Non standard Ricatti solution and linear quadratic pinning control

We study a stochastic linear quadratic (LQ) control problem that arise in the optimal control of linear discrete time invariant stochastic systems characterized by functional uncertainties. The theory of stochastic linear quadratic control has been extensively studied and developed. However, there remains a significant open problem, which is to derive an appropriate Ricatti solution when the models of the stochastic or deterministic systems under consideration are unknown. In such situations, functional uncertainties should be taken into consideration when deriving the optimal control law. This paper solves this problem for stochastic uncertain systems with additive state and control dependent noise. A new type of Ricatti equation is introduced which involves additional terms that depend on the estimated models uncertainties. The derived control result is then demonstrated on pinning control problem where the control matrix is sparse. It is used to synchronize the states of a complex coupled map lattice network with spatiotemporal chaos.