基于策略迭代的连续时间系统的随机线性二次最优控制

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.

     

奇异系统的不定号二次型指标最优控制问题

讨论奇异系统的不定号LQ问题 (二次型指标中的权矩阵含有负特征值的最优控制问题). 首先指出问题的可解性, 并给出了问题等价转化为奇异系统的奇异LQ问题的充要条件. 然后基于等价的奇异系统奇异LQ问题, 给出问题存在唯一最优控制—轨线对的充分条件. 最后用一个算例说明结论的正确性.     

具有乘性噪声的线性离散时间随机控制系统综述

具有乘性噪声的随机不确定系统的控制问题有着广泛的应用背景. 本文概述了具有乘性噪声的线性离散时间随机系统的稳定性分析、均方镇定、最优控制以及最优估计问题和相关结论. 同时, 本文研究了具有状态与控制乘性噪声的线性多变量离散时间系统的均方镇定和最优控制问题, 分析了这两个问题之间的联系, 并讨论了最优状态反馈控制器的设计算法.     

冷连轧系统跟踪问题的最优控制律的仿真研究*

本文根据随机离散系统跟踪问题输出反馈最优控制规律,以武汉钢铁公司冷轧厂冷连轧系统为研究对象,提出了冷连轧系统跟踪问题的最优控制规则;应用这一规则进行了计算机仿真,得到了比较满意的结果。     

离散系统LQ逆问题及其在最优闭环极点配置中的应用

本文采用离散系统LQ逆问题方法得到了最优闭环系统的两个必要条件,分析了单输入单输出系统权阵Q与开环特征多项式系数a_i、及闭环特征多项式系数b_i之间的关系,最后应用所得结论研究了离散系统逆问题方法在最优闭环极点配置中的应用。     

离散系统LQ逆问题及其在最优闭极点配置中的应用

本文采用离散系统LQ逆向问题方法得到了最优闭环系统的两个必要条件，分析了单输入单输出系统权阵Q与开环特征多项式系数ai，及闭环特征多项式系数bi之间的关系，最后应用所得结论研究了离散系统逆问题方法在最优闭环极点配置中的应用。     

基于连续Hopfield网络的多变量时变系统最优控制

针对多变量时变系统提出了一种基于连续Hop fie ld网络的最优控制系统设计方法.该方法不仅从理论上建立了移动时域上的LQ性能指标与连续Hop fie ld网络能量函数间的等价关系,并在此基础上设计出可求解LQ最优控制问题的连续Hop fie ld网络,而且将滚动优化控制策略引入控制系统,形成了包括连续Hop fie ld网络在内的闭环控制结构,实现了多变量时变系统无限域上的动态最优控制.仿真结果验证了该设计方法的有效性.     

《LQ最优控制之逆问题的研究》一文的更正

文[1]中研究了LQ最优控制的逆问题,得到了确定最优离散系统中加权矩阵Q的一个重要定理,但是,经过对方程(3.21)和(3.22)的校验发现,在文[1]的定理4中,H_1的定义有误,H_1的正确定义应为     

无限时间长时延网络控制系统的随机最优控制

考虑二次性能指标下线性网络控制系统的随机最优控制问题,建立了控制器为事件驱动时长时延线性网络控制系统的数学模型,证明了在无限时间情况下离散随机黎卡提代数方程解的存在性,设计出无限时间情况下线性网络控制系统的随机最优控制器,得到相应的最优性能指标的表达形式,并证明了相应的随机最优控制器可使网络控制系统均方指数稳定.最后以网络控制下的倒立摆为对象进行仿真研究,仿真结果表明该方法的正确性和有效性.     

带马尔科夫跳和乘积噪声的随机系统的最优控制

讨论了N个选手随机系统的最优控制问题. 设计了无限时间的带有马尔科夫跳和乘积噪声的随机系统的Pareto最优控制器. 应用推广的Lyapunov方法和解随机Riccati代数方程得到了系统的Pareto最优解, 证明了最优控制器是稳定的反馈控制器, 以及对应于最优控制器的反馈增益中的随机Riccati代数方程的解是最小解.     

线性离散奇异系统的不定二次最优控制问题: Krein空间方法

The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter. Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.     

Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise

This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.     

Infinite horizon linear quadratic differential games for discrete-time stochastic systems

This paper deals with the infinite horizon linear quadratic(LQ)differential games for discrete-time stochastic systems with both state and control dependent noise.The Popov-Belevitch-Hautus(PBH)criteria for exact observability and exact detectability of discrete-time stochastic systems are presented.By means of them,we give the optimal strategies (Nash equilibrium strategies)and the optimal cost values for infinite horizon stochastic differential games.It indicates that the infinite horizon LQ stochastic differential games are associated with four coupled matrix-valued equations.Furthermore, an iterative algorithm is proposed to solve the four coupled equations.Finally,an example is given to demonstrate our results.     

Infinite horizon linear quadratic optimal control for discrete‐time stochastic systems

This paper is concerned with the infinite horizon linear quadratic optimal control for discrete‐time stochastic systems with both state and control‐dependent noise. Under assumptions of stabilization and exact observability, it is shown that the optimal control law and optimal value exist, and the properties of the associated discrete generalized algebraic Riccati equation (GARE) are also discussed. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类双线性随机系统M量测不定LQ控制

研究了带有乘性噪声和受扰动观测的离散时间随机系统不定线性二次(Linear quadratic, LQ) 最优输出反馈控制问题. 对此类问题而言,二次成本函数的加权矩阵不定号,并且最优控制具有对偶效果.为在最优性和计算复杂度间 进行折衷,本文采用了一种M量测反馈控制设计方法.基于动态规划方法,将未来的测量结合到当前控制 计算当中的M量测反馈控制可以通过倒向求解一类与原系统维数相同的广义差分Riccati方程(Generalized difference Riccati equation, GDRE)得到.仿真结果 表明本文提出的算法与目前普遍采用的确定等价性方法相比具有优越性.     

Linear matrix inequalities, Riccati equations, and indefinitestochastic linear quadratic controls

This paper deals with an optimal stochastic linear-quadratic (LQ) control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables. In contrast to the deterministic case, we allow the control and state weighting matrices in the cost functional to be indefinite. This leads to an indefinite LQ problem, which may still be well posed due to the deep nature of uncertainty involved. The problem gives rise to a stochastic algebraic Riccati equation (SARE), which is, however, fundamentally different from the classical algebraic Riccati equation as a result of the indefinite nature of the LQ problem. To analyze the SARE, we introduce linear matrix inequalities (LMIs) whose feasibility is shown to be equivalent to the solvability of the SARE. Moreover, we develop a computational approach to the SARE via a semi-definite programming associated with the LMIs. Finally, numerical experiments are reported to illustrate the proposed approach     

基于风险价值约束的动态均值-方差投资组合的研究

研究了基于风险价值约束的动态均值-方差项目投资组合的数学模型,该模型是控制带约束的随机线性二次型（LQ）控制问题.在讨论该随机LQ控制问题的解之后,给出投资组合动态数学模型对应的随机哈密顿-雅克比-贝尔曼方程的解,得出了有效边界和最佳策略,讨论了风险价值约束的影响.最后,针对某油田勘探开发项目的实际情况,应用上述结论求出该实例的解,并讨论了风险价值约束发挥的作用.     

Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon

This paper is concerned with a stochastic linear-quadratic (LQ) problem in an infinite time horizon with multiplicative noises both in the state and the control. A distinctive feature of the problem under consideration is that the cost weighting matrices for the state and the control are allowed to be indefinite. A new type of algebraic Riccati equation – called a generalized algebraic Riccati equation (GARE) – is introduced which involves a matrix pseudo-inverse and two additional algebraic equality/inequality constraints. It is then shown that the well-posedness of the indefinite LQ problem is equivalent to a linear matrix inequality (LMI) condition, whereas the attainability of the LQ problem is equivalent to the existence of a “stabilizing solution” to the GARE. Moreover, all possible optimal controls are identified via the solution to the GARE. Finally, it is proved that the solution to the GARE can be obtained via solving a convex optimization problem called semidefinite programming.