Globally exponentially stable adaptive control of switched linear systems: A memory augmented approach

Abstract

This paper introduces a switched model reference adaptive control (S-MRAC) architecture for uncertain switched multi-input multi-output (MIMO) linear time-invariant (LTI) systems with a switched reference model. One distinctive aspect of the suggested method is the use of memory to augment the parameter estimator, leading to parameter learning even during inactive periods of the subsystems. Together with an intermittently initial excitation (IIE) condition, the memory augmentation-based approach guarantees exponential stability of the tracking and parameter estimation error systems. An online parameter estimator with a dual-layer low-pass filter and a bank of memory filters is at the heart of the proposed architecture. The addition of the $\sigma -$ modification term in adaptive law facilitates the computation of a unified expression of dwell time that is valid for both excitation and non-excitation scenarios. Further, the dwell time expression is tunable and thus, allows for fast switching. Simulation results are showcased to confirm the efficacy of the suggested outcome.