Identification of Hammerstein–Wiener Systems with State-Space Subsystems Based on the Improved PSO and GSA Algorithm.

This paper investigates the parameter estimation of Hammerstein–Wiener systems whose linear subsystems are observable state-space models. The particle swarm optimization (PSO) and gravitational search (GSA) algorithms are combined to derive a novel method for identifying the discussed systems. To improve the optimization ability, some improvements are employed, including adding the oscillating exponential decay inertia weight and fuzzy membership in PSO (OFPSO) and introducing the chaotic optimization mechanism to GSA (CGSA). Thus, the combination of OFPSO and CGSA (OFPSO-CGSA) method is proposed. Its principle is to utilize coordinated behaviors of the speed in the OFPSO algorithm and the acceleration in the CGSA algorithm to update the particle position. Moreover, the convergence analysis proves that the OFPSO-CGSA algorithm converges to the global solution with probability one. Two simulations of the Hammerstein–Wiener nonlinear systems with two-dimensional and three-dimensional linear state space subsystems verify that the algorithms are effective, and OFPSO-CGSA has the best performance considering the convergence speed and identification accuracy in the algorithm comparison. [ABSTRACT FROM AUTHOR]