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 共查询到17条相似文献,搜索用时 46 毫秒
1.
研究一类带随机跳跃的完全耦合的线性二次随机控制问题. 得到了最优控制的显式解, 并可以证明最优控制是唯一的. 引入了一类推广的黎卡提方程并讨论了其可解性. 利用这一类推广的黎卡提方程的解, 得到了上述带随机跳跃的最优控制问题的线性状态反馈调节器.  相似文献   

2.
讨论一类正倒向随机微分方程解的存在唯一性及其对应的一类线性二次随机最优控制问题,利用单调性方法证明了一类特殊的正倒向随机微分方程解的存在唯一性定理,利用该结果研究一类耦合了一个倒向随机微分方程的线性随机控制系统广义最优指标随机控制问题,得到由正倒向随机微分方程的解所表示的唯一最优控制的显式表达式,并得到精确的线性反馈及其对应的Riccati方程.  相似文献   

3.
线性二次最优控制的精细积分法   总被引:15,自引:1,他引:14       下载免费PDF全文
钟万勰 《自动化学报》2001,27(2):166-173
LQ控制虽然是最优控制的最基本问题,但其数值求解仍有很多问题.黎卡提微分方程的精细积分法利用黎卡提方程的解析特点,求出计算机上高度精密的解,并已证明误差在计算机倍精度数的误差范围之外.这对于Kalman-Bucy滤波,LQG问题以及H∞控制及滤波等都可运用,精细积分还求解了反馈后的状态微分方程.数例验证了其高精度特性.  相似文献   

4.
约束随机线性二次最优控制的研究   总被引:2,自引:0,他引:2       下载免费PDF全文
本文研究线性终端状态约束下不定随机线性二次最优控制问题.首先利用Lagrange Multiplier 定理得到了存在最优线性状态反馈解的必要条件, 而在加强的条件下也得到了最优控制存在的充分条件. 从某种意义上讲, 以往关于无约束随机线性二次最优控制的一些结果可以看成本文主要定理的推论.  相似文献   

5.
王涛  张化光 《控制与决策》2015,30(9):1674-1678

针对模型参数部分未知的随机线性连续时间系统, 通过策略迭代算法求解无限时间随机线性二次(LQ) 最优控制问题. 求解随机LQ最优控制问题等价于求随机代数Riccati 方程(SARE) 的解. 首先利用伊藤公式将随机微分方程转化为确定性方程, 通过策略迭代算法给出SARE 的解序列; 然后证明SARE 的解序列收敛到SARE 的解, 而且在迭代过程中系统是均方可镇定的; 最后通过仿真例子表明策略迭代算法的可行性.

  相似文献   

6.
带有随机通信时滞的状态估计   总被引:1,自引:0,他引:1       下载免费PDF全文
研究了测量值不带时间戳的网络控制系统的最优状态估计问题. 当最大的随机时滞界是一步滞后时, 对可能存在的乱序测量提出新的测量模型. 基于每一时刻收到的所有测量值的平均值构造估计器以保证不稳定网络控制系统的估计器是线性无偏的及估计误差协方差一致有界, 并通过求解离散黎卡提方程得到估计器增益. 在无偏性及误差协方差一致有界的意义下保证估计器是最优的. 最后给出仿真实例验证了该算法的有效性.  相似文献   

7.
随机运动目标搜索问题的最优控制模型   总被引:1,自引:0,他引:1       下载免费PDF全文
提出了Rn空间中做布朗运动的随机运动目标的搜索问题的最优控制模型.采用分析的方法来研究随机运动目标的最优搜索问题,并将原问题转化为由一个二阶偏微分方程(HJB方程)所表示的确定性分布参数系统的等价问题,推导出随机运动目标的最优搜索问题的HJB方程,并证明了该方程的解即是所寻求的最优搜索策略.由此给出了一个计算最优搜索策略的算法和一个实例.  相似文献   

8.
随机系统的鲁棒状态反馈控制   总被引:7,自引:0,他引:7  
对结构参数不确定的随机线性时不变系统的无限时间鲁棒状态反馈控制问题进行了研究.给出了鲁棒控制器的存在条件及其状态空间表达形式,而且也给出了系统输出的渐近协方差所规定的性能界.仿真结果表明,本文所提供的方法大大改善了系统的输出性能,且具有很强的鲁棒性.  相似文献   

9.
肖俊  徐红兵  祝颖 《自动化学报》2007,33(4):373-377
讨论了带有随机丢包的最优控制. 在传感器网络中,控制器与被控对象通过不可靠无线网络通信,因此代数Riccati方程由于通信链路的随机丢包产生了新的参数. 证明了当丢包率大于一临界值时,此Riccati 方程的解不存在. 通过解线性矩阵不等式,得到了这一临界值.  相似文献   

10.
时变广义系统线性二次最优控制   总被引:9,自引:1,他引:8       下载免费PDF全文
研究时变广义系统线性二次最优控制问题.通过引进时变广义系统脉冲能控性及脉冲能观性等概念,建立了这类问题与标准状态空间系统二次指标问题的等价性.进而证明了解的存在唯一性,给出了解的表示和最优反馈综合.  相似文献   

11.
    
A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.  相似文献   

12.
This paper is concerned with the existence and uniqueness of solution for the optimal control problem governed by the stochastic FitzHugh–Nagumo equation driven by a Gaussian noise. First-order conditions of optimality are also obtained.  相似文献   

13.
    
The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by external forces which are feedback controls. To attain our objective we adapt the argument of Lisei (2002) where the existence of optimal controls to the stochastic Navier–Stokes equation was studied. The results obtained in the present paper may be applied to demonstrate the existence of optimal controls to various types of controlled SPDEs such as: a stochastic nonlocal equation and stochastic semilinear equations which are locally monotone equations; we also apply the result to a monotone equation such as the stochastic reaction–diffusion equation and to a stochastic linear equation.  相似文献   

14.
We consider a controlled stochastic linear differential equation with state- and control-dependent noise in a Hilbert space H. We investigate the relation between the null controllability of the equation and the existence of the solution of “singular” Riccati operator equations. Moreover, for a fixed interval of time, the null controllability is characterized in terms of the dual state. Examples of stochastic PDEs are also considered.  相似文献   

15.
    
ABSTRACT

In this paper, we investigate the optimal control problems for delayed doubly stochastic control systems. We first discuss the existence and uniqueness of the delayed doubly stochastic differential equation by martingale representation theorem and contraction mapping principle. As a necessary condition of the optimal control, we deduce a stochastic maximum principle under some assumption. At the same time, a sufficient condition of optimality is obtained by using the duality method. At the end of the paper, we apply our stochastic maximum principle to a class of linear quadratic optimal control problem and obtain the explicit expression of the optimal control.  相似文献   

16.
This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear operators, the problem is formulated as an operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the expectation operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained.  相似文献   

17.
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problem can be interpreted as a stochastic control problem for an evolution system in a Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equation in infinite dimension, plays a crucial role in the formulation of the maximum principle.  相似文献   

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