Fixed-Time Stable Proximal Dynamical System for Solving MVIPs

• 成果类型: Article
• 署名作者: Garg, Kunal; Baranwal, Mayank; Gupta, Rohit; Benosman, Mouhacine
• 署名单位: University of Michigan System; University of Michigan; Tata Sons; Tata Consultancy Services Limited (TCS); University of Michigan System; University of Michigan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3214795
• 发表日期: 2023
• 页码: 5029-5036
• 关键词: Discretization; Fixed-time stability; mixed variational inequality problem (MVIP); proximal dynamical system

摘要

In this article, a novel modified proximal dynamical system is proposed to compute the solution of a mixed variational inequality problem (MVIP) within a fixed time, where the time of convergence is finite and is uniformly bounded for all initial conditions. Under the assumptions of strong monotonicity and Lipschitz continuity, it is shown that a solution of the modified proximal dynamical system exists, is uniquely determined, and converges to the unique solution of the associated MVIP within a fixed time. Furthermore, the fixed-time stability of the modified projected dynamical system continues to hold, even if the assumption of strong monotonicity is relaxed to that of strong pseudomonotonicity. Finally, it is shown that the solution obtained using the forward-Euler discretization of the proposed modified proximal dynamical system converges to an arbitrarily small neighborhood of the solution of the associated MVIP within a fixed number of time steps, independent of the initial conditions.