LQ-Stochastic Multimodel Control

Abstract

The main goal of this chapter is to illustrate the possibilities of the MP approach for a class of Min-Max Control Problems for uncertain systems described by a system of linear stochastic differential equations with a controlled drift and diffusion terms and unknown parameters within a given finite set. The problem belongs to the class of Min-Max Optimization Problems on a fixed finite horizon (where the cost function contains both an integral and a terminal term) and on an infinite one (the loss function is a time-averaged functional). The solution is based on the results on the Robust Stochastic Maximum Principle (RSMP) derived in the previous chapter. The construction of the Min-Max LQ optimal controller is shown to be reduced to a finite-dimensional optimization problem related to the solution of the Riccati equation parametrized by the weights to be found.