A randomized approach to switched nonlinear systems identification

This paper addresses the identification of Switched Nonlinear AutoRegressive eXogenous (SNARX) systems characterized as a collection of nonlinear dynamical systems (modes), each one described via a discrete time Nonlinear AutoRegressive eXogenous (NARX) model, indexed by a discrete-valued variable (switching signal). We propose a novel approach which, given a realization of the input/output signals collected from the system, jointly classifies the data attributing them to the different modes, and identifies the model structure and parameters for each mode. The involved optimization problem is partly combinatorial due to the data classication over modes and the model structure selection, and partly continuous due to the parameter estimation required to complete the identification of the dynamical models assigned to the different modes. A probabilistic framework is employed to address the problem, where Categorical and Bernoulli distributions are respectively used for the assignment of modes over time and for the structure selection of the NARX models describing the modes. A randomized procedure is then proposed to solve the problem, based on a sample-and-evaluate strategy that progressively refines the induced SNARX model probability distribution. The approach is tested on a numerical example taken from the literature, where it shows promising results.