Non-myopic Innovations Dual Controller

Optimal control of a linear discrete stochastic state space system with uncertain parameters is treated. The problem statement leads to design of a dual controllers. Unfortunately, except for few special cases it is not possible to obtain closed-form solution for such controller. Many suboptimal approaches were proposed to overcome this obstacle, however, mostly they restrict the control horizon only to one step ahead and thus suffer from myopic behaviour. This paper presents technique that makes it possible to derive suboptimal dual controller in closed-form for arbitrarily long control horizon. The design of the presented controller is based on the innovations dual controller and use of the partial certainty equivalence principle. The proposed dual controller is compared to other non-dual controllers in a numerical example.