Adaptive regulation in bimodal linear systems

This paper considers an adaptive regulation problem for switched bimodal linear systems where it is desired to achieve regulation against unknown sinusoidal exogenous inputs representing disturbance or reference signals. Switching among plant models as well as among disturbance and reference signals is defined according to a performance variable. The design of the proposed adaptive regulators involves two main steps. First, a set of observer‐based Q‐parameterized stabilizing controllers for the switched system is constructed, and a sufficient regulation condition for the resulting switched closed‐loop system is presented. Second, an adaptation algorithm is developed to tune the Q parameter in the expression of the parameterized controller and make it converge to the desired Q parameter that guarantees regulation for the switched system. The tuning of the Q parameter is performed to compensate for the lack of information on the properties of the sinusoidal exogenous inputs. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.