arXiv subjects

Kasturi Das

Publications and source records attributed to Kasturi Das.

3 recordsLinked to original sources

arXiv2024

An iterative scheme for finite horizon model reduction of continuous-time linear time-varying systems

In this paper, we obtain the functional derivatives of a finite horizon error norm between a full-order and a reduced-order continuous-time linear time-varying (LTV) system. Based on the functional derivatives, first-order necessary conditions for optimality of the error norm are derived, and a projection-based iterative scheme for model reduction is proposed. The iterative scheme upon convergence produces reduced-order models satisfying the optimality conditions. Finally, through a numerical example, we demonstrate the better performance of the proposed model reduction scheme in comparison to the finite horizon balanced truncation algorithm for continuous-time LTV systems.

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arXiv2022

H$_2$ Optimal Model Order Reduction over a Finite Time Interval

For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method involves obtaining a reduced model which minimizes the time-limited H$_2$ norm, formulated as a nonlinear optimization problem. The optimization problem is solved using standard optimization software.

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arXiv2021

Near Optimal Interpolation based Time-Limited Model Order Reduction

This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time intervals of the form, $\begin{bmatrix}0 & τ\end{bmatrix}$ with $τ< \infty$ for linear time invariant (LTI) systems. Using the time limited $H_2$ norm, we derive interpolation based $H_{2,τ}$ optimality conditions. The LT-IRKA yields a near optimal $H_2(τ)$ reduced order system. The nearness to the exact $H_2(τ)$ optimal reduced system is quantized in terms of the errors in the interpolation based $H_2(τ)$ optimality conditions. We demonstrate with numerical examples how the proposed algorithm nearly satisfies the time-limited optimality conditions and also how it performs with respect to the Time-Limited Two sided Iteration Algorithm (TL-TSIA), the Time-Limited Balanced Truncation (TL-BT), the Iterative Rational Krylov Algorithm (IRKA) and the Time-Limited Pseudo Optimal Rational Krylov (TL-PORK) Algorithm over a finite time interval.

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