Predefined Upper Bound of Settling Time based Convergent Gradient Flow Systems

Gradient flow systems provide effortless continuous time optimization. Such systems have inherent property that their solutions move in the direction of descent. This paper proposes a modified gradient flow technique to reach optimal point of an objective function within a priori chosen predefined time. A least square estimation problem and a quadratic programming problem are solved using the proposed continuous-time optimization approach. Simulation results of the aforementioned problems show the efficacy of the proposed method. Further, results obtained with predefined upper bound of settling time based approach are compared with the results using fixed-time stable gradient flow scheme.