Stabilization Learning: A Paradigm Transition Bridging Control Theory and Machine Learning

Stabilization learning is an interdisciplinary paradigm that bridges control theory and machine learning. Its core idea is to enable systems to adjust their policies under perturbations or environmental changes through real-time feedback and adaptive mechanisms. It takes stability as its primary goal, distinguishing itself from certificate learning, which focuses on formal proofs, and reinforcement learning, which pursues optimality. It encompasses a range of methods, including Lyapunov-based analysis and design, deep feature extraction, and data-driven feedback synthesis, and is applicable to complex high-dimensional, nonlinear systems. This paper elaborates on the two major categories of stability in stabilization learning, as well as three typical application scenarios: control, observation, and recognition. It constructs a unified mathematical framework based on a six-tuple, and expands into two types of seven-tuple models: constrained learning with barrier spaces and tracking problems with targets. It also analyzes the roles, meanings, and implementation choices of key elements such as state space, controlled system, metrics, and policy. Through the formal reformulation of 11 types of problems, including multi-agent cooperative tracking, visual servo robot position stabilization, chess games, and Push-T tasks, this paper illustrates the potential applicability of the framework across multiple domains. Finally, it points out that future stabilization learning will focus on two major directions: constructing a unified problem framework and achieving efficient and robust learning, providing solutions for complex system control that combine theoretical rigor with engineering practicality.

Energy-Optimal Spatial Iterative Learning within a Virtual Tube

Due to the limited endurance of embedded energy sources such as lithium-polymer (LiPo) batteries, the flight duration and operational range of unmanned aerial vehicles (UAVs) are severely constrained. Although energy-efficient trajectory planning and control have been widely studied, most existing approaches rely on accurate system models and computationally expensive optimization procedures. This paper proposes a model-free online iterative learning (IL) framework to minimize energy consumption. Without requiring explicit models of UAV dynamics or energy consumption, the proposed method improves energy efficiency while maintaining a low computational cost. The per-iteration computational complexity is O(n), where n denotes the number of path points. In the tested cases, the proposed method is approximately 50--60 times faster than the model-based IPOPT benchmark. Simulation results and real-world flight experiments across multiple UAV platforms validate the effectiveness, computational efficiency, and practical applicability of the proposed approach.

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.

Multi-Modal Agents for Power Distribution Defect Detection: An Evaluation of Foundation Models

The power distribution network is critical to reliable electricity delivery, yet traditional inspection methods face limitations in semantic understanding, generalization, and closed-loop automation. To address these challenges, this paper proposes a Multi-Modal Agent framework specifically for power distribution defect detection. Central to this study is the systematic evaluation of multimodal foundation models as unified cognitive engines. We rigorously assess their integrated performance across three critical capabilities: (1) Perception, where the model must accurately identify equipment and generate expert-level descriptions of defects; (2) Reasoning, where the model interprets visual findings to diagnose causes, assess severity, and plan maintenance strategies based on domain knowledge; and (3) Tool Usage, where the model acts as an autonomous operator to execute actions -- such as querying knowledge bases or generating work orders -- to achieve closed-loop maintenance. To support this evaluation, a domain-specific evaluation dataset and a comprehensive benchmark are developed. Experimental results demonstrate the strengths and limitations of current foundation models in these three dimensions, providing empirical evidence for deploying autonomous agents in high-stakes industrial environments.

Planar-Sector LOS Guidance for Interception of Agile Targets with Lifting-Wing Quadcopters

Autonomous visual interception of agile aerial targets is challenging due to unpredictable target motion, limited sensing, and the strong coupling between target visibility and interceptor maneuverability. Most existing strapdown-camera interception methods preserve visibility using conic line-of-sight (LOS) constraints that keep the target near the image center. While safe, such symmetric constraints unnecessarily restrict maneuverability and can significantly reduce the usable thrust for pursuit. Motivated by the observation that aggressive FPV pilots do not maintain equal visibility margins in all image directions, this paper proposes a Planar-Sector Line-of-Sight (PS-LOS) guidance framework for autonomous interception using a lifting-wing quadcopter equipped with only a strapdown monocular camera. PS-LOS tightly constrains lateral image error while relaxing longitudinal image error within a safe field-of-view margin, preserving visibility while releasing maneuverability for acceleration-intensive pursuit. Under the lifting-wing quadcopter model, PS-LOS provides nearly 50% more available thrust near the LOS direction than conventional conic LOS constraints. To realize LOS-only interception without direct depth measurements, a delay-compensated state-estimation framework and a nonlinear guidance-and-control architecture are developed for lifting-wing quadcopters. Extensive outdoor flight experiments demonstrate autonomous interception of agile targets exhibiting large-amplitude, high-frequency, and unpredictable motion under real wind disturbances. The proposed system achieves successful interceptions at ranges up to 138 m while maintaining continuous visual tracking throughout the engagement. The results validate PS-LOS as a visibility-preserving, maneuverability-aware guidance framework for long-range visual interception of agile aerial targets.

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.

Virtual-Tube-Based Cooperative Transport Control for Multi-UAV Systems in Constrained Environments

This paper proposes a novel control framework for cooperative transportation of cable-suspended loads by multiple unmanned aerial vehicles (UAVs) operating in constrained environments. Leveraging virtual tube theory and principles from dissipative systems theory, the framework facilitates efficient multi-UAV collaboration for navigating obstacle-rich areas. The proposed framework offers several key advantages. (1) It achieves tension distribution and coordinated transportation within the UAV-cable-load system with low computational overhead, dynamically adapting UAV configurations based on obstacle layouts to facilitate efficient navigation. (2) By integrating dissipative systems theory, the framework ensures high stability and robustness, essential for complex multi-UAV operations. The effectiveness of the proposed approach is validated through extensive simulations, demonstrating its scalability for large-scale multi-UAV systems. Furthermore, the method is experimentally validated in outdoor scenarios, showcasing its practical feasibility and robustness under real-world conditions.

MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Control

Achieving provable stability in model-free reinforcement learning (RL) remains a challenge, particularly in balancing exploration with rigorous safety. This article introduces MSACL, a framework that integrates exponential stability theory with maximum entropy RL through multi-step Lyapunov certificate learning. Unlike methods relying on complex reward engineering, MSACL utilizes off-policy multi-step data to learn Lyapunov certificates satisfying theoretical stability conditions. By introducing Exponential Stability Labels (ESL) and a $λ$-weighted aggregation mechanism, the framework effectively balances the bias-variance trade-off in multi-step learning. Policy optimization is guided by a stability-aware advantage function, ensuring the learned policy promotes rapid Lyapunov descent. We evaluate MSACL across six benchmarks, including stabilization and nonlinear tracking tasks, demonstrating its superiority over state-of-the-art Lyapunov-based RL algorithms. MSACL achieves exponential stability and rapid convergence under simple rewards, while exhibiting significant robustness to uncertainties and generalization to unseen trajectories. Sensitivity analysis establishes the multi-step horizon $n=20$ as a robust default across diverse systems. By linking Lyapunov theory with off-policy actor-critic frameworks, MSACL provides a foundation for verifiably safe learning-based control. Source code and benchmark environments will be made publicly available.

RflyUT-Sim: A Simulation Platform for Development and Testing of Complex Low-Altitude Traffic Control

Significant challenges are posed by simulation and testing in the field of low-altitude unmanned aerial vehicle (UAV) traffic due to the high costs associated with large-scale UAV testing and the complexity of establishing low-altitude traffic test scenarios. Stringent safety requirements make high fidelity one of the key metrics for simulation platforms. Despite advancements in simulation platforms for low-altitude UAVs, there is still a shortage of platforms that feature rich traffic scenarios, high-precision UAV and scenario simulators, and comprehensive testing capabilities for low-altitude traffic. Therefore, this paper introduces an integrated high-fidelity simulation platform for low-altitude UAV traffic. This platform simulates all components of the UAV traffic network, including the control system, the traffic management system, the UAV system, the communication network , the anomaly and fault modules, etc. Furthermore, it integrates RflySim/AirSim and Unreal Engine 5 to develop full-state models of UAVs and 3D maps that model the real world using the oblique photogrammetry technique. Additionally, the platform offers a wide range of interfaces, and all models and scenarios can be customized with a high degree of flexibility. The platform's source code has been released, making it easier to conduct research related to low-altitude traffic.

Self-Organizing Aerial Swarm Robotics for Resilient Load Transportation : A Table-Mechanics-Inspired Approach

In comparison with existing approaches, which struggle with scalability, communication dependency, and robustness against dynamic failures, cooperative aerial transportation via robot swarms holds transformative potential for logistics and disaster response. Here, we present a physics-inspired cooperative transportation approach for flying robot swarms that imitates the dissipative mechanics of table-leg load distribution. By developing a decentralized dissipative force model, our approach enables autonomous formation stabilization and adaptive load allocation without the requirement of explicit communication. Based on local neighbor robots and the suspended payload, each robot dynamically adjusts its position. This is similar to energy-dissipating table leg reactions. The stability of the resultant control system is rigorously proved. Simulations demonstrate that the tracking errors of the proposed approach are 20%, 68%, 55.5%, and 21.9% of existing approaches under the cases of capability variation, cable uncertainty, limited vision, and payload variation, respectively. In real-world experiments with six flying robots, the cooperative aerial transportation system achieved a 94% success rate under single-robot failure, disconnection events, 25% payload variation, and 40% cable length uncertainty, demonstrating strong robustness under outdoor winds up to Beaufort scale 4. Overall, this physics-inspired approach bridges swarm intelligence and mechanical stability principles, offering a scalable framework for heterogeneous aerial systems to collectively handle complex transportation tasks in communication-constrained environments.