Control Strategy for Generalized Synchrony in Coupled Dynamical Systems

TL;DR

This paper presents a control method to achieve generalized synchronization in coupled dynamical systems, demonstrated through chaotic Lorenz oscillators and coordinated drone motion.

Contribution

It introduces a novel control strategy for generalized synchronization and provides practical circuit and drone swarm implementations.

Findings

Successful control of chaos in Lorenz oscillators

Effective coordination in autonomous drone swarms

Versatile coupling functions for different systems

Abstract

Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems have a well-specified functional relationship. This process can be viewed as a control technique that ensures generalized synchronization. Depending on the nature of the dynamical systems and the specified submanifold, different coupling functions can be derived in order to achieve a desired control objective. We discuss a circuit implementation of this strategy for coupled chaotic Lorenz oscillators, as well as a demonstration of the methodology for designing coordinated motion (swarming) in a set of autonomous drones.