Neural-Network-Based Adaptive Decentralized Fault-Tolerant Control for a Class of Interconnected Nonlinear Systems

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control of Nonlinear Interconnected Systems With Unmodeled Dynamics and Prescribed Performance

This article proposes two adaptive asymptotic tracking control schemes for a class of interconnected systems with unmodeled dynamics and prescribed performance. By applying an inherent property of radial basis function (RBF) neural networks (NNs), the design difficulties aroused from the unknown interactions among subsystems and unmodeled dynamics are overcome. Then, in order to ensure that the tracking errors can be suppressed in the specified range, the constrained control problem is transformed into the stabilization problem by using an auxiliary function. Based on the adaptive backstepping method, a time-triggered controller is constructed. It is proven that under the framework of Barbalat's lemma, all the variables in the closed-loop system are bounded and the tracking errors are further ensured to converge to zero asymptotically. Furthermore, the event-triggered strategy with a variable threshold is adopted to make more precise control such that the better system performance can be obtained, which reduces the system communication burden under the condition of limited communication resources. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

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.

Event-Triggered Multigradient Recursive Reinforcement Learning Tracking Control for Multiagent Systems

In this article, the tracking control problem of event-triggered multigradient recursive reinforcement learning is investigated for nonlinear multiagent systems (MASs). Attention is focused on the distributed reinforcement learning approach for MASs. The critic neural network (NN) is applied to estimate the long-term strategic utility function, and the actor NN is designed to approximate the uncertain dynamics in MASs. The multigradient recursive (MGR) strategy is tailored to learn the weight vector in NN, which eliminates the local optimal problem inherent in gradient descent method and decreases the dependence of initial value. Furthermore, reinforcement learning and event-triggered mechanism can improve the energy conservation of MASs by decreasing the amplitude of the controller signal and the controller update frequency, respectively. It is proved that all signals in MASs are semiglobal uniformly ultimately bounded (SGUUB) according to the Lyapunov theory. Simulation results are given to demonstrate the effectiveness of the proposed strategy.

Robust Pointing Control of Marching Tank Gun With Matched and Mismatched Uncertainty

This article focuses on a robust control scheme for pointing control of the marching tank gun. Both matched and mismatched uncertainties, which may be nonlinear (possibly fast) time varying but bounded, are considered. First, the pointing control system is constructed as a coupled, nonlinear, and uncertain dynamical system with two interconnected (horizontal and vertical) subsystems. Second, for the horizontal pointing control, robust control is proposed to render the horizontal subsystem to be practically stable. Third, for the vertical pointing control, an uncertainty bound-based state transformation is constructed in a similar way of backstepping to convert the original mismatched system (i.e., the vertical subsystem) to be locally matched and then robust control is proposed to render the transformed system to be practically stable. Finally, it is proved that when the transformed system is rendered to be practically stable, the original system renders the same performance; therefore, vertical pointing control is achieved. This work should be among the first ever endeavor to cast all the coupling, nonlinearity, and (both matched and mismatched) uncertainty into the pointing control framework of the marching tank gun.

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.

Adaptive NN-Based Consensus for a Class of Nonlinear Multiagent Systems With Actuator Faults and Faulty Networks

This article addresses the problem of fault-tolerant consensus control of a general nonlinear multiagent system subject to actuator faults and disturbed and faulty networks. By using neural network (NN) and adaptive control techniques, estimations of unknown state-dependent boundaries of nonlinear dynamics and actuator faults, which can reflect the worst impacts on the system, are first developed. A novel NN-based adaptive observer is designed for the observation of faulty transformation signals in networks. On the basis of the NN-based observer and adaptive control strategies, fault-tolerant consensus control schemes are designed to guarantee the bounded consensus of the closed-loop multiagent system with disturbed and faulty networks and actuator faults. The validity of the proposed adaptively distributed consensus control schemes is demonstrated by a multiagent system composed of five nonlinear forced pendulums.

Decentralized Dynamic Event-Triggered Output Feedback Adaptive Fixed-Time Funnel Control for Interconnection Nonlinear systems

A decentralized dynamic event-triggered output feedback adaptive fixed-time (DDETOFAFxT) funnel controller is described for a class of interconnected nonlinear systems (INSs). A novel dynamic event-triggered mechanism is designed, which includes a triggering control input, fixed threshold, decreasing function of tracking error, and a dynamic variable. To obtain the unknown states, a decentralized linear filter is designed. By introducing a prescribed funnel and using an adding a power integrator technique and a neural network method, a DDETOFAFxT funnel controller is designed to obtain better tracking performance and effectively alleviate the computational burden. Furthermore, it is ensured that the tracking error falls into a preset performance funnel. A simulation example is presented to demonstrate the availability of the designed control scheme.

Adaptive Neural Dynamic Surface Control With Prespecified Tracking Accuracy of Uncertain Stochastic Nonstrict-Feedback Systems

This article addresses the adaptive neural tracking control problem for a class of uncertain stochastic nonlinear systems with nonstrict-feedback form and prespecified tracking accuracy. Some radial basis function neural networks (RBF NNs) are used to approximate the unknown continuous functions online, and the desired controller is designed via the adaptive dynamic surface control (DSC) method and the gain suppressing inequality technique. Different from the reported works on uncertain stochastic systems, by combining some non-negative switching functions and dynamic surface method with the nonlinear filter, the design difficulty is overcome, and the control performance is analyzed by employing stochastic Barbalat's lemma. Under the constructed controller, the tracking error converges to the accuracy defined a priori in probability. The simulation results are shown to verify the availability of the presented control scheme.

Adaptive Actuator Failure Compensation Control Schemes for Uncertain Noncanonical Neural-Network Systems

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.

Distributed Adaptive Consensus of Nonlinear Heterogeneous Agents With Delayed and Sampled Neighbor Measurements

In this article, the adaptive output consensus problem of high-order nonlinear heterogeneous agents is addressed using only delayed, sampled neighbor output measurements. A class of auxiliary variables is introduced which are n -times differentiable functions and include the agent's output along with delayed, sampled output neighbor measurements. It is proven that if these variables are bounded and regulated to zero then asymptotic consensus among all agent outputs is ensured. In view of this property, an adaptive distributed backstepping design procedure is presented that guarantees boundedness and regulation of the proposed variables. This design procedure ensures not only the desired asymptotic output consensus but also the uniform boundedness of all closed-loop variables. The main feature of our approach is that, in the proposed control law for each agent, the entire state vector of the neighbors is not needed and only delayed sampled measurements of the neighbors' outputs are utilized. The simulation results are also presented that verify our theoretical analysis.

Fixed-time disturbance observer-based nearly optimal control for reusable launch vehicle with input constraints

In this paper, a fixed-time disturbance observer-based nearly optimal control (FTDO-NOC) scheme is proposed for reusable launch vehicle (RLV) subject to model uncertainties, input constraints, and unknown mismatched/matched disturbances. The dynamics of RLV attitude motion are divided into outer-loop subsystem and inner-loop subsystem. For the outer-loop subsystem, to address the problems of unknown mismatched disturbances and model uncertainties, a novel adaptive-gain multivariable generalized super-twisting (AMGST) controller is proposed. Two modified gain-adaptation laws are derived for tuning the control gains of AMGST controller, which attenuates chattering efficiently. For the inner-loop subsystem, considering the effect of unknown matched disturbances, a fixed-time disturbance observer (FTDO) is utilized to estimate the matched disturbances and the time derivative of virtual control input. Incorporated with the designed FTDO, a nearly optimal controller (NOC), which is based on the critic-actor neural networks (NNs), is utilized to generate the approximate optimal control moments satisfying the input constraints. The tracking errors of inner-loop subsystem and the weight estimation errors of the critic-actor NNs are proved to be uniformly ultimately bounded (UUB) via Lyapunov technique. Finally, we provide simulation results to validate the effectiveness and superiority of the proposed control scheme.

Adaptive Fuzzy Tracking Control for a Class of Uncertain Switched Nonlinear Systems With Full-State Constraints and Input Saturations

In this article, an adaptive fuzzy tracking control scheme is developed for a class of uncertain switched nonlinear systems with input saturations and full-state constraints. First to surmount the design difficulty with respect to a saturation nonlinearity controller, a nonlinear smooth function approximating the nondifferential saturation function is introduced to establish a standard switched adaptive tracking control strategy based on the mean-value theorem and the input compensation technique. Then, invoking fuzzy-logic systems (FLSs), a novel analysis method of average dwell time for switched nonlinear systems with full-state constraints is proposed by using an artful logarithmic inequality. Furthermore, the designed adaptive controller can ensure that all the states of uncertain switched nonlinear systems are not to violate the set constraint bounds by employing barrier Lyapunov functions (BLFs), and that the system output tracking error can converge to a desired neighborhood of the origin within a suitable compact set. Finally, the simulation results are given to demonstrate the validity of the presented approach.

Decentralized Adaptive Neuro-Output Feedback Saturated Control for INS and Its Application to AUV

This article investigates the problem of the decentralized adaptive output feedback saturated control problem for interconnected nonlinear systems with strong interconnections. A decentralized linear observer is first established to estimate the unknown states. Then, an auxiliary system is constructed to offset the effect of input saturation. With the aid of graph theory and neural network technique, a decentralized adaptive neuro-output feedback saturated controller is designed in a nonrecursive manner. A sufficient criterion is established to achieve the uniform ultimate boundedness (UUB) of the closed-loop system. An application example of autonomous underwater vehicle (AUV) is provided to verify the effectiveness of the developed algorithm.

Adaptive Fixed-Time Neural Network Tracking Control of Nonlinear Interconnected Systems

In this article, a novel adaptive fixed-time neural network tracking control scheme for nonlinear interconnected systems is proposed. An adaptive backstepping technique is used to address unknown system uncertainties in the fixed-time settings. Neural networks are used to identify the unknown uncertainties. The study shows that, under the proposed control scheme, each state in the system can converge into small regions near zero with fixed-time convergence time via Lyapunov stability analysis. Finally, the simulation example is presented to demonstrate the effectiveness of the proposed approach. A step-by-step procedure for engineers in industry process applications is proposed.

Equivalent-input-disturbance estimator-based event-triggered control design for master-slave neural networks

This paper investigates the robust synchronization problem for a class of master-slave neural networks (MSNNs) subject to network-induced delays, unknown time-varying uncertainty, and exogenous disturbances. An equivalent-input-disturbance (EID) estimation technique is applied to compensate for the effects of unknown uncertainty and disturbances in the system output. In addition, to reduce the burden of the communication channel in the addressed MSNNs and improve the utilization of bandwidth an event-triggered control protocol is developed to obtain the synchronization of MSNNs. In particular, event-triggering conditions are verified periodically at every sampling instant in both sensors and actuators to avoid the Zeno behavior in the networks. By designing an appropriate low-pass filter in the EID estimator block, the accuracy of disturbance estimation performance is improved. Moreover, by concatenating the synchronization error, observer, and filter states as a single state vector, an augmented system is formulated. Then the tangible delay-dependent stability condition for that augmented system is established by employing the Lyapunov stability theory and reciprocally convex approach. Based on the feasible solutions of the derived stability conditions, the event-triggering parameters, controller, and observer gains are co-designed. Finally, two toy examples are given to illustrate the established theoretical findings.

Sliding-Mode Surface-Based Approximate Optimal Control for Uncertain Nonlinear Systems With Asymptotically Stable Critic Structure

This article develops a novel sliding-mode surface (SMS)-based approximate optimal control scheme for a large class of nonlinear systems affected by unknown mismatched perturbations. The observer-based perturbation estimation procedure is employed to establish the online updated value function. The solution to the Hamilton-Jacobi-Bellman equation is approximated by an SMS-based critic neural network whose weights error dynamics is designed to be asymptotically stable by nested update laws. The sliding-mode control strategy is combined with the approximate optimal control design procedure to obtain a faster control action. The stability is proved based on the Lyapunov's direct method. The simulation results show the effectiveness of the developed control scheme.

Event-Triggered H∞ Control for T-S Fuzzy Systems via New Asynchronous Premise Reconstruction Approach

This article studies the problem of H_∞ controller design for discrete-time T-S fuzzy systems under an event-triggered (ET) communication mechanism. By proposing a new asynchronous premise reconstruction approach, new types of ET fuzzy controllers are designed to overcome the challenges caused by the mismatch of premise variables, in which the gains of the designed controllers are automatically updated at different triggering instants according to an online algorithm. By constructing discontinuous Lyapunov functions, it is proved that the proposed ET controllers guarantee the stability and H_∞ performance of the closed-loop systems. Two examples are provided to verify the validity of the proposed design method.

Health-diagnosis of electromechanical system with a principal-component bayesian neural network algorithm

This study proposes a cloud tele-measurement technique on an electromechanical system, and uses a neural network algorithm based on principal-component analysis (PCA) to quickly diagnose its performance. Three vibration, three temperature, electrical voltage, and current sensors were mounted on the electromechanical system, and the external braking device was used to provide different load-states to simulate the operating states of the motor under different conditions. Moreover, a single-chip multiprocessor was used through the sensor to instantly measure the various load-state simulations of the motor. The operating states of the electromechanical system were classified as normal, abnormal, and required-to-be-turned-off states using a principal-component Bayesian neural network algorithm (PBNNA), to enable their quick diagnosis. Furthermore, PBNNA successfully reduces the dimensionality of the multivariate dataset for rapid analysis of the electromechanical system’s performance. The accuracy rates of health-diagnosis based on the Bayesian neural network algorithm and PBNNA models were obtained as 97.7% and 98%, respectively. Finally, the single-chip multiprocessor based on PBNNA is used to automatically upload the measurement and analysis results of the electromechanical system to the cloud website server. The establishment of this model system can optimize prediction judgment and decision-making based on the damage situation to achieve the goals of intelligence and optimization of factory reconstruction.

Finite-Horizon H∞ Fault-Tolerant Constrained Consensus for Multiagent Systems With Communication Delays

This article focuses on the fault-tolerant constrained consensus problem for multiagent systems with communication delays. The communication graphs are first assumed to be directed and fixed. Then, a novel delay-dependent fault-tolerant controller is designed such that, in the presence of communication delays and randomly occurring actuator failures, the influence of the projections and the initial states on the closed-loop system can be attenuated with a prespecified level. Based on the provided performance requirement, the initial state of each agent does not need to be identical. The proposed control algorithms ensure that sufficient conditions are met for the fault-tolerant constrained consensus to be achieved according to the prespecified performance index. After this, the controller gains are computed by employing an iterative linear matrix inequality scheme. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Decentralized Output Sliding-Mode Fault-Tolerant Control for Heterogeneous Multiagent Systems

This paper proposes a novel decentralized output sliding-mode fault-tolerant control (FTC) design for heterogeneous multiagent systems (MASs) with matched disturbances, unmatched nonlinear interactions, and actuator faults. The respective iteration and iteration-free algorithms in the sliding-mode FTC scheme are designed with adaptive upper bounding laws to automatically compensate the matched and unmatched components. Then, a continuous fault-tolerant protocol in the observer-based integral sliding-mode design is developed to guarantee the asymptotic stability of MASs and the ultimate boundedness of the estimation errors. Simulation results validate the efficiency of the proposed FTC algorithm.

Two-Level Game-Based Distributed Optimal Fault-Tolerant Control for Nonlinear Interconnected Systems

This article addresses the distributed optimal fault-tolerant control (FTC) issue by using the two-level game approach for a class of nonlinear interconnected systems, in which each subsystem couples with its neighbors through not only the states but also the inputs. At the first level, the FTC problem for each subsystem is formulated as a zero-sum differential game, in which the controller and the fault are regarded as two players with opposite interests. At the second level, the whole interconnected system is formulated as a graphical game, in which each subsystem is a player to achieve the global Nash equilibrium for the overall system. The rigorous proof of the stability of the interconnected system is given by means of the cyclic-small-gain theorem, and the relationship between the local optimality and the global optimality is analyzed. Moreover, based on the adaptive dynamic programming (ADP) technology, a distributed optimal FTC learning scheme is proposed, in which a group of critic neural networks (NNs) are established to approximate the cost functions. Finally, an example is taken to illustrate the efficiency and applicability of the obtained theoretical results.

Cooperative Fault-Tolerant Output Regulation for Multiagent Systems by Distributed Learning Control Approach

In this article, a new distributed learning control approach is proposed to address the cooperative fault-tolerant output regulation problem for linear multiagent systems with actuator faults. First, a distributed estimation algorithm with an online learning mechanism is presented to identify the system matrix of the exosystem and to estimate the state of the exosystem. In particular, an auxiliary variable is introduced in the distributed estimation algorithm to construct a data matrix, which is used to learn the system matrix of the exosystem for each subsystem. In addition, by resetting the state of the estimator and by using the identified matrix to update the estimator, all subsystems can reconstruct the state of the exosystem at an initial period of time, which is used for the neighbor subsystem to learn the system matrix of the exosystem. Based on the designed estimator, a novel distributed fault-tolerant controller is developed. Compared with the existing cooperative output regulation results, the system matrix of the exosystem considered in this article is unknown for all subsystems. Finally, a simulation example is provided to show the effectiveness of the obtained new design techniques.

A Survey on Active Fault-Tolerant Control Systems

Faults and failures in the system components are two main reasons for the instability and the degradation in control performance. In recent decades, fault-tolerant control (FTC) approaches have been introduced to improve the resiliency of control systems against faults and failures. In general, FTC techniques are classified into active and passive approaches. This paper reviews fault and failure causes in control systems and discusses the latest solutions that are introduced to make the control system resilient.The recent achievements in fault detection and isolation (FDI) approaches and active FTC designs are investigated. Furthermore, a thorough comparison of several different aspects is conducted to understand the advantage and disadvantages of various FTC techniques to motivate researchers to further developing FTC and FDI approaches.

Adaptive Neural Output Feedback Compensation Control for Intermittent Actuator Faults Using Command-Filtered Backstepping

Effectively compensating unknown intermittent actuator faults in uncertain decentralized nonlinear systems is a very difficult problem, and very few results have been obtained. In this article, to address this issue, an adaptive neural output feedback compensation control scheme based on command-filtered backstepping is developed. First, we design a bank of observers to estimate the system states and utilize neural networks with random hidden nodes to approximate the unknown functions of these observers. Second, a smooth projection algorithm is used to online update estimated parameters in the controllers such that the possible ceaseless increase in the estimated parameters caused by intermittent actuator faults can be eliminated. Due to the presence of intermittent jumps of unknown parameters, a modified Lyapunov function is developed to analyze the system stability. It is proved that the boundedness of all closed-loop system signals is ensured and the ultimate bound of the tracking error depends on design parameters, adjustable jumping amplitude of Lyapunov function, and minimum fault time interval. Third, by analyzing the system transient performance, the peaking phenomenon at the starting instant of the system operation can be removed, and a root mean square type of bound is established to illustrate that the transient tracking error performance is tunable by design parameters. Finally, simulations studies are done to illustrate the effectiveness of the theoretical results.

Adaptive Neural Network Finite-Time Control for Multi-Input and Multi-Output Nonlinear Systems With Positive Powers of Odd Rational Numbers

This article investigates the adaptive neural network (NN) finite-time output tracking control problem for a class of multi-input and multi-output (MIMO) uncertain nonlinear systems whose powers are positive odd rational numbers. Such designs adopt NNs to approximate unknown continuous system functions, and a controller is constructed by combining backstepping design and adding a power integrator technique. By constructing new iterative Lyapunov functions and using finite-time stability theory, the closed-loop stability has been achieved, which further verifies that the entire system possesses semiglobal practical finite-time stability (SGPFS), and the tracking errors converge to a small neighborhood of the origin within finite time. Finally, a simulation example is given to elaborate the effectiveness and superiority of the developed.

Adaptive Decentralized Neural Network Tracking Control for Uncertain Interconnected Nonlinear Systems With Input Quantization and Time Delay

This study investigates the problem of adaptive decentralized tracking control for a class of interconnected nonlinear systems with input quantization, unknown function, and time-delay, where the time-delay and interconnection terms are supposed to be bounded by some completely unknown functions. An adaptive decentralized tracking controller is constructed via the backstepping method and neural network technique, where a sliding-mode differentiator is presented to estimate the derivative of the virtual control law and reduce the complexity of the control scheme. On the basis of Lyapunov analysis scheme and graph theory, all the signals of the closed-loop system are uniformly ultimately bounded. Finally, an application example of an inverted pendulum system is given to demonstrate the effectiveness of the developed methods.

Output feedback fault-tolerant control for a class of nonlinear systems via dynamic gain and neural network

In this paper, by combining the dynamic gain and the self-adaptive neural network, an output feedback fault-tolerant control method was proposed for a class of nonlinear uncertain systems with actuator faults. First, the dynamic gain was introduced and the coordinate transformation of the state variables of the system was performed to design the corresponding state observers. Then, the observer-based output feedback controller was designed through the back-stepping method. The output feedback control method based on the dynamic gain can solve the adaptive fault-tolerant control problem when there are simple nonlinear functions with uncertain parameters in the system. For the more complex uncertain nonlinear functions in the system, in this paper, a single hidden layer neural network was used for compensation and the fault-tolerant control was realized by combining the dynamic gain. Finally, the height and posture control system of the unmanned aerial vehicle with actuator faults was taken as an example to verify the effectiveness of the proposed method.

Finite-Time Decentralized Control of IT2 T-S Fuzzy Interconnected Systems With Discontinuous Interconnections

This paper investigates the finite-time decentralized control problem for interconnected systems with discontinuous interconnections. By using the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, a unified IT2 T-S fuzzy interconnected system is provided, in which the global system is described as a fuzzy blending of local subsystems under IF-THEN rules. In addition, based on the differential inclusion theory, the solutions of such discontinuous system are defined in the sense of Filippov. In order to stabilize the considered system in finite time, several decentralized discontinuous state feedback controllers are proposed. Furthermore, by the finite-time stabilization theory and generalized Lyapunov functional method, decentralized control is carried out and several sufficient criteria are derived to ensure the finite-time stabilization of the concerned system. Correspondingly, the settling times for stabilization are given. Finally, the proposed methodology is illustrated by an example.

Command filter based adaptive control of asymmetric output-constrained switched stochastic nonlinear systems

In this paper, adaptive tracking control problem is investigated for a class of switched stochastic nonlinear systems with an asymmetric output constraint. By introducing a nonlinear mapping (NM), the asymmetric output-constrained switched stochastic system is first transformed into a new system without any constraint, which achieves the equivalent control objective. The command filter technique is employed to handle the "explosion of complexity" in traditional backstepping design, and neural networks (NNs) are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB), while the output constraint is satisfied and the desired signal can be tracked with a small domain of the origin. Simulation results are offered to illustrate the feasibility of the newly designed control scheme.

Graph-Theory-Based Decentralized Adaptive Output-Feedback Control for a Class of Nonlinear Interconnected Systems

This paper investigates the problem of decentralized output feedback control for a class of interconnected systems with unknown state-dependent interconnections. First, we design a new form of K -filters with extra design parameters to compensate the unmeasurable states. Then by introducing a smooth function, we can design a decentralized output feedback control law by integrating the well-known backstepping framework. Furthermore, from the graph theory and Lyapunov function method, we analyze the stability and tracking property of the closed-loop systems. As an illustrative example, the proposed control scheme is applied to the controller design of a mass-spring-damper system.

Decentralized Adaptive Fuzzy Secure Control for Nonlinear Uncertain Interconnected Systems Against Intermittent DoS Attacks

Cyber-physical systems (CPSs) are naturally highly interconnected and complexly nonlinear. This paper investigates the problem of decentralized adaptive output feedback control for CPSs subject to intermittent denial-of-service (DoS) attacks. The considered CPSs are modeled as a class of nonlinear uncertain strict-feedback interconnected systems. When a DoS attack is active, all the state variables become unavailable and standard backstepping cannot be applied. To overcome this difficulty, a switching-type adaptive state estimator is constructed. Based on an improved average dwell time method incorporated by frequency and duration properties of DoS attacks, convex design conditions of controller parameters are derived in term of solving a set of linear matrix inequalities. The proposed controller guarantees that all closed-loop signals remain bounded, while the error signals converge to a small neighborhood of the origin. As an illustrative example, the proposed control scheme is applied to a power network system.

Development of a New Adaptive Backstepping Control Design for a Non-Strict and Under-Actuated System Based on a PSO Tuner

In this work, a new adaptive block-backstepping control design algorithm was developed for an under-actuated model (represented by a ball–arc system) to enhance the transient and steady-state behaviors and to improve the robustness characteristics of the controlled system against parameter variation (load change and model uncertainty). For this system, the main mission of the proposed controller is to simultaneously hold the ball at the top of the arc and retain the cart at the required position. The stability of a controlled system based on the proposed adaptive controller was analyzed, and its globally asymptotic stability was proven based on the Lyapunov theorem. A comparative study of adaptive and non-adaptive block-backstepping controllers was conducted in relation to the transient, steady-state, and robustness characteristics. The effectiveness of the controller was verified via simulation within a MATLAB/SIMULINK environment. The simulated results show that the proposed adaptive control strategy could successfully stabilize the under-actuated ball–arc system, regardless of both the regulation problem and the tracking problem. This provides a better dynamic performance and a better load rejection capability, and it performs well in solving the uncertainty problem in the model parameter.