Adaptive predictive control for time-varying stochastic systems

In this paper we present an optimal adaptive predictive controller (APC) for general linear time-varying stochastic systems. It is shown that the controller can be explicitly computed for arbitrary prediction horizons. However, for larger predictions horizons than say 3-4, the expression will be quite complicated, due to the need to compute higher order moments of stochastic vectors. We show the explicit expression for the one- and two-step controllers. We also discuss the possibility to use the APC as a suboptimal solution to the dual control problem.