Probabilistic Approach to Analysis and Synthesis of Control Systems

从理论和应用两个方面研究了控制系统分析与综合的概率方法。提出了一种序贯随机化算法，提出了一种基于最大体积椭球中心的概率割平面技术作为其有效的更新规则。利用控制问题的结构，对更新规则进行了进一步修改，提高了算法的收敛速度。利用概率方法，给出了一种新的随机逼近停止准则。

Probabilistic approach to analysis and synthesis of control systems was investigated from both of theoretical and application viewpoints. A sequential randomized algorithm was developed, where a probabilistic cutting plane technique based on maximal volume ellipsoid center was proposed as its effective update rule. The update rule was further modified for improving its convergence, where the structure of control problems was employed. A new stopping rule for stochastic approximation was also developed via probabilistic approach.