Lyapunov-Based Control

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Sep 22, 2026cs.RO

Vision-based Underwater Formation Control With Input Saturations via Barrier Lyapunov Functions

In this work, we propose a communication-free framework for vision-based formation control of fully actuated underwater robots subject to sensing constraints, collision-avoidance requirements, and input saturations. Recentered barrier Lyapunov functions encode sensing and collision-avoidance constraints, while command-filtered backstepping extends the design to the second-order vehicle dynamics. The resulting control objective is enforced through a quadratic program that explicitly accounts for actuator limits. Conservative sensing domains provide margins from the physical limits and are adaptively relaxed when necessary, allowing temporary violation of the conservative bounds. The proposed approach is validated through realistic Software-in-the-Loop (SITL) simulations in Gazebo.

Nicola De Carli, João Zenário, Victor Nan Fernandez-Ayala +1

Multi-Robot Formation ControlLyapunov-Based ControlUnderwater RoboticsFeedback ControlVision-Based Robot Control
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Sep 15, 2026cs.RO

CALOS: Control-Affine Lyapunov On-manifold Safety Layer for Safe Deep Reinforcement Learning for Quadrotors

Deep Reinforcement Learning has demonstrated remarkable capability in quadrotor control, yet learned policies offer no guarantee of respecting safety constraints during training or deployment. We present CALOS (Control-Affine Lyapunov On-manifold Safety), a runtime safety layer that enforces attitude constraints on a quadrotor without modifying the underlying learning algorithm. CALOS formulates four tilt-angle inequalities and a Lyapunov descent condition as a single quadratic program whose solution is the minimum-norm correction to the nominal torque output of the policy. The quadratic program is solved exactly via active-set enumeration over the three-dimensional torque space, with a computational cost low enough to enforce constraints in real time across thousands of parallel simulation environments, as required by modern massively parallel Deep Reinforcement Learning training. Evaluated on trajectory-tracking tasks in NVIDIA Isaac Lab, CALOS reduces lateral tracking error by 55-60% relative to an unconstrained Proximal Policy Optimization baseline while achieving zero attitude-constraint violations on the training trajectory. By restricting exploration to safe regions of the state space, the safety layer also accelerates training convergence and improves data efficiency without producing suboptimal policies.

Fabrizio Cesareo, Sebastiano Mengozzi, Nicola Mimmo +1

Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi” — DEI University of Bologna, Italy

RL ControlLyapunov-Based ControlQuadratic ProgrammingQuadrotor ControlSafe RL
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Jul 19, 2026eess.SY

Optimal Safety Control using High-Order Control Barrier Functions

This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.

Neng Li, Zuodong Pan, Jiaxing Wang +2

Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116024, China

Lyapunov-Based ControlSafety-Critical ControlControl Barrier Functions
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Jul 15, 2026cs.LG

Lyapunov Guidance: A Unified Framework for Stabilizing Generative Flows

Flow matching has emerged as an effective framework for learning complex data distributions, but adapting pretrained flow models to new tasks often requires computationally expensive retraining. Post-training guidance provides a more efficient alternative, but existing methods are largely heuristic and offer no explicit stability guarantees. We address this limitation by proposing LyaGuide, a unified Lyapunov-guided framework that formulates flow guidance as a Lyapunov control problem. Our main theoretical result establishes an equivalence between guided flow matching and Lyapunov control, thereby unifying common guidance strategies, such as classifier guidance, reward guidance, and energy-based guidance, within a single control-theoretic framework. To enforce the Lyapunov condition, we introduce a pseudo-projection operator with a closed-form expression that endows learned or heuristic guidance terms with explicit stability guarantees. LyaGuide supports two practical settings: a model-driven setting, where the target guidance distribution is specified through a known Lyapunov function, and a data-driven setting, where the guidance is adapted from task-specific downstream data. LyaGuide is compatible with existing guidance methods, introduces minimal additional computational overhead, and is straightforward to integrate in practice. Extensive experiments on synthetic benchmarks, image inverse problems, reinforcement learning planning, and energy-based modeling demonstrate consistent improvements in sample quality, guidance fidelity, and robustness, while maintaining computational efficiency.

Jingdong Zhang, Xinze Li, Yize Jiang +3

Department of Mathematics and I-X, Imperial College London, London, United Kingdom · MicroCyto, Beijing, China · Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, China +1

Flow MatchingLyapunov-Based ControlInference-Time Guidance
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Jul 5, 2026cs.LG

Lyapunov-Guided Training for Hardware-Safe Neural Networks Under Fixed-Point Arithmetic

Low-precision neural networks are attractive for resource-constrained hardware, but fixed-point arithmetic introduces failure modes that are often hidden by idealised quantisation models. In particular, two's-complement overflow wrapping can corrupt hidden activations by changing both their magnitude and sign, leading to unstable numerical error propagation and severe accuracy degradation. This paper proposes a Lyapunov-stabilised quantisation framework for low-precision neural networks operating under hardware-style wrapping arithmetic. The hidden-state energy is monitored through a layerwise Lyapunov function, and a monotone projection is applied to enforce bounded and non-increasing state evolution across depth. The method is evaluated on MNIST using a compact patch-based transformer under post-training quantisation and quantisation-aware training with fixed-point bit-widths from 4 to 16 bits. Monte Carlo results show that unconstrained wrapped quantisation-aware training collapses to near-chance accuracy across 6-16 bits, with activation overflow rates exceeding 11%. In contrast, the proposed monotone Lyapunov projection suppresses activation overflow to below 0.012% and restores stable low-precision learning, achieving 86.55% accuracy at 12 bits. These results demonstrate that Lyapunov-based state control can act as a hardware-aware stabilisation mechanism for reliable fixed-point neural inference and training.

Anis Hamadouche, Amir Hussain

The School of Engineering & Physical Sciences Heriot-Watt University Edinburgh EH14 4AS, UK · SDAIA-KFUPM Joint Research Centre for Artificial Intelligence King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia

Lyapunov-Based ControlQuantization-Aware TrainingPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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Jun 26, 2026eess.SY

Reachability Guarantees for Cart-Pole Swing-Up and Stabilization

The cart-pole swing-up is a canonical benchmark for nonlinear control of underactuated systems, yet an end-to-end guarantee linking the global swing-up maneuver to the local stabilizer is seldom formalized. We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium from a compact set of initial conditions. The swing-up law is derived from an energy-error Lyapunov function; canceling the autonomous conservative term yields a strictly sign-definite Lyapunov derivative, and convergence follows from LaSalle's invariance principle. We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence. For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition. Numerical simulations corroborate the theoretical analysis.

Mohamed Khalid M Jaffar

Department of Aerospace Engineering University of Maryland, College Park, USA

Reachability AnalysisLyapunov-Based ControlLyapunov Stability
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Jun 24, 2026cs.RO

Learning to Adapt: Reptile-D-Learning for Robust and Efficient Control Under Parametric Uncertainty

Learning-based Lyapunov Control (LLC) provides formal stability guarantees for nonlinear systems, but its validity relies heavily on accurate system models. Parameter variations and uncertainties may invalidate stability constraints, leading to costly retraining. Although D-learning can estimate Lyapunov derivatives without relying on explicit dynamics models, it remains limited by single-task dynamics and degrades under large parameter shifts. We propose Reptile-D-learning, a framework that leverages the Reptile meta-learning algorithm to capture shared dynamical structures across systems with different parameters, thereby learning a generalizable Lyapunov network initialization and a high-performance controller. Experiments on multiple nonlinear control systems demonstrate that Reptile-D-learning significantly improves both generalization and rapid adaptation to unseen parameter configurations.

Haipeng Cao, Zhaolong Shen, Quan Quan

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, P.R. China

Lyapunov-Based ControlRobust ControlAdaptive Control
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Jun 13, 2026eess.SY

Robust Conformal CBF and CLF Controllers via Iterative Policy Updates

Conformal prediction (CP) has been used to obtain probabilistic bounds on the error between a learned dynamics model and the true but unknown system. Such CP bounds can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm, which we demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

Omid Mirzaeedodangeh, Eliot Shekhtman, Nikolai Matni +1

1Automatic Control Laboratory, ETH Zürich, Switzerland. · 2Computer and Information Science, University of Pennsylvania, USA. · 3Electrical and Systems Engineering, University of Pennsylvania, USA.

Distribution Shift RobustnessLyapunov-Based ControlControl Barrier FunctionsConformal PredictionRobust Control
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May 26, 2026cs.RO

L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking

This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often suffer from performance degradation in dynamic and uncertain environments, data-driven approaches, while more adaptable, are frequently limited by high sample complexity and a lack of rigorous stability guarantees. L-Learning mitigates these challenges by explicitly learning the system's energy function from data, thereby optimizing performance while ensuring closed-loop stability intrinsically. Characterized by superior control accuracy, theoretical stability guarantees, and high sample efficiency, L-Learning represents a promising solution for practical robotic applications.

Quan Quan, Hao Li

1Quan Quan and Hao Li are with School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Robotic ControlRobot Trajectory TrackingLyapunov-Based ControlData-Driven Control
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May 11, 2026cs.LG

Learning When to Act: Communication-Efficient Reinforcement Learning via Run-Time Assurance

Safe reinforcement learning (RL) typically asks what\textit{what} an agent should do. We ask when\textit{when} it needs to act, and show that a single policy can jointly learn control inputs and communication-efficient timing decisions under a pointwise Lyapunov safety shield. We focus on stabilization around a known equilibrium, where CARE-based LQR backups, Lyapunov certificates, and classical Lyapunov-STC are well defined, enabling clean comparison against analytical baselines. A run-time assurance (RTA) layer overrides the policy via a one-step-ahead Lyapunov prediction and a precomputed LQR backup, providing a strictly stronger guarantee than constrained MDP methods that enforce safety only in expectation. On an inverted pendulum, cart--pole, and planar quadrotor, the learned policy achieves 1.91×1.91\times, 1.45×1.45\times, and 3.51×3.51\times higher mean inter-sample interval (MSI) than a Lyapunov-triggered baseline; a fixed LQR controller at the same average rate is unstable on all three plants, showing that adaptive timing, not a lower average rate, makes sparsity safe. A CARE-derived Lyapunov reward transfers across environments without redesign, with a single weight wcw_c controlling the stability--communication tradeoff; ablations confirm the RTA shield is essential, with its removal reducing MSI by 1.271.27--1.84×1.84\times and degrading state norms. A preference-conditioned extension recovers the full tradeoff frontier from one model at 211\tfrac{2}{11} of training compute, and SAC experiments show the results are algorithm-agnostic across discrete and continuous domains. A 12-state 3D quadrotor case study extends the framework to higher-dimensional systems where classical STC is intractable, and robustness to ±30%\pm30\% mass variation and disturbances shows graceful degradation, with the RTA absorbing what the learned policy cannot.

Adam Haroon, Erick J. Rodríguez-Seda, Cody Fleming +1

Department of Mechanical Engineering, Iowa State University, Ames, IA, USA · Navy Center for Applied Research in Artificial Intelligence (NCARAI), U.S. Naval Research Laboratory, Washington, D.C., USA · Department of Weapons, Robotics, and Control Engineering, United States Naval Academy, Annapolis, MD, USA

RL ControlLyapunov-Based ControlRobot SafetyFeedback ControlRuntime AssuranceSafe RL+1
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May 7, 2026cs.LG

Learned Lyapunov Shielding for Adaptive Control

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function VψV_ψ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint V˙ψ+αVψ≤0\dot V_ψ+ αV_ψ\le 0, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.

Giansalvo Cirrincione, Adriano Fagiolini

Laboratoire LTI, Université de Picardie Jules Verne, Amiens, France. · MIRPALab, Department of Engineering, University of Palermo, 90128 Palermo, Italy.

Lyapunov-Based ControlSafe RLAdaptive Control
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