Abstract
In this paper, we consider the design of an optimal identification input for discrete-time linear dynamical systems with unknown structures. Firstly, models with distinct structures are hypothesized, following which, the concept of entropy is used to express the uncertainty of these model structures. The observations of the input-output data from the system can be used to reduce the entropy sequentially. The Kullback's divergence for the various model structures gives the upper bound of the expected decrease of the entropy.
The optimal input is the one which maximizes the Kullback's divergence at each period. This optimal input is given as the solution of a non-linear optimization problem. An approximate solution for the problem is also given which requires significantly less computation.
It is demonstrated by simulation that the optimal input can discriminate the true system structure rapidly, compared to a random input. The estimation error of the parameters and the prediction error using the optimal input signal are also superior to the random input case. The proposed method is more effective when the observation noise is relatively large.
