TY - JOUR
T1 - A bilevel programming approach to the convergence analysis of control-lyapunov functions
AU - Tang, Wentao
AU - Daoutidis, Prodromos
PY - 2019/10
Y1 - 2019/10
N2 - 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.
AB - 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.
KW - Bilevel programming
KW - Control-Lyapunov function
KW - Domain of attraction
KW - Lyapunov stability
UR - http://www.scopus.com/inward/record.url?scp=85075566149&partnerID=8YFLogxK
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U2 - 10.1109/TAC.2019.2892386
DO - 10.1109/TAC.2019.2892386
M3 - Article
AN - SCOPUS:85075566149
VL - 64
SP - 4174
EP - 4179
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 10
M1 - 8610152
ER -