Model Reference Adaptive Control of Almost Periodic Piecewise Linear Systems with Variable Periods and Disturbance Input

This paper studies a class of almost periodic piecewise linear systems (APPLSs), in which each cycle length (or period) is bounded yet subject to variations, making them more complex than strict periodic systems. A model reference adaptive control (MRAC) approach is developed, where the reference model is also constructed as an APPLS. Novel stability criteria are established for APPLSs, including a necessary and sufficient stability criterion for the special case of APPLSs with commuting subsystem matrices, and sufficient conditions for general cases to facilitate MRAC design. An identification technique is proposed to determine the number of subintervals in the controlled system, offering a more practical and efficient solution than existing methods. Based on that, an adaptive gain update law is provided under the formulated reference model, enabling robust adaptive control for APPLSs with variable periods and external disturbances. The proposed MRAC approach ensures state tracking of the controlled system to the desired trajectory and guarantees convergence of the tracking error. The effectiveness of the proposed approach is demonstrated through simulations based on a circuit system.