State and Input Constrained Model Reference Adaptive Control

TL;DR

This paper introduces a novel model reference adaptive control method that guarantees state and input constraints using barrier Lyapunov functions, ensuring safe, bounded control with asymptotic tracking in multivariable LTI systems.

Contribution

It develops a constrained MRAC framework with a simple saturated control and barrier Lyapunov function, ensuring safety and tracking without restrictive assumptions.

Findings

Guarantees state and input constraints for all time.

Achieves asymptotic convergence of tracking error.

Demonstrates improved performance over standard MRAC in simulations.

Abstract

Satisfaction of state and input constraints is one of the most critical requirements in control engineering applications. In classical model reference adaptive control (MRAC) formulation, although the states and the input remain bounded, the bound is neither user-defined nor known a-priori. In this paper, an MRAC is developed for multivariable linear time-invariant (LTI) plant with user-defined state and input constraints using a simple saturated control design coupled with a barrier Lyapunov function (BLF). Without any restrictive assumptions that may limit practical implementation, the proposed controller guarantees that both the plant state and the control input remain within a user-defined safe set for all time while simultaneously ensuring that the plant state trajectory tracks the reference model trajectory. The controller ensures that all the closed-loop signals remain bounded and the trajectory tracking error converges to zero asymptotically. Simulation results validate the efficacy of the proposed constrained MRAC in terms of better tracking performance and limited control effort compared to the standard MRAC algorithm.