随机不确定时滞系统的鲁棒H∞控制

本文研究了随机不确定时滞系统的鲁棒稳定性与鲁棒H∞控制问题,系统的不确性具有凸多面体形式.利用线性矩阵不等式方法,通过依赖于参数的Lyapunov函数,得到了此类系统鲁棒随机镇定的充分条件.在此基础上,又给出了H∞状态反馈控制器的设计.     

不确定多重时滞随机中立系统鲁棒H∞控制

针对一类不确定多重时滞随机中立系统,研究了鲁棒H_∞控制设计问题．该随机中立系统的状态项、控制项、微分项、外部干扰输入项均含有时滞,系统中的不确定性满足广义匹配条件．首先,利用随机Lyapunov稳定性理论和Ito微分法则,推导出系统的随机鲁棒可镇定的充分条件．在此基础上,进一步给出了鲁棒H_∞控制器存在的充分条件．本文的研究结果以线性矩阵不等式的形式给出,仿真结果表明了此控制器设计方法的有效性．     

随机时滞Lurie系统的鲁棒H∞和L2-L∞指数控制

针对一类具有范数有界不确定性和时变时滞的It^o型随机Lurie系统, 研究了鲁棒H_∞和L₂–L_∞指数控制问题. 利用Lyapunov-Krasovskii泛函方法和It^o微分公式, 得到了以线性矩阵不等式(LMIs)表示的控制器存在的充分条件. 对所有容许的参数不确定性, 设计的无记忆状态反馈控制器使闭环系统鲁棒指数均方稳定, 且具有给定的H_∞和L₂–L_∞干扰抑制度. 最后, 通过两个仿真例子说明了所提方法的有效性.     

不确定时滞混沌系统的鲁棒控制

针对不确定时滞混沌系统中不稳定不动点的控制需要，应用线性矩阵不等式（LMI）方法，得到了系统存在时滞反馈控制器的充分条件，并利用该控制器对系统中存在的不稳定周期轨道的跟踪问题进行研究。数值仿真结果表明了该方法的有效性。     

凸多面体不确定随机时滞系统的参数依赖状态反馈控制

考虑了凸多面体不确定随机时滞系统的参数依赖状态反馈控制问题.把参数相关的Lyapunov-Krasovskii泛函方法和自由权矩阵方法相结合,得到了基于线性矩阵不等式(LMI)的时滞相关及参数相关的鲁棒镇定的充分条件.由于在引入自由权矩阵时,减少了所用的自由矩阵数目,使得给出的参数依赖的控制器更易于实现.最后用例子说明了结果的有效性.     

Exponential synchronization of chaotic systems with stochastic noise via periodically intermittent control

The problem of second‐moment exponential synchronization is discussed for chaotic systems. Different from some existing results, a unified drive‐response system is formulated, which involves stochastic noise and the time‐varying delay. Meanwhile, the feedback controller is presented by the periodically intermittent control. By exploiting the Lyapunov stability theory, the improved reciprocally convex inequality and the Itô formula, several new sufficient conditions are obtained to make two systems synchronized. In addition, the controller is determined by the control period and the control width. Finally, simulation results illustrate that the designed controller achieves the desired performance.     

Fully probabilistic control for uncertain nonlinear stochastic systems

This paper develops a novel probabilistic framework for stochastic nonlinear and uncertain control problems. The proposed framework exploits the Kullback–Leibler divergence to measure the divergence between the distribution of the closed-loop behavior of a dynamical system and a predefined ideal distribution. To facilitate the derivation of the analytic solution of the randomized controllers for nonlinear systems, transformation methods are applied such that the dynamics of the controlled system becomes affine in the state and control input. Additionally, knowledge of uncertainty is taken into consideration in the derivation of the randomized controller. The derived analytic solution of the randomized controller is shown to be obtained from a generalized state-dependent Riccati solution that takes into consideration the state- and control-dependent functional uncertainty of the controlled system. The proposed framework is demonstrated on an inverted pendulum on a cart problem, and the results are obtained.     

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional‐derivative control strategy is presented, where the derivative gain is to make the closed‐loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive tracking control for uncertain switched systems under asynchronous switching

This paper addresses the state‐tracking model reference adaptive control problem for a class of switched systems with parametric uncertainties, where switchings between subsystems and designed adaptive controller are asynchronous. First, we establish a stability criterion for a switched reference model and convert the state‐tracking problem into the stability problem of an error switched system. Then, an adaptive law is designed, and the global practical stability of the error switched system is guaranteed under a class of switching signals characterized by a dwell‐time condition. An electrohydraulic system is given as an example to demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust reliable control of uncertain nonlinear stochastic systems subject to actuator fault

This paper addresses the issue of robust reliable stabilization for a class of uncertain nonlinear stochastic systems with both discrete and distributed time-varying delays and possible occurrence of actuator faults. By constructing a new Lyapunov functional and using linear matrix inequality technique, a new set of sufficient conditions is established for the stochastic stability of the uncertain nonlinear stochastic systems. Then, sufficient conditions are obtained for the solvability of the robust stabilization problem via robust reliable controller. More precisely, the derived control law guarantees the robust stabilization of nonlinear stochastic systems in the presence of known actuator failure matrix and uncertainties. Further, the results are extended to study the stabilization of stochastic systems with unknown actuator failure matrix. Moreover, the obtained criteria are formulated in terms of LMIs and also the reliable controller can be designed in terms of the solutions to certain linear matrix inequalities. Finally, numerical examples with simulation result are presented to demonstrate the validity and less conservatism of the obtained results.     

Guaranteed cost PID control for uncertain discrete‐time stochastic systems with additive gain perturbations

This paper investigates a novel design method for robust nonfragile proportional‐integral‐derivative (PID) control that is based on the guaranteed cost control (GCC) problem for a class of uncertain discrete‐time stochastic systems with additive gain perturbations. On the basis of linear matrix inequality (LMI), a class of fixed PID controller parameters is obtained, and some sufficient conditions for the existence of the GCC are derived. Although the additive gain perturbations are included in the feedback systems, both the stability of closed‐loop systems and adequate cost bound are attained. As a sequel, decentralized GCC PID for a class of discrete‐time uncertain large‐scale stochastic systems is also considered. Finally, the numerical results demonstrate the efficiency of the proposed controller synthesis. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Lurie系统的鲁棒量化控制

研究了Lurie系统的鲁棒量化状态反馈控制问题, 其中的量化器为静态对数量化器. 首先, 根据Lurie系统自身特点以及对数量化器的特性, 将量化状态反馈控制作用下的Lurie系统建模成具有两个扇形约束的不确定系统. 然后分别考虑了没有量化和有量化作用两种情形, 利用小增益定理, 得到了闭环系统内稳定的充分必要条件, 并进一步给出了相应的状态反馈控制律. 最后, 数值例子表明了本文方法的有效性.     

不确定高次随机非线性系统的自适应控制

针对一类含有噪声干扰和非线性参数的高次随机非线性系统,研究了依概率全局自适应稳定问题.在噪声的协方差未知的情况下,利用自适应增加幂积分方法和参数分离技术,提出了一种反馈占优设计方法并构造了一个光滑自适应控制器.该控制器能保证闭环系统依概率全局稳定,并且系统的状态几乎必然收敛到零.仿真例子验证了控制方案的有效性.     

Delay-dependent resilient-robust stabilisation of uncertain networked control systems with variable sampling intervals

This work is concerned with the robust resilient control problem for uncertain networked control systems (NCSs) with variable sampling intervals, variant-induced delays and possible data dropouts, which is seldom considered in current literature. It is mainly based on the continuous time-varying-delay system approach. Followed by the nominal case, delay-dependent resilient robust stabilising conditions for the closed-loop NCS against controller gain variations are derived by employing a novel Lyapunov–Krasovskii functional which makes good use of the information of both lower and upper bounds on the varying input delay, and the upper bound on the variable sampling interval as well. A feasible solution of the obtained criterion formulated as linear matrix inequalities can be gotten. A tighter bounding technique is presented for acquiring the time derivative of the functional so as to utilise many more useful elements, meanwhile neither slack variable nor correlated augmented item is introduced to reduce overall computational burden. Two examples are given to show the effectiveness of the proposed method.     

Funnel‐like prescribed tracking control for uncertain nonlinear stochastic switched systems

This paper deals with the funnel‐like prescribed tracking control problem for a class of uncertain nonlinear stochastic switched systems. An improved performance technique is developed to restrain the fluctuation at the moment of switches and a new algorithm is proposed to address the funnel‐like prescribed tracking problem. First, a dynamic gain‐based switched K‐filter is constructed to estimate the unmeasured state information of the switched system. Subsequently, the performance technique is applied to prescribe output tracking error and restrain fluctuations of the system. Thereafter, the dynamic output feedback switched controller is designed by the use of the backstepping method. Moreover, based on the Lyapunov stability theory, it is proved strictly that all signals of the resulting closed‐loop system are bounded in probability if the switching signal satisfies the average dwell time. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed theoretical results.     

基于神经网络的不确定随机非线性时滞系统自适应有界镇定

针对一类不确定严格反馈随机非线性时滞系统的自适应有界镇定问题,利用神经网络参数化和Backstepping方法,提出一种新的且含较少学习参数的神经网络自适应控制策略,以保证系统半全局随机有界.稳定性分析证明闭环系统的所有误差信号概率意义下有界.仿真结果表明所提出控制器设计方法的有效性.     

A two-tier control architecture for nonlinear process systems with continuous/asynchronous feedback

In this work, we introduce a two-tier control architecture for nonlinear process systems with both continuous and asynchronous sensing and actuation. This class of systems arises naturally in the context of process control systems based on hybrid communication networks (i.e. point-to-point wired links integrated with networked wired or wireless communication) and utilising multiple heterogeneous measurements (e.g. temperature and concentration). Assuming that there exists a lower-tier control system which relies on point-to-point communication and continuous measurements to stabilise the closed-loop system, we propose to use Lyapunov-based model predictive control to design an upper-tier networked control system to profit from both the continuous and the asynchronous measurements as well as from additional networked control actuators. The proposed two-tier control system architecture preserves the stability properties of the lower-tier controller while improving the closed-loop performance. The theoretical results are demonstrated using two different chemical process examples.     

LMI-based robust admissible control for uncertain singular delta operator systems

This paper investigates the problem of state feedback robust admissible control for singular delta operator systems with norm-bounded coefficient matrix uncertainties. A necessary and sufficient condition is derived to ensure the admissibility of the closed-loop singular delta operator system for all allowable uncertainties. Then, by specifying the structure of some matrix variables, the existence condition and explicit expression of a robust admissible controller are obtained in terms of strict linear matrix inequalities. Moreover, from the relation between singular discrete systems and singular delta operator systems, the corresponding results are also presented for uncertain singular discrete systems. Finally, some numerical examples are provided to demonstrate the effectiveness of the results in this paper.