Adaptive output feedback quantised tracking control for stochastic nonstrict-feedback nonlinear systems with input saturation

This paper is concerned with the problem of adaptive output feedback quantised tracking control for a class of stochastic nonstrict-feedback nonlinear systems with asymmetric input saturation. Especially, both input and output signals are quantised by two sector-bounded quantisers. In order to solve the technical difficulties originating from asymmetric saturation nonlinearities and sector-bounded quantisation errors, some special technique, approximation-based methods and Gaussian error function-based continuous differentiable model are exploited. Meanwhile, an observer including the quantised input and output signals is designed to estimate the states. Then, a novel output feedback adaptive quantised control scheme is proposed to ensure that all signals in the closed-loop system are 4-moment (2-moment) semi-globally uniformly ultimately bounded while the output signal follows a desired reference signal. Finally, the effectiveness and applicability of the design methodology is illustrated with two simulation examples.     

Robust adaptive backstepping tracking control of stochastic nonlinear systems with unknown input saturation: A command filter approach

This paper studies the problem of adaptive observer‐based radial basis function neural network tracking control for a class of strict‐feedback stochastic nonlinear systems comprising an unknown input saturation, uncertainties, and unknown disturbances. To handle the issue of a non‐smooth saturation input signal, a smooth function is chosen to approximate the saturation function and the state observer is used to estimate unmeasured states. By the so‐called command filter method in the controller design procedure, the implementation complexity is reduced in the proposed backstepping method. Moreover, a radial basis function neural network is deployed to reconstruct the unknown nonlinear functions. In addition, the gains of all radial basis function neural networks are updated through one updating law leading to a minimal learning parameter which is independent of the number of neural nodes and the order of the system. Comparing with the existing results, the proposed approach can stabilize a constrained stochastic system more effectively and with less computational burden. Finally, a practical example shows the performance of the proposed controller design.     

Controller design for nonlinear quadratic Markov jumping systems with input saturation

This paper deals with the controller design problem of nonlinear quadratic Markov jumping systems with input saturation. Both mode-dependent and mode-independent state feedback controllers are designed. By using the concept of domain of attraction in mean square sense, sufficient conditions for stochastic stabilisation for nonlinear quadratic systems are derived in terms of linear matrix inequalities. Certain existing results are improved. Simulation examples are presented to illustrate the effectiveness of the proposed technique.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

输入饱和下非线性系统的事件触发控制器设计

本文研究了具有输入饱和的非线性系统事件触发控制策略设计问题.首先,针对输入饱和下非线性系统,建立混杂系统模型.其次,当非线性函数满足Lipschitz条件下,给出闭环混杂系统局部一致渐近稳定性的稳定判据,并设计了事件触发饱和控制器.然后,当非线性函数满足扇区条件时,给出闭环混杂系统框架下满足局部一致渐近稳定性的LMI条件,并设计了事件触发饱和控制器.进一步地,在事件触发饱和控制器作用下,分析了非线性系统的半全局鲁棒镇定性.最后,结合两个仿真实例说明了所提出事件触发控制策略的有效性.     

Adaptive prescribed performance control for switched nonlinear systems with input saturation

In this paper, an adaptive prescribed performance output-feedback control scheme is proposed for a class of switched nonlinear systems with input saturation. The MT-filters are employed to estimate the unmeasured states and the unknown functions are approximated by the radial basis function neural networks in controller design procedure. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error satisfies the prescribed performance. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.     

具有输入和输出约束的高阶随机系统神经网络控制

针对高阶非线性系统,开展自适应神经网络跟踪控制器设计,系统受到随机扰动的影响.首次把输入和输出约束问题引入到高阶系统的跟踪控制中,并假定系统动态是未知.首先借用高斯误差函数表达连续可微的非对称饱和模型以实现输入约束,和障碍Lyapunov函数保证系统输出受限;其次,针对高阶非线性系统,径向基函数(RBF)神经网络用来克服未知系统动态和随机扰动.在每一步的backstepping计算中,仅用到单一的自适应更新参数,从而克服了过参数问题;最后,基于Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明设计的控制器能保证所有闭环信号半全局最终一致有界,并能使跟踪误差收敛到零值小的邻域内.仿真研究进一步验证了提出方法的有效性.     

Control of switched linear systems with input saturation

The problem of control of switched linear systems with input saturation is considered. A synthesis method based on the minimum dwell time switching together with saturated feedbacks is presented. Sufficient conditions for stability are proposed in term of linear matrix inequalities. An illustrative example is presented to show the validity of the results.     

Stabilisation for switched linear systems with time-varying delay and input saturation

This article investigates the stabilisation problems for continuous-time and discrete-time switched systems with time-varying delay and saturated control input. Based on dwell time switching signals and multiple Lyapunov functional method, stabilisation conditions are well obtained in the context of linear matrix inequalities. To estimate attractive regions as large as possible, the feasibility problems are translated into optimisation problems. In addition, the corresponding results are presented for linear time-delay systems and switched delay-free systems, which improve and supplement some existing ones in the literature. Finally, numerical examples and simulations are given to illustrate the effectiveness and values of the proposed results.     

受饱和输入约束的非线性系统滑模自适应控制

利用神经网络和滑模控制,研究带有饱和输入的一类非线性系统。为了便于问题分析,引入饱和约束模型输出与控制输入的差值这个变量,分5种情况讨论,求得神经网络权值的在线调节律,得到保证闭环系统稳定的控制律。利用Lyapunov函数,证明了闭环系统的稳定性;仿真实验说明了算法的有效性。     

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

In this paper, an adaptive output‐feedback control problem is investigated for nonlinear strict‐feedback stochastic systems with input saturation and output constraint. A barrier Lyapunov function is used to solve the problem of output constraint. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. To overcome the difficulties in designing the control signal in the saturation, we introduce an auxiliary signal in the n + 1th step in the deduction. By combining Nussbaum technique and the adaptive backstepping technique, an adaptive output‐feedback control method is developed. The proposed control method not only overcomes the problem of the compensation for the nonlinear term from the input saturation but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified by the simulation results.     

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.     

Tracking control and disturbance rejection for nonlinear switched control systems with saturation effects

This article focuses on the concerns of a tracking control and active disturbance rejection for nonlinear switched systems described by Takagi–Sugeno fuzzy framework with state-dependent nonlinear perturbations, actuator saturations and disturbances. Especially, a nonlinear equivalent-input-disturbance technique is employed to guarantee that only the external disturbances are rejected while retaining the beneficial nonlinearity of the system. Notably, with the aid of the lifting technique, the modified repetitive control are accurately described by a continuous-discrete two-dimensional model is designed to improve the tracking precision. The fuzzy-membership-function-dependent piecewise Lyapunov–Krasovskii functional (LKF) by exploiting the knowledge of the membership functions are built to assure the exponential stability of the investigated system. Moreover, the controller and observer gains can be obtained as solutions to a set of strict linear matrix inequalities. Finally, an application example based on the cognitive radio model is given to verify the efficacy of the proposed control protocol.     

Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function

This article focuses on the tracking control problem for switched nonlinear systems in strict-feedback form subject to an output constraint. In order to prevent transgression of the constraint, a barrier Lyapunov function is employed, which grows to infinity when its arguments approach domain boundaries. Under the simultaneous domination assumption, a continuous controller for the switched system is constructed. Furthermore, asymptotic tracking is achieved without violation of the constraint, and all closed-loop signals keep bounded, when a mild requirement on the initial condition is satisfied. Finally, a simulation example is provided to illustrate the effectiveness of the proposed results.     

Composite nonlinear feedback design for discrete-time switching systems with disturbances and input saturation

This paper addresses the problem of robust controller design for a class of discrete-time switching systems with input saturation. To this aim, the composite nonlinear feedback method is extended to design a robust controller with improved performances in terms of the response speed and overshoot in the presence of disturbances and input saturation. The proposed approach is theoretically analysed and its closed-loop stability is proved. Then, the performance of the proposed method is verified using numerical simulations.     

Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.     

Output feedback tracking control for lower‐triangular nonlinear time‐delay systems with asymmetric input saturation

In this paper, the problem of output feedback tracking control is investigated for lower‐triangular nonlinear time‐delay systems in the presence of asymmetric input saturation. A novel design program based on a dynamic high gain design approach is proposed to construct an output feedback tracking controller. The innovation here is that the problem of constructing tracking controller can be transformed into the problem of constructing two dynamic equations, with one being utilized to deal with the nonlinear terms and the other one being applied to analyze the influence of asymmetric input saturation. It is proved by an appropriate Lyapunov‐Krasovskii functional that the proposed tracking controller subject to saturation can ensure that all the signals of the closed‐loop system are globally bounded and the tracking error is prescribed sufficiently small when time is long enough. A practical example is given to illustrate the effectiveness of the proposed method.     

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods.     

Output feedback stabilization of stochastic feedforward nonlinear systems with input and state delay

This paper considers the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with input and state delay. Under a set of coordinate transformations, we first design a linear output feedback controller for a nominal system. Then, with the aid of feedback domination technique and an appropriate Lyapunov–Krasovskii functional, it is proved that the proposed linear output feedback controller can drive the closed‐loop system globally asymptotically stable in probability. Copyright © 2015 John Wiley & Sons, Ltd.     

输入受限的非线性系统自适应模糊backstepping控制

针对一类输入受限的非线性系统,提出了一种自适应模糊backsteppig控制器的设计方法.在控制器的设计过程当中,采用模糊系统对不确定非线性函数在线逼近;利用双曲正切函数和Nussbaum函数对系统输入饱和函数进行处理;将动态面法与backstepping法相结合解决"计算膨胀"的问题.通过Lyapunov理论分析证明了所设计的控制器能够使闭环系统所有信号半全局一致有界(SGUUB).最后应用于高超声速飞行器的攻角跟踪控制中,仿真结果表明该方法的有效性.