Abstract
The identification can be considered as a problem to find the optimal model in a set of models chosen a priori. As a criterion function, (1) response error criterion function, (2) equation error criterion function have been usually used. It has been known that only the response error criterion is applicable when the information about the dynamical structure of the system to be identified is not available. But this criterion function is not much desirable in case when only limited number of observed data of input and output, contaminated by noises, are provided.
In the paper, the improved version of the response error criterion is proposed; i.e., the sum of the following three terms, (1) weighted square error of the initial state, (2) sum of the weighted square error between the input to the model and the observed input, (3) sum of the weighted square error between the output of the model and the observed output.
Minimization procedure with the proposed criterion function is achieved by two steps. First, determination of the optimal initial state and input to the model, which minimize the criterion function for a given model. This first step is known as the optimal tracking problem. Second, minimization of the criterion function with respect to the parameters of the model. This second step is a static optimization problem. The computational algorithm for a linear discrete system is presented.
The criterion function is also explained from the statistical viewpoint and found to be equivalent to the likelihood function in parameter estimation when the structure of the system is the same as that of the model.
The computational examples are given to illustrate the proposed identification method.
