Model Order Reduction of Data driven Time Delay Models

Abstract

This thesis addresses the challenge of system identification for large-scale linear time- invariant delay systems, with a focus on the computational complexity involved in their

identification. System identification entails estimating a model based on a known struc- ture using input-output measurement data. The accuracy of the estimated model is

critical for both the analysis and the design of the system. However, in some cases, the

resulting model can become computationally expensive to solve, particularly for large- scale or high-order systems. To address this challenge, we adopt an indirect approach,

where we first use the Hu-Kalman-Kung method to identify a state-space realization with time delay from input-output data. This initial estimation step provides a robust model representation. Following this, we apply model order reduction through iterative rational Krylov projections to simplify the model while maintaining its accuracy. By

first estimating the model and then reducing its order, we effectively manage the compu- tational complexity, making the overall process more efficient. Testing this method on

two benchmark examples from the literature demonstrates that the indirect approach,

which combines identification and model reduction, proves to be computationally effi- cient and accurate compared to the direct method.

Thehindirect approachhenhances bothhaccuracy and speedhin simulations, makinghit efficient for large-scalehsystem identification. It startshwith estimationhtechniques to

identifyhthe model and then reduceshits order, whichhcuts down on computational de- mands comparedhto direct methods. This approach lowers modelhcomplexity, enabling

quicker simulations without losing dynamic precision. In contrast, direct methods re- quire more resources for similar accuracy, making the indirect approach preferable for

real-time applications and extensive system analysis where speed and precision are cru- cial.