Optimal Design of Control-Lyapunov Functions by Semi-Infinite Stochastic Programming

Lyapunov-based control is a common method to enforce closed-loop stability of nonlinear systems, where the choice of a control-Lyapunov function has a strong impact on the resulting performance. In this paper, we propose a generic semi-infinite stochastic programming formulation for the optimal control-Lyapunov function design problem and discuss its various specializations. Specifically, the expected performance evaluated on simulated trajectories under different scenarios is optimized subject to infinite constraints on stability and performance specifications. A stochastic proximal primal-dual algorithm is introduced to find a stationary solution of such a semi-infinite stochastic programming problem. The proposed method is illustrated by a chemical reactor case study.