Identification of composite local linear state space models using a projected gradient search

An identification method is described to determine a weighted combination of local linear state space models from input and output data. Normalized radial basis function are used for the weights, and the system matrices of the local linear models are fully parameterized. By iteratively solving a nonlinear optimization problem, the centers and widths of the radial basis functions and the system matrices of the local models are determined. To deal with the nonuniqueness of the fully parameterized state space system, a projected gradient search algorithm is described. It is pointed out that when the weights depend only on the input, the dynamical gradient calculations in the identification method are stable. When the weights also depend on the output, certain difficulties might arise. The methods are illustrated using several examples that have been studied in the literature before.