Incremental Design of Simplex Basis Function Model for Dynamic System Identification.

Abstract

In this paper, we propose a novel adaptive piecewise linear model for dynamic system identification. It has four unique features. First, the model designs a new kind of basis function for function approximation. It maintains the uniform shape for each basis function, so as to achieve a satisfactory tradeoff between generalization ability and model complexity. Second, the model takes the structure of basis functions as decision variables to optimize the formulated identification problems instead of taking expansion coefficients as decision variables as proposed by many existing approaches. Third, we establish an incremental design strategy to solve the system identification problems. In each step of the identification, the selection of optimal basis function is a Lipschitz continuous optimization problem that is likely to be easily handled with some mature toolboxes. This incremental design strategy greatly reduces the estimation cost. Fourth, we introduce a smoothing mechanism to avoid overfitting, when the output of dynamic systems is disturbed by noise. Tests on several benchmark dynamic systems demonstrate the potential of the proposed model.