Finite-time stochastic control for complex dynamical systems: The estimate for control time and energy consumption

TL;DR

This paper presents a novel finite-time stochastic control method for complex dynamical systems that emphasizes control time and energy, enabling finite-time control and synchronization with demonstrated effectiveness.

Contribution

Introduces a finite-time, stochastic control scheme focusing on control time and energy, applicable to chaotic systems and synchronization, improving over deterministic methods.

Findings

Effective finite-time control demonstrated on Lorenz systems.

Achieved synchronization in unidirectionally coupled systems.

Numerical experiments confirm analytical results.

Abstract

Controlling complex dynamical systems has been a topic of considerable interest in academic circles in recent decades. While existing works have primarily focused on closed-loop control schemes with infinite-time durations, this paper introduces a novel finite-time, closed-loop stochastic controller that pays special attention to control time and energy and their dependence on system parameters. This technique of stochastic control not only enables finite-time control in chaotic dynamical systems but also facilitates finite-time synchronization in unidirectionally coupled systems. Notably, our new scheme offers several advantages over existing deterministic finite-time controllers from a physical standpoint of time and energy consumption. Using numerical experiments based on random ecosystems, neural networks, and Lorenz systems, we demonstrate the effectiveness of our analytical results. It is anticipated that this proposed stochastic scheme will have widespread applicability in controlling complex dynamical systems and achieving network synchronization.