This paper addresses the containment control issue in high-order nonlinear multi-agent systems (MASs) under denial of service (DoS) attacks. First, a neural network-based switching observer with adaptive mechanism is developed to reconstruct unmeasurable agent states under intermittent DoS-induced communication disruptions, establishing new theoretical pathways for directed network topologies. Second, a command-filtered backstepping control framework is proposed to circumvent the inherent complexity explosion in traditional recursive designs by eliminating redundant differentiations of virtual control laws. Ultimately, a distributed adaptive neural network containment control (DANNCC) scheme is established, ensuring all follower agents asymptotically converge into the convex hull spanned by multiple leaders. Furthermore, systematic stability analysis with constructed Lyapunov functions yields boundedness of all closed-loop signals in the system. Moreover, the containment errors can be asymptotically driven to an arbitrarily small magnitude through systematic parameter adjustment. The developed approach’s operational efficacy and real-world applicability are validated through comprehensive simulations across heterogeneous attack scenarios, demonstrating strict adherence to convergence requirements without control performance degradation.

This study develops a reinforcement learning (RL)-based control framework with guaranteed predefined performance for nonlinear switched interconnected systems. This approach effectively addresses challenges arising from unmeasurable states and group average dwell time switching mechanisms, allowing both convergence time and accuracy to be preset via parameter configuration. First, the system equations are reconstructed to target nonlinear and interconnected terms, which are then approximated using neural networks (NNs). Additionally, an NNs-based switching state observer is designed to estimate the unmeasurable states. Second, within the backstepping synthesis framework, a distributed optimal controller is designed by integrating a performance transformation function into the cost function, with the resulting control law approximated via an identifier-actor-critic architecture. Furthermore, the group average dwell time-based stability analysis is generalized to address the optimal control challenges inherent in nonlinear switched interconnected systems. Compared with existing studies, this approach demonstrates enhanced extensibility and practicality for real-world applications. Finally, two simulation examples verify the effectiveness and superiority of the proposed method over state-of-the-art alternatives.

This article addresses the consensus tracking control problem for a class of unparametrizable noncanonical nonlinear multi-agent systems. Most existing consensus tracking control schemes for nonlinear multi-agent systems (MASs) are restricted to canonical-form system models. For noncanonical-form nonlinear MASs, to our best knowledge, there is still no result available so far due to some challenging technical issues encountered in design and analysis. Firstly, existing distributed observers are limited to canonical systems by the assumption that the output matrix of leader is known, rendering them inapplicable to noncanonical nonlinear systems. Moreover, current adaptive distributed observer frameworks only consider first-order differentiability of the system matrix, missing the information of higher-order derivative. Secondly, unlike the traditional Lyapunov method for canonical systems, noncanonical systems require augmented error analysis for stability, and extending this to noncanonical nonlinear MASs is highly challenging. Thirdly, unparametrizable nonlinear functions in the original system complicate control design. To tackle these issues, an approximate Takagi-Sugeno (T-S) fuzzy models are constructed to eliminate non-parametric functions, alongside a novel adaptive distributed observer for estimating leader information. Simulations verify the effectiveness of our control scheme in achieving consensus control tracking.

The dynamic visual servoing problem studied in this paper differs from existing approaches in two key aspects: the dynamics of the aerial mobile robot are underactuated, and the onboard camera is adaptively calibrated. To address the first challenge, a novel cascade visual servoing framework is developed, consisting of three control loops: the image loop, the attitude loop, and the angular velocity loop. Based on this framework, an extended eye‐in‐hand vision system is constructed, in which the perspective projection of feature points onto the image plane is decoupled from the rigid body’s attitude. This design allows the proposed visual controller to effectively compensate for image dynamics. Furthermore, unknown intrinsic and extrinsic camera parameters make compensation for image dynamics more difficult. To overcome this issue, a depth‐independent composite matrix is introduced, enabling the unknown visual dynamics to be linearly parameterized and integrated with an adaptive control technique. A novel online algorithm is developed to estimate the unknown camera parameters in real time, and an additional adaptation mechanism is incorporated to estimate the rotational inertia of the rigid body. Using Lyapunov theory and Barbalat’s lemma, it is proven that the image tracking error asymptotically converges to zero while all physical variables remain locally bounded. Experimental results confirm that the image tracking error converges to zero over time, with a maximum deviation of no more than two pixels, thereby validating the effectiveness of the proposed visual controller.

The piezoelectric actuator will exhibit the problem of unknown control direction under high-speed operating conditions. Hence, the realization of high-speed control for nonlinear systems driven by piezoelectric actuators requires the fixed-time stability to enhance the convergence rate and the Nussbaum technique to handle the problem of unknown control directions. However, these two techniques are incompatible because the required conditional inequalities for each are different. To resolve this incompatibility, we have incorporated the projection operator into the design of the adaptive updating law. On the basis of ensuring that the adaptive estimation parameter is bounded, we have established the conditional inequality for Nussbaum technique. Then, some nonlinear damping terms are incorporated into the stability analysis to counteract a term containing Nussbaum function, thereby reducing the difficulty of the fixed-time stability analysis. Furthermore, the predefined tracking accuracy and fixed-time stability are theoretically proven through the stability analysis. Finally, the efficiency of the proposed control method is validated through semi-physical experiments on a cylindrical piezoelectric actuator.

In this paper, a Zeroing Neural Network (ZNN)-based control framework is proposed for finite-time visual servoing of robotic manipulators, without requiring camera calibration or kinematic modeling. To address the challenge of the unknown robot-camera interaction, a data-driven Jacobian estimator is introduced, enabling real-time mapping without offline training or analytical derivation. A finite-time noise-rejection ZNN (FTNRZNN) controller is developed to ensure robust and fast joint-level control under measurement noise. The continuous-time scheme is further discretized for digital implementation. Rigorous Lyapunov analysis guarantees finite-time convergence. Simulations and real-world experiments validate the effectiveness of the method in both regulation and trajectory tracking, demonstrating strong adaptability to unstructured environments.

The work aims to solve the high-speed high-precision tracking control problem of piezoactuators in the presence of stochastic disturbances. First, a cascade model composed of the Preisach operator and a class of stochastic nonlinear systems is proposed to describe the sophisticated actuator dynamics during high-speed operation, and then a hysteresis decomposition strategy is developed to transform the Preisach model into an appropriate form tractable to control design so that a robust adaptive fuzzy control framework can be constructed successfully to suppress the hysteresis nonlinearities, and to robustify bounded stochastic disturbances. More importantly, based on such a framework, the fixed-time stability (instead of practical fixed-time stability), and the prescribed steady-state tracking performance can be established simultaneously. Besides theoretical analysis, some experimental tests are also conducted to illustrate the effectiveness of the proposed scheme.

Developing a distributed bipartite optimal consensus scheme while ensuring user-predefined performance is essential in practical applications. Existing approaches to this problem typically require a complex controller structure due to adopting an identifier-actor-critic framework and prescribed performance cannot be guaranteed. In this work, an adaptive critic learning (ACL)-based optimal bipartite consensus scheme is developed to bridge the gap. A newly designed error scaling function, which defines the user-predefined settling time and steady accuracy without relying on the initial conditions, is then integrated into a cost function. The backstepping framework combines the ACL and integral reinforcement learning (IRL) algorithm to develop the adaptive optimal bipartite consensus scheme, which contributes a critic-only controller structure by removing the identifier and actor networks in the existing methods. The adaptive law of the critic network is derived by the gradient descent algorithm and experience replay to minimize the IRL-based residual error. It is shown that a compute-saving learning mechanism can achieve the optimal consensus, and the error variables of the closed-loop system are uniformly ultimately bounded (UUB). Besides, in any bounded initial condition, the evolution of bipartite consensus is limited to a user-prescribed boundary under bounded initial conditions. The illustrative simulation results validate the efficacy of the approach.

An inversion-based control strategy has been shown to be effective in compensating the hysteresis nonlinearities modeled by the Preisach operator. However, when the operator is coupled with the dynamics of uncertain nonlinear systems, there is still no result available for constructing the hysteresis inverse controller. To fill in the gap, in this study, we propose an iterative inverse-based adaptive fuzzy control scheme. Technically, an adaptive hysteresis inverse constructed through an iteration algorithm and updated by a projection-based adaptive law is developed as a feedforward hysteresis compensator, and then, the hysteresis inverse compensation error and plant nonlinearities and uncertainties are handled by a newly designed adaptive fuzzy controller. With our scheme, the closed-loop stability in the sense of signal boundedness, the prescribed steady-state tracking performance, and the convergence of the iteration algorithm can be established. Besides theoretical analysis, the effectiveness of our scheme is also validated by simulation and experimental results.

This article investigates the adaptive optimal output-feedback consensus tracking problem for nonlinear multiagent systems (MASs). Although adaptive optimal output-feedback control schemes for nonlinear systems have been developed recently, most results do not consider the two-way interaction between the state observer and its associated subsystem. To address this issue, we formulate the state-observer and the subsystem as a two-player Stackelberg game framework, where the state-observer acts as the follower-player and the subsystem acts as the leader-player. Such a framework helps us to reveal the two-way interaction between the subobserver and the subsystem. Based on this, we design the optimal auxiliary input of the state-observer and the optimal subsystem controller. We implement the optimal policy pair using integral reinforcement learning (IRL) and adaptive critic learning, which provides a critic-only structure. We prove that the Stackelberg-Nash equilibrium is reached and that the closed-loop signals are ultimately uniformly bounded (UUB). We demonstrate the effectiveness of the proposed scheme using a numerical simulation example.

In this article, direct adaptive actuator failure compensation control is investigated for a class of noncanonical neural-network nonlinear systems whose relative degrees are implicit and parameters are unknown. Both the state tracking and output tracking control problems are considered, and their adaptive solutions are developed which have specific mechanisms to accommodate both actuator failures and parameter uncertainties to ensure the closed-loop system stability and asymptotic state or output tracking. The adaptive actuator failure compensation control schemes are derived for noncanonical nonlinear systems with neural-network approximation, and are also applicable to general parametrizable noncanonical nonlinear systems with both unknown actuator failures and unknown parameters, solving some key technical issues, in particular, dealing with the system zero dynamics under uncertain actuator failures. The effectiveness of the developed adaptive control schemes is confirmed by simulation results from an application example of speed control of dc motors.

In our recent work, we propose an indirect adaptive fuzzy control scheme for uncertain unparametrizable nonlinear systems, which ensures that the number of adaptive laws does not increase with the number of fuzzy rules, and the time derivative of the chosen Lyapunov function is negative semidefinite. However, the scheme involves a class of high-order smooth functions and their time derivatives, which can make the controller structure become sophisticated especially when the relative degree of system is quite large. To overcome this problem, in the article, we propose a new direct adaptive fuzzy control scheme based on a class of reduced-order smooth functions. With the scheme, no partial-derivative term is involved in controller and virtual controllers, only one adaptive law is used regardless of the increase of fuzzy rules, and also the time derivative of Lyapunov function can be ensured negative semidefinite. It is proved that all closed-loop signals are bounded, and the output tracking error converges to a prescribed interval asymptotically. The transient tracking performance and robustness of the proposed control scheme are also considered. The effectiveness of the obtained results is illustrated by two practical control systems.

As the control tasks become complex, fulfilling such tasks cooperatively is the first choice in practice. In this article, the output consensus problem of heterogeneous multiagent systems is studied by deploying distributed observers in follower agents. Each observer in the follower only measures part of the leader’s output, which relieves the burden of a simple agent when the leader’s output is of large-scale dimensions. Then, all followers in the system work cooperatively to estimate the full state of the leader. By using parameterized Riccati equation and output regulation theory, sufficient conditions are given to design the distributed observers and the output consensus protocol. Finally, a numerical example is conducted to verify the obtained result.

In this article, we consider the leader-follower consensus control problem of uncertain multiagent systems, aiming to achieve the improvement of system steady state and transient performance. To this end, a new adaptive neural control approach is proposed with a novel design of the Lyapunov function, which is generated with a class of positive functions. Guided by this idea, a series of smooth functions is incorporated into backstepping design and Lyapunov analysis to develop a performance-oriented controller. It is proved that the proposed controller achieves a perfect asymptotic consensus performance and a tunable L2transient performance of synchronization errors, whereas most existing results can only ensure the stability. Simulation demonstrates the obtained results.

It is interesting to study the problem of adaptive fuzzy control for uncertain nonlinear systems with input and state hysteresis. However, since the hysteresis behavior, especially the state hysteresis, present at the sensors is complicated, mainly in view of its multivalues and rate-dependent features, it is a challenging task to develop the backstepping-based control design. So far, there is still no available result in addressing the problem. In this article, we will pursue this task. A novel indirect fuzzy control scheme is proposed with an alternative adaptive hysteresis inverse, which is used to cancel the unknown input hysteresis. To tackle the effects of state hysteresis, a new dynamic compensation is developed to adaptively accommodate the uncertain dynamics involved in the sensors. It is proved that in addition to system stability, the proposed scheme enables the tracking error to approach a prescribed interval asymptotically. Illustrative examples are used to verify the method developed.

In this paper, an adaptive neural network control for stochastic nonlinear systems with uncertain disturbances is proposed. The neural network is considered to approximate an uncertain function in a nonlinear system. And computational burden in operation is reduced by handling the norm of the neural-network vector. However, it will arise chattering issue, which is a challenge to avoid it from the symbolic operation. Further, traditional schemes often view error of estimate as bounded constant, but it is a time-varying function exactly, which may lead control schemes cannot conform to practical situation and guarantee stability of systems. Thus, backstepping technology and the neural network technology combined to stabilize stochastic nonlinear systems together to handle the aforementioned issues. It is proved that the proposed control scheme can guarantee the satisfactory asymptotic convergence performance and predetermined transient tracking error performance. From simulation results, the proposed control scheme is verified that can guarantee the satisfactory effectiveness.

Most of the available results on adaptive control of uncertain nonlinear systems with input dead-zone characteristics are for canonical nonlinear systems whose relative degrees are explicit and for which a Lyapunov-based backstepping design is directly applicable. However, those results cannot be applied to noncanonical form nonlinear systems whose relative degrees are implicit and for which a Lyapunov-based backstepping design may not be applicable. This article solves the adaptive control problem of a class of noncanonical neural-network nonlinear systems with unknown input dead-zones. A complete solution framework is developed, using a new gradient-based design which is applicable to noncanonical nonlinear systems with input dead-zones. Signal boundedness of the closed-loop system and the desired tracking performance are ensured with the developed control schemes. Their effectiveness is illustrated by an application example of speed control of dc motors. This article can be readily extended to handle general parametrizable noncanonical nonlinear systems with unknown dynamics and input dead-zones, to solve such an open problem.

In this paper, we consider the fuzzy controller design problem for output tracking of uncertain strict-feedback nonlinear systems. For comparison, a basic fuzzy control scheme is first constructed based on an existing approach representative in the field. The scheme can effectively reduce the number of parameter estimates, which benefits from the operation of handling the square of the norm of fuzzy weight vector. However, as a tradeoff of such an operation, the asymptotic tracking performance cannot be ensured and the L2-norm transient performance of tracking error cannot be established. To eliminate these performance costs without losing the advantage of the basic fuzzy control scheme, we further propose a performance-oriented fuzzy control scheme. It guarantees that all closed-loop signals are bounded and the tracking error converges to a prescribed interval asymptotically. Moreover, the L2-norm transient performance of tracking error is also established, which explicitly indicates that the transient performance of tracking error can be improved through changing controller design parameters with the performance-oriented fuzzy control scheme. Simulation examples are given to verify the obtained results.

The application of most existing adaptive dead-zone compensation schemes is limited to the situation where the dead-zone parameters remain unchanged during the system operation. If this is not the case in practice, the closed-loop system stability may no longer be ensured with those schemes because the negative-definite or negative semi-definite property of Lyapunov function may not be satisfied when the dead-zone parameters change in real time. Also, the Lyapunov function is not differentiable from the view on the whole time when the dead-zone parameters change piecewise. Motivated by the observations, in this paper we investigate the output tracking problem for uncertain nonlinear systems in the presence of actuator dead-zone nonlinearity with piecewise time-varying parameters. Technically, by using the projection technique and a modified tuning functions approach, a new adaptive fuzzy control design and a new piecewise Lyapunov function analysis are then developed. It is established that in addition to the system stability, a better quantification of the system performance is achieved in the sense that the tracking error will be controlled within prescribed bounds regardless of the abrupt jumps of the parameters. Finally, simulation results demonstrate the obtained theoretical findings.

In this paper, we shall address the problem of guaranteeing transient performance in adaptive tracking control of uncertain strict-feedback nonlinear systems within the framework of event-triggered control. Note that most of the existing literature about event-triggered control focuses on solving exactly known systems or completely parametric systems, but still no result available in handling more general systems with unparameterizable uncertainties. The formidable issue is successfully resolved in this paper by using the fuzzy logic systems to approximate real-time value of the unknown functions, and the square of the norm of fuzzy weight vector is applied to the backstepping recursive design. Furthermore, by constructing a class of new Lyapunov candidates, the chattering phenomenon caused by sign function can be avoided, whereas the transient performance in terms of the tracking error can also be achieved to be an explicit function with the user-defined parameters. It is further proven that our proposed scheme ensures the global boundedness of all the closed-loop signals. Finally, the simulation results verify the effectiveness of the established theoretic.

The problem of direct adaptive compensation for infinite number of time-varying actuator failures/faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems. However, due to the technical difficulties, so far, very limited result is available in addressing such an issue, which thus motivates us to propose a new fuzzy control methodology in this paper. The proposed scheme is established from the techniques of projection adaptation design, a new piecewise Lyapunov function analysis, and an optimized fuzzy adaptation. It is shown that all the closed-loop signals are bounded and the steady-state tracking error converges to a residual around zero, irrespective of a possibility that there are infinite number of time-varying actuator failures. Simulations are provided to illustrate the effectiveness and applicability of the proposed scheme.

This paper concerns with the problem of adaptive inverse compensation control for a class of uncertain pure-feedback nonlinear systems with asymmetric actuator backlash. By resorting to the mean-value theorem, the considered system can be transformed into the strict-feedback form with unknown state-dependent virtual control coefficients. Then, the most challenging difficulty is how to design the adaptive backlash inverse compensator in face of uncertain control gain function. To overcome this challenge, we first propose a smooth inverse model for asymmetric backlash, and based on it, a new expression of adaptive compensation error is further developed, which also paves the way to the embeddedness of fuzzy logic systems to cancel the unknown gain function. Moreover, two mutually learning mechanisms (one is for predicting unknown backlash parameters, while another is to search for optimal fuzzy weights) are further constructed such that the inverse compensator can be updated online. With the backstepping iteration design of compensator input, an adaptive fuzzy compensation controller (i.e., the compensator output) is developed to ensure the asymptotic stability of the closed-loop system. Finally, comparative simulations are conducted to validate the effectiveness and applicability of the proposed control theory.

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.

This paper mainly aims at the problem of adaptive quantized control for a class of uncertain nonlinear systems preceded by asymmetric actuator backlash. One challenging problem that blocks the construction of our control scheme is that the real control signal is wrapped in the coupling of quantization effect and nonsmooth backlash nonlinearity. To resolve this challenge, this paper presents a two-stage separation approach established on two new technical components, which are the approximate asymmetric backlash model and the nonlinear decomposition of quantizer, respectively. Then the real control is successfully separated from the coupling dynamics. Furthermore, by employing the neural networks and adaptation method in control design, a quantized controller is developed to guarantee the asymptotic convergence of tracking error to an adjustable region of zero and uniform ultimate boundedness of all closed-loop signals. Eventually, simulations are conducted to support our theoretical results.

This paper is concentrated on the problem of adaptive fuzzy tracking control for an uncertain nonlinear system whose actuator is encountered by the asymmetric backlash behavior. First, we propose a new smooth inverse model which can approximate the asymmetric actuator backlash arbitrarily. By applying it, two adaptive fuzzy control scenarios, namely, the compensation-based control scheme and nonlinear decomposition-based control scheme, are then developed successively. It is worth noticing that the first fuzzy controller exhibits a better tracking control performance, although it recourses to a known slope ratio of backlash nonlinearity. The second one further removes the restriction, and also gets a desirable control performance. By the strict Lyapunov argument, both adaptive fuzzy controllers guarantee that the output tracking error is convergent to an adjustable region of zero asymptotically, while all the signals remain semiglobally uniformly ultimately bounded. Lastly, two comparative simulations are conducted to verify the effectiveness of the proposed fuzzy controllers.

This paper presents a novel adaptive controller for controlling an autonomous helicopter with unknown inertial matrix to asymptotically track the desired trajectory. To identify the unknown inertial matrix included in the attitude dynamic model, this paper proposes a new structural identifier that differs from those previously proposed in that it additionally contains a neural networks (NNs) mechanism and a robust adaptive mechanism, respectively. Using the NNs to compensate the unknown aerodynamic forces online and the robust adaptive mechanism to cancel the combination of the overlarge NNs compensation error and the external disturbances, the new robust neural identifier exhibits a better identification performance in the complex flight environment. Moreover, an optimized algorithm is included in the NNs mechanism to alleviate the burdensome online computation. By the strict Lyapunov argument, the asymptotic convergence of the inertial matrix identification error, position tracking error, and attitude tracking error to arbitrarily small neighborhood of the origin is proved. The simulation and implementation results are provided to evaluate the performance of the proposed controller.

This paper presents a novel fuzzy adaptive controller for controlling a class of dead-zone output nonlinear systems with time delays. A new approximate model is first designed to describe a special dead-zone phenomenon encountered by the output mechanism of nonlinear systems, and the proposed smooth model can be conveniently fused with available adaptive fuzzy control techniques. In addition, the coupling effect that the dead-zone output and the time-delayed states coexist in a common coupling function makes the tracking control design more complicated. To further address this difficulty, a compensation method using mean-value theorem with Lyapunov-Krasovskii function is presented in this paper. By using the proposed output dead-zone model, and based on Lyapunov synthesis, a new optimized algorithm is developed to guarantee the prescribed convergence of tracking error and the boundedness of all the signals in the closed-loop systems. Simulations have been implemented to verify the performance of the proposed fuzzy adaptive controller.

This paper addresses the problem of adaptive neural output-feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states. A modified Bouc-Wen model is first employed to capture the output hysteresis phenomenon in the design procedure. For its fusion with the neural networks and the Nussbaum-type function, two key lemmas are established using some extended properties of this model. To avoid the bad system performance caused by the output nonlinearity, a barrier Lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error. In addition, a robust filtering method is designed to cancel the restriction that all the system states require to be measured. Based on the Lyapunov synthesis, a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system. Simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper.

This paper investigates the fusion of unknown direction hysteresis model with adaptive neural control techniques in face of time-delayed continuous time nonlinear systems without strict-feedback form. Compared with previous works on the hysteresis phenomenon, the direction of the modified Bouc-Wen hysteresis model investigated in the literature is unknown. To reduce the computation burden in adaptation mechanism, an optimized adaptation method is successfully applied to the control design. Based on the Lyapunov-Krasovskii method, two neural-network-based adaptive control algorithms are constructed to guarantee that all the system states and adaptive parameters remain bounded, and the tracking error converges to an adjustable neighborhood of the origin. In final, some numerical examples are provided to validate the effectiveness of the proposed control methods.