Abstract
In this paper, an identification problem of unknown nonlinear discrete systems is considered from the standpoint of the local estimation of system dynamics and the global function learning.
In the local estimation process, the unknown nonlinear dynamics are expanded into the second order Taylor series about the estimated state and the expansion coefficients are estimated with the system state by using Second Order Filter on the assumption of a slow system variation. After the local estimation has been performed in the wide region of the states, these estimation results are used for the global learning of the unknown nonlinear functions which indicate the state transfer characteristics. In the function learning process, these unknown nonlinear functions in the system are approximated by the linear combination of the independent functions with unknown coefficients and the function learning can be reduced to the linear estimation of these unknown coefficients in which Kalman Filter is directly applicable.
It has been found that by using this method the computing time required for the identification can be remarkably reduced comparing with the usual method using the nonlinear parameter estimation.
Another identification method is also proposed here. In this method, the local estimation of the system dynamics and the global function learning are practiced in parallel, by driving the system to the optimal searching point at which the most effective information for the learning may be obtained.
As identification examples, four types of the nonlinear systems i.e. the saturation, periodic, exponential and polynominal types are considered by the digital computer simulations.
