Optimal Control For Nonlinear Large-Scale Systems: A Successive Approximation Approach

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.