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. The uncertainty in the 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 in terms of 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.