Discrete-Time Gradient Systems Governed by Difference Equation with Minima

This article explores the theory of discrete-time gradient systems that converge in a finite amount of time and are governed by a difference equation with minima. Two algorithms with distinct structures are discussed, both aimed at achieving finite-time stabilization of these systems. These gradient-based algorithms have significant applications in solving optimization problems. Using the finite-time convergent techniques discussed in the article, a quadratic programming problem is solved, and an optimal solution is obtained within a finite time frame. The effectiveness of these proposed methods is demonstrated through simulation results.