Fuzzy linear pulse-transfer function-based sliding-mode control fornonlinear discrete-time systems

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory     

Discrete-time sliding mode control for uncertain systems with state and input delays

This article presents a discrete-time sliding mode control method for the robust stabilisation of linear uncertain multi-input discrete-time systems with state and input delays. The systems are assumed to have structured mismatched time-varying parameter uncertainties. A specified switching surface is proposed and a sliding mode controller is derived to ensure the existence of the quasi-sliding mode. Based on the improved Lyapunov function and linear matrix inequality technique, delay-independent sufficient conditions for the design of a stable switching surface are given and the stability of the overall closed-loop system is guaranteed. Neither chattering phenomenon will occur nor the knowledge of upper bound of uncertainties is required. Finally, simulation results demonstrate the efficacy of the proposed control methodology.     

离散双切换线性正系统的L1增益性能分析

离散时间双切换线性正系统是同时受到确定切换信号和Markov随机切换信号共同影响的系统。鲁棒稳定以及扰动抑制问题是研究混杂系统稳定性的重要问题,但双切换正系统的扰动抑制问题研究较少。基于此研究背景,提出了新型的切换系统——具有指数不确定性的离散时间双切换线性正系统(DDSLPS),通过构建Co-positive Lyapunov能量衰减函数,利用线性编程(LP)得到确保DDSLPS在持续驻留时间(PDT)约束下系统满足鲁棒指数几乎处处稳定(Robust-EAS)的充分条件。另外,将此方法推广到DDSLPS的L1增益分析中,得到闭环系统在鲁棒指数几乎处处稳定下满足L1性能指标x的充分条件。利用Matlab数值仿真,验证了所用方法的有效性和所得结果的正确性。     

Robust Tracking Control of Uncertain MIMO Nonlinear Systems with Application to UAVs

In this paper, we consider the robust adaptive tracking control of uncertain multi-input and multi-output (MIMO) nonlinear systems with input saturation and unknown external disturbance. The nonlinear disturbance observer (NDO) is employed to tackle the system uncertainty as well as the external disturbance. To handle the input saturation, an auxiliary system is constructed as a saturation compensator. By using the backstepping technique and the dynamic surface method, a robust adaptive tracking control scheme is developed. The closed-loop system is proved to be uniformly ultimately bounded thorough Lyapunov stability analysis. Simulation results with application to an unmanned aerial vehicle (UAV) demonstrate the effectiveness of the proposed robust control scheme.      

Robust predictor feedback for discrete-time systems with input delays

This work studies the design problem of feedback stabilisers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping coincides with the predictor-based feedback law used in continuous-time systems with input delays. However, simple examples demonstrate that the sensitivity of the closed-loop system with respect to modelling errors increases as the value of the delay increases. The paper proposes a Lyapunov redesign procedure that can minimise the effect of the uncertainty. Specific results are provided for linear single-input discrete-time systems with multiplicative uncertainty. The feedback law that guarantees robust global exponential stability is a nonlinear, homogeneous of degree 1 feedback law.     

Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

In this paper, an adaptive dynamic programming (ADP) strategy is investigated for discrete-time nonlinear systems with unknown nonlinear dynamics subject to input saturation. To save the communication resources between the controller and the actuators, stochastic communication protocols (SCPs) are adopted to schedule the control signal, and therefore the closed-loop system is essentially a protocol-induced switching system. A neural network (NN)-based identifier with a robust term is exploited for approximating the unknown nonlinear system, and a set of switch-based updating rules with an additional tunable parameter of NN weights are developed with the help of the gradient descent. By virtue of a novel Lyapunov function, a sufficient condition is proposed to achieve the stability of both system identification errors and the update dynamics of NN weights. Then, a value iterative ADP algorithm in an offline way is proposed to solve the optimal control of protocol-induced switching systems with saturation constraints, and the convergence is profoundly discussed in light of mathematical induction. Furthermore, an actor-critic NN scheme is developed to approximate the control law and the proposed performance index function in the framework of ADP, and the stability of the closed-loop system is analyzed in view of the Lyapunov theory. Finally, the numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.      

Robust ℋ2/ℋ∞/reference model dynamic output-feedback control synthesis

This article presents a new strategy to design robust model matching dynamic output-feedback controllers that guarantee tracking response specifications, disturbance rejection and noise attenuation. The proposed synthesis methodology, based on a multi-objective optimisation problem, can be applied to uncertain continuous or discrete-time linear time-invariant systems with polytopic uncertainty, leading to both full-order and reduced-order robust-performance dynamic controllers. The objective functions represent the ?_∞-norm of the difference between the closed-loop transfer function matrix, from the reference signals and the plant outputs and the reference model matrix, the ?_∞-norm of the closed-loop transfer function matrix from the disturbances and the plant outputs and the ?₂-norm of the closed-loop transfer function matrix from the measurement noises and the control inputs. An integral control action is also introduced in order to achieve zero steady-state error. In the case of MIMO systems, the proposed strategy can be applied to decouple the closed-loop control system choosing an appropriated reference model matrix. Two examples are presented to illustrate both SISO and MIMO systems control synthesis.     

Robust Finite-time Attitude Tracking Control of Rigid Spacecraft Under Actuator Saturation

This paper investigates the robust finite-time attitude tracking control problem for rigid spacecraft considering the modeling uncertainty, external disturbance and actuator saturation. An auxiliary system is proposed to directly compensate for the saturated control input. First, the basic controller is formulated based on the fast nonsingular terminal sliding mode surface (FNTSMS), the fast-TSM-type reaching law and the auxiliary system in the presence of upper bounded external disturbance. Then, when facing system uncertainty which consists of both modeling uncertainty and external disturbance and has upper bounded first derivative, the extended state observer (ESO) is associated with the first controller to improve the robustness of control system. Furthermore, to handle more general system uncertainty which is upper bounded by a polynomial function of the closed-loop system states, a continuous adaptive controller is designed to compensate for the total system uncertainty on line. The proposed controllers are able to deal with system uncertainty, input singularity and actuator saturation, while simultaneously providing fast finite-time convergence speed for the control system. And the problems of complex parameters selection process and repeated differentiations of nonlinear functions can be avoided. Rigorous stability analyses are given via the Lyapunov stability theory and digital simulations are conducted to illustrate the effectiveness of the proposed controllers.     

冷带轧机厚控系统自适应鲁棒输出反馈动态控制器设计

冷带轧机厚控系统可被认为是一个受外界干扰的线性不确定时滞系统.本文首先设计了标称系统下的鲁棒输出反馈动态控制器,以改善闭环系统的动静态性能;其次,在系统不需要满足不确定性匹配条件的情况下,将参数和外部扰动不确定性综合考虑.应用Lyapunov稳定性理论设计了系统不确定性上界参数的自适应估计器和系统的自适应控制器,保证了闭环系统的渐近稳定性,减小了设计的保守性;两者结合实现了板带出口厚度的有效控制.最后通过一个仿真实例说明本文所提出的自适应鲁棒控制器的有效性.     

基于区域极点约束的鲁棒H2控制

考虑了在区域极点约束下状态反馈的鲁棒H2控制问题.分别对含多面体不确定性的连 续和离散系统进行了讨论.基于LMI,给出了存在参数相关的Lyapunov矩阵的充分条件.利用 LMI凸优化方法的解,所得静态反馈控制器,不仅保证闭环系统的极点在-给定区域内,而且还 使性能指标H2的一上界达到最小.     

BOUNDED ROBUST CONTROLLER DESIGN FOR MISMATCHED STATE‐DEPENDENT UNCERTAINTY

A bounded robust control is presented for dealing with matched external disturbance and mismatched state‐dependent uncertainty in linear time‐invariart systems. By using the famous pole‐assignment method, an important switching vector is selected first before the controller is designed. Based on the Lyapunov theory, system stability is proven, and the upper bound of the control input is discussed. It is found that the system initial state has to be located in a suitable region determined by the upper bounds on the control input, the matched disturbance and the mismatched uncertainty. A numerical example is used to demonstrate use of the bounded robust controller in simulation.     

Asynchronous control of discrete-time stochastic bilinear systems with Markovian switchings

This paper is concerned with the problem of asynchronous control for a class of discrete-time Markov systems with multiplicative stochastic white noises. Based on a stability analysis scheme developed from mode-dependent Lyapunov function method, we first derive testable conditions in linear matrix inequality (LMI) setting to ensure the robust stability of the closed-loop system. We then recast the proposed stability conditions into equivalent forms that are later utilised to design a multi-mode asynchronous state-feedback controller (ASFC) that makes the closed-loop system stable. An extension to the case of deficient mode information (i.e. transition rates of the system and the controller are not fully accessible) is also presented. Finally, a model of networked control with DC devices is given to demonstrate the efficacy of the proposed design scheme.     

Adaptive nonlinear information fusion preview control for autonomous surface vessels subject to measurement noises and unknown input saturations

This study presents an adaptive nonlinear information fusion preview control (NIFPC) method for trajectory tracking of autonomous surface vessels (ASVs) subject to system uncertainty, measurement noise, and unknown input saturations. The NIFPC is developed based on the nonlinear information fusion estimation methodology, in which the system's future reference trajectory information, noise information, performance index requirements, and system dynamic model are all transformed into information equations related to control input, and then the current control action is obtained by fusing these previewed future information via the nonlinear information fusion optimal estimation. In order to avoid the unknown input saturation constraints, a fuzzy asymmetric saturated approximator (FASA) is designed and integrated into the controller, where the fuzzy logic system (FLS) is used to adaptively adjust the key boundary parameters of the approximator. As a result, the negative effects caused by system uncertainty and measurement noise can be effectively suppressed, while the completely unknown input saturation constraints in the system actuator are guaranteed not to be violated. The convergence of the tracking errors of the closed-loop system is guaranteed via Lyapunov stability theory. Numerical simulation results have been provided to demonstrate the satisfactory performance of the proposed control scheme.     

Construction of Lyapunov–Krasovskii functionals for switched nonlinear systems with input delay

This paper studies the stability issue for switched nonlinear systems with input delay and disturbance. It is assumed that for the nominal system an exponential stabilizing controller is predesigned such that the switched system is stable under a certain switching signal, and a piecewise Lyapunov function for the corresponding closed-loop system is known. However, in the presence of input delay and disturbance, the system may be unstable under the same switching signal. For this case, a new Lyapunov–Krasovskii functional is firstly constructed based on the known Lyapunov function. Then, by employing this new functional, a new switching signal satisfying the new average dwell time conditions is constructed to guarantee the input-to-state stability of the system under a certain delay bound. The bound on the average dwell time is closely related to the bound on the input delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

基于干扰观测器的非线性不确定系统自适应滑模控制

本文研究了一类基于非线性干扰观测器的多输入多输出非线性不确定系统的边界层自适应滑模控制方法并应用于近空间飞行器高精度姿态控制.考虑系统存在不确定性和外部干扰上界未知的情况,设计了基于干扰观测器的边界层自适应滑模控制器,以消除传统滑模控制中的"抖振"现象,使跟踪误差趋近于零.同时,利用李雅普洛夫方法严格证明了闭环系统的稳定性.最后将所研究的自适应滑模控制方法,应用于某近空间飞行器的姿态控制中,仿真结果表明在不确定性和外部干扰作用下能保证姿态控制的稳定性,对参数不确定具有较好的鲁棒性.     

Observations-weighted controllers for linear stochastic systems using a dual criterion: the multivariable case

The solution of a dual criterion observations-weighted control problem is obtained, using the polynomial equation approach, for linear, stochastic, multivariable, discrete-time systems. The system model involves input disturbance, and reference and coloured measurement noise signals. The dual criterion considered here includes the sensitivity functions in addition to the usual observations-weighted cost function. It is shown that the observations-weighted controller presented guarantees the internal stability of the closed-loop system, even in a light control for non-minimum-phase plants, whenever the sensitivity and/or complementary sensitivity weighting matrices are non-zero. The controller is also effective for improving the robustness of the usual observations-weighted controller, but has comparable computation loads to the dual criterion linear quadratic gaussian (LQG) controller in a general situation.     

多采样率不确定离散时滞系统的鲁棒预见控制

研究一类输入多采样率型不确定离散时滞系统的鲁棒预见控制问题.首先,利用离散提升技术从形式上消除输入时滞和多采样率特点,将多采样率不确定系统的鲁棒预见控制问题转化为一个普通的单采样率不确定系统的鲁棒预见控制问题;然后根据预见控制的基本方法,构造出包含未来目标信息的扩大误差系统,并对其相应的标称系统设计预见控制器;最后,根据所设计的控制器和Lyapunov稳定性理论,给出不确定闭环系统的鲁棒稳定性判据.数值仿真结果验证了所提出设计方法的有效性.     

具有输入未建模动态的纯反馈非线性系统自适应控制

对一类具有状态和输入未建模动态且控制增益符号未知的纯反馈非线性系统,利用非线性变换、改进的动态面控制方法以及Nussbaum函数性质,提出两种自适应动态面控制方案.利用正则化信号来约束输入未建模动态,从而有效地抑制其产生的扰动.通过引入动态信号,有效地处理了由状态未建模动态引起的动态不确定性.通过在总的李雅普诺夫函数中引入非负正则化信号,并利用稳定性分析中引入的紧集,证明了闭环控制系统是半全局一致终结有界的.数值仿真验证了所提方案的有效性.     

离散系统的滑动模控制及其在一伺服系统控制中的应用

本文借助李雅普诺夫稳定理论研究了一类具有有界参数和扰动不确定性离散系统的滑动模控制方法，并将其用于一飞行仿真器的高精度伺服控制，得到了较好的仿真和实验结果。     

基于输入状态稳定的离散广义系统预测控制

针对一类具有持续扰动和输入约束的离散广义系统, 研究其鲁棒预测控制器的设计问题. 将输入状态稳定的概念引入广义系统预测控制, 在quasi-min-max 性能指标下, 提出了广义系统双模鲁棒预测控制器的设计方法, 证明了基于双模鲁棒预测控制器的闭环广义系统输入状态稳定, 且具有正则、因果性. 数值仿真结果验证了所提出方法的有效性.