Chaos Synchronization: a Lagrange Programming Network Approach

In this paper we interpret chaos synchronization schemes within the framework of Lagrange programming networks, which form a class of continuous-time optimization methods for solving constrained nonlinear optimization problems. From this study it follows that standard synchronization schemes can be regarded as a Lagrange programming network with soft constraining, where synchronization between state vectors is defined as a constraint to the dynamical systems. New schemes are proposed then which implement synchronization by hard and soft constraints within Lagrange programming networks. A version is derived which takes into account synchronization errors within the problem formulation. Furthermore Lagrange programming networks for achieving partial and generalized synchronization are given. The methods assume the existence of potential functions for the given systems. The proposed Lagrange programming networks with hard and soft constraining show improved performance on many simulation examples for identical and nonidentical chaotic systems. The schemes are illustrated on Chua’s circuit, Lorenz attractor and n-scroll circuits.