Zulfiqar's New Algorithm Allows Imaginary Shifts for Data-Driven Model Reduction
Enables balanced truncation from experimentally measured transfer function samples on the imaginary axis.
Umair Zulfiqar proposes a new low-rank Cholesky-factor alternating direction implicit (LRCF-ADI) algorithm that generalizes the standard method by allowing ADI shifts to be placed anywhere in the complex plane, including on the imaginary axis. The standard LRCF-ADI requires shifts with negative real parts, which is restrictive for applications like frequency-limited data-driven balanced truncation. The new method reduces to the standard version as a special case and extends to frequency-limited and time-limited Lyapunov equations as well as Riccati equations. It also handles approximations of matrix logarithm and exponential products.
The key practical breakthrough is in data-driven model reduction: standard non-intrusive LRCF-ADI balanced truncation requires transfer function samples in the right half-plane, which are not experimentally accessible. The new algorithm’s ability to use imaginary-axis shifts means models can be built purely from measured frequency response data—a critical enabler for real-world control system design where state-space models are unavailable. The paper provides a concrete algorithm for constructing reduced-order models from such measured samples.
- Removes the negative-real-part restriction on ADI shifts, allowing imaginary-axis placements.
- Enables non-intrusive data-driven balanced truncation using experimentally measurable frequency response samples.
- Generalizes standard LRCF-ADI and also applies to frequency-limited Lyapunov and Riccati equations.
Why It Matters
Brings data-driven model reduction closer to practical engineering by accepting real-world frequency measurements instead of requiring unphysical right half-plane samples.