Randomized Algorithms for Uncertain Complex Dynamical Systems Design

In this paper we consider the problem of optimal design of an uncertain discrete time dynamical system. We consider two types of performance criteria, corresponding to an apriori equilibrium measure and asymptotic output measure, respectively, that result in two different optimal design methods. However, these two measures are difficult to obtain analytically for most uncertain complex dynamical systems. In order to derive the optimal controller numerically, we apply randomized algorithms for average performance synthesis to approximate the optimal solution. Results from statistical learning theory, providing the relationship between the sample complexity and the approximation error, show that the obtained design methodology is an efficient algorithm for uncertain system design.