Optimal Control

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Overview

Optimal control asks how to steer a system over time toward goals while minimizing costs such as energy, time, or tracking error and respecting limits on actions and states. Classical approaches include Pontryagin’s maximum principle, dynamic programming and Hamilton–Jacobi–Bellman equations, and numerical methods such as direct collocation, differential dynamic programming, and model predictive control. Recent work also uses reinforcement learning, differentiable simulators, and neural surrogates to speed up planning or handle complex models, with applications ranging from robotics and aerospace to energy systems and PDEs. A central challenge is making these methods fast enough for real-time, high-dimensional tasks without losing reliability when models are uncertain or safety guarantees are needed.

Latest papers

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139 papers11 papers in the last four weeks, up 22% on the four weeks before. 0.1% of all new papers.

  1. Generalizable Optimal Control with Transformers: One Policy Across Diverse Systems

    Mar 16, 2026Turki Bin Mohaya, Maitham F. AL-Sunni, John M. Dolan +1Optimal ControlNeural Network Control

    Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA

  2. State-space models through the lens of ensemble control

    Mar 13, 2026Ye Feng, Jianfeng LuMirror DescentOptimal Control

  3. Parallel-in-Time Nonlinear Optimal Control via GPU-native Sequential Convex Programming

    Mar 11, 2026Yilin Zou, Zhong Zhang, Maxime Robic +1Optimal ControlGPU Acceleration

    School of Aerospace Engineering, Tsinghua University, 100084 Beijing, China. · Department of Aerospace Science and Technology, Politecnico di Milano, 20156 Milan, Italy.

  4. An Optimal Control Approach To Transformer Training

    Mar 10, 2026Kağan Akman, Naci Saldi, Serdar YükselTransformerTransformer Training Dynamics

    Department of Mathematics, Bilkent University, Ankara, 06800, Turkey · Department of Mathematics and Statistics, Queen’s University, Kingston K7L 3N6, ON, Canada

  5. Receding-Horizon Nullspace Optimization for Actuation-Aware Control Allocation in Omnidirectional UAVs

    Mar 6, 2026Riccardo Pretto, Mahmoud Hamandi, Abdullah Mohamed Ali +3Aerial RoboticsOptimal Control

    Tampere University, Finland · New York University Abu Dhabi, Abu Dhabi, UAE

  6. Accelerating Sampling-Based Control via Learned Linear Koopman Dynamics

    Mar 5, 2026Wenjian Hao, Yuxuan Fang, Zehui Lu +1Robotic ControlRobot Trajectory Tracking

    independent researcher

  7. RAmmStein: Regime Adaptation in Mean-reverting Markets with Stein Thresholds -- Optimal Impulse Control in Concentrated AMMs

    Feb 23, 2026Pranay AnchuriHJB EquationsDecentralized Finance

    Offchain Labs

  8. Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs

    Feb 12, 2026Yongcun Song, Xiaoming Yuan, Hangrui Yue +1Optimal ControlConstrained Optimization

    Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore. · Department of Mathematics, The University of Hong Kong, Pok Fu Lam, Hong Kong SAR, China. · School of Mathematical Sciences, Nankai University, Tianjin 300071, China.

  9. Soft Swing-up: Benchmarking Model-Based Optimal Control for Rigid-Soft Underactuated Systems

    Feb 3, 2026Daniele Caradonna, Nikhil Nair, Anup Teejo Mathew +5Robotic ControlModel Predictive Control

    The BioRobotics Institute, Scuola Superiore Sant’Anna, Pisa, Italy · Department of Excellence in Robotics and AI, Scuola Superiore Sant’Anna, Pisa, Italy · Department of Cognitive Robotics, Delft University of Technology, 2628 CN Delft, The Netherlands +3

  10. Emergence of Physical Intelligence via Controllable Information Production

    Jan 30, 2026Tristan Shah, Stas TiomkinRobotic RLReinforcement Learning

    Department of Computer Science, Texas Tech University

  11. Soft Fitted Q-Iteration without Bellman Completeness: Occupancy Reweighting and Temperature Annealing

    Dec 30, 2025Lars van der Laan, Nathan KallusReinforcement LearningKL-Regularized RL

    Department of Statistics, University of Washington · Netflix · Cornell University

  12. Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control

    Sep 24, 2025Teruki Kato, Ryotaro Shima, Kenji KashimaData-Driven ControlModel Predictive Control

    Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi, Japan. · Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan

  13. Observed Control - Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons

    Aug 18, 2025Eugene T. Hamzezadeh, Andrew J. PetruskaNonlinear MPCModel Predictive Control

    Colorado School of Mines, Golden, CO 80401, USA

  14. A statistical physics framework for optimal learning

    Jul 10, 2025Francesca Mignacco, Francesco MoriStatistical Physics of LearningNeural Network Training Dynamics

    1Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA · 2Graduate Center, City University of New York, New York, NY 10016, USA · Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA

  15. Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence

    Jun 9, 2025Qi Feng, Gu WangStochastic Optimal ControlPolicy Iteration

    Department of Mathematics, Florida State University, Tallahassee, 32306 · Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609

  16. BR-MPPI: Barrier-Rate Guided MPPI for Enforcing Multiple Inequality Constraints with Learned Signed Distance Fields

    Jun 8, 2025Hardik Parwana, Taekyung Kim, Kehan Long +4Constrained Motion PlanningControl Barrier Functions

    Robotics Department, University of Michigan, Ann Arbor, MI 48109, USA · Contextual Robotics Institute, University of California San Diego, La Jolla, CA 92093, USA. · Toyota Motor North America, Research & Development, Ann Arbor, MI 48105, USA.

  17. Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method

    Feb 10, 2025Thomas LewStochastic Differential EquationsStochastic Optimal Control

    Toyota Research Institute

  18. Safe Learning Control with Optimality and Stability Guarantees

    Jan 26, 2025Xinyang Wang, Hongwei Zhang, Shimin Wang +2Control Barrier FunctionsRobust Control

    Shenzhen Key Lab for Advanced Motion Control and Modern Automation Equipments, School of Intelligence Science and Engineering, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China · School of Data Science, Lingnan University, Hong Kong · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, with M3S, SMART, and with MIT CSAIL +1

  19. Entropic perspective on AI resilience, data-minimal learning and optimal control

    Oct 19, 2023Illia HorenkoData-Efficient LearningAdversarial Robustness

    Chair for Mathematics of AI, Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, Kaiserslautern, 67663, Germany.