This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min-max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush- Kuhn-Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption.
Bibliographical noteFunding Information:
Manuscript received April 3, 2018; revised August 20, 2018 and December 19, 2018; accepted December 30, 2018. Date of publication January 11, 2019; date of current version September 25, 2019. This work was supported by the National Science Foundation (NSF-CBET). Recommended by Associate Editor F. Mazenc. (Corresponding author: Prodromos Daoutidis.) The authors are with the Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,email@example.com; firstname.lastname@example.org).
© 2019 IEEE.
- Bilevel programming
- Control-Lyapunov function
- Domain of attraction
- Lyapunov stability