Observer-Based Adaptive Fuzzy Tracking Control for Strict-Feedback Nonlinear Systems With Unknown Control Gain Functions

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

Disturbance Observer-Based Adaptive Intelligent Control of Marine Vessel With Position and Heading Constraint Condition Related to Desired Output

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

A health status estimation method based on interpretable neural network observer for HVs

Estimating the health status is a crucial step in learning about the health of hypersonic vehicles beforehand. The estimation results can be used to detect abnormal states and provide data reference for fault diagnosis. However, certain conventional neural network-based estimate techniques rely heavily on data and have limited model interpretability, which challenges the accuracy of the estimation results. This research aims to address the problems of data dependency and model interpretability in estimation models. In this study, a block interpretable neural network model with constraints on the trajectory and attitude equations is established. On the basis of the interpretable neural network model, two health status estimation methods are proposed: one that is unsupervised and the other that is supervised. Additionally, in the supervised health status estimate approach, an FC-LN-Mish structure is created to fit the relationship between the fault residual and the fault state parameters. The results indicate that the proposed estimation methods can fit the system mechanism relationship more accurately, improve the model interpretability, reduce data dependency, and ensure high estimation efficiency and precision. The FC-LN-Mish structure can reduce the missed detection rate and false detection rate to some extent, and perform better than other models under the low fault deviation degree. In conclusion, the interpretable neural network model-based observers accurately observe the health status parameters of rudders and RCS, reduce data dependence and data processing costs, and have better performance under high uncertainty interference. It provides effective method for online health estimation.

Asynchronous Resilent State Estimation of Switched Fuzzy Systems With Multiple State Impulsive Jumps

This work researches the resilent mixed H∞ and energy-to-peak filter design problem of switched Takagi-Sugeno (T-S) fuzzy systems with asynchronous switching and multiple state impulsive jumps. The novelties include three points. First, a novel mixed H∞ and energy-to-peak performance index is proposed, which covers the H∞ performance index and energy-to-peak performance index as special cases. Second, in addition to designing the switching filters, the filter state jump rules are constructed at filter switching instants. Finally, both system states and filter states jump in a asynchronous manner. The switching law is devised through the mode-dependent average dwell time (MDADT) approach. A new type of Lyapunov-like functionals is constructed, which will increase when the subsystem is running with its mismatched filter and jump while the subsystem or the filter is switching. Then, new conditions are deduced to ensure the filtering error systems with multiple state impulsive jumps to be asymptotically stable with a mixed H∞ and energy-to-peak performance level. Filter design conditions expressing as linear matrix inequality (LMI) are obtained. Finally, the effectiveness of the derived results is illustrated by two examples.

Adaptive Event-Triggered Output-Feedback Control Against Unknown Control Directions and Unknown Intrinsic Growth

This article addresses global stabilization via disparate event-triggered output feedback for a class of uncertain nonlinear systems. Typically, the systems allow unknown control directions and unmeasurable-state dependent growth simultaneously. Actually, in the context of the latter ingredient, there has been no any continuous control strategy that has allowed the former ingredient so far. Hence, one cannot solve the event-triggered control problem based on corresponding continuous feedback as done in the emulation-based method. In view of the unsolvability, we pursue a nonemulation-based strategy, directly conducting event-triggered control design. First, a parameterized output feedback controller incorporating a dynamic high gain is designed, which would globally stabilize the system once the adjustable parameter therein is suitable. Then, an event-triggering mechanism is developed to not only decide when the controller is sampled/executed but also determine which constant value the adjustable parameter takes. Just due to the instantly varying (discontinuous) adjustable parameter, the feedback ability of the controller is large enough, making it possible to solve the control design problem in the event-triggered framework. A simulation example is provided to verify the effectiveness and advantage of the proposed approach.

Integral BLF-Based Adaptive Neural Constrained Regulation for Switched Systems With Unknown Bounds on Control Gain

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.

Dynamic Gain Reduced-Order Observer-Based Global Adaptive Neural-Network Tracking Control for Nonlinear Time-Delay Systems

In this article, a globally adaptive neural-network tracking control strategy based on the dynamic gain observer is proposed for a class of uncertain output-feedback systems with unknown time-varying delays. A reduced-order observer with novel dynamic gain is proposed. An n th-order continuously differentiable switching function is constructed to achieve the continuous switching control of the system, thus further ensuring that all the closed-loop signals are globally uniformly ultimately bounded (GUUB). It is proved that by adjusting the designed parameters, the tracking error converges to a region which can be adjusted to be small enough. The effectiveness of the control scheme is demonstrated by two simulation examples.

Observer-Based Decentralized Control for Non-Strict-Feedback Fractional-Order Nonlinear Large-Scale Systems With Unknown Dead Zones

This article addresses the output-feedback decentralized control issue for the fractional-order nonlinear large-scale nonstrict-feedback systems with states immeasurable and unknown dead zones. The unknown nonlinear functions are identified by neural networks (NNs), and immeasurable states are estimated by establishing an NNs' decentralized state observer. The algebraic loop issue is solved by using the property of NN basis functions and designing the fractional-order adaptation laws. In addition, the fractional-order dynamic surface control (FODSC) design technique is introduced in the adaptive backstepping control algorithm to avoid the issue of "explosion of complexity." Then, by treating the nonsymmetric dead zones as the time-varying uncertain systems, an adaptive NNs' output-feedback decentralized control scheme is developed via the fractional-order Lyapunov stability criterion. It is proven that the controlled fractional-order systems are stable, and the tracking and observer errors can converge to a small neighborhood of zero. Two simulation examples are given to confirm the validity of the put forward control scheme.

Adaptive Neural Asymptotic Tracking of Uncertain Non-Strict Feedback Systems With Full-State Constraints via Command Filtered Technique

This brief addresses the adaptive neural asymptotic tracking issue for uncertain non-strict feedback systems subject to full-state constraints. By introducing the significant nonlinear transformed function (NTF), the command filtered technology, and the boundary estimation method into control design, a novel command filtered backstepping adaptive controller is proposed. The proposed control scheme is able to not only deal with full-state constraints but also avoid the "explosion of complexity" issue. By means of a Lyapunov stability analysis, we prove that: 1) the tracking error asymptotically converges to zero; 2) all the variables in the controlled systems are bounded; and 3) all the states are constrained in the asymmetric predefined sets. Finally, a numerical simulation is used to demonstrate the validity of the proposed algorithm.

Performance Improvement of Active Suspension Constrained System via Neural Network Identification

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.

Adaptive Event-Triggered Finite-Time Control for Uncertain Time Delay Nonlinear System

In this article, adaptive event-triggered finite-time control is explored for uncertain nonlinear systems with time delay. First, to handle the time-varying state delays, the Lyapunov-Krasovskii function is used. Fuzzy-logic systems are used to deal with the unknown nonlinearities of the system. Notice that compared to the reporting achievements, our proposed virtual control laws are derivable by using the novel switch function, which avoids "singularity hindrance" problem. Moreover, the dynamic event-triggered controller is designed to reduce the communication pressure and we prove that the controller is Zeno free. Our proposed control strategy ensures that the tracking error is arbitrarily small in finite time and all variables of the closed-loop system remain bounded. Finally, to show the effectiveness of our control strategy, the simulation results are given.

Backstepping Boundary Control for a Class of Gantry Crane Systems

In this article, two boundary feedback controllers are designed via the backstepping approach for a class of gantry crane systems. To provide an accurate and concise representation of the dynamic behavior, the gantry crane with a flexible cable is described by a hybrid system. The hybrid system is formed by an ordinary differential equation coupled with a partial differential equation. In the first control strategy, a backstepping-based boundary state-feedback controller is proposed for the gantry crane to transport a payload to an expected position with less shaking. In the second control strategy, a boundary output-feedback controller is explored with an observer estimating the inaccessible states. By using the backstepping technique and kernel functions, the original systems with different control strategies are transformed into target systems. By using the operator semigroup and Lyapunov stability theories, the target system is proven to be well-posed and exponentially stable, respectively. Finally, numerical simulations and comparisons are provided to illustrate the efficiency and the advantages of the proposed methods.

Neuroadaptive Optimal Fixed-Time Synchronization and its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems

This article investigates the neuroadaptive optimal fixed-time synchronization and its circuit realization along with dynamical analysis for unidirectionally coupled fractional-order (FO) self-sustained electromechanical seismograph systems under subharmonic and superharmonic oscillations. The synchronization model of the coupled FO seismograph system is established based on drive and response seismic detectors. The dynamical analysis reveals this coupled system generating transient chaos and homoclinic/heteroclinic oscillations. The test results of the constructed equivalent analog circuit further testify its complex nonlinear dynamics. Then, a neuroadaptive optimal fixed-time synchronization controller integrated with the FO hyperbolic tangent tracking differentiator (HTTD), interval type-2 fuzzy neural network (IT2FNN) with transformation, and prescribed performance function (PPF) together with the constraint condition is developed in the backstepping recursive design. Furthermore, it is proved that all signals of this closed-loop system are bounded, and the tracking errors fall into a trap of the prescribed constraint along with the minimized cost function. Extensive studies confirm the effectiveness of the proposed scheme.

Event-Triggered Adaptive Neural Network Control for Stochastic Nonlinear Systems With State Constraints and Time-Varying Delays

In this article, we pay attention to develop an event-triggered adaptive neural network (ANN) control strategy for stochastic nonlinear systems with state constraints and time-varying delays. The state constraints are disposed by relying on the barrier Lyapunov function. The neural networks are exploited to identify the unknown dynamics. In addition, the Lyapunov-Krasovskii functional is employed to counteract the adverse effect originating from time-varying delays. The backstepping technique is employed to design controller by combining event-triggered mechanism (ETM), which can alleviate data transmission and save communication resource. The constructed ANN control scheme can guarantee the stability of the considered systems, and the predefined constraints are not violated. Simulation results and comparison are given to validate the feasibility of the presented scheme.

Adaptive Output Feedback Fuzzy Fault-Tolerant Control for Nonlinear Full-State-Constrained Switched 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.

Event-triggered control of flexible manipulator constraint system modeled by PDE

The vibration suppression control of a flexible manipulator system modeled by partial differential equation (PDE) with state constraints is studied in this paper. On the basis of the backstepping recursive design framework, the problem of the constraint of joint angle and boundary vibration deflection is solved by using the Barrier Lyapunov function (BLF). Moreover, based on the relative threshold strategy, an event-triggered mechanism is proposed to save the communication workload between controller and actuator, which not only deals with the state constraints of the partial differential flexible manipulator system, but also effectively improves the system work efficiency. Good damping effect on vibration and the elevated system performance can be seen under the proposed control strategy. At the same time, the state can meet the constraints given in advance, and all system signals are bounded. The proposed scheme is effective, which is proven by simulation results.

Enhanced Fuzzy Fault Estimation of Discrete-Time Nonlinear Systems via a New Real-Time Gain-Scheduling Mechanism

The problem of enhancing the robust performance of nonlinear fault estimation (FE) is addressed by proposing a novel real-time gain-scheduling mechanism for discrete-time Takagi-Sugeno fuzzy systems. The real-time status of the operating point for the considered nonlinear plant is characterized by using these available normalized fuzzy weighting functions at both the current and the past instants of time. To achieve this, the developed fuzzy real-time gain-scheduling mechanism produces different switching modes by introducing key tunable parameters. Thus, a pair of exclusive FE gain matrices is designed for each switching mode on the strength of time-varying balanced matrices developed in this study, respectively. Since the implementation of more FE gain matrices can be scheduled according to the real-time status of the operating point at each sampling instant, the robust performance of nonlinear FE will be enhanced over the previous methods to a great extent. Finally, considerable numerical comparisons are implemented in order to illustrate that the proposed method is much superior to those existing ones reported in the literature.

Resilient Output Synchronization of Heterogeneous Multiagent Systems With DoS Attacks Under Distributed Event-/Self-Triggered Control

This article investigates the resilient output synchronization problem of a class of linear heterogeneous multiagent systems subjected to denial-of-service (DoS) attacks. Two types of control mechanisms, namely, event- and self-triggered control mechanisms, are presented so as to cut down unnecessary information transmission. Both of these two mechanisms are distributed, and thus, only local information of each agent and its neighboring agents is adopted for the event condition design. The DoS attacks are considered to be aperiodic, and the quantitative relationship between the attributes of the DoS attacks and the synchronization is also revealed. It is shown that the output synchronization can be achieved exponentially in the presence of DoS attacks under the proposed control mechanisms. The validness of the provided mechanisms is certified by a simulation example.

Formation Tracking of Multiagent Systems With Time-Varying Actuator Faults and Its Application to Task-Space Cooperative Tracking of Manipulators

This article is concerned with a fault-tolerant formation tracking problem of nonlinear systems under unknown faults, where the leader's states are only accessible to a small set of followers via a directed graph. Under these faults, not only the amplitudes but also the signs of control coefficients become time-varying and unknown. The current setting will enhance the investigated problem's practical relevance and at the same time, it poses nontrivial design challenges of distributed control algorithms and convergence analysis. To solve this problem, a novel distributed control algorithm is developed by incorporating an estimation-based control framework together with a Nussbaum gain approach to guarantee an asymptotic cooperative formation tracking of nonlinear networked systems under unknown and dynamic actuator faults. Moreover, the proposed control framework is extended to ensure an asymptotic task-space coordination of multiple manipulators under unknown actuator faults, kinematics, and dynamics. Lastly, numerical simulation results are provided to validate the effectiveness of the proposed distributed designs.

Distributed Fault-Tolerant Bipartite Output Synchronization of Discrete-Time Linear Multiagent Systems

This article studies the distributed fault-tolerant bipartite output synchronization problem of discrete-time linear multiagent systems (MASs) with process faults under a general directed signed graph. The reference signal is generated by an autonomous exosystem, which can also be seen as a leader. All followers are divided into two subgroups with antagonistic interactions, and the followers in each subgroup are cooperative. We aim to solve the bipartite fault-tolerant control (FTC) problem via the output regulation theory such that bipartite output synchronization can be achieved in the presence of process faults, that is, the outputs of followers with different subgroups can approach the output of exosystem with the same magnitude and the opposite sign regardless of process faults. To estimate the states and the faults of each follower, a simultaneous state and fault estimator based on the neighboring signed output estimation error and the standard discrete-time algebraic Riccati equation (ARE) is designed. Besides, a new exosystem observer with two classes of convergence conditions relying on the respective solutions of standard and modified AREs is provided. All eigenvalues of the exosystem matrix can lie completely outside the unit circle. Based on these estimations, we present a distributed fault-tolerant output feedback controller, which can overcome the no-loops constraint. Finally, simulation results are given to demonstrate the analytic results.

Event-Triggered Adaptive Output-Feedback Control of Switched Stochastic Nonlinear Systems With Actuator Failures: A Modified MDADT Method

This article investigates the adaptive event-triggered output-feedback control problem for a class of switched stochastic nonlinear systems with actuator faults. In the existing works, the developed results on adaptive control for switched stochastic nonlinear systems are almost based on the average dwell-time method, and how to construct a desired adaptive controller in the frame of the mode-dependent average dwell time (MDADT) remains a control dilemma. By presenting a general adaptive control rule based on the MDADT, this article implements the adaptive output-feedback control for the switched stochastic system under interest. In the process of controller design, fuzzy-logic systems, a flexible approximator, are utilized to approximate the unknown nonlinear functions. The dynamic surface design approach is employed to avoid taking derivatives of the constructed virtual controls to decrease the difficulty of complex calculation greatly. Meanwhile, a switched observer is designed to estimate the unknown states. In the frame of backstepping design, an event-triggered-based adaptive output-feedback controller is constructed such that all signals existing in the closed-loop system are ultimately bounded under a class of switching signals with MDADT property. Finally, the simulation results show the validity of the proposed control strategy.

Adaptive-Constrained Impedance Control for Human-Robot Co-Transportation

Human-robot co-transportation allows for a human and a robot to perform an object transportation task cooperatively on a shared environment. This range of applications raises a great number of theoretical and practical challenges arising mainly from the unknown human-robot interaction model as well as from the difficulty of accurately model the robot dynamics. In this article, an adaptive impedance controller for human-robot co-transportation is put forward in task space. Vision and force sensing are employed to obtain the human hand position, and to measure the interaction force between the human and the robot. Using the latest developments in nonlinear control theory, we propose a robot end-effector controller to track the motion of the human partner under actuators' input constraints, unknown initial conditions, and unknown robot dynamics. The proposed adaptive impedance control algorithm offers a safe interaction between the human and the robot and achieves a smooth control behavior along the different phases of the co-transportation task. Simulations and experiments are conducted to illustrate the performance of the proposed techniques in a co-transportation task.

Observer-Based Adaptive Optimized Control for Stochastic Nonlinear Systems With Input and State Constraints

In this work, an adaptive neural network (NN) optimized output-feedback control problem is studied for a class of stochastic nonlinear systems with unknown nonlinear dynamics, input saturation, and state constraints. A nonlinear state observer is designed to estimate the unmeasured states, and the NNs are used to approximate the unknown nonlinear functions. Under the framework of the backstepping technique, the virtual and actual optimal controllers are developed by employing the actor-critic architecture. Meanwhile, the tan-type Barrier optimal performance index functions are developed to prevent the nonlinear systems from the state constraints, and all the states are confined within the preselected compact sets all the time. It is worth mentioning that the proposed optimized control is clearly simple since the reinforcement learning (RL) algorithm is derived based on the negative gradient of a simple positive function. Furthermore, the proposed optimal control strategy ensures that all the signals in the closed-loop system are bounded. Finally, a practical simulation example is carried out to further illustrate the effectiveness of the proposed optimal control method.

Observer-Based Asynchronous Control of Nonlinear Systems With Dynamic Event-Based Try-Once-Discard Protocol

This work investigates the observer-based asynchronous control of discrete-time nonlinear systems with network-induced communication constraints. To avoid the data collisions and side effects in a constrained communication channel, a novel dynamic event-based weighted try-once-discard (DEWTOD) protocol is proposed. In contrast to the existing protocols, the DEWTOD scheduling regulates whether the sampling instant to release and which node to transmit the sampling instant simultaneously. In light of a hidden Markov model, the time-varying detection probability matrix is characterized by a polytopic set. By resorting to the polytopic-structured Lyapunov functional, sufficient conditions are derived such that the closed-loop dynamic is mean-square exponentially stable, and the observer-based controller is designed. In the end, two numerical examples are provided to explicate the validity of the attained methodology.

Global Stabilization for a Class of Stochastic Nonlinear Time-Delay Systems With Unknown Measurement Drifts and Its Application

This article studies the control problem for a class of stochastic nonlinear time-delay systems with uncertain output functions. Under the appropriate assumptions, a stabilization controller is explicitly constructed by applying the adding a power integrator method. Then, using the Lyapunov-Krasovskii functionals to address time-delay, it is proven that the designed controller can guarantee the closed-loop system to be globally asymptotically stable (GAS) in probability. Finally, two simulations show that the control strategy is effective and can be applied to the actual system.

Adaptive Prescribed Performance Control of A Flexible-Joint Robotic Manipulator With Dynamic Uncertainties

An adaptive fuzzy control strategy is proposed for a single-link flexible-joint robotic manipulator (SFRM) with prescribed performance, in which the unknown nonlinearity is identified by adopting the fuzzy-logic system. By designing a performance function, the transient performance of the control system is guaranteed. To stabilize the SFRM, a dynamic signal is applied to handle the unmodeled dynamics. To cut down the communication load of the channel, the event-triggered control law is developed based on the switching threshold strategy. The Lyapunov stability theory and backstepping technique are applied coordinately to design the control strategy. The semiglobally ultimately uniformly boundedness can be ensured for all signals in the closed-loop system. The designed control method can also guarantee that the tracking error can converge to a small neighborhood of zero within the prescribed performance boundaries. At the end of the article, two illustrative examples are shown to validate the designed event-triggered controller.

Finite-Time Robust Intelligent Control of Strict-Feedback Nonlinear Systems With Flight Dynamics Application

The tracking control is investigated for a class of uncertain strict-feedback systems with robust design and learning systems. Using the switching mechanism, the states will be driven back by the robust design when they run out of the region of adaptive control. The adaptive design is working to achieve precise adaptation and higher tracking precision in the neural working domain, while the finite-time robust design is developed to make the system stable outside. To achieve good tracking performance, the novel prediction error-based adaptive law is constructed by considering the estimation performance. Furthermore, the output constraint is achieved by imbedding the barrier Lyapunov function-based design. The finite-time convergence and the uniformly ultimate boundedness of the system signal can be guaranteed. Simulation studies show that the proposed approach presents robustness and adaptation to system uncertainty.

Adaptive Neural Network Control for a Class of Fractional-Order Nonstrict-Feedback Nonlinear Systems With Full-State Constraints and Input Saturation

This article addresses an adaptive neural network (NN) constraint control scheme for a class of fractional-order uncertain nonlinear nonstrict-feedback systems with full-state constraints and input saturation. The radial basis function (RBF) NNs are used to deal with the algebraic loop problem from the nonstrict-feedback formation based on the approximation structure. In order to overcome the problem of input saturation nonlinearity, a smooth nonaffine function is applied to approach the saturation function. To arrest the violation of full-state constraints, the barrier Lyapunov function (BLF) is introduced in each step of the backstepping procedure. By using the fractional-order Lyapunov stability theory and the given conditions, it proves that all the states remain in their constraint bounds, the tracking error converges to a bounded compact set containing the origin, and all signals in the closed-loop system are ensured to be bounded. Finally, the effectiveness of the proposed control scheme is verified by two simulation examples.

Event-Triggered Adaptive Neural Network Sensor Failure Compensation for Switched Interconnected Nonlinear Systems With Unknown Control Coefficients

In this article, a decentralized adaptive neural network (NN) event-triggered sensor failure compensation control issue is investigated for nonlinear switched large-scale systems. Due to the presence of unknown control coefficients, output interactions, sensor faults, and arbitrary switchings, previous works cannot solve the investigated issue. First, to estimate unmeasured states, a novel observer is designed. Then, NNs are utilized for identifying both interconnected terms and unstructured uncertainties. A novel fault compensation mechanism is proposed to circumvent the obstacle caused by sensor faults, and a Nussbaum-type function is introduced to tackle unknown control coefficients. A novel switching threshold strategy is developed to balance communication constraints and system performance. Based on the common Lyapunov function (CLF) method, an event-triggered decentralized control scheme is proposed to guarantee that all closed-loop signals are bounded even if sensors undergo failures. It is shown that the Zeno behavior is avoided. Finally, simulation results are presented to show the validity of the proposed strategy.

Adaptive Optimized Backstepping Control-Based RL Algorithm for Stochastic Nonlinear Systems With State Constraints and Its Application

This article investigates the adaptive neural-network (NN) tracking optimal control problem for stochastic nonlinear systems, which contain state constraints and uncertain dynamics. First, to avoid the violation of state constraints in achieving optimal control, the novel barrier optimal performance index functions for subsystems are developed. Second, under the framework of the identifier-actor-critic, the virtual and actual optimal controllers are presented based on the backstepping technique, in which the unknown nonlinear dynamics are learned by the NN approximators. Moreover, the quartic barrier Lyapunov functions are constructed instead of square ones to cope with the Hessian term to ensure the stability of the systems with stochastic disturbance. The proposed optimal control strategy can guarantee the boundedness of closed-loop signals, and the output can follow the given reference signal. Meanwhile, the system states are restricted within some preselected compact sets all the while. Finally, both numerical and practical systems are carried out to further illustrate the validity of the proposed optimal control approach.

Adaptive Fuzzy Finite-Time Control for Nonstrict-Feedback Nonlinear Systems

This article presents an adaptive fuzzy finite-time control (AFFTC) method for nonstrict-feedback nonlinear systems (NFNSs) with unknown dynamics. With the aid of the backstepping technique, by establishing the smooth switch function (SSF), a novel C¹ AFFTC strategy is recursively constructed, which counteracts the effect of nonstrict-feedback structure and unknown dynamics. Different from the reporting finite-time control achievements, the singularity hindrance derived from the differentiating virtual control law is availably surmounted. Moreover, the developed AFFTC strategy can drive the tracking error to converge into a small neighborhood of the origin in a finite time. Simulation results are conducted to substantiate the efficacy of theoretical findings.

Finite-Time Consensus for Singularity-Perturbed Multiagent System via Memory Output Sliding-Mode Control

In some practical systems, it often remains difficult to directly measure all state variables. This article investigates the memory output sliding-mode control (SMC) for the finite-time consensus of singularly perturbed multiagent systems (SPMASs). First, the virtual state-feedback sliding surface (SFSS) is constructed to ensure the consensus of all agent states. Then, the unknown output derivatives in SFSS are approximated by a moving finite difference method with error estimation and refinement, which gives rise to a new delay-dependent sliding surface. On this basis, the memory output switching control law is designed to stabilize the consensus errors in finite time, even in the presence of estimation biases, singular perturbations, and input noises. Different from the observer-based SMC, the proposed memory output SMC is of simple static form without introducing extra dynamical structures for state estimation. The effectiveness and superiority of the design method are verified in an SPMAS with double-integrator dynamics.

Event-Triggered Adaptive Neural Control for Fractional-Order Nonlinear Systems Based on Finite-Time Scheme

This article addresses the finite-time event-triggered adaptive neural control for fractional-order nonlinear systems. Based on the backstepping technique, a novel adaptive event-triggered control scheme is proposed, and finite-time stability criteria are introduced with the aim to ensure that the tracking error enters into a small region around the origin in finite time. Finally, the stability of the closed-loop system is ensured via a fractional Lyapunov function theory and two simulation examples were used to prove the validity of the designed control scheme.

Asynchronous Impulsive Protocols With Asymmetric Feedback Saturation on Leader-Based Formation Control of Multiagent Systems

Saturation phenomena often exist due to limited system resources, and impulsive protocols can lead to a reduction in communication cost. From these issues, this article investigates a leader-based formation control problem of multiagent systems via asynchronous impulsive protocols with saturated feedback. General linear system models with and without finite time-varying time delays under asymmetric saturated feedback control are concurrently considered. The asynchronous impulsive protocols only permit communication at impulsive instants and each agent has its own communication instants independently. Moreover, to improve system performance, an offset only containing desired formation information is introduced. Finally, because the feedbacks are saturated, admissible regions are proved to exist, which are also estimated by a mean of optimization. Numerical simulations are presented to demonstrate the validity of the proposed schemes.

Fuzzy Adaptive Switching Control for Stochastic Systems With Finite-Time Prescribed Performance

The issue of fuzzy adaptive switching control for stochastic systems with arbitrary switching signal and finite-time prescribed performance is investigated in this article. A piecewise function is adopted to characterize finite-time prescribed performance, and the error signal is converted to a new state variable via the tangent function. Unknown functions are approximated via fuzzy-logic systems (FLSs). Based on the stochastic stability theory and common Lyapunov function, a fuzzy adaptive switching control scheme is presented. The control law is proposed for the stochastic switched closed-loop system so that not only all the signals are ensured to be semiglobally uniformly ultimately bounded (SGUUB) in probability but also a residual error related to the finite-time prescribed performance bound is guaranteed. Eventually, simulation studies for a practical system are given to show the effectiveness of the presented fuzzy adaptive switching control scheme.

H∞ Pinning Control of Complex Dynamical Networks Under Dynamic Quantization Effects: A Coupled Backward Riccati Equation Approach

In this article, a pinning control strategy is developed for the finite-horizon H_∞ synchronization problem for a kind of discrete time-varying nonlinear complex dynamical network in a digital communication circumstance. For the sake of complying with the digitized data exchange, a feedback-type dynamic quantizer is introduced to reflect the transformation from the raw signals into the discrete-valued ones. Then, a quantized pinning control scheme takes place on a small fraction of the network nodes with the hope of cutting down the control expenses while achieving the expected global synchronization objective. Subsequently, by resorting to the completing-the-square technique, a sufficient condition is established to ensure the finite-horizon H_∞ index of the synchronization error dynamics against both quantization errors and external noises. Moreover, a controller design algorithm is put forward via an auxiliary H₂ -type criterion, and the desired controller gains are acquired in terms of two coupled backward Riccati equations. Finally, the validity of the presented results is verified via a simulation example.

Adaptive Fuzzy Output-Feedback Control for Switched Uncertain Nonlinear Systems With Full-State Constraints

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.

Fault-Tolerant Adaptive Fuzzy Tracking Control for Nonaffine Fractional-Order Full-State-Constrained MISO Systems With Actuator Failures

The problem of fault-tolerant adaptive fuzzy tracking control against actuator faults is investigated in this article for a type of uncertain nonaffine fractional-order nonlinear full-state-constrained multi-input-single-output (MISO) system. By means of the existence theorem of the implicit function and the intermediate value theorem, the design difficulty arising from nonaffine nonlinear terms is surmounted. Then, the unknown ideal control inputs are approximated by using some suitable fuzzy-logic systems. An adaptive fuzzy fault-tolerant control (FTC) approach is developed by employing the barrier Lyapunov functions and estimating the compounded disturbances. Moreover, under the drive of the reference signals, a sufficient condition ensuring semiglobal uniform ultimate boundedness is obtained for all the signals in the closed-loop system, and it is proved that all the states of nonaffine nonlinear fractional-order systems are guaranteed to remain inside the predetermined compact set. Finally, two numerical examples are provided to exhibit the validity of the designed adaptive fuzzy FTC approach.

Unknown System Dynamics Estimator for Active Vehicle Suspension Control Systems With Time-Varying Delay

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.

Event-Based Design of Finite-Time Adaptive Control of Uncertain Nonlinear Systems

The problem of finite-time adaptive tracking control against event-trigger error is investigated in this article for a type of uncertain nonlinear systems. By fusing the techniques of command filter backstepping technical and event-triggered control (ETC), an adaptive event-triggered design method is proposed to construct the controller, under which the effect of event-triggered error can be compensated completely. Moreover, the proposed controller can increase robustness against uncertainties and event error in the backstepping design framework. In particular, we establish the finite-time convergence condition under which the tracking error asymptotically converges to zero in finite time with the aid of a scaling function. Detailed and rigorous stability proofs are given by making use of the improved finite time stability criterion. Two simulation examples are provided to exhibit the validity of the designed adaptive ETC approach.

Global Finite-Time Stabilization for Uncertain Systems With Unknown Measurement Sensitivity

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

Reduced-Order Filters-Based Adaptive Backstepping Control for Perturbed Nonlinear Systems

In this article, a robust adaptive output-feedback control approach is presented for a class of nonlinear output-feedback systems with parameter uncertainties and time-varying bounded disturbances. A reduced-order filter driven by control input is proposed to reconstruct unmeasured states. The state estimation error is shown to be bounded by dynamic signals driven by system output. The bound estimation technique is employed to estimate the unknown disturbance bound. Based on the backstepping design with three sets of tuning functions, an adaptive output-feedback control scheme with the flat-zone modification is proposed. It is shown that all the signals in the resulting closed-loop adaptive control systems are bounded, and the output tracking error converges to a prespecified small neighborhood of the origin. Two simulation examples are provided to illustrate the effectiveness and validity of the proposed approach.

Observer-Based Neuro-Adaptive Optimized Control of Strict-Feedback Nonlinear Systems With State Constraints

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.

Distributed Cooperative Compound Tracking Control for a Platoon of Vehicles With Adaptive NN

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

Distributed Finite-Time Containment Control for Nonlinear Multiagent Systems With Mismatched Disturbances

This article proposes a finite-time adaptive containment control scheme for a class of uncertain nonlinear multiagent systems subject to mismatched disturbances and actuator failures. The dynamic surface control technique and adding a power integrator technique are modified to develop the distributed finite-time adaptive containment algorithm, which shows lower computational complexity. In order to overcome the difficulty from the mismatched uncertainties, the disturbance observers are constructed based on the backstepping technique. Moreover, the uncertain actuator faults, including loss of effectiveness model and lock-in-place model, are considered and compensated by the proposed adaptive control scheme in this article. According to the Lyapunov stability theory, it is demonstrated that the containment errors are practically finite-time stable in the presence of actuator faults. Finally, a simulation example is conducted to show the effectiveness of the proposed theoretical results.

Finite-Time-Prescribed Performance-Based Adaptive Fuzzy Control for Strict-Feedback Nonlinear Systems With Dynamic Uncertainty and Actuator Faults

In this article, finite-time-prescribed performance-based adaptive fuzzy control is considered for a class of strict-feedback systems in the presence of actuator faults and dynamic disturbances. To deal with the difficulties associated with the actuator faults and external disturbance, an adaptive fuzzy fault-tolerant control strategy is introduced. Different from the existing controller design methods, a modified performance function, which is called the finite-time performance function (FTPF), is presented. It is proved that the presented controller can ensure all the signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in finite time. The effectiveness of the presented control scheme is verified through the simulation results.