Optimal sensor selection for prediction-based iterative learning control of distributed parameter systems

Abstract

The purpose of this study is to develop an effective computational scheme to solve the optimal tracking control problem for repeated trials in distributed-parameter system in the situation where quantity under control cannot be observed directly. In such situations, the reliability of model predictions becomes more important than the accuracy of model parameters, because the ultimate objective in model-based control is the prediction or forecast of the system states. Particularly, given a finite number of possible spatial locations at which sensors may reside, we select gaged sites so as maximize the prediction accuracy. For that purpose, an suitable output criterion is proposed as a measure of the prediction accuracy and the sensor selection problem formulated in terms of optimization task. To solve it, a specialized technique is adopted based on relaxation of the original discrete optimization problem which amounts to operating on the density of sensors in lieu of their individual positions. As a result, a simple and effective exchange algorithm is outlined to select the gaged sites. Then, the measurement schedule providing the most informative system observations is further incorporated into the adaptive control scheme based on iterative learning control technique for effective solution of underlying tracking control problem. The proposed approach is verified by numerical experiments on the model of the friction welding process of two aluminum plates.