Title: Generalised Riccati solution and pinning control of complex stochastic networks

Authors: Randa Herzallah

Addresses: Nonlinearity and Complexity Research Group, Aston University, Birmingham, UK

Abstract: This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

Keywords: quadratic pinning control; Riccati solution; stochastic control; Lyapunov stability analysis; complex networks; stochastic networks; coupled map lattice networks; modelling; uncertainty; forward dynamics; inverse controller; optimal control.

DOI: 10.1504/IJMIC.2015.070652

International Journal of Modelling, Identification and Control, 2015 Vol.23 No.4, pp.346 - 354

Received: 27 Sep 2014
Accepted: 20 Oct 2014
Published online: 16 Jul 2015 *

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