Greedy Rational Approximation for Parametric LTI Systems
Analysis
This paper addresses the model reduction problem for parametric linear time-invariant (LTI) systems, a common challenge in engineering and control theory. The core contribution lies in proposing a greedy algorithm based on reduced basis methods (RBM) for approximating high-order rational functions with low-order ones in the frequency domain. This approach leverages the linearity of the frequency domain representation for efficient error estimation. The paper's significance lies in providing a principled and computationally efficient method for model reduction, particularly for parametric systems where multiple models need to be analyzed or simulated.
Key Takeaways
- •Proposes a greedy algorithm for model reduction of parametric LTI systems.
- •Utilizes reduced basis methods (RBM) in the frequency domain.
- •Employs an error estimator that exploits the linearity of the frequency domain representation.
- •Provides a computationally efficient approach for rational compression of high-order rational functions.
“The paper proposes to use a standard reduced basis method (RBM) to construct this low-order rational function. Algorithmically, this procedure is an iterative greedy approach, where the greedy objective is evaluated through an error estimator that exploits the linearity of the frequency domain representation.”