# Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis

arXiv: https://arxiv.org/abs/1906.11378 · HTML: https://mlsanity.com/paper/1906.11378/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

## Built on by (most cited first, 30 of 40)

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- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)
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- [Online Learning for Predictive Control with Provable Regret Guarantees](https://mlsanity.com/paper/2111.15041/) (2021)
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- [Robust Learning for Smoothed Online Convex Optimization with Feedback Delay](https://mlsanity.com/paper/2310.20098/) (2023)
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- [AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Control](https://mlsanity.com/paper/2606.23079/) (2026)
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- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control](https://mlsanity.com/paper/2301.07876/) (2023)
- [The Complexity of Sequential Prediction in Dynamical Systems](https://mlsanity.com/paper/2402.06614/) (2024)
- [Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis](https://mlsanity.com/paper/2503.23600/) (2025)
- [Constrained Online Decision-Making: A Unified Framework](https://mlsanity.com/paper/2505.07101/) (2025)
- [Tuning the burn-in phase in training recurrent neural networks improves their performance](https://mlsanity.com/paper/2602.10911/) (2026)
- [RASteer: Retain-Aware Activation Steering for Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2610.01969/) (2026)
- [Regret-Optimal LQR Control](https://mlsanity.com/paper/2105.01244/) (2021)
- [DILF-EN framework for Class-Incremental Learning](https://mlsanity.com/paper/2112.12385/) (2021)

## Abstract (arXiv)

This paper studies the online optimal control problem with time-varying convex stage costs for a time-invariant linear dynamical system, where a finite lookahead window of accurate predictions of the stage costs are available at each time. We design online algorithms, Receding Horizon Gradient-based Control (RHGC), that utilize the predictions through finite steps of gradient computations. We study the algorithm performance measured by dynamic regret: the online performance minus the optimal performance in hindsight. It is shown that the dynamic regret of RHGC decays exponentially with the size of the lookahead window. In addition, we provide a fundamental limit of the dynamic regret for any online algorithms by considering linear quadratic tracking problems. The regret upper bound of one RHGC method almost reaches the fundamental limit, demonstrating the effectiveness of the algorithm. Finally, we numerically test our algorithms for both linear and nonlinear systems to show the effectiveness and generality of our RHGC.