Dual control of linear stochastic systems with unknown parameters

Closed-loop control of linear stochastic control systems with unknown parameters is studied using a dual-control approach. At each state, the cost functional associated with the system objective is decomposed into a certainty equivalence cost and a dual cost. The dual cost is appropriately expressed in terms of filter variables in algebraic form, and it appears to be a sum of dual costs of each future state. It is shown that the dual cost at the next immediate stage dominates the future uncertainties, and the resulting optimal control problem is solved in closed form using this property.<>