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1.
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.  相似文献   

2.
Ping   《Automatica》2008,44(12):3120-3125
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.  相似文献   

3.
研究了一类随机非线性系统的逆最优增益设计问题,系统中除了方差未知的Wiener噪声之外,还含有Markov跳跃参数. 首先,给出此类系统逆最优增益设计问题可解的一个充分条件. 其次,针对一类具有严格反馈形式的随机非线性系统,利用积分反推法,给出了依概率全局渐近稳定和逆最优控制策略的设计方法. 其中,所设计的Lyapunov函数和控制策略与模态显式无关,克服了由于Markov跳跃模态引起的耦合项所带来的设计困难. 最后,通过仿真验证了控制策略的有效性.  相似文献   

4.
The minimum variance estimator algorithm is derived for a class of linear continuous systems modulated by a multivalued jump Markov process. The approach adopted in this paper is as follows. First, we express the jump Markov process in terms of its initial value, the jump times and the values taken by the jump process after the jump, and then we apply the Bayes' rule and the general likelihood-ratio formula to obtain the a posteriori probability distribution of the jump process. The minimum variance estimate is given in terms of the a posteriori probability distribution of the jump process and the Kalman-filter estimates corresponding to the admissible values of the jump process. Simulation studies are also carried out to illustrate the behavior of the optimal estimator presented here.  相似文献   

5.
A class of linear, stochastic, jump parameter systems is studied in which the probability law of the parameter processes depends upon the control policy used. An optimal controller is given when the loss function is quadratic. Because of difficulties inherent in the design equations, a more easily evaluated, near optimal controller is provided for problems in which the parameter processes are weakly dependent on the control policy.  相似文献   

6.
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.  相似文献   

7.
Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and H -control of Markovian jump linear systems are considered. First, the equations that arise from the quadratic optimal control problem are studied. The matrix cost is only assumed to be hermitian. Conditions for the existence of the maximal hermitian solution are derived in terms of the concept of mean square stabilizability and a convex set not being empty. A connection with convex optimization is established, leading to a numerical algorithm. A necessary and sufficient condition for the existence of a stabilizing solution (in the mean square sense) is derived. Sufficient conditions in terms of the usual observability and detectability tests for linear systems are also obtained. Finally, the coupled algebraic Riccati equations that arise from the H -control of discrete-time Markovian jump linear systems are analyzed. An algorithm for deriving a stabilizing solution, if it exists, is obtained. These results generalize and unify several previous ones presented in the literature of discrete-time coupled Riccati equations of Markovian jump linear systems. Date received: November 14, 1996. Date revised: January 12, 1999.  相似文献   

8.
研究线性Markov切换系统的随机Nash微分博弈问题。首先借助线性Markov切换系统随机最优控制的相关结果,得到了有限时域和无线时域Nash均衡解的存在条件等价于其相应微分(代数) Riccati方程存在解,并给出了最优解的显式形式;然后应用相应的微分博弈结果分析线性Markov切换系统的混合H2/H∞控制问题;最后通过数值算例验证了所提出方法的可行性。  相似文献   

9.
含参数不确定性的马尔可夫跳变过程鲁棒正实控制   总被引:5,自引:0,他引:5  
刘飞  苏宏业  褚健 《自动化学报》2003,29(5):761-766
讨论一类具有随机跳变参数的线性系统正实控制问题,其跳变参数的跃迁由有限状态的马尔可夫过程描述.基于随机李亚普诺夫函数的方法,并结合线性矩阵不等式,分别提出依赖于模态的状态反馈和输出反馈控制,以保证相应闭环系统的严格正实性.进一步针对系统含参数不确定性的情形,引入鲁棒正实性分析,得到鲁棒正实控制器存在的充分条件和设计方法.  相似文献   

10.
This paper deals with the robust H2-control of discrete-time Markovian jump linear systems. It is assumed that both the state and jump variables are available to the controller. Uncertainties satisfying some norm bounded conditions are considered on the parameters of the system. An upper bound for the H2-control problem is derived in terms of a linear matrix inequality (LMI) optimization problem. For the case in which there are no uncertainties, we show that the convex formulation is equivalent to the existence of the mean square stabilizing solution for the set of coupled algebraic Riccati equations arising on the quadratic optimal control problem of discrete-time Markovian jump linear systems. Therefore, for the case with no uncertainties, the convex formulation considered in this paper imposes no extra conditions than those in the usual dynamic programming approach. Finally some numerical examples are presented to illustrate the technique.  相似文献   

11.
Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between appropriately defined controllability, stabilizability properties, and the solution of the infinite time jump linear quadratic (JLQ) optimal control problems is also examined. Although the solution of the continuous-time Markov JLQ problem with finite or infinite time horizons is known, only sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite time problem appear in the literature. In this paper necessary and sufficient conditions are established. These conditions are based on new definitions of controllability, observability, stabilizability, and detectability that are appropriate for continuous-time Markovian jump linear systems. These definitions play the same role for the JLQ problem as the deterministic properties do for the linear quadratic regulator (LQR) problem  相似文献   

12.
陈珺  高泽峰  刘飞 《自动化学报》2013,39(5):587-593
研究了一类模糊双线性跳变系统的随机镇定问题. 采用T-S模糊建模技术来构建模糊双线性跳变模型, 然后通过并行分布补偿 (Parallel distributed compensation, PDC) 方法和选择合适的模糊隶属度函数, 将整个非线性控制器表示为一组局部线性控制器的模糊综合. 此外, 还推导出了保证闭环模糊双线性跳变系统随机稳定的充分条件, 并且这些条件最终可归结为一组线性矩阵不等式 (Linear matrix inequalities, LMIs)的可行性问题. 最后, 连续搅拌反应釜(Continuous stirred tank reactor, CSTR)系统的数值示例表明该设计方法的合理性和有效性.  相似文献   

13.
We consider coupled Riccati equations that arise in the optimal control of jump linear systems. We show how to reliably solve these equations using convex optimization over linear matrix inequalities (LMIs). The results extend to other nonstandard Riccati equations that arise, e.g., in the optimal control of linear systems subject to state-dependent multiplicative noise. Some nonstandard Riccati equations (such as those connected to linear systems subject to both state- and control-dependent multiplicative noise) are not amenable to the method. We show that we can still use LMI optimization to compute the optimal control law for the underlying control problem without solving the Riccati equation  相似文献   

14.
This paper deals with the class of linear discrete-time systems with random abrupt changes also known as class of Markovian jump singular systems. The problems of stochastic stability and the stochastic stabilisation (using state-feedback control and static output feedback control) are tackled. Conditions in the LMI setting to design the appropriate gains of the controllers are developed. It is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities (LMIs) are feasible. Numerical examples are employed to show the usefulness of the proposed results.  相似文献   

15.
The notion of input–output finite-time mean square (IO-FTMS) stability is introduced for Itô-type stochastic systems with Markovian jump parameters. Concerning a class of random input signals W, sufficient conditions are presented for the IO-FTMS stability and stabilisation of stochastic nonlinear Markov jump systems in terms of coupled Hamilton–Jacobi inequalities. When specialising to the linear case, these criteria are turned into coupled linear matrix inequalities. Moreover, the quadratic IO-FTMS stabilisation is addressed when polytopic uncertainty appears in the transition rate. Finally, a numerical example with simulations is exploited to illustrate the proposed techniques.  相似文献   

16.
A New Method for Stabilization of Networked Control Systems With Random Delays   总被引:11,自引:0,他引:11  
We consider the stabilization problem for a class of networked control systems in the discrete-time domain with random delays. The sensor-to-controller and controller-to-actuator delays are modeled as two Markov chains, and the resulting closed-loop systems are jump linear systems with two modes. The necessary and sufficient conditions on the existence of stabilizing controllers are established. It is shown that state-feedback gains are mode-dependent. An iterative linear matrix inequality (LMI) approach is employed to calculate the state-feedback gains.  相似文献   

17.
Markov跳变系统的有限时间状态反馈镇定   总被引:2,自引:2,他引:0  
讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.  相似文献   

18.
This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.  相似文献   

19.
祝超群  郭戈 《控制与决策》2014,29(5):802-808

针对随机事件驱动的网络化控制系统, 研究其中的有限时域和无限时域内最优控制器的设计问题. 首先, 根据执行器介质访问机制将网络化控制系统建模为具有多个状态的马尔科夫跳变系统; 然后, 基于动态规划和马尔科夫跳变线性系统理论设计满足二次型性能指标的最优控制序列, 通过求解耦合黎卡提方程的镇定解, 给出最优控制律的计算方法, 使得网络化控制系统均方指数稳定; 最后, 通过仿真实验表明了所提出方法的有效性.

  相似文献   

20.
张远敬  彭力 《测控技术》2019,38(9):113-117
讨论了含执行器饱和的离散时滞Markov跳变系统在未知但有界扰动的情况下,针对系统模态转移概率部分未知的系统进行有限时间镇定的分析和研究。利用构造的Lyapunov函数和饱和非线性处理技术,对具有执行器饱和的离散时滞Markov系统进行研究,并提出了系统状态有限时间镇定的充分条件,结合线性矩阵不等式的方法,设计并实现了有限时间镇定状态反馈控制器。通过数值仿真,示例验证了该设计方法的有效性及潜在的应用性。  相似文献   

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