Adaptive Control with Memory for Switched Linear Systems

This work proposes a switched model reference adaptive control (S-MRAC) architecture for a multi-input multi-output (MIMO) switched linear system with memory for enhanced learning. A salient feature of the proposed method that separates it from most previous results is the use of memory that store the estimator states at switching and facilitate parameter learning during both active and inactive phases of a subsystem, thereby improving the tracking performance of the overall switched system. Specifically, the learning experience from the previous active duration of a subsystem is retained in the memory and reused when the subsystem is inactive and when the subsystem becomes active again. Parameter convergence is shown based on an intermittent initial excitation (IIE), which is significantly relaxed than the classical persistence of excitation (PE) condition. A common Lyapunov function is considered to ensure closed-loop stability with S-MRAC. Further, under IIE, the exponential stability of tracking and parameter estimation error dynamics are guaranteed.