Singular perturbation methods in the synthesis of feedback-control laws for eigenvalue-assignment in multivariable linear systems

In this paper, a computationally attractive method for the synthesis of feedback -control laws which effect asymptotic eigenvalue-assignment in plants containing ‘ parasitic ’ elements is developed by invoking certain results from the singular perturbation theory of multivariate linear systems. It is demonstrated that the synthesis of feedback-control laws which effect asymptotic eigenvalue assignment in (n+m)th-order plants can be reduced to the separate determination of control laws for plants of mth and nth orders, respectively. The salient features of the method are illustrated by synthesizing a feedback-control law for a fourth-order plant.     

非部分嵌套信息结构的LQG动态队决策问题的可解性（II）*

本文讨论非嵌套信息结构的递阶队决策问题和控制均享信息结构的LQG分散控制问题,文中首先证明这两类问题的信息结构都是“部分控制嵌入”的,进而给出最优策略(或控制)存在的充要条件和当此条件成立时最优策略(或控制)的表达式。     

Equivalence condition of optimal control problems†

Two optimal control problems which have the same optimal feedback control laws and identical minimum costs are said to be equivalent. The conditions for the equivalence of two optimal control problems have been presented by other authors, but it seems that the equivalence conditions given by other authors are not complete. In this paper, a necessary and sufficient condition for the equivalence classes is derived.     

一类具有状态反馈NCS的H∞优化控制

研究一类网络控制系统(NCS)的H∞优化控制问题.状态反馈是兼顾系统性能和敏感性的最有效的控制方式,因此,针对一类不确定时延和有限能量干扰输入的状态反馈NCS,将其建模为不确定的线性时滞系统,并利用Lyapunov理论和线性矩阵不等式(LMI)研究H∞优化控制问题.首先给出NCS的鲁棒稳定的充分条件;然后给出NCS状态反馈次优和最优H;∞控制律的设计方法.仿真结果表明了该方法的可行性和有效性.

Abstract：

The H∞ optimal control problems of a class of networked control systems(NCS) is studied. The statefeedback is the most effective control mode, which combines system function and sensibility. Therefore, a class of state-feedback NCS with uncertain time-delay and limited energy disturbance input is modeled as the uncertain linear time-delay system. Then by using the Lyapunov theory and LMI, the problems about the H∞ optimal control are researched. The sufficient condition is first given for the robust stability of networked control system, and then the design methods of NCS state-feedback suboptimum and optimum H∞ control laws are obtained consequently. The simulation results show the feasibility and effectiveness of the results.     

Decentralized,stochastic control for a static LQ problem

An original problem statement for the optimal control laws design is presented. A large scale system composed of M linear static subsystems with an interaction and quadratic performance index is considered. A two-level hierarchical control structure is assumed, in which a coordinator and local controllers have access to different information. The so-called elastic constraint (Gessing 1985) is used for coordination. For the problem the possibility of partial decomposition of calculations and a decentralization of the control, as well as an analytical form of the optimal laws are obtained. The influence of the particular subsystem on the control quality is investigated.     

具有不确定Wiener噪声随机非线性系统的自适应逆最优控制

针对一类具有不确定Wiener噪声扰动和未知定常参数的随机非线性系统,采用随 机微分方程描述系统,基于Backstepping算法,利用随机控制Lyapunov函数,研究了自适 应逆最优控制问题的可解定理,系统地给出了全局依概率渐近稳定和自适应逆最优控制策略 的设计方法.这种方法可同时获得控制律和自适应律,仿真结果表明该控制算法的有效性.     

基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

严格反馈随机非线性系统的自适应逆最优控制

讨论了自适应逆最优控制问题可解定理，基于Ito微分规则和Backstepping方法，给出了具有标准Wiener噪声扰动和未知定常参数的严格反馈随机非线性系统的全局依概率渐近稳定和自适应逆最优控制策略的设计方法，该方法可同时获得控制律和自适应律。仿真结果表明了控制算法的有效性。     

Optimal digital feedback control systems counting computation time of control laws

Since microprocessors are easily obtained, multivariable control theory can be applied to many practical control problems, for example control of robots. However, when the time constant of the plant is short and the dynamic order of the plant is high, the time delay due to the computation time of the control law cannot be neglected. In this paper, the author proposes design methods for linear optimal regulators and linear optimal servosystems in which the delay arising from the computation time of the processors is counted properly. From the theoretical point of view, the results are interesting since all the control laws derived in this paper are obtained using only conventional results of optimal regulator theory.     

Parallel Optimal Control for Weakly Coupled Nonlinear Systems Using Successive Galerkin Approximation

This technical note presents a new algorithm for the closed-loop parallel optimal control of weakly coupled nonlinear systems with respect to performance criteria using the successive Galerkin approximation (SGA). By using the weak coupling theory, the optimal control law can be obtained from two reduced-order optimal control problems in parallel, but the resulting problem is difficult to solve for nonlinear systems. In order to overcome the difficulties inherent in the nonlinear optimal control problem, the parallel optimal control laws are constructed in terms of the approximated solutions to two independent Hamilton-Jacobi-Bellman equations using the SGA method. One of the purposes of this note is to design the closed-loop parallel optimal control law for the weakly coupled nonlinear systems using the SGA method. The second is to reduce the computational complexity when the SGA method is applied to the high-order weakly coupled systems.