# Regularity Properties of Optimization-Based Controllers

arXiv: https://arxiv.org/abs/2311.13167 · HTML: https://mlsanity.com/paper/2311.13167/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2023.

## Built on by (most cited first, 5 of 5)

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- [Convex Chance-Constrained Stochastic Control under Uncertain Specifications with Application to Learning-Based Hybrid Powertrain Control](https://mlsanity.com/paper/2601.18313/) (2026)
- [Data-driven Reachable Set Estimation with Tunable Adversarial and Wasserstein Distributional Guarantees](https://mlsanity.com/paper/2604.12654/) (2026)

## Abstract (arXiv)

This paper studies regularity properties of optimization-based controllers, which are obtained by solving optimization problems where the parameter is the system state and the optimization variable is the input to the system. Under a wide range of assumptions on the optimization problem data, we provide an exhaustive collection of results about their regularity, and examine their implications on the existence and uniqueness of solutions and the forward invariance guarantees for the resulting closed-loop systems. We discuss the broad relevance of the results in different areas of systems and controls.