An adaptive controller for uncertain nonlinear systems with multiple time delays

Abstract

This paper leverages the predictor-based model reference adaptive control (PMRAC) architecture to develop an adaptive compensation scheme for uncertain nonlinear systems with multiple input and state delays. The controller is composed of a state predictor, an auxiliary system, and adaptive laws. The adaptive laws are designed through a Lyapunov function in such a way that the predictor state and the auxiliary state asymptotically converge to the system state given that a stability condition holds. Satisfying this delay-dependent stability condition, formulated in the form of a linear matrix inequality (LMI), also ensures the input-to-state stability of the closed-loop control system. Numerical case studies with a standard F-16 aircraft model are discussed to illustrate the efficacy of the proposed control framework.