Global Asymptotic Stability of Nonlinear Systems while Exploiting Properties of Uncertified Feedback Controllers via Opportunistic Switching

Paul K. Wintz, Ricardo G. Sanfelice, and João P. Hespanha

American Control Conference, 2022

Abstract

A hybrid control strategy is introduced that renders a compact set uniformly globally asymptotically stable for a continuous-time plant by switching between a Lyapunov-certified feedback controller and an uncertified controller. This control strategy allows for the opportunistic use of a controller that has desirable performance but lacks a Lyapunov certificate. A pair of tunable threshold functions determine conditions for switching between the controllers. To establish global uniform asymptotic stability, a nonsmooth Lyapunov function is constructed for the closed-loop hybrid system using an auxiliary memory variable and the Lyapunov certificate associated with the certified controller. Examples illustrate improvements to control effort and rate of convergence resulting from the proposed hybrid control strategy when applied to state-feedback and model-predictive control.

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