Showing papers by "Ron J. Patton published in 2004"

Approximation capability of TP model forms

Abstract: The tensor product (TP) based models have been applied widely in approximation theory, and approximation techniques. Recently, a controller design framework working on dynamic systems has also been established based on TP model transformation combined with Linear Matrix Inequalities (LMI) within Parallel Distributed Compensation (PDC ) framework. The effectiveness of the control design framework strongly depends on the approximation property of the TP model used. Therefore, the primary aim of this paper is to investigate the approximation capabilities of dynamic T P model. It is shown that the set of functions that can be approx imated arbitrarily well by TP forms with bounded number of components lies no-where dense, i.e. “almost discretely ” in the set of continuous functions. Consequently, this pape r points out that in a class of control problems this drawback necessitates the application of trade-off techniques betw een accuracy and complexity of TP form. Such requirements are very difficult to consider in the analytical framework, but T P model transformation offers an easy way to deal with them.

On the approximation properties of TP model forms

Abstract: The tensor product (TP) based models have been applied widely in approximation theory and approximation techniques. Recently, a controller design framework working on dynamic systems has also been established based on TP model transformation combined with linear matrix inequalities (LMI) within parallel distributed compensation (PDC) framework. The effectiveness of the control design framework strongly depends on the approximation property of the TP model used. Therefore, the primary aim of this paper is to investigate the approximation capabilities of dynamic TP model. It is shown that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. This drawback necessitates the application of trade-off techniques between accuracy and complexity of TP form. Such requirements are very difficult to consider in the analytical framework, but TP model transformation offers an easy way to deal with them.