Model reference switched adaptive control with nonnegative orthant state constraints

Abstract

This work proposes for the first time a model reference adaptive asymptotic tracking method for a class of uncertain switched linear systems with nonnegative orthant state constraints and dwell time switching. In contrast with the state-of-the-art switched adaptive methods, the main characteristic of this method consists in guaranteeing that the systems states remain in the nonnegative orthant of the state space. To achieve asymptotic tracking, an interpolated Lyapunov function is adopted. To ensure the positivity of the system states, a parameter projection law is needed, because some knowledge of the bounds of the parameter estimates is required to guarantee that the closed-loop system is a switched positive system. A benchmark traffic flow example (a switched positive linear system commonly used in literature) is adopted to verify the effectiveness of the proposed approach.