Persistence of excitation, RBF approximation and periodic orbits

Satisfying the persistence of excitation (PE) condition is an important and yet challenging problem in system identification and adaptive control. In this paper, it is shown that a regressor vector consisted of radial basis functions can satisfy the PE condition. Specifically, for radial basis function networks (RBFN) constructed on a regular lattice, any periodic orbit that stays within the regular lattice can lead to the satisfaction of a partial PE condition. The significance of this result lies in that, with the partial PE condition satisfied, accurate RBFN approximation of unknown system dynamics can be achieved in a local region along the periodic orbit. This result will be very useful in identification, control and recognition of nonlinear systems using RBFN.