Alternating Minimization Approach for Identification of Piecewise Continuous Hammerstein Systems

Identification of piecewise continuous Hammerstein systems, which consist of the cascade of memoryless piecewise continuous systems followed by linear systems, is an important problem in engineering. In the identification process, major existing approaches approximate exact minimization of the non-convex cost function for the piecewise continuous system, which degrades the identification accuracy in some occasions. In this paper, we propose an alternating minimization approach for identification of the piecewise continuous Hammerstein system by alleviating the difficulty in minimization of the cost function for the piecewise continuous system. We first decompose this minimization into quadratic subproblems by sorting the magnitudes of input signals. Then, based on this decomposition, the proposed method exactly minimizes the cost function by finite comparison of the solutions of the subproblems. Numerical examples show the effectiveness of the proposed method.