  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.
