Markov跳跃非线性系统逆最优增益设计

证明了一类严格反馈Markov跳跃系统是依概率输入–状态可稳定的.其次,证明了逆最优增益设计问题可解的一个充分条件是存在一组满足小控制量的依概率输入–状态稳定控制李雅普诺夫函数.最后,利用积分反推方法,给出了严格反馈Markov跳跃系统逆最优增益设计问题的一个构造性解.其中,为了克服由于Markov跳跃引起的耦合项所带来的困难,所设计的李雅普诺夫函数以及控制器是与模态无关的.     

具有跳跃时滞的跳跃线性离散系统的控制器设计

研究一类具有Markov随机时滞的Markov跳跃线性离散系统的控制器设计问题.给出了系统随机稳定的充分必要条件,在公共控制器不存在时,所给出的依赖于模态和时滞的控制器可以保证系统随机稳定,并可以利用锥补线性化等方法求出控制器.仿真结果验证了所提出的控制器设计方法的有效性.     

转移概率未知下具有双Markov 链的网络控制系统控制器设计

研究一类基于Markov模型的网络控制系统的稳定性和镇定控制器设计问题.针对网络控制系统中受控对象模型的随机切换和通信过程中的丢包问题,利用具有两个独立Markov链的离散时间Markov跳跃系统进行建模.在该Markov跳跃系统模态转移概率矩阵部分元素未知的情况下,充分考虑转移概率的约束条件,给出系统可镇定的充要条件和状态反馈控制器的设计方法.最后通过仿真示例验证了所提出方法的有效性.     

具有跳跃时滞的跳跃线性离散系统的控制器设计

研究一类具有Markov随机时滞的Markov跳跃线性离散系统的控制器设计问题.给出了系统随机稳定的充分必要条件,在公共控制器不存在时,所给出的依赖于模态和时滞的控制器可以保证系统随机稳定,并可以利用锥补线性化等方法求出控制器.仿真结果验证了所提出的控制器设计方法的有效性.

     

模态跳变概率可控的Markov跳变线性系统的优化

研究模态跳变概率可控的Markov跣变线性二次模型的最优控制问题,考虑两类模态跳变控制策略:开环模态控制和闭环模态控制,应用策略迭代和性能势的概念,给出了最优的闭环模态控制优于最优的开环模态控制的充分条件,以指导最优控制器的设计,在已知最优的开环模态控制策略的基础上,应用策略迭代给出了构造闭环模态控制策略的方法,以进一步改善系统的性能.     

非齐次马尔可夫跳跃正线性系统的稳定与镇定

本文研究一类非齐次马尔可夫跳跃正线性系统的稳定与镇定问题.该系统中模态的变化服从非齐次马尔可夫过程,其模态转移速率/概率矩阵是随时间随机变化的,且变化规律由一个高层马尔可夫过程描述,本文提出一种双层马尔可夫跳跃正系统模型来刻画此类系统特征.在此基础上,利用切换线性余正李雅普诺夫函数给出此类连续和离散时间非齐次马尔可夫跳跃正线性系统平均稳定的判据.然后,运用线性规划方法设计依赖于模态–模态转移速率/概率矩阵的状态反馈控制器,进而实现闭环系统的平均稳定性.最后,以功率分配系统为例给出仿真算例,验证了所设计控制策略的有效性.     

转移概率部分未知的随机Markov 跳跃系统的镇定控制

研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式（LMIs）的可行性问题;最后,通过数值仿真验证了所得结论的正确性.     

一类离散时间非齐次马尔可夫跳跃系统最优控制

本文研究了一类离散时间非齐次马尔可夫跳跃线性系统的线型二次高斯(linear quadratic Gaussian,LQG)问题,其中系统模态转移概率矩阵随时间随机变化,其变化特性由一高阶马尔可夫链描述.对于该系统的LQG问题,文中首先给出了线性最优滤波器,得到最优状态估计;其次,验证分离定理成立,并利用利用动态规划方法设计了系统最优控制器;最后,数值仿真结果验证了所设计控制器的有效性.     

一种新型的滑模变结构增益调度控制器设计方法

研究影响一般滑动模态变结构控制性能的因素,并给出了根据切换函数选择滑动模态系数、边界层厚度以及控制器增益系数的一般要求．针对一类含参数不确定性的非线性系统,采用新型增益调度变结构控制策略进行控制,以切换函数作为调度变量对滑动模态系数、边界层厚度以及控制器增益系数进行调度,以提高滑动模态变结构控制系统的控制性能,抑制颤振,降低控制能耗．仿真算例验证了所提出控制策略的有效性．     

一类Markov跳跃非线性系统的鲁棒自适应镇定

研究一类具有Markov 跳跃参数的随机非线性系统的鲁棒自适应镇定问题.利用随机控制的Lyapunov 设计方法,对受Wiener 噪声干扰的参数严格反馈形式的跳跃系统,利用backstepping 方法设计参数自适应律和控制律,使得闭环系统状态在4 阶矩意义下全局一致有界,并能收敛到平衡点的任意小邻域内.仿真结果表明了该设计方法的有效性.     

Inverse optimal adaptive stochastic gain assignment for a class of nonlinear systems with Markovian jump

This paper deals with the inverse optimal adaptive stochastic gain assignment problem for a class of Markovian jump nonlinear systems with constant unknown parameters. The Wiener noises have bounded but unknown covariance. It is shown that a sufficient condition to solve this problem is the existence of a Lyapunov function for a corresponding auxiliary system. By employing backstepping technique and common Lyapunov function method, an adaptive control law is designed, which solves this problem for a class of Markovian jump nonlinear systems in strict-feedback form. A numerical example is given to illustrate the theoretical analysis result.     

Finite horizon quadratic optimal control and a separation principle for Markovian jump linear systems

In this note, we consider the finite-horizon quadratic optimal control problem of discrete-time Markovian jump linear systems driven by a wide sense white noise sequence. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati difference equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a principle of separation for the finite horizon quadratic optimal control problem for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the linear quadratic Gaussian control of discrete-time linear systems.     

Jump linear quadratic regulator with controlled jump rates

Deals with the class of continuous-time linear systems with Markovian jumps. We assume that jump rates are controlled. Our purpose is to study the jump linear quadratic (JLQ) regulator of the class of systems. The structure of the optimal controller is established. For a one-dimensional (1-D) system, an algorithm for solving the corresponding set of coupled Riccati equations of this optimal control problem is provided. Two numerical examples are given to show the usefulness of our results     

A geometric approach to H∞ control of nonlinear Markovian jump systems

This paper first discusses the H_∞ control problem for a class of general nonlinear Markovian jump systems from the viewpoint of geometric control theory. Following with the updating of the Markovian jump mode, the appropriate diffeomorphism can be adopted to transform the system into special structures, which establishes the basis for the geometric control of nonlinear Markovian jump systems. Through discussing the strongly minimum-phase property or the strongly γ-dissipativity of the zero-output dynamics, the H_∞ control can be designed directly without solving the traditional coupled Hamilton–Jacobi inequalities. A numerical example is presented to illustrate the effectiveness of our results.     

Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays

The notions of the practical stability in probability and in the pth mean, and the practical controllability in probability and in the pth mean, are introduced for some stochastic systems with Markovian jump parameters and time-varying delays. Sufficient conditions on such practical properties are obtained by using the comparison principle and the Lyapunov function methods. Besides, for a class of stochastic nonlinear systems with Markovian jump parameters and time-varying delays, existence conditions of optimal control are discussed. Particularly, for linear systems, optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters.     

Dissipativity of diffusion Itô processes with Markovain switching and problems of robust stabilization

Consideration is given to a class of systems described by a finite set of controlled diffusion Itô processes that are control-affine, with jump transitions between them, and are defined by the evolution of a uniform Markovian chain (Markovian switching). Each state of this chain corresponds to a certain system mode. A stochastic version of the notion dissipativity by Willems is introduced, and properties of diffusion processes with Markovian switching are studied. The relationship between passivity and stabilizability in the process of output-feedback control is established. The obtained results are applied to the problem of robust simultaneous stabilization for the set of nonlinear systems with undetermined parameters. As a partial case, a problem of robust simultaneous stabilization for the set of linear systems where final results are obtained in terms of linear matrix inequalities.     

<Emphasis Type="BoldItalic">H</Emphasis><Subscript>2</Subscript>-Control and the Separation Principle for Discrete-Time Markovian Jump Linear Systems

In this paper we consider the H₂-control problem of discrete-time Markovian jump linear systems. We assume that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system is mean square stable and minimizes the H₂-norm of the system. As in the case with no jumps, we show that an optimal controller can be obtained from two sets of coupled algebraic Riccati equations, one associated with the optimal control problem when the state variable is available, and the other associated with the optimal filtering problem. This is the principle of separation for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the H₂-control of discrete-time linear systems. Date received: June 1, 2001. Date revised: October 13, 2003.     

Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults

This article investigates the stability analysis and control design of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults and saturation. It is assumed that the actuator faults of each subsystem are varying and governed by a Markovian process. The nonlinear term is located in a sector. First, sufficient conditions for stochastic stability of the underlying systems are established using a stochastic copositive Lyapunov function. Then, a family of reliable L₁‐gain controller is proposed for nonlinear positive Markovian jump systems with actuator faults and saturation in terms of a matrix decomposition technique. Under the designed controllers, the closed‐loop systems are positive and stochastically stable with an L₁‐gain performance. An optimization method is presented to estimate the maximum domain of attraction. Furthermore, the obtained results are developed for general Markovian jump systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.     

Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach

This paper considers the stabilization problems for interconnected nonlinear stochastic Markovian jump systems from the viewpoint of dissipativity theory. Based on the strongly stochastic passivity theory, the feedback equivalence and global stabilization problems are studied for interconnected nonlinear stochastic Markovian jump systems. The strongly stochastic γ-dissipativity sustains a direct H_∞ control for this class of systems instead of solving coupled Hamilton–Jacobi inequalities.