This article proposes an adjustable-error neural network (NN) approximator and incorporates it into the adaptive neural tracking controller design of uncertain nonlinear systems. Noted that the error between the unknown nonlinear function and the NN approximator cannot be adjusted under the traditional NN control framework, as it is solely determined by the selection of neurons, basis functions, and the estimation of the ideal weight vector. This inherent constraint compromises the precision of the NN approximation and the convergence accuracy of the tracking error. To improve the approximation accuracy of unknown nonlinear functions in adaptive neural control systems, an adjustable-error NN approximator is designed, in which the error between the approximator and the unknown nonlinear function can be adjusted by designed parameters. Based on the proposed NN approximator, an adaptive neural tracking controller is designed for a class of uncertain nonlinear systems, which achieves higher accuracy of the tracking error compared with traditional methods. The stability of the resulting closed-loop system is proved in the Lyapunov sense, and the convergence of the tracking error is also analyzed. The effectiveness of the proposed scheme is verified by simulation and experiment.

This work investigates the fault-prediction optimal output regulation problem for the structural reliability feedback (SRF) system, and it aims to design a reliability feedback controller that minimizes the probability of fault (PoF) of the SRF system. Distinguished from the existing feedback control, the tracking of the upper bound of the PoF is considered to ensure the fault-prediction in the feedback control. The proposed design converts the PoF tracking problem into the satisfaction of the generalized damage energy (GDE). Furthermore, the impact of inaccurate measurement is eliminated by tolerating the epistemic uncertainty via a novel probabilistic policy iteration (PI). Moreover, the uniformly ultimately bounded (UUB) condition of the SRF system is guaranteed by employing the subset method. Finally, comparative investigations are conducted to examine the superiority of the proposed approach.

The total least squares (TLS) algorithm is a superior identification tool for low-order errors-in-variables (EIV) systems, where the estimate can be obtained by solving an eigenvector of the minimum eigenvalue of an augmented matrix. However, the TLS algorithm demonstrates inefficiency when applied to high-order EIV systems. This study introduces two innovative TLS algorithms: an iterative TLS algorithm, offering superior performance for low-order EIV models, and a two-step TLS algorithm, designed to effectively handle high-order EIV models. In comparison to the conventional TLS algorithm, these proposed methodologies present noteworthy advantages, including: 1) reduced computational costs, 2) the utilization of an iterative technique to calculate the inverse, and 3) the diversification of EIV identification methods. Simulation bench test examples are selected to show the efficacy of the proposed algorithms and transparent procedure for applications. Note to Practitioners—This paper was motivated by the problem of identifying network systems which are contaminated by noises. For network systems, the input and output data are usually contaminated by noises. Existing approaches to estimating such systems have the assumption that the noises are in little level scenarios or only the output data are contaminated by noises. This paper suggests two new total least squares approaches which can deal with systems contaminated by noises in medium level scenarios or whose input and output are both contaminated by noises. These two algorithms, using iterative technique and two-step technique, can: 1) avoid the matrix inverse calculation; 2) reduce the computational efforts; 3) increase the convergence rates. The proposed algorithms can also be extended to various fields such as inverse scattering, pattern recognition, image restoration, and computer vision.

In this paper, a simple but effective control scheme is proposed for bilateral teleoperation systems with variable communication time-delays. The robotic models are first reformulated and an unknown system dynamics estimator (USDE) is constructed to estimate the lumped uncertainties without using the accelerations, where only low-pass filtering operations and trivial algebraic calculations are used. The USDE is then incorporated into the controller design to compensate for the effects of uncertainties. The stability of the closed-loop system is rigorously proven via the Lyapunov theorem for all three motion states: free motion, tracking motion, and contact motion. The salient feature over traditional control strategies is that apart from position and velocity synchronization, compliance can be guaranteed in the tracking motion and force transparency can be obtained in the contact motion. Moreover, the proposed USDE and control have simple structures and less parameters, which facilitate their practical application. Both simulation and experimental results are presented to demonstrate the effectiveness of the proposed methods.Note to Practitioners—Bilateral teleoperation systems are widely used in nuclear science, space research, telesurgery, microassembly and other fields, where human or unmanned robotics cannot perform certain tasks. However, in the teleoperation, several factors such as external forces and communication delays between local and remote robotics will affect the control performance, e.g., synchronization, compliance and transparency. This paper proposes a USDE-based control method that can handle unknown system dynamics and variable time-delays without using the acceleration signals, while the system’s stability in all the three motion states: free motion, tracking motion and contact motion can be retained, and the corresponding position and velocity synchronization objectives can be achieved. This method has the certain advantages including simpler structures, less tuning parameters and better control performances, facilitating its practical applications. Finally, both simulation and experiments are illustrated to verify the theoretical claims.

Flexibility models based on the virtual joint approach (VJA) are essential for error compensation to improve the positioning accuracy of industrial robots across a range of payloads. However, current flexibility models are not accurate enough due to less consideration of deformation, or incorporate too many factors leading to difficulties in practical applications. This paper proposes a flexibility model based on the error sensitivity analysis to improve the positioning accuracy and stability of industrial robots. First, the effects of the six directions flexible deformation of the joint on the positioning error are analyzed by introducing the Sobol’s method. It indicates that the rotational deformations around X, Y and Z-axes cause the majority of positioning errors, and only a tiny minority is originated from translational deformations along X, Y, and Z-axes. Then, a mapping equation between the flexible deformations around X, Y and Z-axes and the positioning error is derived based on this observation. Finally, a flexibility model for N degrees of freedom (DoF) industrial robots is established and an identification method is presented for flexibility coefficients. The verification experiments are performed on a 6-DoF robot, and an application example is provided for error compensation in robotic assembly tasks. The experimental results show that the proposed model has higher accuracy and stability but lower calculation cost than conventional models. Moreover, after compensation, the pose error is reduced to 0.1mm and 0.03° meeting the assembly requirements in the application example. Note to Practitioners—The joint deformation under payload and link gravity is mainly responsible for the degraded positioning accuracy of industrial robots. Error compensation by flexibility models is an effective way to improve positioning accuracy. Traditional 6-DoF flexibility models are too complex to be used in industrial scenarios, while 1-DoF flexibility models are not accurate enough. This paper proposes an error sensitivity flexibility compensation that considers the main factors affecting the positioning error, while removing factors with less impact. Compared with traditional models, the proposed model combines both high accuracy and applicability. Through establishing the mathematical equation between the joint deformation and the positioning error, a new flexibility model is derived, and an easy-to-implement method is provided to identify flexibility coefficients. The proposed model can be used conveniently for high-precision compensation of errors, including applications with constant payloads, such as assembly, cutting and welding, as well as tasks with variable payloads, such as milling, drilling and de-burring. In addition, the model can also be used to optimize poses to reduce robot flexibility and enhance resistance to deformation in one workspace. Experiments indicate that high compensation accuracy can be obtained by applying the flexibility model to robot assembly tasks.

The inherent hysteresis nonlinearity in the magnetostrictive actuators (MAs) restricts their application in high-precision positioning systems. While direct inverse compensation has been widely used to mitigate hysteresis effects, it suffers from complexities in computing the inverse model, and addressing the residual modeling and compensation errors. In this respect, this paper introduces a composite control strategy to enhance the control performance of magnetostrictive actuated positioning system (MAPS) by presenting a new inverse-based compensator for the hysteresis. The key innovation lies in the derivation of an analytical expression for the inverse compensation error based on a generalized Prandtl-Ishlinskii (GPI) model, and the design of an unknown system dynamics estimator (USDE) to estimate this residual error. The USDE has a simple structure and easy parameter tuning, and can be trivially integrated into the closed-loop control system. Furthermore, a fast reaching law (FRL) is developed to design a composite sliding mode control (SMC), which uses both the inverse-based compensator and the USDE. This control with the FRL can achieve both the enhanced control response and the reduced chattering, compared with the standard SMC techniques. Finally, the effectiveness of the proposed approaches is confirmed by comparative simulations and experiments.

Admittance control is an effective technique for enhancing compliance with the interaction between the exoskeleton and the wearer. In practice, obtaining the desired admittance model parameters is a challenging task under various interaction scenarios with different wearers, especially when the human impedance parameters are indeterminate. In this paper, we propose a hierarchical optimal admittance control consisting of a higher-level admittance learning and a lower-level position control. First, finding the desired admittance model parameters is reformulated as a linear quadratic regulator (LQR) problem, and then a policy iteration (PI) algorithm is proposed to solve the derived LQR problem even with unknown system dynamics and human impedance parameters. With the obtained admittance model, the virtual trajectory is regulated to adapt the human-robot interaction (HRI) torque. Finally, an unknown system dynamics estimator (USDE) is integrated into a lower-level position controller to accommodate the lumped system uncertainties. This approach reduces the computational burden of admittance control while improving the tracking performance of position control. Comparative simulations are conducted to validate the effectiveness of the proposed hierarchical admittance control, and multiple knee joint flexion/extension movement experiments with surface electromyographic (sEMG) measurements are also carried out on three subjects to evaluate its improved compliance performance.

This article addresses the tracking control problem of uncertain nonlinear strict-feedback systems. First, to enhance the tracking performance of control system, an improved prescribed performance function (PPF) is constructed, which yields that the convergence accuracy of tracking error can reach a preset factor than that of the traditional PPF-based control method. Then, the fuzzy logic system (FLS) is used to approximate the unknown nonlinear dynamics on a compact set integrated by an ideal controller, from which an adaptive fuzzy control law is designed by combining the improved PPF and FLS. The stability of closed-loop system and the convergence of tracking error are analyzed in the Lyapunov sense. Finally, simulation and experimental results show the feasibility and effectiveness of the proposed method.

The control problem for connected vehicular platoons requires balancing control optimality, saving computational and communication resources, and ensuring security. In this paper, a fuzzy prescribed performance adaptive optimal control strategy is developed for platoon system, and a distributed event-triggered (ET) mechanism is introduced. The main contributions include: 1) A prescribed performance adaptive dynamic programming (ADP) control architecture under distributed event-triggering is developed. The designed control method not only ensures the safety distance requirements of the platoon, but also significantly reduces the computing and communication costs, while guaranteeing the control optimality under the above objectives; 2) The stability proof of the platoon system considering the above complex control objectives is completed. Stable convergence of fuzzy logic system (FLS) is ensured by designing an experience replay-based critic update rule; 3) Considering the practicability in real working conditions, the cost function of the ADP controller robust to actuator saturation and disturbance is designed. Compared with existing methods, our approach achieves optimal control, robustness, and enhanced communication efficiency. Finally, the effectiveness and applicability of the controller are verified by simulations.

The exponential asynchronous stabilization (EAS) issue for a category of neural networks (NNs) with semi-Markov jump (SMJ) parameters and additive time-varying delays (ATDs) is addressed in this article. Here, the SMJ parameters in the controller gain are supposed to be distinct from those in the system structure, which is more consistent with the actual situation. To further relieve the communication load of the network, a new discrete adaptive event-triggered impulsive control (DAEIC) scheme is proposed, where the impulsive moments are the sampling instants satisfying event-triggered constraints, and the triggering threshold can be dynamically adjusted by an adaptive update rule (AUR) related to the current sampling state and the last triggered state. A more flexible looped Lyapunov-Krasovski functional (LLKF) is constructed to commendably capture the available information about impulsive instants, triggering state, sampling interval, ATDs, and heterogeneous SMJ parameters. Combined with the LLKF, DAEIC scheme, and other inequality analysis approaches, some novel results guaranteeing the EAS of the underlying systems are exported. Finally, three explanatory examples are presented to check the validity of our results.

This paper proposes an adaptive bipartite secure consensus asymptotic tracking control scheme based on event-triggered strategy for the nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. First, by incorporating the concept of shortest path into the hierarchical algorithm, the bipartite consensus control problem in the presence of unbalanced communication topology is successfully addressed. Further, an anti-attack bipartite control strategy by designing the improved forms of the tracking errors and virtual controllers is proposed under DoS attacks. Then, a modified event-triggered mechanism based on the relative threshold strategy is proposed, which can ensure that the bipartite consensus tracking errors converge to zero asymptotically by utilizing the Barbalat’s Lemma. Under the Lyapunov stability theory, it is guaranteed that the outputs of all agents can reach agreement with an identical magnitude but opposite signs and all the signals of the closed-loop MASs are bounded. Finally, the simulation results on the model of damping pendulums are given to verify the efficiency of the proposed secure controller.Note to Practitioners—In this paper, the adaptive bipartite secure consensus asymptotic tracking control problem is considered for nonlinear MASs subject to DoS attacks, whose models can describe many critical applications, such as bidirectional formation of unmanned vehicles and robots. The research on the secure tracking control problem will be rather complicated yet challenging if the DoS attacks of the communication channels are taken into account in the insecure complex network environment. In addition, the event-triggered mechanism is used to reduce the usage of communication resources, which makes the proposed control scheme more easier to implement and more friendly for control engineers.

The path tracking control problem for autonomous vehicle with uncertain dynamics requires simultaneous consideration of control optimality and safety-based performance constraints. In this paper, an adaptive optimal control method with prescribed performance is proposed to solve this problem, which contains two contributions: 1) by introducing a prescribed performance function (PPF) into adaptive dynamic programming (ADP), the controller can constrain the tracking error of the system within a specified performance boundary while optimizing the control cost; 2) the critic-only ADP is used for the controller design, which simplifies the commonly used actor-critic ADP scheme, and the convergence of the estimation error is guaranteed under FE conditions. On this basis, the neural network identification technique is introduced to deal with the unknown dynamic parameters of the vehicle system. The control scheme is able to strictly guarantee user-defined vehicle performance specifications with approximately optimal control performance. The stability of the closed-loop system is rigorously demonstrated by the Lyapunov method. In addition, the controller also embeds a radial basis function neural network (RBFNN) compensator to approximate the nonlinear external disturbances of the autonomous vehicle. Finally, the efficiency of the controller to achieve autonomous vehicle path tracking is verified by CarSim-Simulink simulation.

In this paper, the mixed traffic scenario with human-driven vehicles (HDVs) and connected and autonomous vehicles (CAVs) on freeway is considered. In this partly known nonlinear system, an optimal control algorithm using adaptive dynamic programming (ADP) is proposed to deal with the communication latence and drivers’ reaction time, which can stabilize the system under the influence of dead zone and saturation with minimal cost. There are three contributions in this paper. Firstly, in the used ADP algorithm, a critic neural network (NN) is designed to estimate the optimal value of the cost function, which is updated using online data instead of pre-gathered data. This means that the proposed controller can adapt to different parameters of different systems. Secondly, the reaction time of human driver and the time latence of the V2V communication are considered as the state and input delay of the nonlinear system, by adding the terms of delayed states to the optimal value function, the influence of the time delay can be minimized in the process of the critic NN updating. Thirdly, the saturation and dead zone of actuator are considered, by designing a new utility function of control value, the control value is limited from being out of the expected range. Under this condition, the stabilization of the overall system and the effectiveness of the proposed algorithm is proved and validated by means of simulation results.

This paper proposes a new adaptive estimation approach to online estimate the model parameters of a piezoelectric cantilever beam. The beam behavior is firstly modeled using partial differential equations (PDE) considering the Kelvin-Voigt damping. To facilitate the estimation of unknown model parameters, the Galerkin’s method is introduced to extract desired vibration modes by separating the time and space variables of the PDE. Then, considering two major vibration modes, the corresponding system model can be represented by a fourth-order ordinary differential equation (ODE). Finally, by using measured input and output information, a novel adaptive parameter estimation strategy is introduced to estimate the unknown parameters of the derived ODE model in real time. For the purpose of driving the parameter updating law, the estimation error is extracted by using an auxiliary variable and a time-varying gain. Consequently, the convergence of the parameter estimation error is rigorously proved based on the Lyapunov theory. Simulations and experimental results show the validity and practicability of the proposed estimation method.

In this article, a generalized fuzzy subset (GFS) method is proposed to assess the time-varying multistate reliability of the perturbation failure coupling measurement system. First, a perturbation-failure coupling mechanism is designed to define the propagation chain of perturbations so as to integrate all the possible perturbations as the inputs of the GFS method. Second, to assess the time-varying multistate reliability, a GFS reliability model is constructed based on the composite limit state. Furthermore, the concept of the uncertain subset boundary is presented to conduct the reliability assessment via a group of embedded interval type-2 fuzzy sets. To address the deficiency of the GFS reliability model, a data-driven strategy is designed to establish the implicit relation between the limited expert knowledge and the membership function. Finally, the experimental tests are carried out to examine the superiority of the GFS method, and parametric studies are also conducted to study the reliability of the PFCM system.

This article studies the multi- [Formula: see text] controls for the input-interference nonlinear systems via adaptive dynamic programming (ADP) method, which allows for multiple inputs to have the individual selfish component of the strategy to resist weighted interference. In this line, the ADP scheme is used to learn the Nash-optimization solutions of the input-interference nonlinear system such that multiple [Formula: see text] performance indices can reach the defined Nash equilibrium. First, the input-interference nonlinear system is given and the Nash equilibrium is defined. An adaptive neural network (NN) observer is introduced to identify the input-interference nonlinear dynamics. Then, the critic NNs are used to learn the multiple [Formula: see text] performance indices. A novel adaptive law is designed to update the critic NN weights by minimizing the Hamiltonian-Jacobi-Isaacs (HJI) equation, which can be used to directly calculate the multi- [Formula: see text] controls effectively by using input-output data such that the actor structure is avoided. Moreover, the control system stability and updated parameter convergence are proved. Finally, two numerical examples are simulated to verify the proposed ADP scheme for the input-interference nonlinear system.

This article investigates a finite-time composite learning-based elliptical enclosing control for nonholonomic robots under a global positioning system (GPS)-denied environment. At the kinematic level, following a prediction and innovation architecture, a novel bearing measurement-based relative position observer formulated in a local coordinate is proposed to assure an exponential decaying of estimation errors without the aid of GPS. Utilizing the observation outcomes, an elliptical guidance law with a time-varying enclosing radius and nonorthogonal tangential and axial vectors is established to yield the reference velocity and angular rate to be tracked. At the kinetic level, by constructing filtering operations and auxiliary variables to extract weight errors, a special finite-time composite neural learning driven by weight and tracking errors is devised to reinforce parameter convergences, then an anti-disturbance kinetic control rule is designed to achieve online precise disturbance compensation and finite-time error convergence. The distinct merit is that an elliptical surrounding concerning an unknown target can be fulfilled with the finite-time neural learning capability while eliminating the deployment of GPS, which is nontrivial and challenging than reported circumnavigation alternatives either relying on the accessibility of GPS or neglecting kinetic uncertainties. An input-to-state stable criterion is applied to demonstrate the boundedness of a closed-loop system. Simulations are provided to confirm the utility of the considered strategy.

This article proposes a novel control method for vehicle active suspension systems in the presence of time-varying input delay and unknown nonlinearities. An unknown system dynamics estimator (USDE), which employs first-order low-pass filter operations and has only one tuning parameter, is constructed to deal with unknown nonlinearities. With this USDE, the widely used function approximators (e.g., neural networks and fuzzy-logic systems) are not needed, and the intermediate variables and observer used in the traditional estimators are not required. This estimator has a reduced computational burden, trivial parameter tuning and guaranteed convergence. Moreover, a predictor-based compensation strategy is developed to handle the time-varying input delay. Finally, we combine the suggested USDE and predictor to design a feedback controller to attenuate the vibrations of vehicle body and retain the required suspension performances. Theoretical analysis is carried out via the Lyapunov-Krasovkii functional to prove the stability of the closed-loop system. Simulation results based on professional vehicle simulation software Carsim are provided to show the efficiency of the proposed control scheme.

In this article, we studied the parameters identification problem for the single sinusoidal signal based on the finite-time observer technique. After representing the sinusoidal signal with known frequency as a second-order time-invariant system, a finite-time observer-based estimation strategy is designed based on the homogeneous system theory to obtain unknown amplitude and phase angle. When the signal frequency is unknown, the original signal will be constructed into a third-order nonlinear system, which is challenging to design the corresponding state estimator. Based on the Lyapunov analysis method and adding a power integrator technique, a finite-time estimation scheme is developed and analyzed strictly. Finally, for a single-phase grid signal, some experimental results are provided to illustrate the efficacy of the proposed method.

This article presents an adaptive control method for dual-arm robot systems to perform bimanual tasks under modeling uncertainties. Different from the traditional symmetric bimanual robot control, we study the dual-arm robot control with relative motions between robotic arms and a grasped object. The robot system is first divided into two subsystems: a settled manipulator system and a tool-used manipulator system. Then, a command filtered control technique is developed for trajectory tracking and contact force control. In addition, to deal with the inevitable dynamic uncertainties, a radial basis function neural network (RBFNN) is employed for the robot, with a novel composite learning law to update the NN weights. The composite learning is mainly based on an integration of the historic data of NN regression such that information of the estimate error can be utilized to improve the convergence. Moreover, a partial persistent excitation condition is employed to ensure estimation convergence. The stability analysis is performed by using the Lyapunov theorem. Numerical simulation results demonstrate the validity of the proposed control and learning algorithm.

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.

This article presents and practically validates an identifier-critic-based approximate dynamic programming (ADP) method to online address the optimal tracking control problem for nonlinear continuous-time unknown systems. The imposed assumption on precisely known system dynamics is obviated via a neural network (NN) identifier. A static control is first adopted to retain the steady-state tracking response, while an optimal control derived via the ADP method is proposed to regulate the tracking error by minimizing a cost function. A critic NN is then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation. The learning of the identifier NN and critic NN is performed online simultaneously by tailoring a novel adaptation method, which can guarantee the convergence of the estimated NN weights. Consequently, the critic NN can be used to construct the optimal control policy directly, such that the actor NN used in the previous ADP schemes is avoided. Simulations are performed to verify the suggested control, and experiments on a helicopter plant are carried out to show its feasibility and improved control response.

Although robust control has been studied for decades, the output-feedback robust control design is still challenging in the control field. This article proposes a new approach to address the output-feedback robust control for continuous-time uncertain systems. First, we transform the robust control problem into an optimal control problem of the nominal linear system with a constructive cost function, which allows simplifying the control design. Then, a modified algebraic Riccati equation (MARE) is constructed by further investigating the corresponding relationship with the state-feedback optimal control. To solve the derived MARE online, the vectorization operation and Kronecker's product are applied to reformulate the output Lyapunov function, and then, a new online data-driven learning method is suggested to learn its solution. Consequently, only the measurable system input and output are used to derive the solution of the MARE. In this case, the output-feedback robust control gain can be obtained without using the unknown system states. The control system stability and convergence of the derived solution are rigorously proved. Two simulation examples are provided to demonstrate the efficacy of the suggested methods.

This article investigates the integrated lane-keeping and roll control for autonomous ground vehicles (AGVs) considering the transient performance and system disturbances. The robust integral of the sign of error (RISE) control strategy is proposed to achieve the lane-keeping control purpose with rollover prevention, by guaranteeing the asymptotic stability of the closed-loop system, attenuating systematic disturbances, and maintaining the controlled states within the prescribed performance boundaries. Three contributions have been made in this article: 1) a new prescribed performance function (PPF) that does not require accurate initial errors is proposed to guarantee the tracking errors restricted within the predefined asymptotic boundaries; 2) a modified neural network (NN) estimator which requires fewer adaptively updated parameters is proposed to approximate the unknown vertical dynamics; and 3) the improved RISE control based on PPF is proposed to achieve the integrated control objective, which analytically guarantees both the controller continuity and closed-loop system asymptotic stability by integrating the signum error function. The overall system stability is proved with the Lyapunov function. The controller effectiveness and robustness are finally verified by comparative simulations using two representative driving maneuvers, based on the high-fidelity CarSim-Simulink simulation.

This paper presents an alternative adaptive parameter estimation framework for nonlinear systems with time-varying parameters. Unlike existing techniques that rely on the polynomial approximation of time-varying parameters, the proposed method can directly estimate the unknown time-varying parameters. Moreover, this paper proposes several new adaptive laws driven by the derived information of parameter estimation errors, which achieve faster convergence rate than conventional gradient descent algorithms. In particular, the exponential error convergence can be rigorously proved under the well-recognized persistent excitation condition. The robustness of the developed adaptive estimation schemes against bounded disturbances is also studied. Comparative simulation results reveal that the proposed approaches can achieve better estimation performance than several other estimation algorithms. Finally, the proposed parameter estimation methods are verified by conducting experiments based on a roto-magnet plant.

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method.

In this paper, a force sensorless control scheme based on neural networks (NNs) is developed for interaction between robot manipulators and human arms in physical collision. In this scheme, the trajectory is generated by using geometry vector method with Kinect sensor. To comply with the external torque from the environment, this paper presents a sensorless admittance control approach in joint space based on an observer approach, which is used to estimate external torques applied by the operator. To deal with the tracking problem of the uncertain manipulator, an adaptive controller combined with the radial basis function NN (RBFNN) is designed. The RBFNN is used to compensate for uncertainties in the system. In order to achieve the prescribed tracking precision, an error transformation algorithm is integrated into the controller. The Lyapunov functions are used to analyze the stability of the control system. The experiments on the Baxter robot are carried out to demonstrate the effectiveness and correctness of the proposed control scheme.

This paper presents a new adaptive fuzzy control scheme for active suspension systems subject to control input time delay and unknown nonlinear dynamics. First, a predictor-based compensation scheme is constructed to address the effect of input delay in the closed-loop system. Then, a fuzzy logic system (FLS) is employed as the function approximator to address the unknown nonlinearities. Finally, to enhance the transient suspension response, a novel parameter estimation error-based finite-time (FT) adaptive algorithm is developed to online update the unknown FLS weights, which differs from traditional estimation methods, for example, gradient algorithm with e -modification or σ -modification. In this framework, both the suspension and estimation errors can achieve convergence in FT. A Lyapunov-Krasovskii functional is constructed to prove the closed-loop system stability. Comparative simulation results based on a dynamic simulator built in a professional vehicle simulation software, Carsim, are provided to demonstrate the validity of the proposed control approach, and show its effectiveness to operate active suspension systems safely and reliably in various road conditions.

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.

This paper proposes an adaptive funnel control (FC) scheme for servo mechanisms with an unknown dead-zone. To improve the transient and steady-state performance, a modified funnel variable, which relaxes the limitation of the original FC (e.g., systems with relative degree 1 or 2), is developed using the tracking error to replace the scaling factor. Then, by applying the error transformation method, the original error is transformed into a new error variable which is used in the controller design. By using an improved funnel function in a dynamic surface control procedure, an adaptive funnel controller is proposed to guarantee that the output error remains within a predefined funnel boundary. A novel command filter technique is introduced by using the Levant differentiator to eliminate the "explosion of complexity" problem in the conventional backstepping procedure. Neural networks are used to approximate the unknown dead-zone and unknown nonlinear functions. Comparative experiments on a turntable servo mechanism confirm the effectiveness of the devised control method.

This article presents a new adaptive parameter estimation method and the corresponding control design for nonlinear servo mechanisms with friction compensation. A continuous friction model is employed to capture the friction dynamics of servo mechanisms. Then, the unknown system parameters including friction model parameters are online estimated via the derived adaptive law. Hence, a new adaptive law is proposed to achieve faster and more accurate parameter estimation over classical adaptive laws so as to suppress the undesired transient dynamics. For this purpose, an auxiliary filter is introduced to extract the estimation error for driving the parameter updating law. Moreover, an adaptive control is designed in conjunction with a robust integral of the sign of the error feedback term to address the bounded disturbances and enhance the tracking precision. Simulations and experiments are given to validate the efficiency of the developed control scheme.

Due to strongly coupled nonlinearities of the grasped dual-arm robot and the internal forces generated by grasped objects, the dual-arm robot control with uncertain kinematics and dynamics raises a challenging problem. In this paper, an adaptive fuzzy control scheme is developed for a dual-arm robot, where an approximate Jacobian matrix is applied to address the uncertain kinematic control, while a decentralized fuzzy logic controller is constructed to compensate for uncertain dynamics of the robotic arms and the manipulated object. Also, a novel finite-time convergence parameter adaptation technique is developed for the estimation of kinematic parameters and fuzzy logic weights, such that the estimation can be guaranteed to converge to small neighborhoods around their ideal values in a finite time. Moreover, a partial persistent excitation property of the Gaussian-membership-based fuzzy basis function was established to relax the conventional persistent excitation condition. This enables a designer to reuse these learned weight values in the future without relearning. Extensive simulation studies have been carried out using a dual-arm robot to illustrate the effectiveness of the proposed approach.

In this paper, we propose real-time adaptive parameter estimation methods for a polymer electrolyte membrane fuel cell (PEMFC) to facilitate the modeling and the subsequent control synthesis. Specifically, the electrochemical model of this fuel cell is in a nonlinearly parametric formulation. Hence, most of existing parameter estimation techniques for PEMFC mainly rely on the optimization approaches, requiring heavy computational costs or even offline implementation. In comparison to those methods, real-time adaptive parameter estimation methods for nonlinearly parametric system are developed in this paper. First, the nonlinearly parametric function is linearized by using the Taylor series expansion. Then, adaptive parameter estimation methods are proposed for estimating the constant or time-varying parameters of PEMFC. Different from the well-recognized adaptive parameter estimation methods, the proposed adaptive laws are driven by the extracted estimation errors, so that exponential convergence of the parameter estimation error can be guaranteed, without using any predictors or observers. Finally, practical experiments in a H-100 PEMFC system are conducted, which illustrate satisfactory performances of the presented parameter estimation methods under different operation scenarios

This article proposes a novel nonlinear receding horizon optimal control algorithm for wave energy converter (WECs) with nonlinear dynamics. It is well accepted that the WEC control problem is essentially a noncausal constrained optimal control problem, where the energy output can be improved by incorporating the short-term wave prediction into the control synthesis. Inspired by this fact, we suggest a new nonlinear noncausal optimal control (NNOC) for WECs based on the principle of approximate dynamic programming, which can, first, explicitly use the wave prediction to improve the energy conversion efficiency; second, handle the state and control input constraints; third, reduce the computational burden. Different to the existing linear noncausal optimal control, the derived Hamilton-Jacobi-Bellman equation for NNOC does not have an analytic solution. To tackle this problem, a critic neural network (NN) is adopted to approximate its solution in a receding horizon manor. The weights of NN are determined via a policy iteration algorithm. The resulting NNOC consists of a causal state feedback part and a noncausal feedforward part to explicit incorporate wave prediction information. Numerical simulations are provided to verify the efficacy of the proposed NNOC method.

Most function approximator (e.g., neural network or fuzzy system) based control designs can only prove uniform ultimate boundedness of the controlled system due to the unavoidable approximation errors. Moreover, the transient response of conventional adaptive control may be sluggish because high-gain learning is not preferable for guaranteeing system safety. To address these issues, this paper proposes and experimentally validates an alternative robust adaptive control for servo mechanisms with unknown dynamics and bounded disturbances. This control can guarantee asymptotic tracking error convergence in the steady-state, while the transient response can also be prescribed by using an improved prescribed performance function. An echo state network augmented by a smooth friction model is used to accommodate the unknown nonlinearities. The residual approximation error and other bounded disturbances are compensated by using a robust integral of sign of the error term. Comparative experiments based on a practical turntable servo mechanism are conducted to validate the effectiveness of the proposed control scheme and show improved control performance.

In this paper, an approximation-free funnel feedback controller is proposed for a class of nonlinear servomechanisms to achieve prescribed tracking error performance. An improved funnel function is proposed to guarantee the transient and asymptotic behavior of the tracking error within a given funnel boundary. The proposed funnel function removes the imposed assumption used in conventional funnel controls (e.g., systems with relative degree one or two) and avoids the potential singularity problem in prescribed performance controls. Moreover, an extended state observer (ESO) is used to address the effect of unknown dynamics in the control system (e.g., friction and disturbances), where the ESO parameters can be easily designed based on the control system bandwidth. The stability of the proposed control system with ESO and funnel function is analyzed via the Lyapunov theory. Comparative simulations and experimental results are conducted based on a practical turntable servomechanisms to validate the efficacy of the proposed method.

Many well-established singular perturbation theories for singularly perturbed systems require the full knowledge of system model parameters. In order to obtain an accurate and faithful model, a new identification scheme for singularly perturbed nonlinear system using multitime-scale recurrent high-order neural networks (NNs) is proposed in this paper. Inspired by the optimal bounded ellipsoid algorithm, which is originally designed for discrete-time systems, a novel weight updating law is developed for continuous-time NNs identification process. Compared with other widely used gradient-descent updating algorithms, this new method can achieve faster convergence, due to its adaptively adjusted learning rate. Based on the identification results, a control scheme using singular perturbation theories is developed. By using singular perturbation methods, the system order is reduced, and the controller structure is simplified. The closed-loop stability is analyzed and the convergence of system states is guaranteed. The effectiveness of the identification and the control scheme is demonstrated by simulation results.

In this paper, we study the power allocation problem for the downlink transmission in a set of closed-access femtocells which underlay a number of macrocells. We introduce a mutli-step pricing mechanism for the macrocells to control the cross- tier interference by femtocell transmissions without explicit coordination. We model the cross- tier joint power allocation process in the heterogeneous network as a non-cooperative, average-reward Markov game. By investigating the structure of the instantaneous payoff functions in the game, we propose a self-organized strategy learning scheme based on learning automata for both the macrocell base stations and the femtocell access points to adapt their transmit power simultaneously. We prove that the proposed learning scheme is able to find a pure-strategy Nash equilibrium of the game without the need for the femtocell access points to share any local information. Simulation results show the efficiency of the proposed learning scheme.

In this paper, the position tracking control with finite-time convergence has been studied for a class of nonliear uncertain robot manipulators. Radial basis function neural network (RBFNN) based adaptive control is designed to compensate for the effect of the unknown dynamics. To achieve the finite-time convergence of both trajectory tracking error and RBFNN learning error, barrier Lyapunov functions (BLFs) and and filtering techniques are employed to design a performance function and a tracking error region to ensure position tracking error converge to a pair of specified bounds in a finite time. The effectiveness and efficiency of the proposed control method is tested and verified by simulation studies.

In this paper, an alternative solution for adaptive optimal tracking control of nonlinear completely unknown systems is proposed. Firstly, an adaptive identifier is used to estimate the unknown system dynamics. Then, a recently developed system augmentation approach is adopted to design the optimal control, where the reference signal is incorporated into the augmented system. Thus, both the feedforward control and feedback control can be obtained simultaneously. Then, a critic neural network (NN) is used to estimate the augmented performance index, and calculate the optimal control action. Thus, the widely used actor NN is not needed. Finally, a new adaptive law recently proposed by the authors is used to online update the NN weight. The closed-loop stability and the convergence of the optimal control are all proved. The feasibility of the suggested approach is demonstrated by a simulation example.

Most of the available control schemes for pure-feedback systems are derived based on the backstepping technique. On the contrary, this paper presents a novel adaptive control design for nonlinear pure-feedback systems without using backstepping. By introducing a set of alternative state variables and the corresponding transform, state-feedback control of the pure-feedback system can be viewed as output-feedback control of a canonical system. Consequently, backstepping is not necessary and the previously encountered explosion of complexity and circular issue are also circumvented. To estimate unknown states of the newly derived canonical system, a high-order sliding mode observer is adopted, for which finite-time observer error convergence is guaranteed. Two adaptive neural controllers are then proposed to achieve tracking control. In the first scheme, a robust term is introduced to account for the neural approximation error. In the second scheme, a novel neural network with only a scalar weight updated online is constructed to further reduce the computational costs. The closed-loop stability and the convergence of the tracking error to a small compact set around zero are all proved. Comparative simulation and practical experiments on a servo motor system are included to verify the reliability and effectiveness.

This paper presents a discrete control design for time-delay systems subjected to the periodical command signal or exogenous disturbances. Unlike other dead-time compensators (DTC), we take profit of the system components to construct an internal model. In addition, a novel disturbance observer is developed to compensate the effect of disturbances, and thus to achieve tracking and disturbance rejection simultaneously. The possible fractional delay from discretization is also handled by using a fractional delay filter. The stability conditions and robustness analysis under model uncertainties are provided. Two numerical examples including a supply chain management (SCM) is provided to illustrate the feasibility of the results.