On the stabilizing control of a class of nonlinear stochastic systems

A class of discrete-time nonlinear stochastic control systems is considered. By using previously established proper mean-square stabilizability and observability conditions, the author shows the relationship between the stabilization conditions for the moving- and infinite-horizon quadratic optimal controllers. In this way, the existence of the mean-square stabilizing infinite-horizon controller implies the existence of a multitude of moving finite-horizon controllers with different horizon lengths with the same stability property. The results allow the use of finite-stage solutions of a Riccati-like matrix equation in a stabilizing control design which can drastically reduce the computation time