A novel APSO-aided maximum likelihood identification method for Hammerstein systems

Identification of Hammerstein nonlinear models has received much attention due to its ability to describe a wide variety of nonlinear systems. In this paper the maximum likelihood estimator which was originally derived for linear systems is extended to work for Hammerstein nonlinear systems in colored-noise environment. The maximum likelihood estimate is known to be statistically efficient, but can lead to complex nonlinear multidimensional optimization problem; traditional methods solve this problem at the computational cost of evaluating second derivatives. To overcome these shortcomings, a particle swarm optimization (PSO) aided maximum likelihood identification algorithm (Maximum Likelihood-Particle Swarm Optimization, ML-PSO) is first proposed to integrate PSO’s simplicity in implementation and computation, and its ability to quickly converge to a reasonably good solution. Furthermore, a novel adaptive strategy using the evolution state estimation technique is proposed to improve PSO’s performance (maximum likelihood-adaptive particle swarm optimization, ML-APSO). A simulation example shows that ML-APSO method outperforms ML-PSO and traditional recursive least square method in various noise conditions, and thus proves the effectiveness of the proposed identification scheme.