# Sensitivity-conditioning: Beyond Singular Perturbation for Control Design on Multiple Time Scales

arXiv: https://arxiv.org/abs/2101.04367 · HTML: https://mlsanity.com/paper/2101.04367/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [Towards a Systems Theory of Algorithms](https://mlsanity.com/paper/2401.14029/) (2024)
- [Maximum likelihood inference for high-dimensional problems with multiaffine variable relations](https://mlsanity.com/paper/2409.03495/) (2024)

## Abstract (arXiv)

A classical approach to design controllers for interconnected systems is to assume that the different subsystems operate at different time scales, then design simpler controllers within each time scale, and finally certify stability of the interconnected system via singular perturbation analysis. In this work, we propose an alternative approach that also allows to design the controllers of the individual subsystems separately. However, instead of requiring a sufficiently large time-scale separation, our approach consists of adding a feed-forward term to modify the dynamics of faster systems in order to anticipate the dynamics of slower ones. We present several examples in bilevel optimization and cascade control design, where our approach improves the performance of currently available methods.