Probabilistic Synchronization of Pinning Control

TL;DR

This paper introduces a probabilistic control approach for synchronizing complex stochastic networks with noise and uncertainties, demonstrating robustness and defining stochastic pinning controllability, validated through coupled map lattice examples.

Contribution

It presents a novel probabilistic control method for adaptive synchronization of stochastic networks with unknown models, including robustness proof and the concept of stochastic pinning controllability.

Findings

Robust probabilistic controller proven via Lyapunov method.

Successful synchronization of stochastic networks demonstrated.

Validation on coupled map lattice examples confirms theoretical results.

Abstract

This paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty. A probabilistic control method for adaptive synchronization is presented. All required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength, the state and control values. Robustness of the probabilistic controller is proved via the Liapunov method. Furthermore, based on the residual error of the network states we introduce the definition of stochastic pinning controllability. A coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments. The theoretical derivation is complemented by its validation on two representative examples.