An optimal control formulation for dual control problems

A systematic procedure is introduced, which allows converting a stochastic control problem involving a tradeoff between minimizing control effort and maximizing estimation performance into a deterministic two-point boundary value problem. The proposed approach can be applied to calculating control inputs for a system whose observability is affected by the system´s state trajectory due to nonlinear coupling between estimation and control, called the dual effect. A parameter estimation problem is considered in order to demonstrate the feasibility of the proposed approach. The parameter estimation problem is formulated as a nonlinear two-point boundary problem and then solved numerically using a collocation method.