Towards Dual MPC

We present a novel approach to performing closed-loop system identification with minimal deterioration of output regulation. The adaptive control algorithm excites the system to improve model identification but does not disturb the plant when parameter estimates are good, so that a balance between output regulation and excitation for identification is found without requiring persistent excitation. The formulation of the problem is such that standard state-of-the-art optimization codes can be used in the controller rather than techniques like stochastic dynamic programming, which may lead to a more complicated control design. The approach is based on model predictive control (MPC) and can be implemented with only minor modifications to an existing MPC algorithm. The method is illustrated on an example system where the input gain is unknown, and is shown to intelligently excite the system only when the parameter estimates are uncertain. We also show how a slight increase in system excitation by the controller can greatly enhance parameter identification with minimal effect on the system output.