Identification and control of nonlinear systems via piecewise affine approximation

Piecewise affine model represents an attractive model structure for approximating nonlinear systems. In this paper, a procedure for obtaining the piecewise affine ARX models of nonlinear systems is proposed. Two key parameters defining a piecewise affine ARX model, namely the parameters of locally affine subsystems and the partition of the regressor space, will be estimated, the former through a least-squares based identification method using multiple models, and the latter using standard procedures such as neural network classifier or support vector machine classifier. Having obtained the piecewise affine ARX model of the nonlinear system, a controller is then derived to control the system for reference tracking. Simulation studies show that the proposed algorithm can indeed provide accurate piecewise affine approximation of nonlinear systems, and the designed controller provides good tracking performance.