Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.     

Robust output tracking of uncertain nonlinear time‐delay systems with unknown dead‐zone inputs via control schemes with a simple structure

The adaptive robust output tracking control problem is considered for a class of uncertain nonlinear time‐delay systems with completely unknown dead‐zone inputs. A new design method is proposed so that some adaptive robust output tracking control schemes with a rather simple structure can be constructed. It is not necessary to know the nonlinear upper bound functions of uncertain nonlinearities. In fact, the constructed output tracking control schemes are structurally linear in the state and have a self‐tuning control gain function that is updated by an adaptation law. In this paper, the dead‐zone input is nonsymmetric, and its information is assumed to be completely unknown. In addition, a numerical example is given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.     

Adaptive control for switched uncertain nonlinear systems with time‐varying output constraint and input saturation

This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example.     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

Experience replay–based output feedback Q‐learning scheme for optimal output tracking control of discrete‐time linear systems

This paper focuses on solving the adaptive optimal tracking control problem for discrete‐time linear systems with unknown system dynamics using output feedback. A Q‐learning‐based optimal adaptive control scheme is presented to learn the feedback and feedforward control parameters of the optimal tracking control law. The optimal feedback parameters are learned using the proposed output feedback Q‐learning Bellman equation, whereas the estimation of the optimal feedforward control parameters is achieved using an adaptive algorithm that guarantees convergence to zero of the tracking error. The proposed method has the advantage that it is not affected by the exploration noise bias problem and does not require a discounting factor, relieving the two bottlenecks in the past works in achieving stability guarantee and optimal asymptotic tracking. Furthermore, the proposed scheme employs the experience replay technique for data‐driven learning, which is data efficient and relaxes the persistence of excitation requirement in learning the feedback control parameters. It is shown that the learned feedback control parameters converge to the optimal solution of the Riccati equation and the feedforward control parameters converge to the solution of the Sylvester equation. Simulation studies on two practical systems have been carried out to show the effectiveness of the proposed scheme.     

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.     

Adaptive finite-time control for output regulation of nonlinear systems with completely unknown control directions

This article studies the finite-time output regulation problem for nonlinear strict-feedback systems with completely unknown control directions and unknown functions. First, according to the necessary conditions for the solvability of the output regulation problem, the output regulation problem of nonlinear strict-feedback systems and the external system is transformed into a stabilization problem of nonlinear systems. Second, an internal model with external signals is designed. Third, based on finite time, fuzzy control, output feedback control, and Nussbaum gain functions, the control law is designed so that all signals of the closed-loop system are the semi-global practically finite-time stable (SGPFS), and the tracking error converges to a small neighborhood of the origin in a finite-time. Finally, the proposed algorithm is applied to the finite-time tracking problem of Chua's oscillator system.     

Adaptive state tracking of switched systems based on a hyperstability criterion

The adaptive state tracking problem of switched systems is studied in this paper. The desirable state trajectory is generated by a switched reference model. First, a condition for asymptotical hyperstability of switched systems is proposed and a switching law is designed, which is a generalization of the classical hyperstability condition for non‐switched systems. Then, the result is applied to uncertain switched systems to achieve state tracking. An individual adaptive law is designed for each subsystem such that the Popov inequality is satisfied. Asymptotical state tracking is achieved under non‐persistent exciting input when the error system switches in a certain way. The result is demonstrated by a numerical example and a practical system of Highly Maneuverable Aircraft Technology vehicle, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive fuzzy finite-time fault-tolerant control of nonlinear systems with state constraints and input quantization

This article concentrates on an adaptive finite-time fault-tolerant fuzzy tracking control problem for nonstrict feedback nonlinear systems with input quantization and full-state constraints. By utilizing the fuzzy logic systems and less adjustable parameters method, the unknown nonlinear functions are addressed in each step process. In addition, a dynamic surface control technique combined with fuzzy control is introduced to tackle the variable separation problem. The problem for the effect of quantization and unlimited number of actuator faults is tackled by a damping term with smooth function in the intermediate control law. Finite-time stability is achieved by combining barrier Lyapunov functions and backstepping method. The finite-time controller is designed such that all the responses of the systems are semiglobal practical finite-time stable and ensured to remain in the predefined compact sets while tracking error converges to a small neighborhood of the origin in finite time. Finally, simulation examples are utilized to testify the validity of the investigated strategy.     

Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint

This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed‐loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Adaptive control design for MIMO switched nonlinear systems with full state constraints

This paper presents an adaptive fuzzy control approach of multiple‐input–multiple‐output (MIMO) switched uncertain systems, which involve time‐varying full state constraints (TFSCs) and unknown disturbances. In the design procedure, the fuzzy logic systems are adopted to approximate the unknown functions in the systems. The adaptive fuzzy controller is set up by backstepping technique. According to the tangent barrier Lyapunov function (BLF‐Tan), a novel adaptive MIMO switched nonlinear control algorithm is designed. Under the rule of arbitrary switchings and the proposed control laws, it is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero with TFSCs. Furthermore, the simulation example validates the effectiveness of presented control strategy.     

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.     

Predictor‐based adaptive dynamic surface control for consensus of uncertain nonlinear systems in strict‐feedback form

This paper investigates the leader–follower consensus problem of uncertain nonlinear systems in strict‐feedback form. By parameterizations of unknown nonlinear dynamics of the agents, an adaptive dynamic surface control with the aid of predictors, tracking differentiators is proposed to realize output consensus of the multi‐agent systems. Unlike the existing adaptive consensus methods, the predictor errors are used to learn the unknown parameters, which can achieve fast learning without high‐frequency signals in control inputs. As a fast precise signal filter, the tracking differentiator is used in the control design instead of first‐order filters, which can further improve the control performance. Based on graph theory and Lyapunov stability theory, it is shown that the outputs of all followers ultimately synchronize to that of the leader with bounded tracking errors. Simulation results are provided to validate the effectiveness and advantage of the proposed consensus algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

非线性时滞系统自适应神经网络Backstepping控制

针对一类未知非线性时滞系统,提出了一种自适应神经网络控制设计方案,将Backstepping、占有方法以及自适应界化技术结合起来构造了一个鲁棒自适应神经网络跟踪控制器,采用神经网络逼近未知时滞函数,放松了对非线性时滞函数的要求。通过构建一个恰当的Lyapunov-Krasoviskii泛函证明了闭环系统所有信号半全局一致最终有界,调节设计参数可以实现任意输出跟踪精确度。实例仿真说明了该方案的可行性。     

Adaptive neural tracking control for high angle of attack maneuver with average dwell time

This article attempts to study the high angle of attack maneuver from the perspective of switched system control. In view of the complex aerodynamic characteristics, an improved longitudinal attitude motion model is presented, which is a switched stochastic nonstrict feedback nonlinear system with distributed delays. The significant design difficulty is the completely unknown diffusion and drift terms and distributed delays with all state variables. Based on a technical lemma and neural networks, an improved smooth state feedback control law for nonstrict feedback systems is proposed without any growth assumptions. To eliminate the influence of distributed delays, an improved Lyapunov–Krasovskii function is constructed, which skillfully removes the constraint of the upper bound of the delay change rate. Then, by combining the average dwell-time scheme and stochastic backstepping technique, an adaptive neural network tracking control law is designed, which extends a newly proposed switched system stability condition to the stochastic switched system. Theoretical analysis and flight control simulation experiments are provided to illustrate the effectiveness of the proposed control method.     

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。     

Adaptive finite-time output feedback control for Markov jumping nonlinear systems

In this article, the problem of output feedback tracking control for uncertain Markov jumping nonlinear systems is studied. A finite-time control scheme based on command filtered backstepping and adaptive neural network (NN) technique is given. The finite-time command filter solves the problem of differential explosions for virtual control signals, the NN is utilized to approximate the uncertain nonlinear dynamics and the adaptive NN observer is applied to restructure the state of system. The finite-time error compensation mechanism is established to compensate the errors brought by filtering process. The proposed finite-time tracking control algorithm can ensure that the solution of the closed-loop system is practically finite-time stable in mean square. Two simulation examples are employed to demonstrate the effectiveness of the proposed control algorithm.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.