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.     

Controller design for Markov jumping systems subject to actuator saturation

In this paper, the stochastic stabilization problem for a class of Markov jumping linear systems (MJLS) subject to actuator saturation is considered. The concept of domain of attraction in mean square sense is used to analyze the closed-loop stability. When the jumping mode is available, a mode-dependent state feedback controller is developed. Otherwise, we give a less conservative approach to design the mode-independent state feedback controller. Both design procedures can be converted into a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the techniques.     

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.     

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.     

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。     

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.     

Observer-based adaptive output-constrained control design of switched stochastic nonlinear systems with input saturation

In this article, the problem of adaptive fuzzy control for output-constrained switched stochastic nonlinear systems subject to input saturation is addressed. By employing the trigonometric function mapping method, the constrained systems are transformed into unconstrained ones, and the control goals of the original constrained systems are not affected. Meanwhile, an auxiliary system is established to deal with the issue of input saturation, and an observer is constructed to estimate the unmeasured states. Then, the unknown nonlinear functions in the system are approximated by the fuzzy logic systems (FLSs). Based on the backstepping technique and Lyapunov function method, an output feedback control strategy is designed, where the dynamic surface control technique is applied in the backstepping design process to overcome the issue of a large number of online calculations. The designed controller can guarantee that all the signals of the system satisfy bounded conditions, and the output can track given reference signals within a small error range. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.     

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.     

一类输入饱和非仿射非线性系统的非线性动态逆控制

输入饱和是实际系统中经常遇到的问题,很多已有的控制方法要求被控系统具有仿射结构.本文针对一类具有输入饱和的非仿射纯反馈非线性系统提出了一种基于奇异值摄动理论的非线性动态逆控制方法.首先构建一个快变子系统,在慢时间尺度下将非仿射非线性系统转换为具有仿射结构的线性系统,从而应用已有的控制算法实现控制目的.为了消除输入饱和带...     

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.     

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

This paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.     

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.     

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.     

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.     

Constructive stabilization for quadratic input nonlinear systems

In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions, the feasible control set is parameterized, and continuous feedback stabilizing controls are designed. Then for the general case, piecewise continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.     

Truncated adaptation design for decentralised neural dynamic surface control of interconnected nonlinear systems under input saturation

This paper studies decentralised neural adaptive control of a class of interconnected nonlinear systems, each subsystem is in the presence of input saturation and external disturbance and has independent system order. Using a novel truncated adaptation design, dynamic surface control technique and minimal-learning-parameters algorithm, the proposed method circumvents the problems of ‘explosion of complexity’ and ‘dimension curse’ that exist in the traditional backstepping design. Comparing to the methodology that neural weights are online updated in the controllers, only one scalar needs to be updated in the controllers of each subsystem when dealing with unknown systematic dynamics. Radial basis function neural networks (NNs) are used in the online approximation of unknown systematic dynamics. It is proved using Lyapunov stability theory that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. The tracking errors of each subsystems, the amplitude of NN approximation residuals and external disturbances can be attenuated to arbitrarily small by tuning proper design parameters. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Controller design for a class of nontriangular nonlinear systems with input dependent growth rate

In this paper, we consider the global control problem for a class of high‐order nonlinear systems in the nontriangular form. Compared with the existing results, the growth rate of the nonlinearities depends on the control input, which cannot be dominated by the traditional constant gain. Under the assumption that the nonlinear terms satisfy the homogeneous growth conditions, a dynamic state‐feedback controller is elaborately designed to stabilize the system based on the adding a power integrator technique and the domination methodology. Moreover, by choosing the dynamic gain appropriately, the assumptions on the nonlinearities can be further relaxed to the polynomial case. Numerical simulations are provided to show the effectiveness of the proposed control laws.     

Neuroadaptive containment control of nonlinear multiagent systems with input saturations

This paper investigates the output containment tracking problem of nonlinear multiagent systems with mismatched uncertain dynamics and input saturations. A neural network–based distributed adaptive command filtered backstepping (CFB) scheme is given, which can guarantee that the containment tracking errors reach to the desired neighborhood of origin and all signals in the closed‐loop system are bounded. Note that error compensation system and virtual control laws established in CFB only use local information, so the given scheme is completely distributed. Moreover, the applied sliding mode differentiator (SMD) can make the outputs of SMD fast approximate the virtual signal and its derivative at each step of backstepping, which can further improve the control quality. Finally, a simulation example is given to show the effectiveness of the proposed scheme.     

具有输入饱和的非线性关联大系统的分散控制

考虑了一类具有输入饱和的不确定非线性关联大系统的分散输出反馈鲁棒镇定问题,利用Riccati方程的方法和矩阵的Moore-Penrose逆给出了这类系统的一种分散输出反馈鲁棒镇定控制器的设计方法.同时,考虑了一类具有输入饱和的不确定非线性相似关联大系统,利用相似系统的结构特点,简化了分散输出反馈鲁棒镇定的条件.