A fixed-time inverse-free dynamical system for solving the system of absolute value equations

TL;DR

This paper introduces a new inverse-free dynamical system with fixed-time convergence to efficiently solve absolute value equations, providing guaranteed settling time and demonstrating effectiveness through numerical simulations.

Contribution

The paper proposes a novel inverse-free dynamical system with fixed-time convergence for AVEs, including a conservative settling-time estimate, which improves upon existing methods.

Findings

Convergence to AVE solutions is proven under mild conditions.

The method has a guaranteed fixed settling time.

Numerical simulations confirm the effectiveness of the approach.

Abstract

In this paper, an inverse-free dynamical system with fixed-time convergence is presented to solve the system of absolute value equations (AVEs). Under a mild condition, it is proved that the solution of the proposed dynamical system converges to the solution of the AVEs. Moreover, in contrast to the existing inverse-free dynamical system \cite{chen2021}, a conservative settling-time of the proposed method is given. Numerical simulations illustrate the effectiveness of the new method.