Min-max feedback control of uncertain systems

In general a saddle point solution does not exist to the problem of min-max control for a system with uncertain parameters. By introduction of mixed strategies over the uncertainty set a min-max theorem is proven enabling interchange of the order of minimization and maximization without assumption of a saddle point solution. The min-max feedback control can then be characterized in terms of the solution of an integro-differential equation which is the analog of the Hamilton Jacobi equation obtained in the deterministic case. Consideration of the linear system quadratic criterion case leads to the usual form of linear feedback, however determination of the feedback matrix requires solution of coupled systems of Riccati differential equations. The equations obtained are also valid for the random parameter case.