Finite Horizon Minimax Optimal Control of Stochastic Partially Observed Time Varying Uncertain Systems

We consider a linear-quadratic problem of minimax optimal control for stochastic uncertain control systems with output measurement. Uncertainty in a system satisfies a stochastic integral quadratic constraint. To convert the constrained optimization problem into an unconstrained one, a special S-procedure is applied. The resulting unconstrained game-type optimization problem is then converted into a risk sensitive stochastic control problem with an exponential-of-integral cost functional. This is achieved via a certain duality relation between stochastic dynamic games and risk sensitive stochastic control. The solution of the risk sensitive stochastic control problem based on a pair of differential matrix Riccati equations is then used to establish a minimax optimal control law for the original uncertain system with uncertainty subject to the stochastic integral quadratic constraint.