Comparison of several adaptive controllers according to their robustness metrics

This paper compares the performance and the robustness of several linear adaptive controllers using a linear system with time-varying disturbance in the presence of measurement noise. For the purpose of comparison we select the direct and indirect model reference adaptive controller (MRAC), the direct MRAC with σ-modification, and the ℒ ₁ adaptive controller. Using tools from linear systems theory we compute the stability margins of these controllers and examine the performance of these closed-loop systems via analysis of several important transfer functions between the system's inputs and outputs. In this paper we also investigate some properties of the piecewise constant update laws, introduced in recent ℒ ₁ papers, and provide an interpretation to draw some insights. Finally, we validate the conclusions in simulations.