Trade-off Properties of Tensor Product Model Transformation: A Case Study of the TORA System

Abstract

The Tensor Product (TP) based models have been applied widely in approximation theory, and approximation techniques. Re-cently, 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 Compen-sation (PDC) framework. The effectiveness of the control design frame-work strongly depends on two main properties of the TP model used. One of them is the approximation accuracy, and the other one is compu-tational complexity. Therefore, the primary aim of this paper is to inves-tigate the relation of the two contradictory goals, namely, the trade-off between the dynamic TP model's accuracy and complexity. The study is conducted through the example of Translational Oscillations with a Rotational Actuator (TORA) system.