A modified DFC method based on full state and periodic gain for stabilization and chaos control

TL;DR

This paper introduces a modified delayed feedback control method using full state information and periodic gain to stabilize unstable equilibria and control chaos, with a systematic design process and analytical validation.

Contribution

It presents a novel control scheme combining delayed state differences and periodic gain, providing a rigorous analytical framework for stabilization and chaos control.

Findings

Successfully stabilizes hyperbolic unstable equilibria

Effectively controls chaos by stabilizing embedded equilibrium points

Demonstrates the method's performance through simulated examples

Abstract

A novel delayed feedback control based on full state is proposed. The designed scheme combines the difference between two delayed states and a periodic control gain. System stabilization is achieved in any hyperbolic unstable equilibrium point. The procedure to build the control is systematic and, the set of the stabilizing control parameters is rigorously featured by analytical arguments. An ad-hoc strategy based on the proposed scheme is implemented for control of chaos by stabilizing equilibrium points embedded in chaotic attractors. Simulated examples illustrate this strategy performance.