Deterministic learning and nonlinear observer design

A " deterministic learning " (DL) theory was recently proposed for identification of nonlinear system dynamics under full-state measurements. In this paper, for a class of nonlinear systems undergoing periodic or recurrent motions with only output measurements, firstly, it is shown that locally-accurate identification of nonlinear system dynamics can still be achieved. Specifically, by using a high gain observer and a dynamical radial basis function network (RBFN), when state estimation is achieved by the high gain observer, along the estimated state trajectory, a partial persistence of excitation (PE) condition is satisfied, and locally-accurate identification of system dynamics is achieved in a local region along the estimated state trajectory. Secondly, by embedding the learned knowledge of system dynamics into a RBFN-based nonlinear observer, it is shown that correct state estimation can be achieved according to the internal matching of the underlying system dynamics, rather than by using high gain domination. The significance of this paper is that it reveals that the difficult problems in nonlinear observer design can be successfully resolved by incorporating the deterministic learning mechanisms. Simulation studies are included to demonstrate the effectiveness of the approach