On the optimizing-adaptive control problem

The optimizing-adaptive control problem arises in applications where the desired behavior is not specified explicitly, but instead, an objective function of the plant behavior and the unknown plant itself is to be optimized. In these cases, the control task involves the explicit determination of the optimal behavior and the control action to achieve that behavior. The difficulty with this problem is that it involves a conflict between identification and optimisation on the one hand, and control on the other. In this paper, we study this problem in the context of the intelligent exercise machine application. We propose two related excitation supervisors which switch between an excitation phase and a control phase, based on an internally generated optimality error signal.