mlsanityData to 14 Oct 2026

Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems

arXiv 2106.10497 ↗First posted 19 Jun 2021math.OC cs.SY eess.SYcited by 25

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Abstract (arXiv)

We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future k time steps. We show that when the prediction window k is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of O(λk T), where λ < 1 is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. Under more assumptions on the terminal costs, we also show that predictive control obtains the first competitive bound for the control of linear time-varying systems: 1 + O(λk). Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Jun 2021.

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Citing papers per year: 2021: 2; 2022: 2; 2023: 7; 2024: 6; 2025: 4; 2026: 4.

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  1. 2023Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictionscited by 8
  2. 2024Reinforcement Learning with Lookahead Informationcited by 8
  3. 2024The Value of Reward Lookahead in Reinforcement Learningcited by 6
  4. 2021Online Optimization with Feedback Delay and Nonlinear Switching Costcited by 5
  5. 2023Near-Optimal Adversarial Reinforcement Learning with Switching Costscited by 4
  6. 2024Long-term Safe Reinforcement Learning with Binary Feedbackcited by 4
  7. 2024CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Designcited by 4
  8. 2025On the Hardness of Reinforcement Learning with Transition Look-Aheadcited by 4
  9. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  10. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  11. 2025Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approachcited by 3
  12. 2026AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Controlcited by 3
13 more
  1. 2023Best of Both Worlds Guarantees for Smoothed Online Quadratic Optimizationcited by 2
  2. 2024Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Informationcited by 2
  3. 2022Bayesian Learning Approach to Model Predictive Controlcited by 1
  4. 2023Anytime-Competitive Reinforcement Learning with Policy Priorcited by 1
  5. 2023Out-of-Distribution-Aware Electric Vehicle Chargingcited by 1
  6. 2025Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learningcited by 1
  7. 2022Learning to Control under Time-Varying Environmentcited by 0
  8. 2023Sub-linear Regret in Adaptive Model Predictive Controlcited by 0
  9. 2023Data-Guided Regulator for Adaptive Nonlinear Controlcited by 0
  10. 2025Smoothed Online Optimization for Target Tracking: Robust and Learning-Augmented Algorithmscited by 0
  11. 2026SCaLE: Switching Cost aware Learning and Explorationcited by 0
  12. 2026Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batchingcited by 0
  13. 2026Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regretcited by 0