Lyapunov Analysis of Least Squares Based Direct Adaptive Control

Abstract

Adaptive control studies mostly utilize gradient based parameter estimators for convenience in Lyapunov analysis based constructive design. However, simulations and real-time experiments reveal that, compared to gradient based online parameter identifiers, least squares (LS) based parameter identifiers, with proper selection of design parameters, exhibit better transient performance from the aspects of speed of convergence and robustness to measurement noise. The existing literature on LS based adaptive control mostly follow the indirect adaptive control approach as opposed to the direct one, because of the difficulty in integrating an LS based adaptive law within the direct approaches starting with a certain Lyapunov-like cost function to be driven to (a neighborhood) of zero. In this paper, a formal constructive analysis framework for integration of recursive LS (RLS) based estimation to direct adaptive control is proposed following the typical steps for gradient adaptive law based direct model reference adaptive control, but constructing a new Lyapunov-like function for the analysis. Adaptive cruise control simulation application is studied in Matlab/Simulink and CarSim.