Globally Finite time and Globally Fixed-time stable Dynamical Systems for solving Inverse Quasi-variational inequality problems

Nam Van Tran; Le Thi Thanh Hai

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arXiv · 2503.04590

Globally Finite time and Globally Fixed-time stable Dynamical Systems for solving Inverse Quasi-variational inequality problems

Nam Van Tran·Le Thi Thanh Hai

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Abstract

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.

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Nam Van Tran, Le Thi Thanh Hai. 2025-03-06. Globally Finite time and Globally Fixed-time stable Dynamical Systems for solving Inverse Quasi-variational inequality problems. https://arxiv.org/abs/2503.04590

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