Neural Lyapunov Control

Abstract

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.

NeurIPS 2019

Cited by in corpus (37)

• Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview
• Formal Synthesis of Lyapunov Neural Networks
• Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach
• Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates
• Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers
• Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimization
• Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
• Learning Stability Certificates from Data
• Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions
• On the Sample Complexity of Stability Constrained Imitation Learning
• Neural Termination Analysis
• Learning Certified Control using Contraction Metric
• Neural Lyapunov Differentiable Predictive Control
• Towards Learning and Verifying Maximal Neural Lyapunov Functions
• Enforcing robust control guarantees within neural network policies
• Offline Reinforcement Learning for Autonomous Driving with Safety and Exploration Enhancement
• Almost Surely Stable Deep Dynamics
• Value Iteration in Continuous Actions, States and Time
• Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Data-driven invariant set for nonlinear systems with application to command governors
• Neural Identification for Control
• Composed Physics- and Data-driven System Identification for Non-autonomous Systems in Control Engineering
• Learning Safe Neural Network Controllers with Barrier Certificates
• Transient Stability Assessment of Networked Microgrids Using Neural Lyapunov Methods
• Learning Density Distribution of Reachable States for Autonomous Systems
• Lyapunov-Regularized Reinforcement Learning for Power System Transient Stability
• Neural Lyapunov Redesign
• Lyapunov-stable neural-network control
• Learning Dynamics Models with Stable Invariant Sets
• Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems
• Continuous Lyapunov Controller and Chaotic Non-linear System Optimization using Deep Machine Learning
• Formal controller synthesis for hybrid systems using genetic programming
• Stabilizing Neural Control Using Self-Learned Almost Lyapunov Critics
• Robustly Learning Regions of Attraction from Fixed Data
• Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guarantees
• Learning Region of Attraction for Nonlinear Systems