Linear Quadratic Regulator

Also known as LQR

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Overview

Linear quadratic regulation (LQR) finds feedback policies that balance goals such as tracking and low control effort in systems modeled by linear dynamics and quadratic costs. Riccati equations provide the classical solution, while iterative LQR extends the approach to nonlinear trajectories and learning-based methods estimate controllers when system dynamics are unknown. Current work addresses safe and online learning, robustness to disturbances or intermittent communication, and faster computation through parallel algorithms and learned Riccati solvers. A central challenge is extending LQR’s efficient, well-understood guarantees to nonlinear or high-dimensional settings without sacrificing safety, stability, or computational practicality.

Latest papers

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33 papers5 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. Personalized Rollout Allocation for Federated LQR Policy Optimization under Heterogeneous Process Noise

    Oct 31, 2026Mohammadreza Rostami, Shahriar Talebi, Solmaz S. KiaLinear Quadratic RegulatorFederated Learning

    University of California, Irvine, CA, US · University of California, Los Angeles, CA, US

  2. How Tuning, Reference Preview, Actuator Modeling, and Fallback Policies Change Quadrotor Controller Comparisons: A Reproducible Simulation Study

    Oct 26, 2026Xuan-Quy Dao, Le-Minh Nguyen, Ngoc-Bich LeQuadrotor ControlModel Predictive Control

    Eastern International University Binh Duong, Vietnam · Industrial University of Ho Chi Minh City Ho Chi Minh City, Vietnam

  3. Reinforcement learning for constrained stochastic linear--quadratic control in continuous time

    Oct 26, 2026Weiping Wu, Qitong Pan, Xun Li +1Stochastic Optimal ControlLinear Quadratic Regulator

    School of Economics and Management, Fuzhou University, Fuzhou, 350108, Fujian, China · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

  4. Performance Gaps Between Open-Loop, Certainty-Equivalent, and Optimal Control Under Action-Dependent Observations

    Oct 24, 2026Leo Maynard-Zhang, Sunmook Choi, Yahya Sattar +3Stochastic Optimal ControlOptimal Control

    U Washington · Cornell · Imperial College London +1

  5. Solvable models of learning to pursue a moving target

    Oct 22, 2026John J. Vastola, Kanaka RajanLinear Quadratic RegulatorPolicy Learning

    Department of Neurobiology, Harvard Medical School · Department of Psychology and Center for Brain Science, Harvard University · Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University

  6. Square Root Gauss-Newton iLQR

    Sep 17, 2026Maximilian Haas-Heger, Jur van den BergTrajectory OptimizationLinear Quadratic Regulator

    Waabi Innovation Inc.

  7. Closing the Loop on the Poppy Humanoid: Bipedal Locomotion with Linear-Quadratic Control and Learned Cost Functions

    Aug 27, 2026Xulin Chen, Borui He, Ruipeng Liu +3Humanoid Robot LocomotionRobotic Control

    Syracuse University, Syracuse NY 13244, USA

  8. Wasserstein Policy Gradient for Entropy-Regularized Linear-Quadratic Control

    Aug 7, 2026Zhaoyu Zhu, Rui Gao, Shuang LiMaximum Entropy RLPolicy Gradient Methods

    University of Illinois Urbana-Champaign · The University of Texas at Austin · The Chinese University of Hong Kong, Shenzhen

  9. Rake-Compress Riccati Recursions for Parallel Scenario-Tree Model Predictive Control

    Aug 2, 2026João Sousa-PintoModel Predictive ControlLinear Quadratic Regulator

    independent researcher

  10. When Can Safe Controllers Adapt? Information before Commitment

    Jul 18, 2026Venkatesh SaligramaRL ExplorationLinear Quadratic Regulator

    Department of Electrical and Computer Engineering, Boston University, MA 02215

  11. Steering Robustness into World Action Models via Mechanistic Interpretability and Optimal Control

    Jul 16, 2026Jihoon Hong, Julian Skifstad, Qiyue Dai +2World Models for RoboticsAction-Conditioned World Models

    Georgia Institute of Technology

  12. LQG solution for POMDP without estimating states: A minimum variance approach

    Jul 13, 2026Ranjan Sarkar, Prabhat K. MishraStochastic Optimal ControlFeedback Control

    Department of Artificial Intelligence at Indian Institute of Technology Kharagpur, West Bengal, India

  13. Parallel Dynamic Programming for Conic Linear Quadratic Control

    Jun 23, 2026Luyao Zhang, Gabriel Bravo-Palacios, Brian Plancher +1Dynamic ProgrammingFeedback Control

    Delft Center for Systems and Control, TU Delft, The Netherlands · Barnard College, Columbia University, New York, NY 10027 USA · & Dartmouth College, Hanover, NH 03755, USA

  14. Horizon-Uniform Sensitivity Certificates for Finite-Horizon Pontryagin Systems

    Jun 16, 2026Pyuyi Chufeng Huang, Zikang Song, Xingshu ChenDynamical SystemsFeedback Control

    School of Cyber Science and Engineering, Sichuan University, Chengdu, Sichuan, China · School of Mathematics, Sichuan University, Chengdu, Sichuan, China

  15. Activation Steering of Video Generation Models via Reduced-Order Linear Optimal Control

    Jun 3, 2026Jihoon Hong, Alice Chan, Qiyue Dai +2T2V GenerationVideo Generation

    Georgia Institute of Technology Atlanta, GA 30308

  16. When Mean Age Is Not Enough: Distribution-Aware Scheduling for Networked LQR Control

    Jun 3, 2026Abdullah Y. Etcibasi, C. Emre Koksal, Eylem EkiciAge of InformationFeedback Control

    Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA.

  17. SeaVis: Modeling and Control of a Remotely Operated Towed Vehicle for Seabed Visualization and Mapping

    May 14, 2026Abdelhakim Amer, Aske Alstrup, Frederik Rasmussen +3Robotic ControlRobust Control

    Artificial Intelligence in Robotics Laboratory (AiR Lab), Department of Electrical and Computer Engineering, Aarhus University, 8000 Aarhus C, Denmark · EIVA a/s, 8660 Skanderborg, Denmark · Automatic Control Group (RAT), Department of Electrical Engineering and Information Technology, Paderborn University, Paderborn, Germany

  18. Layerwise LQR for Geometry-Aware Optimization of Deep Networks

    May 5, 2026Simon Dufort-Labbé, Pierre-Luc Bacon, Razvan Pascanu +2Deep Learning OptimizationSecond-Order Optimization

    Mila, Université de Montréal · Samsung – SAIL Montreal

  19. Analytic Bridge Diffusions for Controlled Path Generation

    May 3, 2026Michael ChertkovStochastic Optimal ControlSchrödinger Bridges

    Program in Applied Mathematics & Department of Mathematics University of Arizona, AZ 85721, USA

  20. Rate-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulator

    Apr 24, 2026Spencer Hutchinson, Nanfei Jiang, Mahnoosh AlizadehStochastic Linear Dynamical SystemsStochastic Optimal Control

    Department of Electrical and Computer Engineering, University of California Santa Barbara

  21. Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control

    Apr 21, 2026Julian Skifstad, Xinyue Annie Yang, Glen ChouLLM AlignmentLanguage Model-Based Control

    1Georgia Institute of Technology, Atlanta, GA, USA. Schools of Electrical and Computer Engineering · 2Computer Science · 3Cybersecurity and Privacy, Aerospace Engineering

  22. Learning the Riccati solution operator for time-varying LQR via Deep Operator Networks

    Apr 20, 2026Jun Chen, Umberto Biccari, Junmin WangFeedback ControlDeep Operator Networks

  23. FNO∠θ^{\angle θ}: Extended Fourier neural operator for learning state and optimal control of distributed parameter systems

    Apr 6, 2026Zhexian Li, Ketan SavlaFourier Neural OperatorPDE Operator Learning

    Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089, USA. · Sonny Astani Department of Civil and Environmental Engineering, the Daniel Epstein Department of Industrial and Systems Engineering, and the Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA 90089, USA.

  24. Scalar Federated Learning for Linear Quadratic Regulator

    Apr 6, 2026Mohammadreza Rostami, Shahriar Talebi, Solmaz S. KiaFederated LearningLinear Quadratic Regulator

    University of California, Irvine, CA, US · University of California, Los Angeles, CA, US

  25. A Novel Hybrid PID-LQR Controller for Sit-To-Stand Assistance Using a CAD-Integrated Simscape Multibody Lower Limb Exoskeleton

    Apr 4, 2026Ranjeet Kumbhar, Rajmeet Singh, Appaso M Gadade +2Assistive RoboticsLinear Quadratic Regulator

    Department of Mechanical Engineering Thapar Institute of Engineering and Technology Patiala, India · Khalifa University Center for Autonomous Robotic Systems (KUCARS) Khalifa University Abu Dhabi, UAE

  26. Optimistic Online LQR via Intrinsic Rewards

    Mar 30, 2026Marcell Bartos, Bruce D. Lee, Lenart Treven +3Linear Quadratic RegulatorRegret Minimization in RL

    ETH Zürich, Zürich, Switzerland

  27. Separation is Optimal for LQR under Intermittent Feedback

    Mar 29, 2026Abdullah Y. Etcibasi, C. Emre Koksal, Eylem EkiciSequential Decision MakingStochastic Optimal Control

    The Ohio State University

  28. A Schrödinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control

    Mar 24, 2026Louis Claeys, Artur Goldman, Zebang Shen +1Stochastic Optimal ControlHJB Equations

    ETH Zürich, Department of Mathematics · ETH Zürich, ETH AI Center, Institute for Machine Learning · ETH Zürich, Institute for Machine Learning

  29. Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part II

    Mar 8, 2026Yi Tian, Kaiqing Zhang, Russ Tedrake +1Linear Quadratic RegulatorState Representation Learning

    Massachusetts Institute of Technology · University of Maryland, College Park · Technical University Munich

  30. Douglas-Rachford Splitting for Group-Sparse Feedback Linear-Quadratic Control

    Jul 26, 2025Lechen Feng, Xun Li, Yuan-Hua NiDistributed OptimizationDistributed Control

    Department of Applied Mathematics, The Hong Kong Polytechnic University, China · College of Artificial Intelligence, Nankai University, Tianjin, China