2025/03/06 by Nam Van Tran, Van Tran, Nam, Lê Thị Thanh Hải +1
Computer Science · Engineering · Mathematics · #47J20 #47J30 #49J40 #49J53 #49M37 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2503.04590
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose two projection dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces-one ensuring finite-time stability and the other guaranteeing fixed-time stability. We first establish the connection between these dynamical systems and the solutions of inverse quasi-variational problems. Then, under mild conditions on the operators and parameters, we analyze the global finite-time and global fixed-time stability of the proposed systems. Both approaches offer accelerated convergence, however, while the settling time of a finite-time stable dynamical system depends on initial conditions, the fixed-time stable system achieves convergence within a predefined time, independent of initial conditions. To demonstrate their effectiveness, we provide numerical experiments, including an application to the traffic assignment problem.