On selecting the MIMO Generalized Orthonormal Basis Functions poles by using Particle Swarm Optimization

This paper deals with the problem of finding the pole(s) in Orthonormal Basis Functions (OBF) models. In fact, any stable system can be exactly represented by an infinite orthonormal functions series, assuming that the basis used in such representation is complete. However, in practice a truncated basis functions expansion is used. For certain basis choice and fixed number of functions, there is a pole or set of poles that minimizes the truncation error. The problem is then to find such set. Therefore, the present paper is focused on the problem of finding the basis functions poles when more than one dynamic is involved, for instance, in SISO Generalized Orthonormal Basis Functions (GOBF) models or MIMO Laguerre, Kautz and/or GOBF models. It is proposed and analyzed here the use of Particle Swarm Optimization (PSO) for such problem. Simulation results presented shows the validity of the proposed method.