Direct Model Reference Adaptive Control of Periodic Slow Time-Varying Systems with Disturbance Input
Zhuolin Tan, Xiaochen Xie, Jiantai Huang · 2024
This paper investigates the direct model reference adaptive control (MRAC) of periodic systems with slow time-varying dynamics and disturbance input. It is necessary to approximate the periodic slow time-varying system as a periodic piecewise linear system for MRAC. Based on the stability criteria of the periodic piecewise linear reference system,a new sufficient condition in terms of linear matrix inequalities (LMIs) is established to obtain the Lyapunov matrices and design the adaptive update law for the state feedback controller gains. Different from previous studies, where asymptotic tracking was possible only in the presence of a common Lyapunov function for the reference models, the asymptotic tracking in this work is achieved through a periodic time-varying Lyapunov matrix function. A numerical example validates the proposed MRAC scheme, and the effectiveness of the modified approach is discussed.