连续系统观测时滞的 H∞控制

研究一类连续系统观测时滞的H∞控制问题．基于Krein空间的重组新息分析方法，给出了观测时滞系统H∞输出反馈控制问题的解存在的充要条件．H∞输出反馈控制器依赖于一个倒向Riccati方程和一个正向Riccati方程的解．与传统的方法相比，重组新息分析方法不需要增广系统的维数。从而减少了计算量．仿真例子验证了该方法的有效性．     

具Frobenius有界不确定性广义系统的鲁棒稳定性

研究了具Frobenius有界不确定性广义系统的稳定与鲁棒镇定问题. 通过对代数Riccati不等式或代数Riccati方程的求解, 获得了不确定广义系统广义二次稳定的充要条件, 使得对所有容许的不确定参数, 系统是稳定, 正则和无脉冲. 而且, 根据一类矩阵方程, 构造了使不确定广义系统鲁棒镇定的状态反馈控制器的设计方法. 实例说明了上述方法的有效性.     

一类不确定动态时滞系统的无记忆鲁棒镇定控制

针对状态和控制均存在滞后,同时具有未知且有界的一类时变不确定线性时滞系 统,提出了一种无记忆鲁棒镇定控制器设计算法.给出了闭环系统二次稳定的充分条件,并利 用一等价线性时不变系统的H∞标准问题综合方法来构造出所需的线性状态反馈控制律,即 可通过求解一代数Riccati型方程来求得控制律静态增益阵,从而保证了解的存在性和可解 性.     

基于策略迭代算法的连续时间线性Markov跳变系统非零和微分反馈Nash控制

针对一类连续时间线性Markov跳变系统,本文提出了一种新的策略迭代算法用于求解系统的非零和微分反馈Nash控制问题.通过求解耦合的数值迭代解,以获得具有线性动力学特性和无限时域二次成本的双层非零和微分策略的Nash均衡解.在每一个策略层,采用策略迭代算法来计算与每一组给定的反馈控制策略相关联的最小无限时域值函数.然后,通过子系统分解将Markov跳变系统分解为N个并行的子系统,并将该算法应用于跳变系统.本文提出的策略迭代算法可以很容易求解非零和微分策略所对应的耦合代数Riccati方程,且对高维系统有效.最后通过仿真示例证明了本文设计方法的有效性和可行性.     

关于不确定对称组合系统的稳定化

研究不确定对称组合系统的二次稳定化问题,给出这类系统可二次稳定的一些充分条件 及计算反馈控制律的方法.这些条件的检验和反馈控制律的计算都由两个低阶系统关于相应 问题的求解来完成.     

无限维最优控制问题中的Riccati方程

本文讨论分布参数系统二次最优控制问题中出现的一类算子值Riccati方程。在很一般的条件下证明了Riccati方程与一个线性Fredholm积分方程的等价性,为Riccati方程的研究提供了一条新的途径。在此基础上证明了Riccati方程的解的存在唯一性,并给出了计算无限维Riccati方程的一个有限维逼近公式。     

不确定离散时间系统鲁棒稳定控制

根据Lyapunov稳定性定理,针对不确定离散时间系统鲁棒稳定状态反馈控制问题,提出 一种方法,即通过不确定矩阵秩1分解,计算加权矩阵,沿用线性最优调节器问题的Riccati代 数方程,设计鲁棒稳定调节器,并讨论了控制矩阵的不确定程度与鲁棒稳定调节器的存在性关 系问题.     

线性不确定中立型时滞系统的鲁棒二次性能

研究具有非匹配条件的范数有界线性不确定中立型时滞系统的稳定和二次性能控制问题．基于Lyapunov方法，提出了系统鲁棒渐近稳定并满足给定二次性能指标的时滞相关型条件，该条件等价干线性矩阵不等式(LMI)可解性问题，并根据LMI的可行解，构造了状态反馈控制器设计方法．     

不确定脉冲系统的鲁棒H∞控制

首次提出并研究了不确定脉冲系统的鲁棒H∞控制问题.基于代数Riccati方程正定矩阵解的存在性,建立了不确定脉冲闭环系统具有鲁棒H∞特性的充分性准则,同时给出了相应的状态反馈控制设计方法,并用数值例子说明了所得结果的有效性.     

饱和系统鲁棒控制及其在飞行控制中的应用

给出一种饱和系统鲁棒稳定性的分析和设计方法.通过对不确定系统的H∞优化过程的分析,并根据其反馈控制原理,按全部和部分输入超过限制分别考虑不同指标下的优化计算问题,得到了输入受限制条件下的3种Riccati方程.飞行控制器设计和仿真结果表明,采用该方法可给出满意的控制效果.     

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.     

Separation theorem for nonlinear measurements

General solutions to the optimal stochastic control problem, or the combined estimation and control problem, are extremely difficult to compute since dynamic programming is required. However, if the system is linear, if the measurements are linear, and if the cost is quadratic, then the optimal stochastic controller is separated into 1) a filter to generate the conditional mean of the state, and 2) the optimum (linear) controller that results when all uncertainties are neglected. By altering the system configuration a new separation theorem is derived for arbitrary nonlinear measurements, discrete-time linear systems, and a quadratic cost. If a feedback loop is placed around the nonlinear measurement device (e.g., an analog-to-digital converter), then the stochastic control can be found without dynamic programming and is computed by cascading a nonlinear filter and the optimum (linear) controller. The primary advantage is the significant saving in computation. The performance of this new system configuration relative to the system without feedback depends on the nonlinearity, and it is not necessarily superior. A numerical example is presented.     

约束随机线性二次最优控制的研究

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.     

Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems

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.     

Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems

In this paper we consider the stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations. For the case in which the quadratic-term matrices are non-negative, this necessary and sufficient condition can be written in a more explicit way. The results are applied to a problem of portfolio optimization.     

Stochastic optimal linear discrete-time feedback control system using available measurements

The stochastic optimal feedback control of linear discrete-time systems with partially observable parameters is synthesized. A quadratic performance criterion is used with discrete noisy measurements. The structure of the regulator is given and the optimal solution is reduced to a two-point boundary-value problem. Comments on the numerical solution schemes are included.     

On a general optimal algorithm for multirate output feedbackcontrollers for linear stochastic periodic systems

A modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed. By combining the discrete-time linear quadratic regulation (LQR) control problem and the discrete-time stochastic linear quadratic regulation (SLQR) control problem to obtain an extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages of the optimal transient response of the LQR control problem and the optimal steady-state regulation of the SLQR control problem. In general, the solution of this algorithm is obtained by solving a set of coupled matrix equations. Special cases for which the coupled matrix equations can be reduced to a discrete-time algebraic Riccati equation are discussed. A reducable case is the optimal algorithm derived by H.M. Al-Rahmani and G.F. Franklin (1990), where the system has complete state information and the discrete-time quadratic performance index is transformed from a continuous-time one     

带有随机跳跃干扰的线性二次随机最优控制问题

给出一类布朗运动和泊松过程混合驱动的正倒向随机微分方程解的存在唯一性结果, 应用这一结果研究带有随机跳跃干扰的线性二次随机最优控制问题,并得到最优控制的显式形 式,可以证明最优控制是唯一的.然后,引入和研究一类推广的黎卡提方程系统,讨论该方程系统 的可解性并由该方程的解得到带有随机跳跃干扰的线性二次随机最优控制问题最优的线性反馈.     

Characterizing all optimal controls for an indefinite stochasticlinear quadratic control problem

This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite-time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation is introduced and all the possible optimal controls, including the ones in state feedback form, of the underlying LQ problem are explicitly obtained in terms of the two Riccati equations