# Robust Regret Optimal Control

arXiv: https://arxiv.org/abs/2307.14297 · HTML: https://mlsanity.com/paper/2307.14297/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2023.

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

- [Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis](https://mlsanity.com/paper/2503.23600/) (2025)
- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)

## Abstract (arXiv)

This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant model and given full knowledge of the disturbance. Robust regret is defined relative to the performance of this optimal non-causal control. It is shown that a controller achieves robust regret if and only if it satisfies a robust H_∞ performance condition. DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret. The approach is demonstrated three examples: (i) a simple single-input, single-output classical design, (ii) a longitudinal control for a simplified model for a Boeing 747 model, and (iii) an active suspension for a quarter car model. All examples compare the robust regret optimal against regret optimal controllers designed without uncertainty.