Basic Structure and Design of Hybrid Controllers including logic information process

本文的主要研究成果如下：1.建模：提出了一种新的混合系统模型，称之为采样数据分段仿射系统，其中离散切换是根据状态条件在给定的采样时间内执行的，采样时间由数字设备中的编程确定。2.适定性、稳定性、可控性分析：对于分段仿射系统和线性互补系统，定义了解的概念，并给出了易于检验的适定性条件。针对分段线性系统，提出了一种新的基于系统极点的稳定性分析方法。此外，本文还提出了一种分段仿射系统的概率能控性方法，它使我们能够确定更大类混杂系统的能控性。本文导出了一类采样分段仿射系统的最优控制器，并给出了混合控制器的一种基本结构。该方法已应用于CPU的控制问题，数值仿真结果表明，该方法是十分有效的。同时，本文还提出了一种求解混合整数二次规划问题的有效算法，并将最优控制问题转化为混合整数二次规划问题，从而通过本学期的一系列研究，发展了混杂控制系统的基本理论，这对于混杂系统的实际系统控制理论具有重要的意义。

This research have obtained the following results.1.Modelling : We have proposed a new model of hybrid systems, which we call the sampled-data piecewise affine systems, where the discrete switching is executed according to the state condition at a given sampling time fixed by the programming in the digital device.2.Well-posedness, Stability, Controllability analysis : For the class of piecewise affine systems and linear complementarity systems, the solution concept is defined and well-posedness conditions, which can be easily checkable, are derived. A new analytical method of stability based on the poles of the systems has been proposed for the piecewise linear systems. In addition, a probabilistic controllability method of piecewise affine systems has been developed, which allows us to determine the controllability of a larger class of hybrid system3.Optimal control : We have derived an optimal controller for the class of sampled-data piecewise affine systems, and have shown one of the basic structures of the hybrid controller The approach has been applied to the control problem of CPU, and it has been shown that the proposed method is quite useful by numerical simulation, using the CPU model obtained identification. Furthermore, an efficient algorithm to solving the mixed integer quadratic programming problem, to which the optimal control problem is reduced, has been developed.In this way, we have developed the basic theory of hybrid control systems by a series of research in this term, which will be important results toward the practical system control theory of hybrid systems.