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

Controlling complex dynamical systems has garnered significant attention within academic circles in recent decades. While most existing works have focused on closed-loop control schemes with infinite-time durations, this paper introduces a novel finite-time, closed-loop stochastic controller that considers control time, energy consumption, and their dependence on system parameters. This stochastic control technique not only enables finite-time control in chaotic dynamical systems but also facilitates finite-time synchronization in unidirectionally coupled systems. Importantly, our proposed scheme offers several advantages over existing deterministic finite-time controllers, particularly in terms of time and energy consumption. Through numerical experiments utilizing random ecosystems, neural networks, and Lorenz systems, we provide evidence of the effectiveness of our analytical results. We anticipate that this stochastic scheme will find wide-ranging applications in the control of complex dynamical systems and in achieving network synchronization.