Sampled-Data Stabilization with Control Lyapunov Functions via Quadratically Constrained Quadratic Programs

Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap between design with continuous time models and the discrete time sampled implementation of the resulting controllers, often leading to poor performance on hardware platforms. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CLF-based controllers, specified as quadratically constrained quadratic programs (QCQPs). Assuming feedback linearizability and stable zero-dynamics of a system's continuous time model, we derive practical stability guarantees for the resulting sampled-data system. We demonstrate improved performance of the proposed approach over continuous time counterparts in simulation. ; © 2021 IEEE. Manuscript received March 4, 2021; revised May 10, 2021; accepted May 16, 2021. Date of publication June 2, 2021; date of current version June 29, 2021. The work of Andrew J. Taylor and Aaron D. Ames was supported by NSF under Award 1932091. The work of Victor D. Dorobantu and Yisong Yue was supported in part by DARPA, in part by Beyond Limits, and in part by a Kortschak Fellowship. The work of Paulo Tabuada was supported in part by NSF under Award 1705135. Recommended by Senior Editor L. Menini. ; Submitted - 2103.03937.pdf