Abstract

Ordinary differential equations, and in general a dynamical system viewpoint, have seen a resurgence of interest in developing fast optimization methods, mainly thanks to the availability of well established analysis tools. In this study, we purs a similar objective and propose a class of hybrid control systems that adopts a 2nd-order differential equation as its continuous flow. A distinctiv feature of the proposed differential equation in comparison with the existing literature is a state dependent, time-invariant damping term that acts as a feedback control input. Given a user-defined scalar α, it is shown that the proposed control input steers the state trajectories to the global mizer of a desired objective function with a guaranteed rate of convergence Our framework requires that the objective function satisfie the so called Polyak–Łojasiewicz inequality. Furthermore, a discretization method is introduced such that the resulting discrete dynamical system possesses an exponential rate of convergence.