Simultaneous identification and tracking of uncertain systems

The problem of optimal simultaneous identification and tracking of uncertain linear systems on a finite time interval is formulated. The tracking objective is minimization of a quadratic criterion of the difference between the desired trajectory and the trajectory of the plant. The identification criterion is maximization of the Fisher information matrix. The combined objective is the simultaneous minimization of the quadratic criterion and maximization of the information matrix. The inherent conflict between tracking and identification, as they are competing for the only available resource, namely the input to the plant, is posed. An algorithm based on optimal simultaneous state estimation and parameter identification and a certainty equivalence control algorithm is proposed. The novelty in the presented approach is that the certainty equivalence control has, in addition to its control properties, qualities that are suitable for identification. Examples of application of the approach to a second order system are presented.