# Towards a constructive framework for control theory

arXiv: https://arxiv.org/abs/2501.02267 · HTML: https://mlsanity.com/paper/2501.02267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 51 references that are in the map.
- First posted on arXiv 4 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [Adversarial Robustness Against the Union of Multiple Perturbation Models](https://mlsanity.com/paper/1909.04068/) (2019)
- [Robustifying Reinforcement Learning Agents via Action Space Adversarial Training](https://mlsanity.com/paper/2007.07176/) (2020)
- [Practical sample-and-hold stabilization of nonlinear systems under approximate optimizers](https://mlsanity.com/paper/1803.02203/) (2018)
- [Local Policy Optimization for Trajectory-Centric Reinforcement Learning](https://mlsanity.com/paper/2001.08092/) (2020)
- [Deductive Stability Proofs for Ordinary Differential Equations](https://mlsanity.com/paper/2010.13096/) (2020)
- [On inf-convolution-based robust practical stabilization under computational uncertainty](https://mlsanity.com/paper/2102.04309/) (2021)
- [Analysis of extremum value theorems for function spaces in optimal control under numerical uncertainty](https://mlsanity.com/paper/1709.05836/) (2017)
- [On constructive extractability of measurable selectors of set-valued maps](https://mlsanity.com/paper/2403.05858/) (2024)

## Abstract (arXiv)

This work presents a framework for control theory based on constructive analysis to account for discrepancy between mathematical results and their implementation in a computer, also referred to as computational uncertainty. In control engineering, the latter is usually either neglected or considered submerged into some other type of uncertainty, such as system noise, and addressed within robust control. However, even robust control methods may be compromised when the mathematical objects involved in the respective algorithms fail to exist in exact form and subsequently fail to satisfy the required properties. For instance, in general stabilization using a control Lyapunov function, computational uncertainty may distort stability certificates or even destabilize the system despite robustness of the stabilization routine with regards to system, actuator and measurement noise. In fact, battling numerical problems in practical implementation of controllers is common among control engineers. Such observations indicate that computational uncertainty should indeed be addressed explicitly in controller synthesis and system analysis. The major contribution here is a fairly general framework for proof techniques in analysis and synthesis of control systems based on constructive analysis which explicitly states that every computation be doable only up to a finite precision thus accounting for computational uncertainty. A series of previous works is overviewed, including constructive system stability and stabilization, approximate optimal controls, eigenvalue problems, Caratheodory trajectories, measurable selectors. Additionally, a new constructive version of the Danskin's theorem, which is crucial in adversarial defense, is presented.