【作者】 孙亮；

【导师】 唐功友；

【作者基本信息】 中国海洋大学 ， 信号与信息处理， 2004， 硕士

【摘要】 随着科学技术的发展，涉及到大系统理论的问题越来越多，如复杂的社会系统、经济系统、生态系统以及大规模过程控制系统等，都属于复杂大系统研究的范畴。由于动态大系统具有“规模庞大，结构复杂，因素众多，功能综合”等特点，用常规的控制理论和方法处理大系统的分析与综合问题一般是不现实的。在复杂的大系统中，非线性现象是普遍存在的。因此，对于非线性大系统的分析，无论在理论上还是在实际应用中都是很有意义的。如何寻求对非线性大系统比较简单的分析方法或控制策略，且又能得到人们期望的结果是摆在大系统研究工作者面前的重要任务。 本文首先简要回顾了大型动力系统和非线性系统的理论的发展过程，综述了有关研究的最新动态及其在自动控制领域的应用情况。通过对当前大系统和非线性系统最优控制的研究现状的分析，本文将逐次逼近法引入到非线性大系统的最优控制研究中。针对一般的非线性互联耦合大系统和一类仿射非线性相似组合大系统提出一种最优控制律设计的逐次逼近方法，首先利用该方法将求解高阶耦合的非线性两点边值问题简化为求解一族解耦的线性两点边值问题序列；然后证明该线性两点边值问题序列的解一致收敛于非线性互联动态大系统的最优控制；最后在最优控制律中截取共态向量序列的有限逼近项得到非线性互联大系统次优控制律。最后经仿真表明，本文提出的非线性大系统最优控制律设计的逐次逼近方法是有效的。更多还原

【Abstract】 Along with the development of technology, more and more problems about large-scale system appear, such as complicated social systems, economic systems , biology systems, large-scale process control systems and so on. While it is hard to deal with the analysis and synthesis of dynamic large-scale systems with general control theory and methods, which are featuring in large scale, complicated structure, numerous factors, integrated functions. On the other hand, complicated large-scale systems always have nonlinear phenomena. Therefore it is meaningful to study nonlinear large-scale systems not only in theory but also in practice. How to analyze and control large-scale systems easily and effectively is faced with the researchers.This paper firstly reviews the development process of large-scale systems theory and nonlinear systems theory, and then summarizes the recent development of related research and the application in field of automatic control. Having analyzed the research status on optimal control of large-scale systems and nonlinear systems, a successive approximation approach is introduced to the field of optimal control of nonlinear large-scale systems. The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach designing optimal controller is proposed with respect to quadratic performance indexes. By using the approach, a high order, coupling, non-linear two-point boundary value problem is transformed to a linear decoupling two-point boundary value problem sequence. We prove that the two-point boundary value problem sequence uniformly converges to the optimal control for non-linear interconnected large-scale system. A suboptimal controllaw is obtained by intercepting a finite iterative result of optimal control law sequence.更多还原