Novel model reference adaptive control laws for improved transient dynamics and guaranteed saturation constraints

• Published in: Journal of the Franklin Institute 2021-08, Vol.358 (12), p.6281-6308
• Main Authors: Anderson, Robert B., Marshall, Julius A., L’Afflitto, Andrea
• Format: Article
• Language: English
• Subjects: Actuators; Adaptive control; Closed loop systems; Constraint modelling; Control theory; Convergence; Errors; Feedback control; Iterative methods; Liapunov functions; Model reference adaptive control; Nonlinear systems; Saturation; Steering; Studies; Tracking control; Tracking control systems; Tracking errors; Trajectory control
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.06.020

In classical model reference adaptive control (MRAC), the adaptive rates must be tuned to meet multiple competing objectives. Large adaptive rates guarantee rapid convergence of the trajectory tracking error to zero. However, large adaptive rates may also induce saturation of the actuators and excessive overshoots of the closed-loop system’s trajectory tracking error. Conversely, low adaptive rates may produce unsatisfactory trajectory tracking performances. To overcome these limitations, in the classical MRAC framework, the adaptive rates must be tuned through an iterative process. Alternative approaches require to modify the plant’s reference model or the reference command input. This paper presents the first MRAC laws for nonlinear dynamical systems affected by matched and parametric uncertainties that constrain both the closed-loop system’s trajectory tracking error and the control input at all times within user-defined bounds, and enforce a user-defined rate of convergence on the trajectory tracking error. By applying the proposed MRAC laws, the adaptive rates can be set arbitrarily large and both the plant’s reference model and the reference command input can be chosen arbitrarily. The user-defined rate of convergence of the closed-loop plant’s trajectory is enforced by introducing a user-defined auxiliary reference model, which converges to the trajectory tracking error obtained by applying the classical MRAC laws before its transient dynamics has decayed, and steering the trajectory tracking error to the auxiliary reference model at a rate of convergence that is higher than the rate of convergence of the plant’s reference model. The ability of the proposed MRAC laws to prescribe the performance of the closed-loop system’s trajectory tracking error and control input is guaranteed by barrier Lyapunov functions. Numerical simulations illustrate both the applicability of our theoretical results and their effectiveness compared to other techniques such as prescribed performance control, which allows to constrain both the rate of convergence and the maximum overshoot on the trajectory tracking error of uncertain systems.