Autonomous navigation requires real-time trajectory optimization with limited onboard computational resources, where traditional optimization-based methods often impose heavy computational burdens and require extensive parameter tuning. To achieve transparent navigation results and minimize computational burden, this paper introduces an iterative learning planning (ILP) approach for navigation. By dynamically integrating the control layer into the planning layer, ILP can achieve efficient trajectory optimization through functional iterative learning, providing transparent results that enhance navigation efficiency. This approach significantly improves real-time performance, achieving a time complexity ofO(k*n), wherek*represents the number of iterations andnrepresents the number of waypoints. Simulations and quadcopter experiments are conducted to verify the proposed framework. Results show that ILP significantly improves computational efficiency, ensures safe navigation, and maintains robustness against disturbances, demonstrating its potential as a practical solution for real-world autonomous systems.

To enhance the control effectiveness and operational efficiency of the wastewater treatment process (WWTP), this article proposes a multivariable optimal control scheme based on an identifier–critic–actor reinforcement learning (RL) framework with an event-triggered mechanism (ETM) for dissolved oxygen (DO) and nitrate nitrogen (NO) concentrations. First, the first fuzzy neural network (FNN) is used to estimate the unknown dynamics in WWTP, and the second FNN is implemented within the critic–actor optimization framework. Second, the RL algorithm is applied to design optimal controllers for DO and NO concentrations by constructing a tangent barrier Lyapunov function. Moreover, a dynamic ETM based on the adaptive threshold strategy is proposed to balance the control performance and energy consumption in the wastewater system. Finally, stability analysis and the benchmark simulation model no. 1 are conducted to verify that the control scheme proposed in this article demonstrates effectiveness and enhanced performance.

In this article, we investigate the adaptive safety-constrained control problem for quadrotor unmanned aerial vehicle (QUAV) clusters in dense forest environments to achieve adaptive navigation and obstacle avoidance. Compared to traditional methods, obstacle avoidance constraints are introduced for the first time, and the limitations of fixed formations and the need for prior data are eliminated. First, a cluster constraint mechanism is developed to constrain the distance between QUAVs within the cluster and the distance between the QUAV and the desired trajectory. Then, considering the lack of targeted obstacle avoidance constraint mechanisms in previous methods and the extensive prior data required by learning-based approaches, an obstacle constraint model is established to ensure that the QUAV maintains a safe distance from obstacles to avoid collisions. Finally, an adaptive safety control strategy for QUAV clusters is proposed by combining constraint conditions and stability criteria. Under the proposed control strategy, the QUAV clusters can achieve stable, safe, and efficient navigation and obstacle avoidance, and all constraints will always be satisfied. Furthermore, a numerical simulation experiment on a QUAV cluster navigation demonstrates the effectiveness and flexibility of this strategy.

In soft deformable terrain environments, the robot slips due to dynamic changes in wheel-ground contact, which poses a great challenge to the design of the driving torque of its motion control system. To solve the trajectory tracking control problem of wheeled mobile robots in soft deformation terrain, an event triggering mechanism based on wheel-ground mechanical parameters was designed, in which wheel-terrain mechanics has an important influence on the driving torque and is included in the control system design process. Aiming at the wheeled mobile robot in the working environment of soft ground, considering the rolling resistance of the wheel during its driving process, a dynamic model based on wheel-ground interaction is established. Estimation of unmodelled dynamic and rolling resistance terms for wheeled mobile robots in soft deformable terrain environments by adaptive neural networks. Based on the static event triggering strategy based on constant threshold, a hybrid threshold dynamic event triggering strategy based on rolling resistance is proposed. By proving that there is a positive lower bound on the inter-event time, which means that Zeno behavior is avoided. Meanwhile, the lower bound of inter-event time will change with the designed dynamic threshold. Finally, the good control performance of the proposed algorithm under different ground environments is verified by simulation. Note to Practitioners—With the advancement of detection tasks, the working environment of wheeled mobile robots has become increasingly complex. In the motion control of a wheeled mobile robot in a soft deformable terrain working environment, the influence of the robot ’s wheel-to-ground contact is crucial to the successful realization of the task. The existing wheeled mobile robot control methods for soft deformable terrain working environment usually ignores the influence between wheels and ground, which cannot meet the application requirements of this complex scene. Aiming at the problem of tracking control of wheeled mobile robots in soft deformable terrain working environment, this paper, the traction force change caused by wheel-ground contact mechanics is taken as the main factor of event-triggered mechanism, and the force feedback event-triggered tracking control method is designed. Theoretical algorithms and simulation results show that a trade-off between robot tracking performance and communication resources in different ground environments is realized.

In this paper, an adaptive neural network control algorithm based on event-triggered reinforcement learning is proposed for a four-wheel independent steering and four-wheel independent driving (4WS4WD) mobile robot. A kinematic model is established based on the kinematic relationship between the robot wheels and the body under the consideration of the effect of slip-turn perturbation. The dynamics model is established using the Lagrangian dynamics equations. An improved performance metric function is designed and approximated using the Critic neural network and the Actor neural network to approximate the unknown long-term performance metric function and controller respectively. A threshold band event triggering is proposed for reducing the consumption of communication and computational resources. It is rigorously demonstrated using Lyapunov analysis that both the neural network error and the system error are up to the final consistent bound. As well as proved that the proposed event-triggered mechanism can eliminate the Zeno phenomenon. Finally, comparative experiments demonstrated the effectiveness of the proposed algorithm.

This paper presents an adaptive boundary control design for flexible riser systems with external disturbances and boundary position constraint. An integral barrier Lyapunov function (iBLF) is used to solve the boundary position constraint problem. Since the iBLF directly constrains the boundary position, this relaxes the conservative restriction on the state constraint of conventional BLF control. A new auxiliary signal is designed to offset the effect of the coupling term that cannot be eliminated. Compared to time triggering, the controller and actuator communicate less when using event triggering. Therefore, an event-triggered control scheme is designed to achieve effective suppression of riser vibration by introducing a relative threshold strategy. The Lyapunov stability theory is used to demonstrate that the flexible riser system is finally constrained. The efficiency of the control strategy is then further verified by numerical simulationsNote to Practitioners—This paper investigates the control problem of flexible riser systems with external disturbances. Since the riser needs to consider the uninterrupted marine distribution disturbance and external disturbance, the riser will inevitably distort and vibrate. So the stability of the ship is extremely challenging. The riser is regarded as an Euler-Bernoulli beam construction because of its small diameter and lengthy length. Using Hamilton’s principle, the riser is represented as a fourth-order partial differential equation and two ordinary differential equations. In contrast to the logarithmic BLF and tangent BLF, the integral BLF has direct constraints on the boundary positions, which relaxes the conservative restrictions on state constraints imposed by conventional BLF control. Event-triggered control has attracted the interest of many flexible system control researchers due to its benefits in preserving communication, cost and other resources, and is widely used in practical engineering fields. The complexity and uncertainty attributed to the PDE system itself makes the design of event-triggered strategies more difficult. Based on the original ODE event triggering, it discusses the PDE-based event-triggered strategy of flexible riser systems.

This paper introduces an event-triggered saturation-tolerant prescribed control (STPC) framework for rigid spacecraft subject to actuator faults and actuator saturation via a fixed-time disturbance observer (FTDO). An FTDO with time-varying observer gains is initially developed to reconstruct the lumped perturbations caused by external disturbances, parameter uncertainties, and actuator faults. A fixed-time auxiliary system is employed to counter the adverse effects of actuator saturation. Additionally, asymmetric prescribed performance and shift functions are skillfully incorporated to handle arbitrary bounded initial conditions. Subsequently, a novel FTDO-based event-triggered STPC strategy is formulated, ensuring that attitude-tracking errors converge to predefined performance bounds within a predetermined time while minimizing unnecessary control signal updates. The practical fixed-time stability of all closed-loop signals is validated, with the strict avoidance of Zeno behavior. Finally, simulation studies are conducted to verify the accuracy and effectiveness of the proposed approach.

This article presents a bearing-based formation control method for autonomous aerial vehicle (AAV) swarms, allowing users to specify both convergence time and precision in advance. Unlike traditional distance-based methods, which rely on intricate distance measurements, our approach simplifies constraints using bearing information, reducing hardware and sensing requirements. It also eliminates the need to update control commands for each AAV, as formation reconfiguration can be achieved solely by adjusting the motion trajectory of formation leaders. Moreover, the strategy demonstrates enhanced robustness in addressing real-world input constraints. A continuous hyperbolic tangent saturation function and an input saturation compensation system are incorporated, ensuring system convergence and precision while addressing singularity issues. In addition, unlike conventional bearing-based strategies focusing primarily on convergence time, the proposed algorithm enables preset control over both convergence time and precision. Finally, the effectiveness of the proposed approach is validated through several illustrative examples, including a 6-degree-of-freedom (6DoF) quadrotor AAV swarm, highlighting its practical applicability and performance.

This article investigates for the first time the predefined-time relative position tracking and attitude synchronization control problem with asymptotic tracking errors for spacecraft. Compared to previous studies, this article considers convergence speed and control accuracy simultaneously, ensuring the predefined-time stability and asymptotic convergence of the spacecraft relative tracking errors. The fuzzy logic systems are introduced to estimate the unknown nonlinear terms in the relative dynamic model. By combining the adaptive backstepping control method and the command filter technique, a relative position tracking and attitude synchronization control method is proposed. The improved filter compensation signals are designed to eliminate the impact of filtering errors on the control performance. With the proposed control method, the closed-loop spacecraft position and attitude control system can achieve predefined-time stability, and the spacecraft relative tracking errors can reach zero as time approaches infinity. Finally, simulation results are provided, fully demonstrating the effectiveness of the proposed method.

In the soft deformable terrain environment, the running state of the wheeled mobile robot is easily affected by the complex wheel-ground interaction, which limits its running state variables and input torque. In this paper, the tracking control of wheeled mobile robot under soft deformable terrain is studied, and a dynamic event trigger mechanism is proposed. Based on the proposed trigger strategy, an adaptive event trigger optimal tracking control algorithm for wheeled mobile robot system with nonlinear constraints is designed. By analyzing the nonlinear constraint problem faced by the dynamic model of wheeled mobile robot considering skidding and slipping, the dynamic model of wheeled mobile robot in soft deformable terrain environment with force-speed mixed constraints is constructed. Combining the force-speed constraint and the state error event-triggered idea, a dynamic event-triggered mechanism containing constraint information is designed, and Zeno behavior is avoided. An adaptive event-triggered optimal controller is constructed by combining adaptive dynamic programming algorithm and policy iteration algorithm. To make the wheeled mobile robot complete the tracking control. Finally, it is verified by simulation.

Autonomous exploration in large-scale environments is impeded by two critical challenges, namely, suboptimal viewpoint selection resulting from inadequate feature extraction and the continuously rising computational costs as the environment expands. Existing methods struggle to simultaneously tackle these dual challenges within cohesive frameworks. In response, we present an efficient autonomous exploration framework with contrastive-driven reinforcement learning. Inspired by human cognitive mechanisms that reinforce crucial information recognition through contrast, our study implements contrastive constraints on nodes of varying utility levels within high-dimensional feature spaces, achieving a decoupling of their latent representations. This capability empowers decision networks to explicitly capture key regional characteristics, thereby enhancing the precision of optimal viewpoint selection. Moreover, to mitigate the issues of backtracking and redundant exploration, we design specialized training rules that enforce effective action constraints, further enhancing viewpoint selection. Additionally, we propose a novel graph rarefaction algorithm to tackle computational costs, simplifying computational complexities while maintaining performance standards. Compared to the state-of-the-art (SOTA) approaches, our method achieves 6.7% shorter path lengths, while also demonstrates robust generalization capabilities through real-world robotic experiments across multiple real-world scenarios.

In this article, a novel adaptive control method based on neural networks is proposed for a class of multiagent systems (MASs) with nonlinear functions and external disturbances. First, the approximation properties of neural networks are used to approximate the MAS partial differential equation (PDE) model with nonlinear terms containing two variables, time ${t}$ , and spatial variable ${x}$ . Second, an adaptive controller is constructed to actuate the parabolic MAS to reach consensus under external disturbances. Based on this, the finite-time theorem and special inequalities are applied to prove the stability of the closed-loop system. Thus, MAS that have nonlinear functions and external disturbances are enabled with finite-time consensus. Finally, the effectiveness of the proposed control method is demonstrated by numerical simulations.

In this article, the problem of adaptive event-triggered tracking control is investigated for a class of nonlinear multiagent systems (MASs) with asymmetric multi-information-related (MIR) constraints on all states. The fuzzy-logic systems (FLSs) are utilized to model the system unknown items by virtue of their universal approximation properties. The appropriate integral barrier Lyapunov functions (IBLFs) are selected to prevent the states from exceeding the asymmetric constraint boundaries associated with multi-information, which include historical states, time and neighbor outputs. The event-triggered mechanism (ETM) with varying threshold is employed to reduce the update frequency of the controller, thereby achieving the purpose of saving network resources, including communication bandwidth and computation abilities. Under the backstepping technique framework, the required control scheme is designed by integrating the adaptive controller with triggering mechanism. And it is proven that the controlled plant with state constraint conditions is stable, the consensus tracking errors can eventually remain near the origin, and the Zeno behavior does not exist. Finally, the simulation results corroborate the view that the designed control scheme is effective.

To address the challenges posed by flight envelope limitation, external disturbances, model uncertainties and actuator failures in quadrotor unmanned aerial vehicles (UAVs), we propose an adaptive neural attitude control method that incorporates a Nussbaum function and nonlinear disturbance observer (NDO). By designing the Nussbaum function, we effectively address potential actuator failures while leveraging the NDO enables us to employ feedforward compensation strategy to mitigate perturbation effects. To handle the flight envelope limitation and model uncertainties, we introduce a nonlinear state-dependent function (NSDF) and neural networks (NNs), respectively. The NSDF is utilized to directly constrain the attitude, while the NNs are constructed to estimate the unknown components. Simulation results demonstrate that this approach successfully addresses the flight envelope limitation and maintains robust tracking performance even in the presence of external disturbances, model uncertainties and actuator failures in the controlled system.

An adaptive irregular constraint control problem is investigated in this study based on an output feedback control strategy. Nonlinear systems with irregular constraints are widely used in engineering fields such as the robot flexible operation. We consider such constraints referring to ones that may not only be asymmetric, but may also emerge in stages, or even be positive and negative at times. Ancillary constraint boundaries, which extend the originally imposed constraints to the full period of the system operation, are designed to accommodate the irregular constraints. Furthermore, the state observer is used to calculate the unmeasured states. Meanwhile, to get past the constraint that the nonlinearities in the system rely exclusively on the measured output, we employ the small-gain approach. Through the utilization of the input-state-practically stability (ISpS) theory, it is demonstrated that when the recommended adaptive control technique is applied, the system is semiglobal stable. Also, the output of the system follows the relevant trajectory. The validation of the findings from the simulation further highlights the advantages of the advised control program.

A novel adaptive constraint control approach is proposed for flexible riser systems characterized by uncertain parameters and external disturbances, aimed at achieving the desired transient performance. By combining Hamilton’s principle with partial differential equations (PDEs), the physical model is transformed into a dynamic model. Considering the boundary position constraint, a boundary controller is built using the tangent barrier Lyapunov function (BLF) to mitigate vibrations. In order to ensure the convergence of the boundary position error at a predetermined rate, the control approach incorporates a performance function to attain the necessary transient performance. An auxiliary term is defined to counteract the impact of coupling terms that remain during the decoupling process of PDEs. Finally, the above scheme is further validated through MATLAB simulations.

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It$\hat {\rm \textbf {o}}$differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method.Note to Practitioners—In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

In this article, an adaptive neural tracking control based on saturation disturbance observer (SDO) and command filter is studied for multiple-input-multiple-output nonlinear systems with time-varying constraints and system uncertainties. By employing neural networks (NNs), the system uncertainties are approximated. The SDO is proposed to estimate the composited disturbances which consist of NN approximation errors and the external bounded disturbances. Compared with the traditional disturbance observer, the SDO can reduce the estimation error to some extent. The control requirements are achieved based on the multiconstraints which contain three layers: 1) prescribed performance functions (PPFs); 2) actual constraints; and 3) virtual constraints. The errors remain within the prescribed small neighborhood of zero by using the PPFs, the error constraints ensure that the time-varying constraints are never violated even if the PPFs are not available, and the virtual constraints are applied in a new time-varying barrier Lyapunov function (TVBLF) to design virtual controllers and controller to solve the singularity problem of the traditional TVBLF. In addition, the command filter is introduced to solve the problem of "explosion of complexity." Finally, a numerical simulation verifies the effectiveness of the proposed scheme for a flight control of unmanned aerial vehicle.

This paper presents a decentralized adaptive event-triggered fault-tolerant control (FTC) method for switched interconnected nonlinear systems with multiple unpredictable actuator faults, input saturation, and asymmetrical time-varying full-state constraints. Uncertain items and interconnected items are identified by a fuzzy logic system, and a state observer is designed to estimate the unavailable states. By integrating backstepping and command filtering technology, the shortcomings of computational explosion in traditional backstepping are solved. The barrier Lyapunov function (BLF) and the auxiliary system are designed to solve the full-state time-varying constraints and input saturation respectively. By adopting an event-triggered mechanism and estimating the boundaries of unknown fault parameters, an event-triggered FTC controller is designed to achieve the ability of flexibly coordinate control performance and communication burden, and compensate for unpredictable actuator failures. The scheme realizes the situation where arbitrary switching signals and states are unavailable, whether a fault occurs or not, all signals are bounded, and the input and state satisfy the constraints. Finally, the effectiveness of the proposed control method is verified by simulation example.

In this paper, for a class of uncertain nonlinear multi-agent systems (MASs) with external disturbances, it investigates adaptive state-based event-triggered predefined-time fuzzy formation control protocol. In order to decrease the hardware requirements of the systems and the interaction between agents, the protocol adopts the state-based event-triggered mechanism (ETC). Compared with most output-triggered mechanisms, the mechanism can reduce the computation and transmission load more effectively, and requires less information interaction. The fuzzy logic systems (FLSs) and distributed disturbance observer are used respectively to handle uncertain nonlinear functions and external disturbances in MASs. Furthermore, considering the convergence rate of the closed-loop system, a predefined-time tuning function is introduced to preset the system stabilization time. Considering the problem of decreasing the computational complexity, the dynamic surface control technique is introduced. The stability of the controlled system is analyzed by Lyapunov function theory. Finally, the feasibility and effectiveness of the control strategy are validated by the simulation.

This article studies the predefined time control design issue for uncertain nonlinear systems with full-state error constraints and unmeasurable states for the first time. Compared with existing works, this study enables the controlled system to stabilize within a predetermined time and ensures that the full-state tracking errors converge to a desired control accuracy range, even in the absence of measurable state information. Fuzzy logic systems (FLSs) are applied to handle unknown nonlinear dynamics, and FLSs-based nonlinear state observer is constructed to estimate unmeasurable states. With the universal barrier Lyapunov function and the dynamic surface control technique, an output-feedback-based full-state error constrained control strategy with predefined time stability is proposed, in which a nonsingular predefined time filter is constructed to avoid high computational complexity. Under this control strategy, the predefined time stability of the closed-loop system is achieved and the full-state error constraints are satisfied. Finally, a series of simulation results confirm the effectiveness and superiority of the proposed control strategy.

This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

This paper investigates the finite-time consensus problem for nonlinear parabolic networks by designing a new tracking controller. For undirected topology, the newly designed controller allows to optimize the consensus time by adjusting the parameter β (0 < β < 1). Firstly, the neural network approximation property is utilized to counteract the uncertain nonlinear dynamics of agents, and the event-triggered mechanism is designed to save energy and reduce the communication burden. Secondly, a tracking control protocol is proposed based on event-triggered mechanism, which drives the multi-agent system to reach leader-follower consensus in finite time. Then, by considering appropriate Lyapunov generalization functions and using some important inequalities, the sufficient condition for achieving finite-time consensus in the multi-agent system is obtained. Finally, the effectiveness of the presented method is verified by simulation.

This article deals with adaptive event-triggering control for nonholonomic systems. Based on state feedback, we fulfill the cooperative design of control law and event-triggering strategy. The crucial method is to use the set-valued map to cover the discontinuous set of event sampling. At the same time, combining the set-valued derivative with backstepping technique to achieve adaptive event control and neural networks are used to fit the unknown functions. The nonholonomic constraints of the system are removed by state-scale systematic design. Through transforming the event-triggering control system into a cascade network with two layers of subsystems, the stability of the entire system is proved based on the input-to-state stable small-gain theorem. The proof that Zeno phenomenon does not occur works in two ways: on the one hand, it ensures that the event trigger is effective; on the other hand, it ensures that there are limited jump discontinuities so that adaptive control can be carried out. Finally, the effectiveness of the adaptive event-triggering control method based on the small-gain theorem is verified by simulation.

In this article, the problem of full state constraints for a class of uncertain nonlinear switched systems with time-varying delays under average dwell time is studied, and an adaptive event-triggered mechanism is proposed. The Lyapunov–Krasovskii function (LKF) is employed to solve the trouble caused by time-varying delays, neural networks are selected to approximate the uncertain terms in the system, and the state constraint problem is solved by constructing tan barrier Lyapunov function (Tan-BLF). What’s more, the constraint boundaries considered in this article can be expressed as functions that rely on time and historical information of the system. In addition, the mismatch behavior between subsystem and its controller is also considered. Finally, numerical simulation results verify the availability of the control strategy.

An optimal tracking control system using neural adaptive techniques is introduced for nonlinear systems subjected to time delay and inequality constraints, which is partially uncertain. The nonlinear inequality constraints and partial uncertain time delay of the state are considered in the discrete-time nonlinear system. By transforming the inequality constraint information into augmented system state variables, and using the precompensator method, an augmentation system that contains constraints and transformed controller information is obtained. The Lyapunov–Krasovskii functionals (LKFs) can be used to deal with the partial uncertain state time delay. Subsequently, the optimal controller, the long-term cost function, the uncertain resistance, and system dynamics can be approximated by the action, critic, the disturbance, and the state estimation NNs, and suitable adaptive laws are obtained. Furthermore, the uniform ultimate boundedness (UUB) of the signals in the closed-loop control system can be obtained by the designed near-optimal controller. The inequality constraints are satisfied and the challenge arising from partial uncertain time delay has been successfully addressed, while a numerical simulation verification example is presented.

In this article, a novel visual-inertial-lidar odometry (VILO) system named TCK-VILO is proposed to assist unmanned ground vehicles in reaching high localization performance. We introduce an adaptive sensor reliability evaluation method to configure weights of visual and lidar measurements dynamically in the backend optimization, which can improve both the accuracy and robustness of the localization in real-world outdoor scenarios. A two-stage initialization method is proposed to initialize the system by solving the spatio-temporal alignment of system states. In the TCK-VILO system, a lightweight frontend is designed to update system states while lidar or visual data is fed into the system, and then a tightly-coupled and keyframe-based backend is used to refine system states. We evaluate the proposed TCK-VILO pipeline on the public Newer College dataset and a self-collected real-world dataset. Experimental results show that our system can achieve low drifts in various challenging scenes and outperforms competing state-of-the-art VILO systems.

In this article, an output feedback adaptive fuzzy tracking control method for a class of switched uncertain nonlinear systems with actuator failures and full-state constraints is proposed under an arbitrary switching signal combining the dynamic surface technique. Since the state variables of the system under study are not measurable, a fuzzy observer is constructed to identify the unmeasured states. The actuator failures are considered in the system. To compensate this failure, a fault-tolerant controller is proposed. Moreover, each state needs to be kept within the constraints, so the tangent Barrier Lyapunov function is selected to solve the full-state constraint problem, and the unknown nonlinear function is approximated by fuzzy-logic systems (FLSs). We also proved that all signals in the closed-loop system are bounded. Furthermore, the states can be kept within the predetermined range even if the actuator fails. Finally, a simulation example is given to verify the effectiveness of the proposed control strategy.

In this article, the problems of state-triggered sampling and self-triggered tracking control for nonlinear systems with constraints are studied. First, the fuzzy observer is designed for the unknown state. In the presence of state-triggered sampling error, the cooperative design of constraint controller is a key problem to be solved. The median value theorem provides help to solve this problem and an asymmetric state-triggering strategy is presented. In addition, it is proved that the closed-loop signals are input-to-state stable, and the sampling error and tracking error are bounded. Then, a general self-triggered tracking control scheme is presented. In order to compare the control performance of different triggering mechanisms, fuzzy observer and logarithmic barrier Lyapunov function are selected also, and the scheme is designed under the framework of backstepping method. Co-designing controllers and scheduling functions is a key issue, so that the physical implementation benefits from not requiring constant monitoring of the state. Finally, the effectiveness of the proposed method is verified by case study, and the control performance of different triggering mechanisms is compared.

In this article, an adaptive fuzzy tracking control scheme based on a fuzzy state observer is proposed for a class of uncertain, nonstrict feedback, nonlinear systems with function constraints. In the first place, based on the approximation characteristic of fuzzy logic systems (FLSs), a fuzzy state observer is designed to estimate the immeasurable state variables in the controlled system. Next, under the framework of adaptive backstepping control technology, FLSs are selected not only to approximate unknown nonlinear functions but also to avoid the algebraic loop problem caused by nonstrict feedback structure. At the same time, asymmetric Barrier Lyapunov functions are selected to solve the problem that system states are subject to function constraints, which are related to states and time. Then, Lyapunov stability theory is utilized to prove the stability of the controlled system, the realizability of function constraints, and the convergence of output tracking errors. Finally, a simulation is given to check the effectiveness of the proposed control scheme.

In this article, an adaptive tracking control problem is addressed for nonstrict-feedback stochastic nonlinear systems subject to state constraints. Fuzzy logic systems (FLSs) are used to model unknown nonlinearities and avoid the algebraic loop arising from the system structure. Appropriate integral Barrier Lyapunov functions (IBLFs) are chosen so that time-varying full state constraints can be guaranteed directly rather than by transforming the constraint object. In the framework of backstepping technology, the relative threshold strategy is introduced to modify the adaptive control scheme so that the controller can be updated only after the trigger condition has been met, which reduces the update frequency of the controller and the loss of the actuator. Combined with Lyapunov stability theory, it is shown that all closed-loop signals are bounded in probability, in which the states remain within the specified constraints, and there is no Zeno behavior. A series of simulation results are given to reveal the effectiveness of the constructed control scheme.

This article presents an adaptive fuzzy fixed time time-varying formation control (TVFC) method for uncertain heterogeneous nonlinear multiagent systems (HNMASs) with full state constraints. Meanwhile, both partial loss of effectiveness and bias fault are considered in HNMASs. The fuzzy logic systems are selected as an effective tool to approximate uncertain nonlinear functions. The original constrained states of the systems will be converted to unconstrained states by the nonlinear transformed function. Compared with previous papers, it is the first time to handle the TVFC problem of HNMASs with full state constraints. In addition, formation control based on an adaptive fuzzy fixed time strategy not only ensures fast convergence of the system, but also the convergence time doesn't depend on any initial conditions. The stability of HNMAs is proven by the fixed time stability theory. Finally, a simulation is given to testify the effectiveness of the control method.

An adaptive fuzzy-based event-triggered control (ETC) scheme is putted forward in this article, targeted at multi-input multioutput switched nonlinear systems with the situation of control directions are unknown. By designing a state observer and by means of fuzzy logic system, the unmeasurable state and unknown nonlinear function is resolved. The command filter is introduced to backstepping design process, combine with the Nussbaum function technology, overcome the trouble of calculation explosion derived from the partial derivative of the virtual controller, and also solves the influence of unknown control directions on the controller design. By construct multiple Lyapunov functions and under the designed ETC mechanism, an adaptive ETC scheme is developed. In addition, the stability of the system is verified by combining the average dwell time method. Finally, a numerical simulation verification example is given.

This study examined the control problem triggered by an adaptive fuzzy event for uncertain fractional-order switched systems. First, an observer was designed to estimate unknown system states, and fuzzy logic systems were introduced to approximate unknown nonlinear functions. Furthermore, the dynamic surface technique is employed to solve complex differential problems of fractional-order switched systems. This article proposes a threshold-based event-triggered control scheme that avoids Zeno behavior to decrease the waste of communication resources. An event-triggered mechanism updates the control signal only when necessary to ensure system performance. The proposed control strategy enables all signals of a closed-loop system to be uniformly bounded and the tracking error of output has good convergence performance near the origin under an arbitrary switching mechanism. Finally, a numerical example is presented that demonstrates the effectiveness of the designed scheme.

This article researches the adaptive fuzzy tracking control problem for uncertain nonlinear systems with multiple actuators and sensors faults. Compared with previous studies, all states of the system cannot be measured accurately in this article due to the existence of multiple sensors faults, and it brings significant difficulties to the design of the control scheme. Moreover, multiple actuators faults and external disturbance can also bring challenges to controller design. To solve these problems, we design different adaptive update laws to relieve the effects of unknown actuators faults, sensors faults, and external disturbance, respectively. Furthermore, the actual states can be estimated by combining sensors outputs with adaptive parameters. On this basis, the unknown nonlinear functions are approximated through the combining of fuzzy logic systems and the estimation of states. Then, a novel adaptive fuzzy tracking control algorithm is completed by the backstepping method. By employing the Lyapunov function, the presented novel fault-tolerant control algorithm can guarantee all signals of the system are bounded in spite of the occurrence of multiple faults. Finally, we verify the availability of the novel algorithm by comparing the control performance of the two algorithms.

In this paper, an adaptive fuzzy control problem is studied for a connected automated vehicles platoon subject to unknown dead-zone input and constraints. To better handle the unknown nonlinear dynamical functions and disturbances, the nonlinear dynamics model is transformed to a new model. Then, the fuzzy logic system (FLS) is used to identify the unknown nonlinear functions. A dead-zone inverse technique is introduced to eliminate the negative effects of the unknown dead-zone input nonlinearity. In the framework of backstepping, the tangent barrier Lyapunov function (BLF) is introduced in this paper, and a distributed adaptive fuzzy control scheme is designed so that the position, velocity and acceleration of the vehicle platoon do not violate the given constrained boundaries. Finally, based on the Lyapunov stability theory, it is noted that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is validated by simulation results.

In this article, the problem of tracking control for a class of nonlinear time-varying full state constrained systems is investigated. By constructing the time-varying asymmetric barrier Lyapunov function (BLF) and combining it with the backstepping algorithm, the intelligent controller and adaptive law are developed. Neural networks (NNs) are utilized to approximate the uncertain function. It is well known that in the past research of nonlinear systems with state constraints, the state constraint boundary is either a constant or a time-varying function. In this article, the constraint boundaries both related to state and time are investigated, which makes the design of control algorithm more complex and difficult. Furthermore, by employing the Lyapunov stability analysis, it is proven that all signals in the closed-loop system are bounded and the time-varying full state constraints are not violated. In the end, the effectiveness of the control algorithm is verified by numerical simulation.

A robust adaptive control method for a certain type of quarter active suspension system (ASS) is proposed in this work. The constraint issue of ASS is put into consideration primarily. Due to the limitation of the traditional barrier Lyapunov functions (BLFs), the integral barrier Lyapunov function (iBLF) is introduced to exert direct constraints on state variables in each stage under the backstepping frame, and neural networks (NNs) are applied to identify those unknown functions. Then, an adaptive law based on the projection operator is defined to eliminate the influence caused by the actuator failure. It is widely known that only the vertical displacement and velocity constraints are not violated, can the ASSs become stable and secure. It can be ultimately confirmed that all signals in the closed-loop system are bounded, and the control goals are satisfied. Last but not least, the feasibility of the approach is illustrated directly through a contrast simulation example.

In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.

In this article, an integral barrier Lyapunov-function (IBLF)-based adaptive tracking controller is proposed for a class of switched nonlinear systems under the arbitrary switching rule, in which the unknown terms are approximated by radial basis function neural networks (RBFNNs). The IBLF method is used to solve the problem of state constraint. This method constrains states directly and avoids the verification of feasibility conditions. In addition, a completely unknown control gain is considered, which makes it impossible to directly apply previous existing methods. To offset the effect of the unknown control gain, the lower bound of the control gain is added into the barrier Lyapunov function, and a regulating term is introduced into the controller. The proposed control strategy realizes three control objectives: 1) all the signals in the resulting system are bounded; 2) the system output tracks the reference signal to a arbitrarily small compact set; and 3) all the constraint conditions for system states are not violated. Finally, a simulation example is used to show the effectiveness of the proposed method.

This article addresses the adaptive tracking control problem for switched uncertain nonlinear systems with state constraints via the multiple Lyapunov function approach. The system functions are considered unknown and approximated by radial basis function neural networks (RBFNNs). For the state constraint problem, the barrier Lyapunov functions (BLFs) are chosen to ensure the satisfaction of the constrained properties. Moreover, a state-dependent switching law is designed, which does not require stability for individual subsystems. Then, using the backstepping technique, an adaptive NN controller is constructed such that all signals in the resulting system are bounded, the system output can track the reference signal to a compact set, and the constraint conditions for states are not violated under the designed state-dependent switching signal. Finally, simulation results show the effectiveness of the proposed method.

This article presents the adaptive tracking control scheme of nonlinear multiagent systems under a directed graph and state constraints. In this article, the integral barrier Lyapunov functionals (iBLFs) are introduced to overcome the conservative limitation of the barrier Lyapunov function with error variables, relax the feasibility conditions, and simultaneously solve state constrained and coupling terms of the communication errors between agents. An adaptive distributed controller was designed based on iBLF and backstepping method, and iBLF was differentiated by means of the integral mean value theorem. At the same time, the properties of neural network are used to approximate the unknown terms, and the stability of the systems is proven by the Lyapunov stability theory. This scheme can not only ensure that the output of all the followers meets the output trajectory of the leader but also make the state variables not violate the constraint bounds, and all the closed-loop signals are bounded. Finally, the efficiency of the proposed controller is revealed.

In this article, an adaptive tracking control method for the bionic active suspension system with the event-triggered mechanism is proposed. In order to achieve the ideal control objectives, a nonlinear suspension system structure is proposed based on the biological inspiration. In the existing research, the suspension system tracking control methods are only aimed at a single part of the mass, respectively. But this article adopts a novel tracking method for the vertical displacement difference, which can track the ideal reference model more accurately. For the sake of alleviating the problem of limited resources in the process of vehicle communication, a control method combined with the events triggering of the relative threshold is proposed. The design of the controller makes the vertical displacement and vertical moving speed of the bionic suspension system close to zero. It can effectively improve the communication efficiency between the actuator and the controller. In the design of this system, all the signals involved are bounded. The Zeno behavior is successfully avoided among the event-triggered control mechanism. Finally, the feasibility and rationality of this method are verified by the simulation analysis of the bionic suspension system.

In this article, a novel coverage algorithm is designed to realize dynamic tracking coverage of unmanned ground vehicles (UGVs) by unmanned aerial vehicles (UAVs) with quantity-adjustment behavior, which can adjust the quantity of UAVs to cover the moving UGVs. In traditional coverage control, the paths of UAVs are preplanned to achieve regional coverage. Additionally, the quantity of UAVs remains unchanged, resulting in a waste of resources and a lack of flexibility. To overcome these problems, we present a novel coverage algorithm. First, the tracking coverage algorithm is designed, in which the positions of the UGVs are sampled at a certain interval, and$k$-means is used to obtain the optimal expected positions of UAVs. Then, to realize the quantity-adjustment behavior of UAVs, an evaluation mechanism is proposed to determine whether the UAVs should be added or withdrawn. UAVs should reach the expected positions during the sample interval. As a result, a finite-time terminal sliding-mode controller is designed to drive the UAVs to follow expected positions. Furthermore, we design a Lyapunov function to prove the stability of the controller. Finally, three simulation examples are put forward, and the results demonstrate the effectiveness of the proposed algorithm and controller.

In this paper, a class of flexible riser systems modeled by partial differential equations (PDEs) with the backlash is considered. The backlash is formulated as the addition of a linear input and a interference-like term, then an new auxiliary item is introduced to compensate for the impact of this backlash. In addition, the constraint problem for the position and the velocity is also taken into consideration. To solve this constrain problem, the logarithmic barrier Lyapunov function is employed. For the flexible riser system, two kinds of adaptive controllers are proposed under the following two cases. One controller is designed when only the parameter of backlash is unknown. On the basis of this result, the other controller is presented when some system parameters cannot be measured through actual measurement. Then, combing the theory of Lyapunov stability, the two controllers can guarantee the boundedness of all signals in the closed-loop flexible riser system. Further, both the position and the velocity satisfy their corresponding constraint condition. Finally, the simulation example verifies that the proposed control method is effective.

In this article, an adaptive sliding-mode control scheme is developed for a class of uncertain quarter vehicle active suspension systems with time-varying vertical displacement and speed constraints, in which the input saturation is considered. The integral terminal SMC is adopted to improve convergence accuracy and avoid singular problems. In addition, neural networks are used to model unknown terms in the system and the backstepping technique is taken into account to design the actual controller. To guarantee that the time-varying state constraints are not violated, the corresponding Barrier Lyapunov functions are constructed. At the same time, a continuous differentiable asymmetric saturation model is developed to improve the stability of the system. Then, the Lyapunov stability theory is used to verify that all signals of the resulting system are semi globally uniformly ultimately bounded, time-varying state constraints are not violated, and error variables can converge to the small neighborhood of 0. Finally, results of the simulation of the designed control strategy are given to further prove the effectiveness.

This article proposes an adaptive finite-time tracking control based on fuzzy-logic systems (FLSs) for an uncertain nonstrict nonlinear multi-input-multi-output (MIMO) full-state-constrained system with the coupled uncertain dead-zone input. By using three kinds of FLSs: the uncertain system, the uncertain dead zone, and the uncertain input transfer inverse matrix are approximated using the system function FLS, dead-zone FLS, and input transfer inverse matrix FLS, respectively. After defining the barrier Lyapunov function, the fuzzy-based adaptive tracking controllers are designed, and the fuzzy weights are updated through the proposed adaptive laws. Then, based on the extended finite-time convergence theorem, with the design parameters chosen properly, the target uncertain nonlinear system is guaranteed to be semiglobal practical finite-time stable (SGPFS); and the full-state constraints are not violated while avoiding the effects of the dead zones. Furthermore, a simulation is presented to verify the validity of the proposed algorithm.

This article investigates an adaptive fuzzy tracking control approach via output feedback for a class of switched uncertain nonlinear systems with full-state constraints under arbitrary switchings. The adaptive observer and controller are designed based on fuzzy approximation. The main characteristic of discussed systems is that the state variables are not available for measurement and need to be kept within the constraint set. In order to estimate the unmeasured states, the adaptive fuzzy state observer is constructed. To guarantee that all the states do not violate the time-varying bounds, the tangent barrier Lyapunov functions (BLF-Tans) are selected in the design procedure. Based on the common Lyapunov function method, the stability of considered systems is analyzed. It is demonstrated that all the signals in the resulting system are bounded, and all the states are limited in their constrained sets. Furthermore, the simulation example is used to validate the effectiveness of the presented control strategy.

This article investigates the attitude stabilization problem of a rigid spacecraft with actuator saturation and failures. Two neural network-based control schemes are proposed using anti-saturation adaptive strategies. To satisfy the input constraint, we design two controllers in a saturation function structure. Taking into account the modeling uncertainties, external disturbances, and adverse effects from actuator faults and failures, the first anti-saturation adaptive controller is implemented based on radial basis function neural networks (RBFNNs) with a fixed-time terminal sliding mode (FTTSM) containing a tunable parameter. Then, we upgrade the proposed controller to a fully adaptive-gain anti-saturation version, in order to strengthen the robustness and adaptivity with respect to actuator faults and failures, unknown mass properties, and external disturbances. In the two schemes, all of the designed adaptive parameters are scalars, thus they only require light computational load and can avoid the redesign process of the controller during spacecraft operation. Finally, the feasibility of the proposed methods is illustrated via two numerical examples.

This article addresses a new adaptive fuzzy fast finite-time state-constraint protocol for leader-follower formation control. Each agent in uncertain nonlinear dynamic multiagent systems is represented by second-order integrator, which synchronously governs its position and velocity. The fuzzy logic systems are employed to compensate and approximate uncertain functions. On the premise of maintaining formation structure and coupling communication topology, time-varying transformation equations containing exponential signals are introduced to ensure that state capability boundaries for different physical quantities of agents are not violated. It not only guarantees own state performance and collision avoidance among agents, but also realizes the specified transient and steady formation performance. Furthermore, focusing on convergence rate, the adaptive fuzzy fast finite-time strategy is designed that can guarantee all agents will follow the desired formation configuration in fast finite-time. Through the abovementioned approaches provide a good way to improve the convergence and ensure the security for decentralized formation control. Finally, the validity of the theoretical method is proved by fast finite-time stable theory and Lyapunov stability theory. The effectiveness of the protocol is verified by digital simulation and simulation comparison.

In this article, a fuzzy adaptive output feedback control strategy is designed for a class of uncertain nonlinear switched system with full state constraints under arbitrary switching signal. The states of the system studied in this article are unmeasurable, so a fuzzy observer is designed to estimate the unmeasurable states. At the same time, in order to ensure that the states of the system do not violate the constraints related to the desired output and states, the log-type barrier Lyapunov function method is selected to solve this constraint problem. Finally, through Lyapunov stability theory analysis, it is found that the designed control strategy can ensure that all signals in the closed-loop system are bounded, and the states of the system do not violate their corresponding constraints. In addition, a numerical simulation verifies the effectiveness of the control strategy.

In this article, an adaptive tracking control approach is developed for a class of strict-feedback nonlinear systems with time-varying full state constraints. As a breakthrough in this system, the special function constraints (whose constraint boundary is relevant to both state variables and time) are considered, which are rarely studied by research work. And there is no doubt that this method increases the complexity of designing this scheme. Furthermore, the time-varying integral barrier Lyapunov functions combining with backstepping technique is introduced to break the limitation of traditional methods as well as achieve the full state constraints. Meanwhile, fuzzy logic systems are selected to approximate unknown nonlinear functions. It is verified that all closed-loop signals are bounded and all states are forced in the time-varying boundness. In addition, the proposed control strategy has a good performance. The effectiveness of the theoretical analysis results is proved via a simulation example.

This article concentrates on the event-driven controller design problem for a class of nonlinear single input single output parametric systems with full state constraints. A varying threshold for the triggering mechanism is exploited, which makes the communication more flexible. Moreover, from the viewpoint of energy conservation and consumption reduction, the system capability becomes better owing to the contribution of the proposed event-triggered mechanism. In the meantime, the developed control strategy can avoid the Zeno behavior since the lower bound of the sample time is provided. The considered plant is in a lower triangular form, in which the match condition is not satisfied. To ensure that all the states retain in a predefined region, a barrier Lyapunov function (BLF) based adaptive control law is developed. Due to the existence of the parametric uncertainties, an adaptive algorithm is presented as an estimated tool. All the signals appearing in the closed-loop systems are then proven to be bounded. Meanwhile, the output of the system can track a given signal as far as possible. In the end, the effectiveness of the proposed approach is validated by an aircraft wing rock motion system.

A novel adaptive control scheme is developed for active suspension systems (ASSs) based on neural networks (NNs) and backstepping control strategies. Since the springs and piecewise dampers are nonlinear, the unknown internal dynamics are approximated by radial basis function neural networks (RBFNNs). Then, to solve the time-varying constrains of both vertical displacement and corresponding speed in vehicle body, the Tangent Barrier Lyapunov Functions (TBLFs) are incorporated into the controller design. Furthermore, the adaptive controller and adaptive laws are designed to improve the riding comfortable, handling stability and driving safety. In the end, the simulation results show the effectiveness and feasibility of the proposed adaptive algorithm compared with unconstrained adaptive approach.

This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.

In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

A reliable, efficient, and simple control is presented and validated for a quarter-car active suspension system equipped with an electro-hydraulic actuator. Unlike the existing techniques, this control does not use any function approximation, e.g., neural networks (NNs) or fuzzy-logic systems (FLSs), while the unmolded dynamics, including the hydraulic actuator behavior, can be accommodated effectively. Hence, the heavy computational costs and tedious parameter tuning phase can be remedied. Moreover, both the transient and steady-state suspension performance can be retained by incorporating prescribed performance functions (PPFs) into the control implementation. This guaranteed performance is particularly useful for guaranteeing the safe operation of suspension systems. Apart from theoretical studies, some practical considerations of control implementation and several parameter tuning guidelines are suggested. Experimental results based on a practical quarter-car active suspension test-rig demonstrate that this control can obtain a superior performance and has better computational efficiency over several other control methods.

Aiming at a class of switched uncertain nonlinear strict-feedback systems under the action of average dwell time switching signal, this paper proposes a novel adaptive neural network output feedback tracking control based on the consideration of the full state constraints. The controller is proposed based on neural networks. One of the key characteristics of the system discussed is that the state variables cannot be measured and the system states need to be kept within the constraint ranges. For the sake of estimating the unmeasured states, the observer is constructed. In order to ensure all states which are within the time-varying boundary, the tangent barrier Lyapunov function (BLF-Tan) is selected in the design process. The boundedness of the closed-loop signals with average dwell time is guaranteed by the designed controllers and all the states limit in their constrained sets. It has been proved that the output tracking error converge to a small neighborhood of zero. In addition, the significance of the presented control strategy is verified and tested by a simulation example.

Considering the uncertain nonstrict nonlinear system with dead-zone input, an adaptive neural network (NN)-based finite-time online optimal tracking control algorithm is proposed. By using the tracking errors and the Lipschitz linearized desired tracking function as the new state vector, an extended system is present. Then, a novel Hamilton-Jacobi-Bellman (HJB) function is defined to associate with the nonquadratic performance function. Further, the upper limit of integration is selected as the finite-time convergence time, in which the dead-zone input is considered. In addition, the Bellman error function can be obtained from the Hamiltonian function. Then, the adaptations of the critic and action NN are updated by using the gradient descent method on the Bellman error function. The semiglobal practical finite-time stability (SGPFS) is guaranteed, and the tracking errors convergence to a compact set by zero in a finite time.

In this paper, an adaptive neural network (NN) control scheme is developed for a class of stochastic nonlinear systems with time-varying full state constraints. In the controller design, RBF NNs are employed to approximate the unknown terms, and the backtracking technique is introduced to overcome the restriction of matching conditions. At the same time, tangent type time-varying barrier Lyapunov functions (tan-TVBLFs) are constructed to ensure the full state constraints are never violated, where tan-TVBLFs are beneficial to integrate constraint analysis into a common method. Furthermore, the Lyapunov stability theory is used to prove that all closed-loop signals are semiglobal uniformly ultimately bounded in probability and error signals remain in the compact set do not violate the time-varying constraints. A simulation example will be used to exhibit the effectiveness of the proposed control scheme.

This article presents an adaptive output feedback approach of nonlinear multi-input-multi-output (MIMO) systems with time-varying state constraints and unmeasured states. An adaptive approximator is designed to approximate the unknown nonlinear functions existing in the state-constrained systems with immeasurable states. To deal with the tracking problem of such systems, a state observer with time-varying barrier Lyapunov functions (BLFs) is introduced in the controller design procedure. The backstepping design with time-varying BLFs is utilized to guarantee that all system states remain within the time-varying-constrained interval. The constant constraint is only the special case of the time-varying constraint which is more general in the real systems. The proposed control approach guarantees that all signals in the closed-loop systems are bounded and the tracking errors converge to a bounded compact set, and time-varying full-state constraints are never violated. A simulation example is given to confirm the feasibility of the presented control approach in this article.

This article proposes an adaptive fuzzy controller for a class of uncertain strict-feedback nonmatching nonlinear single-input single-output systems with fuzzy dead zone and full time-varying state constraints. The states considered here are immeasurable and full states of the systems are constrained in a bounded set with time-varying regions. Following the adaptive backstepping design framework, the tangent barrier Lyapunov functions are introduced to the integrated design to address the problems in such systems. Fuzzy logic systems are used to identify the unknown smooth functions and unknown parameters. An input-driven observer is designed to estimate the immeasurable states. To distinguish the conventional deterministic dead zone models, the output of dead zone is uncertainty. The form of indeterminate dead zone as a combination of a liner and a disturbance-like term is extended by the fuzzy algorithms. Even though the output of dead zone is fuzzy and adopting the integrated design, the proposed fuzzy controller can ensure that all the signals in the closed-loop systems are semiglobal uniformly ultimately bounded and guarantee the tracking performance. Finally, simulation results are shown to verify the effectiveness and reliability of the proposed approach.

This article investigates an adaptive finite-time neural control for a class of strict feedback nonlinear systems with multiple objective constraints. In order to solve the main challenges brought by the state constraints and the emergence of finite-time stability, a new barrier Lyapunov function is proposed for the first time, not only can it solve multiobjective constraints effectively but also ensure that all states are always within the constraint intervals. Second, by combining the command filter method and backstepping control, the adaptive controller is designed. What is more, the proposed controller has the ability to avoid the "singularity" problem. The compensation mechanism is introduced to neutralize the error appearing in the filtering process. Furthermore, the neural network is used to approximate the unknown function in the design process. It is shown that the proposed finite-time neural adaptive control scheme achieves a good tracking effect. And each objective function does not violate the constraint bound. Finally, a simulation example of electromechanical dynamic system is given to prove the effectiveness of the proposed finite-time control strategy.

In this article, an adaptive neural network (NN) decentralized output-feedback control design is studied for the uncertain strict-feedback large-scale interconnected nonlinear systems with nonconstant virtual and control gains. NNs are utilized to approximate the unknown nonlinear functions, and the immeasurable states are estimated via designing an NN decentralized state observer. By constructing the logarithm Lyapunov functions, an observer-based NN adaptive decentralized backstepping output-feedback control is developed in the framework of the decentralized backstepping control. The proposed adaptive decentralized backstepping output-feedback control can make that the closed-loop system is semiglobally uniformly ultimately bounded (SGUUB) and that the tracking and observer errors converge to a small neighborhood of the origin. The most important contribution of this article is that it removes the restrictive assumption in the existing results that both virtual and control gain functions in each subsystem must be constants. A numerical simulation example is provided to validate the effectiveness of the proposed control method and theory.

In this article, the adaptive sliding mode (ASM) control scheme of half-car active suspension systems with prescribed performance is studied. Because of the affected by model uncertainty, time-varying parameter, pavement roughness excitation, etc., the study of suspension systems can be regarded as the multivariable nonlinear control problem. First of all, the prescribed performance function (PPF) is applied to constrain the displacement and pitch angle of the suspension systems to ensure the transient and steady-state suspension responses. Second, an integral terminal sliding mode control method with strong robustness is put forward, which can make the system converge rapidly in a finite-time when it is far from the equilibrium point, solve the singularity problem in the control process, and reduce the chattering phenomenon in the traditional sliding mode control. Then, the neural networks (NNs) approximation characteristics are used to deal with unknown items in the design of the controller, and the Lyapunov stability theory is employed to analyze the stability of the closed-loop system. In the end, the comparative simulation results demonstrate the feasibility and effectiveness of the proposed control scheme.

A novel adaptive controller for the half-car active suspension systems (ASSs), which can improve the riding comfortability and handling stability of the driver, is proposed in this paper. By using nonlinear mapping, it is demonstrated that the nonlinear ASSs with partial performance constraints are transformed into the novel pure-feedback systems without constraints. By introducing a modified dynamic surface control (DSC) into the Lyapunov function, the adaptive neural network (NN) controller is discussed. The unknown continuous functions are estimated by the NNs, and the boundedness of all signals in the closed-loop systems is guaranteed by the Lyapunov stability theory. Meanwhile, the performance constraints are not violated. Finally, the simulations are performed to clarify and verify the effectiveness of the proposed scheme.

In this paper, an adaptive dynamic programming-based online adaptive tracking control algorithm is proposed to solve the tracking problem of the partial uncertain time-delayed nonlinear affine system with uncertain resistance. Using the discrete-time Hamilton-Jacobi-Bellman function, the input time-delay separation lemma, and the Lyapunov-Krasovskii functionals, the partial state and input time delay can be determined. With the approximation of the action and critic, and resistance neural networks, a near-optimal controller and appropriate adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the target system, and the tracking error convergence to a small compact set to zero. A numerical simulation of the wheeled mobile robotic system is presented to verify the validity of the proposed method.

In this article, the adaptive fault-tolerant control (FTC) problem is solved for a switched resistance-inductance-capacitance (RLC) circuit system. Due to the existence of faults which may lead to instability of subsystems, the innovation of this article is that the unstable subsystems are taken into account in the frame of output constraint and unmeasurable states. Obviously, there are not any unstable subsystems in unswitched systems. The unstable subsystems will involve many serious consequences and difficulties. Since the system states are unavailable, a switched state observer is designed. In addition, the fuzzy-logic systems (FLSs) are employed to approximate unknown internal dynamics in the controller design procedure. Then, the barrier Lyapunov function (BLF) is exploited to guarantee that the system output satisfy its constrained interval. Moreover, by using the average dwell-time method, all signals in the resulting systems are proofed to be bounded even when faults occur. Finally, the proposed strategy is carried out on the switched RLC circuit system to show the effectiveness and practicability.

Although adaptive control design with function approximators, for example, neural networks (NNs) and fuzzy logic systems, has been studied for various nonlinear systems, the classical adaptive laws derived based on the gradient descent algorithm with σ -modification or e -modification cannot guarantee the parameter estimation convergence. These nonconvergent learning methods may lead to sluggish response in the control system and make the parameter tuning complex. The aim of this paper is to propose a new learning strategy driven by the estimation error to design the alternative adaptive laws for adaptive control of nonlinear servo systems. The parameter estimation error is extracted and used as a new leakage term in the adaptive laws. By using this new learning method, the convergence of both the estimated parameters and the tracking error can be achieved simultaneously. The proposed learning algorithm is further tailored to retain finite-time convergence. To handle unknown nonlinearities in the servomechanisms, an augmented NN with a new friction model is used, where both the NN weights and some friction model coefficients are estimated online via the proposed algorithms. Comparisons with the σ -modification algorithm are addressed in terms of convergence property and robustness. Simulations and practical experiments are given to show the superior performance of the suggested adaptive algorithms.

In this paper, the problem of adaptive neural tracking control for a type of uncertain switched nonlinear nonlower-triangular system is considered. The innovations of this paper are summarized as follows: 1) input to state stability of unmodeled dynamics is removed, which is an indispensable assumption for the design of nonswitched unmodeled dynamic systems; 2) the design difficulties caused by the nonlower-triangular structure is handled by applying the universal approximation ability of radial basis function neural networks and the inherent properties of Gaussian functions, which avoids the restriction that the monotonously increasing bounding functions of the nonlower-triangular system functions must exist; and 3) multiple Lyapunov functions are utilized to develop a backstepping-like recursive design procedure such that the solvability of the adaptive neural tracking control issue of all subsystems is unnecessary. Based on the proposed controller design methods, it can be obtained that all signals in the closed-loop switched system remain bounded and the tracking error can eventually converge to a small neighborhood of the origin. In the simulation study, two examples are supplied to prove the practicability and feasibility of the developed design schemes.

This paper is concerned with the switched decentralized adaptive control design problem for switched interconnected nonlinear systems under arbitrary switching, where the actuator failures may occur infinite times and the control directions are allowed to be unknown. By introducing a Nussbaum-type function and an integrable auxiliary signal, a switched decentralized adaptive control scheme is developed to deal with the potentially infinite times of actuator failures and the unknown control directions. The basic idea is to design different parameter update laws and control laws for distinct switched subsystems. It is proved that the state variables of the resulting closed-loop system are asymptotically stable. Finally, a numerical simulation on a double-inverted pendulum model is given to verify the proposed control scheme.

In this paper, a novel adaptive fuzzy tracking control strategy is developed for nonlinear time-varying delayed systems with full state constraints. State constraints and time delays are normally found in various real-life plants, which are two important factors for degrading system performance significantly. In the framework of adaptive control, the effects of state constraints and time-varying delays are removed simultaneously. The integral Barrier Lyapunov functionals (IBLFs) are applied to achieve full-state-constraint satisfactions and remove the need of the transformed error constraints in previous BLFs. The unknown time-varying delays are completely compensated by introducing the separation technique and Lyapunov–Krasovskii functionals (LKFs). The unknown functions existing in systems are approximated by employing fuzzy logic systems (FLSs). With the help of less-adjustable parameters, only one parameter is needed to be adjusted online in each step of control design. The novel strategy can guarantee that a satisfactory tracking performance is achieved and the signals existing in the closed-loop system are bounded. Finally, by presenting simulation results, the efficiency of the proposed approach is revealed.

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified.

In this paper, a reinforcement learning-based adaptive control algorithm is proposed to solve the tracking problem of a discrete-time (DT) nonlinear state and input time delayed system of the wheeled mobile robot (WMR). With the typical model of the WMR transformed into an affine nonlinear DT system, a delay matrix function and appropriate Lyapunov-Krasovskii functionals are introduced to overcome the problems caused by the state and input time delays, respectively. Furthermore, with the approximation of the radial basis function neural networks (NNs), the adaptive controller, the critic NN, and action NN adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the WMR system, and the tracking errors convergence to a small compact set to zero. Two examples of simulation are given to illustrate the effectiveness of the proposed algorithm.

In this paper, an adaptive neural network (NN) controller is proposed for a class of nonlinear active suspension systems (ASSs) with hydraulic actuator. To eliminate the problem of “explosion of complexity” inherently in the traditional backstepping design for the hydraulic actuator, a dynamic surface control technique is developed to stabilize the attitude of the vehicle by introducing a first-order filter. Meanwhile, the presented scheme improves the ride comfort even when the uncertain parameter exists. Due to the existence of uncertain terms, the NNs are used to approximate unknown functions in the ASSs. Finally, a simulation for a servo system with hydraulic actuator is shown to verify the effectiveness and reliability of the proposed approach.

In the novel, an adaptive neural network (NN) controller is developed for a category of nonlinear stochastic systems with full state constraints and unknown time delays. The control quality and system stability suffer from the problems of state time delays and constraints which frequently arises in most real plants. The considered systems are transformed into new constrained free systems based on nonlinear mappings, such that full state constraints are never violated and the feasibility conditions on virtual controllers (the values of virtual controllers and its derivative are assumed to be known) are removed. To compensate for unknown time delayed uncertainties, the exponential type Lyapunov-Krasovskii functionals (LKFs) are employed. NNs are utilized to approximate unknown nonlinear functions appearing in the design procedure. In addition, by employing dynamic surface control (DSC) technique and less adjustable parameters, the online computation burden is lightened. The control method presented can achieve the semiglobal uniform ultimate boundedness of all the closed-loop system signals and the satisfactions of full state constraints by rigorous proof. Finally, by presenting simulation examples, the efficiency of the presented approach is revealed.

This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.

This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

In this paper, a framework of adaptive control for a switched nonlinear system with multiple prescribed performance bounds is established using an improved dwell time technique. Since the prescribed performance bounds for subsystems are different from each other, the different coordinate transformations have to be tackled when the system is transformed, which have not been encountered in some switched systems. We deal with the different coordinate transformations by finding a specific relationship between any two different coordinate transformations. To obtain a much less conservative result, in contrast to the common adaptive law, different adaptive laws are established for both active and inactive time-interval of each subsystem. The proposed controllers and switching signals guarantee that all signals appearing in the closed-loop system are bounded. Furthermore, both transient-state and steady-state performances of the switched system are obtained. Finally, the effectiveness of the developed method is verified by the application to a continuous stirred tank reactor system.

This paper proposes an adaptive neural control method for a class of nonlinear time-varying delayed systems with time-varying full-state constraints. To address the problems of the time-varying full-state constraints and time-varying delays in a unified framework, an adaptive neural control method is investigated for the first time. The problems of time delay and constraint are the main factors of limiting the system performance severely and even cause system instability. The effect of unknown time-varying delays is eliminated by using appropriate Lyapunov-Krasovskii functionals. In addition, the constant constraint is the only special case of time-varying constraint which leads to more complex and difficult tasks. To guarantee the full state always within the time-varying constrained interval, the time-varying asymmetric barrier Lyapunov function is employed. Finally, two simulation examples are given to confirm the effectiveness of the presented control scheme.

In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm.

In this paper, we design an adaptive neural network (NN) controller of uncertain n-joint robotic systems with time-varying state constraints. By proposing a nonlinear mapping, the robotic systems are transformed into the multiple-input, multiple-output systems. Compared with constant constraints, the time-varying state constraints are more general in the real systems. To overcome the design challenge, the time-varying barrier Lyapunov function is introduced to ensure that the states of the robotic systems are bounded within the predetermined time-varying range. The NN approximations are employed to approximate the uncertain parametric and unknown functions in the robotic systems. Based on the Lyapunov analysis, it can be proved that all signals of robotic systems are bounded; the tracking errors of system output converge on a small neighborhood of zero and the time-varying state constraints are never violated. Finally, a simulation example is performed to demonstrate the feasibility of the proposed approach.

An adaptive control approach based on the fuzzy systems for a class of uncertain nonlinear multi-input multi-output (MIMO) systems is presented in this paper. This class of systems is in the nested multiple coupling structure and their states are constrained in the corresponding compact sets. The properties of the system structure are inevitable to bring about a complicated design and a difficult task. The fuzzy logic systems are employed to approximate the unknown functions of systems, and the decoupling backstepping way is proposed to design the stability controller and adaptation laws. Barrier Lyapunov functions (BLFs) are constructed in the backstepping design to guarantee that the constraint bounds are not violated. Based on Lyapunov analysis in barrier form, we can prove the stability of the closed-loop system. Two simulation examples are viewed to verify the feasibility of the approach.

In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example.

This paper concentrates on the adaptive critic design (ACD) issue for a class of uncertain multi-input multioutput (MIMO) nonlinear discrete-time systems preceded by unknown backlashlike hysteresis. The considered systems are in a block-triangular pure-feedback form, in which there exist nonaffine functions and couplings between states and inputs. This makes that the ACD-based optimal control becomes very difficult and complicated. To this end, the mean value theorem is employed to transform the original systems into input-output models. Based on the reinforcement learning algorithm, the optimal control strategy is established with an actor-critic structure. Not only the stability of the systems is ensured but also the performance index is minimized. In contrast to the previous results, the main contributions are: 1) it is the first time to build an ACD framework for such MIMO systems with unknown hysteresis and 2) an adaptive auxiliary signal is developed to compensate the influence of hysteresis. In the end, a numerical study is provided to demonstrate the effectiveness of the present method.

This paper deals with the tracking control problem for a class of nonlinear multiple input multiple output unknown time-varying delay systems with full state constraints. To overcome the challenges which cause by the appearances of the unknown time-varying delays and full-state constraints simultaneously in the systems, an adaptive control method is presented for such systems for the first time. The appropriate Lyapunov-Krasovskii functions and a separation technique are employed to eliminate the effect of unknown time-varying delays. The barrier Lyapunov functions are employed to prevent the violation of the full state constraints. The singular problems are dealt with by introducing the signal function. Finally, it is proven that the proposed method can both guarantee the good tracking performance of the systems output, all states are remained in the constrained interval and all the closed-loop signals are bounded in the design process based on choosing appropriate design parameters. The practicability of the proposed control technique is demonstrated by a simulation study in this paper.

A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example.

In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called "explosion of complexity" problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.

Compared with the existing neural network (NN) or fuzzy logic system (FLS) based adaptive consensus methods, the proposed approach can greatly alleviate the computation burden because it needs only to update a few adaptive parameters online. In the multiagent agreement control, the system uncertainties derive from the unknown nonlinear dynamics are counteracted by employing the adaptive NNs; the state delays are compensated by designing a Lyapunov-Krasovskii functional. Finally, based on Lyapunov stability theory, it is demonstrated that the proposed consensus scheme can steer a multiagent system synchronizing to the predefined reference signals. Two simulation examples, a numerical multiagent system and a practical multimanipulator system, are carried out to further verify and testify the effectiveness of the proposed agreement approach.

This paper proposes an adaptive fuzzy asymptotic control method for multiple input multiple output (MIMO) nonlinear systems with unknown input coefficients, with a focus on handling unknown input nonlinearities and control directions. For all the existing Nussbaum gain-based approaches, it is difficult to investigate unknown input coefficients problem since multiple time-varying coefficients and disturbances coexist and should be simultaneously tackled in the stability analysis. To overcome the above difficulty, we propose a robust Nussbaum gain-based approach for the adaptive fuzzy asymptotic control of MIMO nonlinear systems. Benefiting from the proposed Nussbaum gain-based approach, bounded disturbances including unmodeled system dynamics and universal approximation errors are handled. Furthermore, the proposed approach helps extend the bounded fuzzy control result to the asymptotic convergence. Hence, both the control robustness and control accuracy are prompted within the frame of the developed Nussbaum gain approach. Finally, a simulation example is carried out to illustrate the effectiveness of the proposed control method.

This paper solves the problem of adaptive fuzzy inverse compensation control for an uncertain nonlinear system whose actuator is subjected to generalized dead-zone nonlinearity. By defining a continuous connection function and combining with the mean-value theorem, the generalized dead zone is first decomposed into a nominal asymmetric dead zone multiplying an uncertain continuous input function. Afterward, a smooth inversion and its parameterization are further proposed such that a new expression of adaptive asymmetric dead-zone compensation error is established in Theorems 1 and 2. With such an expression, the fuzzy systems can be successfully embedded into a compensation structure to indirectly handle uncertain input dynamics. In addition, a separation scheme is developed to construct two online estimators. Based on the above design procedure, an adaptive inverse compensator for generalized dead zone is built eventually. With the backstepping iteration design of compensator input, an adaptive fuzzy controller is developed to establish the closed-loop system stability. Finally, two simulations are conducted to illustrate the effectiveness and applicability of the proposed control scheme.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

In this paper, an adaptive neural network (NN)-based tracking control algorithm is proposed for the wheeled mobile robotic (WMR) system with full state constraints. It is the first time to design an adaptive NN-based control algorithm for the dynamic WMR system with full state constraints. The constraints come from the limitations of the wheels' forward speed and steering angular velocity, which depends on the motors' driving performance. By employing adaptive NNs and a barrier Lyapunov function with error variables, then, the unknown functions in the systems are estimated, and the constraints are not violated. Based on the assumptions and lemmas given in this paper and the references, while the design and the system parameters chose properly, our proposed scheme can guarantee the uniform ultimate boundedness for all signals in the WMR system, and the tracking error converge to a bounded compact set to zero. The numerical experiment of a WMR system is presented to illustrate the good performance of the proposed control algorithm.

In this paper, model identification and adaptive control design are performed on Devanit-Hartenberg model of a humanoid robot. We focus on the modeling of the 6 degree-of-freedom upper limb of the robot using recursive Newton-Euler (RNE) formula for the coordinate frame of each joint. To obtain sufficient excitation for modeling of the robot, the particle swarm optimization method has been employed to optimize the trajectory of each joint, such that satisfied parameter estimation can be obtained. In addition, the estimated inertia parameters are taken as the initial values for the RNE-based adaptive control design to achieve improved tracking performance. Simulation studies have been carried out to verify the result of the identification algorithm and to illustrate the effectiveness of the control design.

In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example.

An adaptive control-based neural network for a n-link robot is studied and the considered robot can be transformed as a class of multi-input-multioutput systems. The position of the robot or the output of the transformed systems is constrained in a time-varying compact set. It is commonly known that the constant constraint belongs to a special case of the time-varying constraint, and thus, it can be more general for handling practical problem as compared with the existing methods for robot. The neural approximation is used to estimate the unknown functions of systems and the time-varying barrier Lyapunov function is used to overcome the violation of constraints. It can prove the stability of the closed-loop systems by using Lyapunov analysis. The feasibility of the approach is demonstrated by performing a simulation example.

Combined with backstepping techniques, an observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form. By constructing the neural network-based state observer for each follower, the proposed consensus control method solves the unmeasurable state problem of high-order nonlinear multiagent systems. The control algorithm can guarantee that all signals of the multiagent system are semi-globally uniformly ultimately bounded and all outputs can synchronously track a reference signal to a desired accuracy. A simulation example is carried out to further demonstrate the effectiveness of the proposed consensus control method.

In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.

This paper studies an adaptive neural control for nonlinear multiple-input multiple-output systems in interconnected form. The studied systems are composed of N subsystems in pure feedback structure and the interconnection terms are contained in every equation of each subsystem. Moreover, the studied systems consider the effects of Prandtl-Ishlinskii (PI) hysteresis model. It is for the first time to study the control problem for such a class of systems. In addition, the proposed scheme removes an important assumption imposed on the previous works that the bounds of the parameters in PI hysteresis are known. The radial basis functions neural networks are employed to approximate unknown functions. The adaptation laws and the controllers are designed by employing the backstepping technique. The closed-loop system can be proven to be stable by using Lyapunov theorem. A simulation example is studied to validate the effectiveness of the scheme.

In this paper, an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems. The controlled systems are in a strict-feedback frame and contain unknown functions and nonsymmetric dead-zone. For this class of systems, the control objective is to design a controller, which not only guarantees the stability of the systems, but achieves the optimal control performance as well. This immediately brings about the difficulties in the controller design. To this end, the fuzzy logic systems are employed to approximate the unknown functions in the systems. Based on the utility functions and the critic designs, and by applying the backsteppping design technique, a reinforcement learning algorithm is used to develop an optimal control signal. The adaptation auxiliary signal for unknown dead-zone parameters is established to compensate for the effect of nonsymmetric dead-zone on the control performance, and the updating laws are obtained based on the gradient descent rule. The stability of the control systems can be proved based on the difference Lyapunov function method. The feasibility of the proposed control approach is further demonstrated via two simulation examples.

In this paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples.

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.

In the paper, an adaptive tracking control design is studied for a class of nonlinear discrete-time systems with dead-zone input. The considered systems are of the nonaffine pure-feedback form and the dead-zone input appears nonlinearly in the systems. The contributions of the paper are that: 1) it is for the first time to investigate the control problem for this class of discrete-time systems with dead-zone; 2) there are major difficulties for stabilizing such systems and in order to overcome the difficulties, the systems are transformed into an n-step-ahead predictor but nonaffine function is still existent; and 3) an adaptive compensative term is constructed to compensate for the parameters of the dead-zone. The neural networks are used to approximate the unknown functions in the transformed systems. Based on the Lyapunov theory, it is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero. Two simulation examples are provided to verify the effectiveness of the control approach in the paper.

The adaptive fuzzy identification and control problems are considered for a class of multi-input multi-output nonlinear systems with unknown functions and unknown dead-zone inputs. The main characteristics of the considered systems are that 1) they are composed of n subsystems and each subsystem is in nested lower triangular form, 2) dead-zone inputs are in nonsymmetric nonlinear form, and 3) dead-zone inputs appear nonlinearly in the systems and their parameters are not required to be known. The controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions, the couplings among the nested subsystems, and the dead-zone inputs. In the controller design, the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead-zone inputs. To compensate for dead-zone inputs, the compensative terms are designed in the controllers. The stability of the closed-loop system is proved via the Lyapunov stability theorem. A simulation example is provided to validate the feasibility of the approach.

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

This paper studies an adaptive tracking control for a class of nonlinear stochastic systems with unknown functions. The considered systems are in the nonaffine pure-feedback form, and it is the first to control this class of systems with stochastic disturbances. The fuzzy-neural networks are used to approximate unknown functions. Based on the backstepping design technique, the controllers and the adaptation laws are obtained. Compared to most of the existing stochastic systems, the proposed control algorithm has fewer adjustable parameters and thus, it can reduce online computation load. By using Lyapunov analysis, it is proven that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded in probability and the system output tracks the reference signal to a bounded compact set. The simulation example is given to illustrate the effectiveness of the proposed control algorithm.

In this paper, an adaptive fuzzy robust output feedback control problem is considered for a class of single-input and single-output nonlinear systems in a strict-feedback form. The considered systems possess the unstructured uncertainties, unknown dead zone, and the dynamics uncertainties, and they do not assume the states being available for the controller design. In the controller design, fuzzy logic systems are first used to approximate the unstructured uncertainties, and by utilizing the information of the bounds of the dead-zone slopes and treating the time-varying inputs coefficients as a system uncertainty, a fuzzy state observer is designed to estimate the unmeasured states. By combining a backstepping technique with a nonlinear small-gain approach, a new adaptive fuzzy robust output feedback control has been developed. It is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed-loop systems. Simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach.

An adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper. The considered systems are of the discrete-time form in a triangular structure and include the backlash and the external disturbance. By using the prediction function of future states, the systems are transformed into an n-step ahead predictor. The fuzzy logic systems (FLSs) are used to approximate the unknown functions, unknown backlash, and backlash inversion, respectively. A discrete-time tuning algorithm is developed to estimate the optimal fuzzy parameters. Compared with the previous works for the discrete-time systems with backlash, the main contributions of the paper are that 1) the rigorous restriction for the functional estimation error is removed, and 2) the external disturbance is bounded, but the bound is not required to be known. A novel controller and the adaptation laws are constructed by using the discrete Taylor series expansion and the difference Lyapunov analysis, and thus, those limitations in the previous works are overcome. It is proven that all the signals in the closed-loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Because of the complexity of consensus control of nonlinear multiagent systems in state time-delay, most of previous works focused only on linear systems with input time-delay. An adaptive neural network (NN) consensus control method for a class of nonlinear multiagent systems with state time-delay is proposed in this paper. The approximation property of radial basis function neural networks (RBFNNs) is used to neutralize the uncertain nonlinear dynamics in agents. An appropriate Lyapunov-Krasovskii functional, which is obtained from the derivative of an appropriate Lyapunov function, is used to compensate the uncertainties of unknown time delays. It is proved that our proposed approach guarantees the convergence on the basis of Lyapunov stability theory. The simulation results of a nonlinear multiagent time-delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm.

In this paper, the problems of stability and tracking control for a class of large-scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach. Because the dynamic surface control technique is introduced, the designed controllers can avoid the issue of “explosion of complexity,” which comes from the traditional backstepping design procedure that deals with large-scale nonlinear systems with unmodeled dynamics. In addition, a reduced-order observer is designed to estimate those immeasurable states. Based on the Lyapunov stability method, it is proven that all the signals in the closed-loop system are bounded, and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately. The simulation examples are given to verify the effectiveness of the proposed techniques.

In this paper, an adaptive observer control is proposed for a class of uncertain chaotic systems. Because the system states are assumed to be unavailable, an observer is designed to estimate those unavailable states. The main advantage of this algorithm can overcome the problem of “explosion of complexity” inherent in the backstepping design. The stability analysis shows that the system is stable in the sense that all signals in the closed-loop system are uniformly ultimately bounded (GUUB) and the system output can track the reference signal to a bounded compact set. Finally, an example is provided to illustrate the effectiveness of the proposed control system.

In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques.

This brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi-input-multi-output (MIMO) systems in the discrete-time form. The considered MIMO systems are composed of n subsystems with the couplings of inputs and states among subsystems. In order to solve the noncausal problem and decouple the couplings, it needs to transform the systems into a predictor form. The higher order neural networks are utilized to approximate the desired controllers. By using Lyapunov analysis, it is proven that all the signals in the closed-loop system is the semi-globally uniformly ultimately bounded and the output errors converge to a compact set. In contrast to the existing results, the advantage of the scheme is that the number of the adjustable parameters is highly reduced. The effectiveness of the scheme is verified by a simulation example.

An adaptive output feedback control is studied for uncertain nonlinear single-input-single-output systems with partial unmeasured states. In the scheme, a reduced-order observer (ROO) is designed to estimate those unmeasured states. By employing radial basis function neural networks and incorporating the ROO into a new backstepping design, an adaptive output feedback controller is constructively developed. A prominent advantage is its ability to balance the control action between the state feedback and the output feedback. In addition, the scheme can be still implemented when all the states are not available. The stability of the closed-loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to validate the effectiveness of the proposed scheme.

In this paper, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of "explosion of complexity" inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches.

A robust adaptive fuzzy control approach is developed for a class of multi-input-multi-output (MIMO) nonlinear systems with modeling uncertainties and external disturbances by using both the approximation property of the fuzzy logic systems and the backstepping technique. The MIMO systems are composed of interconnected subsystems in the strict-feedback form. The main characteristics of the developed approach are that the online computation burden is alleviated and the robustness to dynamic uncertainties and external disturbances is improved. It is proven that all the signals of the resulting closed-loop system are uniformly bounded and that the tracking errors converge to a small neighborhood around zero. Two simulation experiments are presented to demonstrate the feasibility of the approach developed in this paper.