Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronization 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 neighbors states. For such networks we derive a generalized Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalized Riccati solution is derived using the Liapunov approach. A probabilistic approximation type algorithms are employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying models uncertainty. The theoretical derivation is complemented by its validation on a set of representative examples.