# Stable Online Control of Linear Time-Varying Systems

arXiv: https://arxiv.org/abs/2104.14134 · HTML: https://mlsanity.com/paper/2104.14134/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 29 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [Learning-based Control of Unknown Linear Systems with Thompson Sampling](https://mlsanity.com/paper/1709.04047/) (2017)
- [Impact of Low Rotational Inertia on Power System Stability and Operation](https://mlsanity.com/paper/1312.6435/) (2013)
- [Regret-optimal control in dynamic environments](https://mlsanity.com/paper/2010.10473/) (2020)

## Built on by (most cited first, 3 of 3)

- [Learning Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2201.11211/) (2022)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2206.01704/) (2022)

## Abstract (arXiv)

Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.