模糊系统的Bang-Bang最优控制

系统受到模糊信息干扰时可由模糊微分方程描述，基于模糊微分方程的最优控制问题是模糊最优控制问题，该类问题由申请者在前一基金项目中提出并研究。在最有控制理论中，时间最优控制问题是一类非常重要的Bang-Bang控制问题。即当输入控制变量有界时，最优控制只在边界上取得。所以研究模糊系统的Bang-Bang最优控制问题在理论及应用上都是极其有意义的，该工作是前一项目研究的深入和继续。本项目主要研究：有限（无限）时间内模糊仿射系统的Bang-Bang正常（奇异）最优控制问题，模糊开关系统Bang-Bang最优控制问题，基于模糊系统的首次通过时间Bang-Bang控制问题，时间延迟模糊系统的Bang-Bang最优控制问题，以及Bang-Bang最优控制在讨论模糊微分对策的Nash平衡点与鞍点问题中的应用。本项目将丰富和发展模糊最优控制的研究，较为系统地形成模糊系统Bang-Bang最优控制理论。

A system disturbed by fuzzy information may be described by a fuzzy differential equation. An optimal control problem subject to a fuzzy differential equation is called a fuzzy optimal control problem, which was introduced by the author in a previous project supported by the NSFC. Time optimal control problem in optimal control theory is an important Bang-Bang one in practice. That is, optimal control attains at the boundary of a control variable if it is bounded. Therefore, it is very significative to study Bang-Bang optimal control problem subject to fuzzy system not only in theory but in applications. We will deal with some key problems on fuzzy Bang-Bang optimal control in this project, which is an in-depth and continuous work of our previous project. The contents of our study include Bang-Bang control normal (or Singular) problems of fuzzy affine systems in finite (or infinite) time, Bang-Bang optimal control problems subject to switched fuzzy systems, Bang-Bang optimal control problems of first passage time subject to fuzzy systems, Bang-Bang optimal control problems subject to fuzzy systems with time-delay, and Nash-equilibrium and saddle point problems of fuzzy differential game systems, which are studied by Bang-Bang control method. The investigation in this project will enrich and develop the study of fuzzy optimal control. It is a hope systematically to form the theory of Bang-Bang optimal control for fuzzy systems.