Continuous Piecewise Linear Identification with Moderate Number of Subregions*

A continuous piecewise linear (CPWL) function equals an affine function in each of the subregions which tessellate the domain. By CPWL identification, one nonlinear system can be approached by a set of linear systems and then linear techniques are applicable. For the convenience of further application, the number of subregions should be moderate. However, because the relation between the subregions and parameters of a CPWL model is very complicated, existing identification methods usually lead to a lot of unexpected subregions, when training the parameters of traditional CPWL models. In this paper, domain partition based CPWL neural network, which is recently proposed, is utilized to solve the problem above. The relation between parameters and subregion structure of such model is analyzed. Then an algorithm of adjusting vertices is proposed to improve approximation precision with moderate number of subregions. Compared with some prior identification methods, the proposed algorithm uses much less subregions and achieves satisfactory precision in numerical study.