Composite adaptive finite-time fuzzy control for switched nonlinear systems with preassigned performance

This article investigates the composite adaptive fuzzy finite-time prescribed performance control issue of switched nonlinear systems subject to the unknown external disturbance and performance requirement. First, by utilizing the compensation and prediction errors, the piecewise switched composite parameter update law is employed to improve the approximation accuracy of the unknown nonlinearity. Then, the improved fractional-order filter and error compensation signal are introduced to cope with the influences caused by the explosive calculation and filter error, respectively. Meanwhile, the effect of the compound disturbances consisting of the unknown disturbances and approximation errors is reduced appropriately by designing the piecewise switched nonlinear disturbance observer. Moreover, stability analysis results prove that the proposed preassigned performance control scheme not only ensures that all states of the closed-loop system are practical finite-time bounded, but also that the tracking error converges to a preassigned area with a finite time. Ultimately, the simulation examples are given to demonstrate the effectiveness of the proposed control strategy.     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

In this study, an adaptive output feedback control with prescribed performance is proposed for unknown pure feedback nonlinear systems with external disturbances and unmeasured states. A novel prescribed performance function is developed and incorporated into an output error transformation to achieve tracking control with prescribed performance. To handle the unknown non-affine nonlinearities and avoid the algebraic loop problem, the radial basis function neural network (RBFNN) is adopted to approximate the unknown non-affine nonlinearities with the help of Butterworth low-pass filter. Based on the output of the RBFNN, the coupled design between sate observer and disturbance observer is presented to estimate the unmeasured states and compounded disturbances. Then, the adaptive output feedback control scheme is proposed for unknown pure feedback nonlinear systems, where a first-order filter is introduced to tackle with the issue of “explosion of complexity” in the traditional back-stepping approach. The boundedness and convergence of the closed-loop system are proved rigorously by utilizing the Lyapunov stability theorem. Finally, simulation studies are worked out to demonstrate the effectiveness of the proposed scheme.     

Adaptive event-triggered consensus control of multi-agent systems with prescribed performance and input quantization

This paper focuses on the adaptive fuzzy event-triggered consensus control problem for multi-agent systems (MAS) with prescribed performance and input quantization. Based on a prescribed performance function and an input quantization decomposition method, a new adaptive fuzzy event-triggered consensus protocol is presented. The instances in the event-triggered mechanism are triggered only when the event-triggered error exceeds a specified threshold, which can save limited communication resources. It is demonstrated that the event-triggered control protocol ensures that all signals in the MAS are semi-globally uniformly ultimately bounded. As a result, the consensus tracking errors converge to prescribed limits. Finally, simulation examples are provided to validate effectiveness of the proposed event-triggered control methods.     

Adaptive fuzzy dual-performance fault-tolerant control for interconnected nonlinear systems

This article focuses on the decentralized adaptive fuzzy fixed-time fault-tolerant control issue for the error-constrained interconnected nonlinear systems with unknown actuator faults possessing dead zone. The unknown nonlinear functions can be modeled via fuzzy logic systems. By utilizing the parameter estimation method, the effect of unknown actuator faults possessing dead zone can be compensated. To guarantee the predefined dynamic performance of state tracking errors, the barrier Lyapunov functions and prescribed performance functions are introduced. Then, a dual-performance fault-tolerant control method that can guarantee fast transient performance and predefined performance of state tracking errors is proposed via using the decentralized backstepping technique. In addition, on the basis of the Lyapunov stability theory and the fixed-time criterion, it is proved that the predefined performance of full-state errors and the stability of closed-loop systems can be guaranteed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed control scheme.     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Observer-based adaptive event-triggered neural tracking control for nonlinear cyber-physical systems with incomplete measurements

In this paper, an adaptive event-triggered neural networks (NNs) tracking control problem is investigated for cyber-physical Systems (CPSs) with incomplete measurements. The state variables can get unavailable or distorted in incomplete measurements because of data transmission problems, which can degrade the performance of the system. To solve these problems, the radial basis function neural networks (RBF NNs) control is used to approximate the unknown nonlinear function in CPSs, and the Butterworth Low-pass Filter (LPF) is used to construct the NNs observer, which can estimate the immeasurable states. By using the Lyapunov function, the tracking error of the controller has limited to a small boundary. Based on backstepping control theory and event-triggered theory, the control signal of the fixed threshold strategy is obtained and two adaptive controllers for CPSs are established, it can ensure that all the closed-loop signals are uniformly ultimately bounded (UUB) in mean square and avoid the Zeno-behavior. The simulation results confirm the feasibility and effectiveness of the controller.     

Adaptive controller design with prescribed performance for switched nonstrict feedback nonlinear systems with actuator failures

This article is concerned with the adaptive output-feedback control of switched nonstrict feedback nonlinear systems. By introducing a novel error surface, an adaptive control strategy is proposed for the general case where the nonlinear functions and the control gain functions are unknown, and the states are unmeasurable. The considered switched nonlinear system contains unknown actuator failures, which are modeled as both loss of effectiveness and lock-in-place. In order to improve the transient performance in the presence of unknown actuator failures, the prescribed performance approach is used. The “explosion of complexity” problem is avoided through using low-pass filters. The stability of the closed-loop system under arbitrary switching is shown using Lyapunov stability theory, based on which, the tracking error is shown to converge to a small residual set with the prescribed performance bounds. The advantages of the proposed technique are verified through simulations of two numerical and practical examples.     

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

This paper addresses the issue of the adaptive output tracking control for switched nonlinear systems with uncertain parameters. The solvability of the tracking control problem for each subsystem is not necessary to hold. Individual update laws corresponding to different unknown parameters are adopted to reduce the conservativeness produced from the adoption of a common undated law. By means of the dual design of the adaptive controllers and a state‐dependent switching law using multiple storage functions technique, several conditions are obtained under which the adaptive output tracking control problem for switched nonlinear systems is solvable. Finally, an example shows the effectiveness of the proposed method.     

Adaptive multi-dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

In view of the result and performance of control are affected by the existence of input constraints and requirements, adaptive multi-dimensional Taylor network (MTN) funnel control problem is studied for a class of nonlinear systems with asymmetric input saturation in this paper. Firstly, the effect of asymmetric input saturation can overcome by introducing the Gaussian error function, namely, the asymmetric saturation model is represented as a simple linear model with a bounded disturbance. Secondly, MTNs are employed to approximate the unknown functions in the controller design. Then, an adaptive MTN tracking controller is developed by blends the idea of funnel control into backstepping, which can guarantee that the tracking error always meets the given prescribed performance regarding the transient and steady state responses as well as the output of system tracks the give continuous reference signal. Finally, the effectiveness of the proposed control is demonstrated using two examples.     

Observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances

This paper studies the problem of observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances. Based on mean value theorem and convex combination method, a adaptive neural observer with virtual control coefficients is designed to estimate the systems states. Then, by using funnel Lyapunov function and backstepping method, a finite time control scheme is designed in the presence of disturbances and actuator faults. The stability analysis proves that tracking errors can converge to the prescribed performance bound in a finite time and all signals are uniformly ultimately bounded. Finally, simulation results verify efficiency of the studied approach.     

Adaptive prescribed performance control for hydraulic system with disturbance compensation

In this article, an adaptive prescribed performance controller is developed for hydraulic system with uncertainties. An extraordinary feature is that better prescribed performance control can be achieved by compensating the uncertainties including parameter uncertainties and disturbances. For this reason, the transformation of system output error is realized by a prescribed performance function, which is employed to constrain the boundary of tracking error and convergence rate, then the tracking error of the original system with a priori prescribed performance can be realized by stabilizing the transformed system. Adaptive control is employed to solve the system parametric uncertainties; extended state observers are built to estimate the multiple disturbances. Based on the backstepping method, they are integrated into the design of the novel controller to guarantee prescribed tracking error performance. The stability analysis of the proposed controller is carried out via the Lyapunov theory. Finally, experimental results indicate good performance of the proposed algorithm.     

一类具有高增益观测器的非线性系统的输出调节

针对具有由非线性外部系统产生的未知不确定性函数和未建模动态的非线性不确定系统,研究了其跟踪和干扰抑制问题。首先运用状态变换将输出调节问题转化为非线性系统的镇定问题,接着引入动态信号解决了动态扰动,并设计出高增益的状态观测器去估计不可测的状态。然后根据外系统信息设计自适应的非线性内模,结合自适应控制理论、Backstepping设计方法、模糊控制方法和Lyapunov法给出了输出反馈的自适应模糊控制器和自适应控制律,所提出的输出反馈控制器和自适应律能够实现整个闭环系统的跟踪和干扰抑制,并使得跟踪误差能渐近收敛到给定的任意小的领域内。最后仿真结果验证了所提出的控制器的有效性。     

Neural network‐based adaptive attitude tracking control for flexible spacecraft with unknown high‐frequency gain

Adaptive control design using neural networks (a) is investigated for attitude tracking and vibration stabilization of a flexible spacecraft, which is operated at highly nonlinear dynamic regimes. The spacecraft considered consists of a rigid body and two flexible appendages, and it is assumed that the system parameters are unknown and the truncated model of the spacecraft has finite but arbitrary dimension as well, for the purpose of design. Based on this nonlinear model, the derivation of an adaptive control law using neural networks (NNs) is treated, when the dynamics of unstructured and state‐dependent nonlinear function are completely unknown. A radial basis function network that is used here for synthesizing the controller and adaptive mechanisms is derived for adjusting the parameters of the network and estimating the unknown parameters. In this derivation, the Nussbaum gain technique is also employed to relax the sign assumption for the high‐frequency gain for the neural adaptive control. Moreover, systematic design procedure is developed for the synthesis of adaptive NN tracking control with L₂ ‐gain performance. The resulting closed‐loop system is proven to be globally stable by Lyapunov's theory and the effect of the external disturbances and elastic vibrations on the tracking error can be attenuated to the prescribed level by appropriately choosing the design parameters. Numerical simulations are performed to show that attitude tracking control and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive compensation of persistent actuator failures of nonlinear systems

In this article, adaptive compensation designs are developed for nonlinear systems with uncertainties from the system functions and persistent actuator failures of characterizations that (i) some unknown system inputs are stuck at some unknown fixed or varying values at unknown time instants and (ii) the failure pattern always switches from one to another and the switching does not stop. Such a controlled plant is described by an uncertain time-varying nonlinear system, and some robust adaptive feedback linearization based failure compensation results are studied for closed-loop system stabilization and bounded output tracking for some specific conditions. To improve the tracking performance in the presence of persistent actuator failures, a new adaptive control scheme is developed, using the failure indicator function which contains the failure pattern and failure time in the formulation. Detailed stability and tracking performance are shown. Simulation results are shown to verify the effectiveness of the proposed adaptive actuator failure compensation method.     

Adaptive fuzzy practical fixed-time control for uncertain nonlinear systems with actuator constraints

This article addresses an adaptive fuzzy practical fixed-time tracking control for nonlinear systems with unknown actuator constraints and uncertainty functions. First, fuzzy logic systems (FLSs) are used to identify uncertain functions. Then, by utilizing FLSs, backstepping technique, and finite-time stability theory, an adaptive fuzzy practical fixed-time control is proposed to obtain satisfactory tracking performance even when the actuator faults. The theoretical analysis verified that the closed-loop systems is practical fixed-time stable under the proposed control strategy, the tracking error converges to a small neighborhood of the origin in a fixed time, and the convergence time is independent of the state conditions. Finally, both numerical simulation and physical example demonstrates the effectiveness of the proposed control strategy.     

Adaptive finite-time tracking control for output-constrained nonlinear systems with non-strict-feedback structure

This article investigates the issue of adaptive finite-time tracking control for a category of output-constrained nonlinear systems in a non-strict-feedback form. First, by utilizing the structural characteristics of radial basis function neural networks (RBF NNs), a backstepping design method is extended from strict-feedback systems to a kind of more general systems, and NNs are employed to approximate unknown nonlinear functions. In addition, the system output is constrained to the specified region by applying the barrier Lyapunov function (BLF) technique. Furthermore, the finite-time stability of the system is proved by employing the Bhat and Bernstein theorem. As a result, an adaptive finite-time tracking control scheme for the output-constrained nonlinear systems with non-strict-feedback structure is proposed by applying RBF NNs, BLF, finite-time stability theory, and adaptive backstepping technique. It is demonstrated the finite-time stability of the system, the prescribed convergence of the system output and tracking error, the boundedness of adaptive parameters and state variables. Finally, a simulation example is implemented to illustrate the effectiveness of the presented neural control scheme.     

Neural network–based direct adaptive robust control of unknown MIMO nonlinear systems using state observer

This paper focuses on the problem of adaptive robust tracking control for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear system. Unlike most previous research studies, model dynamics, disturbances, and state variables are unknown in this paper. A novel observer-based direct adaptive neuro-sliding mode control approach is proposed of which the only required knowledge is the system output. By incorporating the Adaptive Linear Neuron (ADALINE) neural network (NN) into the conventional sliding mode observer, the proposed observer has favorable performance. In the controller, a radial basis function (RBF) NN is constructed to approximate the unknown equivalent control laws and the estimation of the sliding surface is applied as the input. A gain-adaptation sliding mode term is designed to enhance the robustness of the control system. Besides, the free parameters of the ADALINE NN and the RBFNN are updated online by adaptive laws to obtain optimal approximation performance. Finally, the comparative simulations are given to show the effectiveness and merits of proposed scheme.     

Optimal model‐free control for a generic MIMO nonlinear system with application to autonomous mobile robots

In this paper, the design procedure for optimal model‐free control algorithm is presented for the tracking problem of completely unknown nonlinear dynamic systems operating under unknown disturbances. The procedure includes a new structure in the context of model‐free control and data‐driven control algorithms. In the new structure, the unknown nonlinear functions are segmented into 1 unknown linear‐in‐states part and another unknown nonlinear part. The adaptive laws proposed for estimating the unknown system dynamics are regressor‐free estimation methods in which there is no need for regressor parameters and, consequently, the persistent excitation condition is not required anymore. Moreover, the main controller gains are updated online, incorporating the adapted values of linear terms in the system dynamics. A comparative study is presented to show that the proposed optimal model‐free control outperforms the state‐of‐the‐art model‐free control algorithms. In addition, the simulation results for the application of the algorithm on autonomous mobile robots are provided.     

Neural networks-based adaptive finite-time prescribed performance fault-tolerant control of switched nonlinear systems

In this article, the adaptive finite-time fault-tolerant control problem is considered for a class of switched nonlinear systems in nonstrict-feedback form with actuator fault. The problem of finite-time fault-tolerant control is solved by introducing a finite-time performance function. Meanwhile, the completely unknown nonlinear functions exist in the switched system are identified by the neural networks. Based on the common Lyapunov function method with adaptive backstepping technique, the finite-time fault-tolerant controller is designed. The proposed control strategy can guarantee that the tracking error converges to a prescribed zone at a finite-time and all system variables remain semiglobally practical finite-time stable. Numerical examples are offered to verify the feasibility of the theoretical result.