Combined MRAC for Unknown MIMO LTI Systems With Parameter Convergence

Abstract

This work proposes a novel combined model reference adaptive controller (MRAC) for unknown multi input multi output (MIMO) LTI systems with guaranteed parameter convergence. An online plant-parameter identification method is developed in conjunction with a direct control-parameter update law to ensure exponential convergence (after a tunable finite time) of tracking error as well as plant and control-parameter estimation errors to zero. Unlike the restrictive persistence of excitation (PE) condition required in classical MRAC approaches, this method guarantees parameter convergence by imposing a significantly milder initial excitation condition on the relevant signals. The introduction of a low-pass filter obviates the need for state derivative knowledge, whereas, the novel inclusion of an integral-like update in the plant-parameter estimation law overcomes the requirement of the restrictive PE condition. As far as the authors are aware, this is the first work on MRAC for MIMO linear time invariant (LTI) systems, which guarantees exponential convergence of the error dynamics without requiring the PE condition as well as the structural knowledge of the system matrices.