Iterative identification of block-oriented nonlinear systems based on biconvex optimization

Abstract We investigate the identification of a class of block-oriented nonlinear systems which is represented by a common model in this paper. Then identifying the common model is formulated as a biconvex optimization problem. Based on this, a normalized alterative convex search (NACS) algorithm is proposed under a given arbitrary nonzero initial condition. It is shown that we only need to find the unique partial optimum point of a biconvex cost function in order to obtain its global minimum point. Thus, the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions. By applying the results to Hammerstein-Wiener systems with an invertible nonlinear function, the long-standing problem on the convergence of iteratively identifying such systems under arbitrary nonzero initial conditions is also now solved.