Model reference safety‐critical adaptive control for nonlinear and switched systems

Abstract

SummaryThis paper studies the problem of model reference safety‐critical adaptive control for a class of nonlinear and switched systems with nonlinear reference models. An adaptive law is designed to estimate unknown parameters, while an energy function is proposed to guarantee the boundedness and safety of nonlinear systems. Also, a model reference safety‐critical adaptive control framework is established to ensure that the state trajectory of nonlinear systems is always within the safe set in the presence of unknown parameters. Moreover, the results obtained are extended to switched uncertain nonlinear systems under arbitrary switchings. A switched adaptive controller is designed to reduce the conservativeness caused by adoption of a common update law for all subsystems. Also, the safety of switched systems under arbitrary switchings is guaranteed as well as the boundedness of the error states between the switched nonlinear systems and the switched reference models by utilizing the common Lyapunov function method. Finally, two illustrative numerical examples are given to demonstrate the effectiveness of the proposed control architecture.