Recent Developments in Probabilistic Approaches to Optimal Control Theory

Modeling and control design of modern complex systems entail an appreciable degree of uncertainty due to modeling approximations, noise and tolerances in components, random effects, parametric errors and other changes. Probabilistic approaches to complex control systems often lead to linear ordinary differential/difference equations with multiplicative and additive noise. The characteristics of such systems are different from regular linear quadratic Gaussian systems, the basic difference being the inapplicability of the separation or the certainty equivalence principle. An optimal controller may not exist in some cases, and the optimal filter is of infinite dimension. Control systems with multiplicative and additive noise are presented and new results that extend the existing theory on linear stochastic systems are given.