Analysis and Synthesis of Control Systems via Randomized Algorithms

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Randomized algorithms are recently recognized as viable tools for control systems design. In fact, in this research field, more and more complex problems arise, and probabilistic approach gives efficient algorithms to solve these problems. For example, robust optimal control is recast as a global optimization in general, where the size of the problem is quite large due to uncertainty contained in systems. Thus, to solve it within a reasonable time is very difficult via deterministic algorithms, which is known as the curse of dimensionality. On the other hand, algorithms based on random sampling of uncertainties enables us to obtain a probabilistic solution, without heavy computational effort, though a certain risk-level should be accepted.In this research project, analysis and synthesis of control systems via randomized algorithms are further investigated, which leads to a novel framework of control systems theory. In particular the following important results are obtained.(i) Randomized Algorithms for Analysis and Synthesis of Control Systems: Specific randomized algorithms are developed for probabilistic design of guaranteed cost regulator, fixed order controller, and switched systems.(ii) Characterizations of Randomized Algorithms in Control: Fundamental procedures of randomized algorithms are investigated for typical control problems with multiple constraints and/or nonconvex constraints, in particular, constraints described ed by a logical sum of convex constraints.(iii) Related Applications: The approach is further applied to a robust identification, where the size of the membership set is estimated probabilistically in the presence of disturbance and parameter uncertainty.