# Online Gradient Descent for Linear Dynamical Systems

arXiv: https://arxiv.org/abs/1912.09311 · HTML: https://mlsanity.com/paper/1912.09311/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Online Decision Making for Trading Wind Energy](https://mlsanity.com/paper/2209.02009/) (2022)
- [Predictor-corrector algorithms for stochastic optimization under gradual distribution shift](https://mlsanity.com/paper/2205.13575/) (2022)
- [Prediction techniques for dynamic imaging with online primal-dual methods](https://mlsanity.com/paper/2405.02497/) (2024)
- [Online optimisation for dynamic electrical impedance tomography](https://mlsanity.com/paper/2412.12944/) (2024)

## Abstract (arXiv)

In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then, performance guarantees are derived in terms of regret analysis. We show that the proposed control scheme achieves sublinear regret if the variation of the cost functions is sublinear. In addition, as a special case, the system converges to the optimal equilibrium if the cost functions are invariant after some finite time. Finally, the performance of the resulting closed loop is illustrated by numerical simulations.