Quasistatic Control of Dynamical Systems

Abstract

This paper investigates a control strategy in which the state of a dynamical system is driven slowly along a trajectory of stable equilibria. This trajectory is a continuum set of points in the state space, each one representing a stable equilibrium of the system under some constant control input. Along the continuous trajectory of such constant control inputs, a slowly varying control is then applied to the system, aimed to create a stable quasistatic equilibrium that slowly moves along the trajectory of equilibria. As a stable equilibrium attracts the state of system within its vicinity, by moving the equilibrium slowly along the trajectory of equilibria, the state of system travels near this trajectory alongside the equilibrium. Despite the disadvantage of being slow, this control strategy is attractive for certain applications, as it can be implemented based only on partial knowledge of the system dynamics. This feature is in particular important for the complex systems for which detailed dynamical models are not available.