基于终端不变集的 Markov 跳变系统约束预测控制

针对离散 Markov 跳变系统, 研究带输入输出约束的有限时域预测控制问题. 对于给定预测时域内的每条模态轨迹, 设计控制输入序列, 驱动系统状态到达相应的终端不变集内, 在预测时域外, 则寻求一个虚拟的状态反馈控制器以保证系统的随机稳定性, 在此基础上, 分别给出了以线性矩阵不等式 (LMI) 描述的带输入、输出约束预测控制器的设计方法.     

多面体不确定线性系统具有约束满足保证的预测控制

基于不变集理论, 拓展了Chiscil等人提出的约束不变预测控制方法(ICPC), 提出了一种适用于带约束多面体不确定线性系统的预测控制的框架. 其关键在于为针对标称系统设计的在线优化问题附加适当的额外的鲁棒可行约束. 若优化问题在初始阶段可行, 则此约束可保证在线优化问题始终可行, 从而保证了实际系统中约束条件的始终满足. 同时提出了闭环系统鲁棒稳定的一个充分条件, 可为成本函数的选择提供指导以保证预测控制器的鲁棒镇定.     

Markov跳变系统的输出反馈鲁棒预测控制

对离散时间Markov跳变系统, 当系统状态不完全可测时, 研究了一类基于输出反馈的鲁棒模型预测控制问题. 所研究系统为准线性参数时变的, 考虑在当前时刻系统的时变参数是已知的, 将来时刻未知的情况. 综合考虑系统存在多胞不确定性和有界噪声等因素, 通过运用线性矩阵不等式方法及变量变换思想, 将无穷时域性能指标的最小最大鲁棒预测控制问题转化为具有线性矩阵不等式约束的凸优化问题, 得到了系统的输出反馈控制律. 引入二次有界概念, 在满足输入输出约束的情况下, 保证闭环系统的随机稳定性. 数值算例验证了方法的有效性.     

Markov跳变系统的稳定自适应控制研究

研究一类据有严参数反馈的Markov跳变系统的自适应稳定控制问题,传统的参数估计是基于某种等价原理得到,估计形式单一,收敛速度较慢,且很难保证参数收敛时系统收敛。应用参数估计与控制器设计分离的方法,先应用微分几何中的流形浸入与不变的概念,得到一种新的参数估计表示式,再应用积分反推方法设计了Markov跳跃非线性系统的控制率,证明了在该控制律的作用下系统平衡点依概率全局渐近稳定。该方法解决了传统参数估计存在的问题,系统的动态性能可通过参数收敛的快慢来调节。仿真实验结果表明了该方法的有效性。     

一类离散不确定系统的Tube不变集离线鲁棒模型预测控制

针对一类输入和状态受限的离散线性不确定系统,提出了一种基于Tube不变集的离线鲁棒模型预测控制方法.首先针对输入和状态约束线性时不变标准系统,设计了改进的基于多面体不变集的离线模型预测控制算法,并证明了稳定性.其次对于存在未知有界干扰的实际不确定系统,引入了Tube不变集策略,通过设计对应标准模型的最优控制序列和状态轨迹,给出了实际不确定系统的离线Tube不变集控制策略,保证系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

计及随机传感器时滞的不确定半Markov跳变系统鲁棒滑模控制

在实际系统中,系统参数与结构随机变化、未知外界干扰、传感器时滞等现象时有发生并严重影响了系统的稳定运行.为了解决这一问题,本文提出计及随机传感器时滞的一类不确定半Markov跳变系统鲁棒滑模控制方法,其中系统的传感器时滞通过使用Bernoulli随机分布进行描述.考虑系统状态信息不可测量条件下,文章设计模态依赖Luenberger观测器去估计半Markov跳变系统的运行状态.然后,本文构造一个积分滑模面并借助随机Lyapunov理论,提出两种半Markov跳变系统的随机稳定性分析方法.进而,文章提出基于观测器的滑模控制方法使得系统状态能够在有限时间内到达滑模面上以及滑模动态在H_∞性能指标γ下是随机稳定的.最后,通过一种基于他励直流电动机模型的数值仿真例子验证所设计的滑模控制方法的有效性与正确性.     

一类不确定离散Markov 跳变系统滑模状态反馈控制

针对具有不确定的离散Markov跳变系统,研究其滑模状态反馈控制问题.考虑系统的不确定满足匹配条件,以线性矩阵不等式形式给出了离散滑模面存在的充分条件,设计了具有指数趋近律的滑模控制器,保证了系统状态到达滑模面并在滑模带上随机镇定.数值仿真验证了所提出的控制方案的有效性.     

模型不确定非线性Markov 跳变系统的滤波算法

针对模型不确定非线性Markov跳变系统,提出一种新的滤波算法.相比于传统交互多模型粒子滤波,该方法通过引入前一时刻的滤波误差来增强原先由于不精确模型而造成权值较小的真实粒子在滤波过程中的作用,以此来改善算法的估计性能.仿真结果表明,该方法在处理含不确定模型参数的非线性Markov跳变系统状态估计问题时具有较好的性能.     

一类非线性广义马尔可夫跳变系统的耗散控制

将耗散理论的二次型供给率中的矩阵Q推广到正定的情况.进而研究了在状态转移概率未知的情况下一类连续时间非线性广义马尔可夫跳变系统的严格耗散控制问题.在应用范围更广的Willems耗散性定义的基础上,首先基于一类Lyapunov函数,给出了相应的随机容许的条件,然后设计导数比例反馈控制器,通过一系列的矩阵构造和合同变换,将双线性矩阵不等式(BMI)转化为可用LMI工具箱解决的线性矩阵不等式(LMI).最后通过数值算例并结合Matlab给出实例,证明其可行性.     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Constrained receding horizon predictive control for nonlinear systems

The paper concerns the receding horizon predictive control of constrained nonlinear systems and presents an algorithm which relies on the online solution of a simple linear program (LP). Use is made of a finite control horizon in conjunction with a terminal inequality constraint and a predicted cost that includes a terminal penalty term. The optimization procedure is based on predictions made by linearized incremental models at points of a given seed trajectory and the effects of linearization error are taken into account to give a bound on the predicted tracking error. The algorithm is posed in the form of an LP and the proper selection of the terminal penalty term of the predicted cost guarantees the asymptotic stability. The results of the paper are illustrated by means of a simple example.     

Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates

In this paper, based on sliding mode control approach, the robust stabilisation problem for a class of continuous-time Markovian jump linear uncertain systems with partly unknown transition rates is investigated. The transition rate matrix under consideration covers completely known, boundary known and completely unknown elements. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. Then a sliding mode control law is designed to drive the state trajectory of the closed-loop system to the specified linear switching surface in finite time in spite of the existing uncertainties and unknown transition rates. Finally, an example is given to verify the validity of the theoretical results.     

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

Model predictive control (MPC) for Markovian jump linear systems with probabilistic constraints has received much attention in recent years. However, in existing results, the disturbance is usually assumed with infinite support, which is not considered reasonable in real applications. Thus, by considering random additive disturbance with finite support, this paper is devoted to a systematic approach to stochastic MPC for Markovian jump linear systems with probabilistic constraints. The adopted MPC law is parameterized by a mode‐dependent feedback control law superimposed with a perturbation generated by a dynamic controller. Probabilistic constraints can be guaranteed by confining the augmented system state to a maximal admissible set. Then, the MPC algorithm is given in the form of linearly constrained quadratic programming problems by optimizing the infinite sum of derivation of the stage cost from its steady‐state value. The proposed algorithm is proved to be recursively feasible and to guarantee constraints satisfaction, and the closed‐loop long‐run average cost is not more than that of the unconstrained closed‐loop system with static feedback. Finally, when adopting the optimal feedback gains in the predictive control law, the resulting MPC algorithm has been proved to converge in the mean square sense to the optimal control. A numerical example is given to verify the efficiency of the proposed results.     

Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems

This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlying systems is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix at each time instant. This robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters. The proposed controller is obtained using semidefinite programming.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.     

Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.