On the optimal control of discrete-time linear systems with random parameters

This work is concerned with the optimal control of a discrete-time linear system with random parameters. It is assumed that the parameters of the system vary randomly during the process, namely, the parameters constitute sequences of random variables. These random variables are not necessarily independent. An important particular case occurs where there are unknown constant parameters in the system. The measurements of the state of the system contain additive noise. A quadratic function of the state and controller, with appropriate weighting, serves as the criterion function. The solutions for the open-loop controller and the open-loop feedback controller are presented. The method of solution is based on the dynamic programming approach which leads to functional recurrence equations.