Control-Barrier-Function-Based Design of Gradient Flows for Constrained Nonlinear Programming

• 成果类型: Article
• 署名作者: Allibhoy, Ahmed; Cortes, Jorge
• 署名单位: University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3306492
• 发表日期: 2024
• 页码: 3499-3514
• 关键词: Optimization; Heuristic algorithms; stability analysis; asymptotic stability; dynamical systems; linear programming; CONVERGENCE; Control barrier functions; gradient flows; nonlinear programming; optimization; projected dynamical systems

摘要

This article considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning it returns a feasible solution regardless of when it is terminated. Our approach augments the gradient flow of the objective function with inputs defined by the constraint functions, treats the feasible set as a safe set, and synthesizes a safe feedback controller using techniques from the theory of control barrier functions. The resulting closed-loop system, termed safe gradient flow, can be viewed as a primal-dual flow, where the state corresponds to the primal variables and the inputs correspond to the dual ones. We provide a detailed suite of conditions based on constraint qualification under which (both isolated and nonisolated) local minimizers are asymptotically stable with respect to the feasible set and the whole state space. Comparisons with other continuous-time methods for optimization in a simple example illustrate the advantages of the safe gradient flow.