Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods (2202.11762v2)

Abstract: Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies -- these certificates provide concise, data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned controller but also provide supervision during training, allowing safety and stability requirements to influence the training process itself. In this paper, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this paper will serve as an accessible introduction to the theory and practice of certificate learning, both to those who wish to apply these tools to practical robotics problems and to those who wish to dive more deeply into the theory of learning for control.

• The paper presents neural network methods for synthesizing certificates that ensure stability and safety without relying on a predefined controller.
• It demonstrates joint learning of certificates and control policies, broadening safe control applications in complex, nonlinear systems.
• The work addresses real-world challenges like state estimation errors and model uncertainties, offering robust strategies for autonomous systems.

Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control

The paper, "Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control," authored by Charles Dawson, Sicun Gao, and Chuchu Fan, explores the development of safe control systems in robotics facilitated by learning algorithmic certificates. These certificates ensure stability and safety, presenting a significant advancement given the historically challenging problem of synthesizing such control assurances for nonlinear systems.

Overview

The authors present a comprehensive survey on the development and application of neural network-based methods for crafting control-theoretic certificates. Certificates, such as Lyapunov functions, barrier functions, and contraction metrics, serve critical roles in defining and proving desirable properties like stability and safety in dynamical systems. Traditional approaches to synthesizing these certificates, such as Sum-of-Squares (SoS) optimization and simulation-guided synthesis, often suffer from scalability and applicability limitations, particularly with complex nonlinear dynamics. The neural certificate approach, by contrast, leverages the representation power of neural networks to address these challenges by learning certificates from data directly.

Key Contributions

• Learning Certificates Independent of Controllers: The paper discusses methods for synthesizing certificates like Lyapunov functions without a predefined controller. The neural approach here allows the system to find a stabilizing certificate that optionally can also imply a controller, notably a Control Lyapunov Function (CLF) or Control Barrier Function (CBF).
• Joint Learning with Control Policies: It expands on frameworks where both certificates and control policies are learned simultaneously. Techniques for embedding these into reinforcement learning contexts are also explored, significantly broadening the applicability of certificates to more complex settings with unknown models.
• Implementation Considerations: Acknowledging real-world challenges such as state estimation errors, observation-feedback control, and model uncertainty, the survey presents techniques to mitigate these effects. Frameworks for robust control that accommodate bounded uncertainties and methods for verifying neural network-derived certificates using optimization and learning theory provide robust strategies for deployment.

Implications and Future Directions

The application of neural network-based certificate learning is poised to significantly impact the design of safe controllers for complex autonomous systems. Real-time considerations, such as control frequency and actuation limits, are elegantly addressed by leveraging the capabilities of neural networks, providing a viable pathway for deploying learning-enabled controllers on resource-constrained hardware.

The paper sets the stage for future developments in several domains:

• Model-Free Certificate Learning: Advancing reinforcement learning techniques that integrate certificates without relying on precise model knowledge.
• Distributed and Multi-Agent Systems: Addressing the scalability aspects in systems with numerous interacting agents, potentially benefiting from graph neural networks to model inter-agent dynamics.
• Generalization and Verification: Establishing firmer theoretical guarantees on generalization and robust methodologies for certificate verification in high-dimensional spaces.

In conclusion, the survey synthesizes existing research and outlines a pathway for leveraging neural certificates to address the safety and stability challenges in robotic control systems. By leveraging the representational capacity of neural networks, this framework offers promising scalability and adaptability for designing robust control solutions in increasingly complex autonomous systems.