A New Property of Noninvasive Control Methods Applied to Stabilize Unstable Periodic Orbits

Abstract

This paper is devoted to present a theorem on a new property of noninvasive control methods applied to stabilize unstable periodic orbits (UPOs). This property is related to the optimal energy consumption of the controller in the presence of noise. The approach of parameter optimization is applied to study optimal energy consumption of the controller. Throughout this paper, the problem of energy consumption of the controller is studied when the system state is close to the UPO, and fluctuates around it because of the presence of noise.