Discrete-time Adaptive Mixing Control with Stability-preserving Interpolation: the Output Regulation Problem

The main result of this paper is the extension of the Adaptive Mixing Control (AMC) approach, to the discrete-time setting. The stability and robustness properties of the adaptive mixing control scheme are analyzed. It is shown that in the ideal case, when no disturbances or unmodelled dynamics are present, the regulation error converges to zero; otherwise the mean-square regulation error is of the order of the modeling error provided the unmodelled dynamics satisfy a norm-bound condition. A stability preserving method for the synthesis of the multicontroller is also proposed, by interpolating a family of precomputed candidate controllers. A two carts system is used to show, via simulations, the effectiveness of the method.