# Predictive Linear Online Tracking for Unknown Targets

arXiv: https://arxiv.org/abs/2402.10036 · HTML: https://mlsanity.com/paper/2402.10036/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 67 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 30 of 36)

- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributions](https://mlsanity.com/paper/1301.6677/) (2013)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [Online Learning for Time Series Prediction](https://mlsanity.com/paper/1302.6927/) (2013)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Making Non-Stochastic Control (Almost) as Easy as Stochastic](https://mlsanity.com/paper/2006.05910/) (2020)
- [On the Regret Analysis of Online LQR Control with Predictions](https://mlsanity.com/paper/2102.01309/) (2021)
- [Online Learning of the Kalman Filter with Logarithmic Regret](https://mlsanity.com/paper/2002.05141/) (2020)
- [Online Optimal Control with Affine Constraints](https://mlsanity.com/paper/2010.04891/) (2020)
- [Introduction to Online Control](https://mlsanity.com/paper/2211.09619/) (2022)
- [No-Regret Prediction in Marginally Stable Systems](https://mlsanity.com/paper/2002.02064/) (2020)
- [On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters](https://mlsanity.com/paper/1809.05870/) (2018)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond](https://mlsanity.com/paper/1909.03118/) (2019)
- [SLIP: Learning to Predict in Unknown Dynamical Systems with Long-Term Memory](https://mlsanity.com/paper/2010.05899/) (2020)
- [A Historical Perspective of Adaptive Control and Learning](https://mlsanity.com/paper/2108.11336/) (2021)
- [Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems](https://mlsanity.com/paper/2201.01680/) (2022)
- [The Power of Linear Controllers in LQR Control](https://mlsanity.com/paper/2002.02574/) (2020)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Machine Learning for Mechanical Ventilation Control](https://mlsanity.com/paper/2102.06779/) (2021)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Online Linear Quadratic Tracking with Regret Guarantees](https://mlsanity.com/paper/2303.10260/) (2023)

## Built on by (most cited first, 5 of 5)

- [Model-free Online Learning for the Kalman Filter: Forgetting Factor and Logarithmic Regret](https://mlsanity.com/paper/2505.08982/) (2025)
- [Online Residual Learning from Offline Experts for Pedestrian Tracking](https://mlsanity.com/paper/2409.04069/) (2024)
- [Logarithmic Regret and Polynomial Scaling in Online Multi-step-ahead Prediction](https://mlsanity.com/paper/2511.12467/) (2025)
- [Online Multi-Agent Control with Adversarial Disturbances](https://mlsanity.com/paper/2506.18814/) (2025)
- [Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regret](https://mlsanity.com/paper/2607.26370/) (2026)

## Abstract (arXiv)

In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with O(√TVT), where VT is the total variation of the target dynamics and T is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement PLOT on a real quadrotor and provide open-source software, thus, showcasing one of the first successful applications of online control methods on real hardware.