Probabilistic Approach to Analysis and Synthesis of Control Systems

从理论和应用两方面研究了控制系统分析与综合的概率方法。提出了一种序列随机化算法，提出了基于最大体积椭球中心的概率切割平面技术作为其有效的更新规则。为了提高其收敛性，对更新规则进行了进一步的修改，其中采用了控制问题的结构。利用概率方法提出了一种新的随机逼近停止规则。

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.