Robust adaptive control using multiple models, switching and tuning

The supervisory control problem is analysed as an online robust design problem using switching to select the relevant models for designing the control law. The proposed supervisory control algorithm is based on the integration of concepts used in supervisory adaptive control, robust control and receding horizon control. It involves a two-stage adaptive control algorithm: (i) the identification of a time-varying set of models P-L(k), from the set of admissible models P-L, that explains the input-output behaviour of the system, followed by (ii) the design of the control law using a parametric linear optimisation problem. The authors show that under the proposed supervisory control algorithm, the system output remains bounded for any bounded disturbance. The use of superstability concepts, together with certain assumptions on P-L, allows us to establish overall performance and robust stability guarantees for the supervisory scheme and to include constrains in the closed-loop variables as well as in the controller structure. The relevant features of the proposed control algorithm are demonstrated in a numerical simulation.