Analysis of problems on probabilistically optimal control of linear systems with discrete time (Q1316255)

Three types of problems on probabilistically optimal control of linear autonomous systems in the presence of uncertainty with discrete time and polyhedral constraints are analyzed. The first problem concerns optimal control with random initial state; the second, optimal control in the presence of additive random noise; the third, optimal control with a noise of a different type. The conditions are formulated and proved for existence of solutions of these problems which are independent of the distribution of the random variables.