Coupled Map Lattice Model Identification of Stochastic Distributed Parameter Systems

The identification of Coupled Map Lattice models of linear and nonlinear distributed parameter systems from discrete noisy observations is considered. In the first part of the paper the stochastic CML model is introduced together with some basic tools, the Frobenius-Perron and the equivalent transfer operator, which are used to describe the evolution of densities under the action of the CML transformation. A more general form off the transfer operator that accounts for external stochastic perturbations, which are not necessarily additive or multiplicative, is derived. The identification of the lattice equations which make up the CML model, in the presence of noise, is addressed and some particular implementation issues are discussed. A new identification algorithm for stochastic CML's is introduced and tested using simulated data.