# Maximum Hands-Off Control: A Paradigm of Control Effort Minimization

arXiv: https://arxiv.org/abs/1408.3025 · HTML: https://mlsanity.com/paper/1408.3025/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2014.

## Built on by (most cited first, 6 of 6)

- [Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments](https://mlsanity.com/paper/2205.00446/) (2022)
- [Sharper Bounds for Proximal Gradient Algorithms with Errors](https://mlsanity.com/paper/2203.02204/) (2022)
- [Let it Cook: Learning to Wait in Sequential Decision Making](https://mlsanity.com/paper/2608.11511/) (2026)
- [Fast Algorithm for Constrained Linear Inverse Problems](https://mlsanity.com/paper/2212.01068/) (2022)
- [Randomized algorithms and PAC bounds for inverse reinforcement learning in continuous spaces](https://mlsanity.com/paper/2405.15509/) (2024)
- [Tractable downfall of basis pursuit in structured sparse optimization](https://mlsanity.com/paper/2503.19126/) (2025)

## Abstract (arXiv)

In this paper, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.