Adaptive Actuator Failure Compensation on the Basis of Contraction Metrics

TLDR: In this article, an adaptive actuator failure compensation method for nonlinear systems with unmatched parametric uncertainty based on contraction metrics is proposed, which ensures the closed-loop stability and asymptotic tracking of the desired trajectory in the presence of actuator failures.

Abstract: This letter develops an adaptive actuator failure compensation method for nonlinear systems with unmatched parametric uncertainty based on contraction metrics. The proposed method, which is constructed by benefiting from the recent achievements on contraction metrics based adaptive control techniques, ensures the closed-loop stability and asymptotic tracking of the desired trajectory in the presence of actuator failures. In particular, a sufficient convex condition is derived for constructing a valid metric, by which a quadratic program-based controller is obtained to determine the inputs of the actuators. The introduced method is more general than the common adaptive actuator failure compensation methods, as it does not require the system to have an identical relative degree for all inputs and be transformable into the parametric strick-feedback or feedback linearization form. Besides, it can be enriched with learning-based algorithms and common robust modifications. Simulation results are presented to verify the effectiveness of the proposed controller.