Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes

Abstract

Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller renders an equilibrium point asymptotically stable. The ROA is typically estimated based on a model of the system. However, since models are only an approximation of the real world, the resulting estimated safe region can contain states outside the ROA of the real system. This is not acceptable in safety-critical applications. In this paper, we consider an approach that learns the ROA from experiments on a real system, without ever leaving the true ROA and, thus, without risking safety-critical failures. Based on regularity assumptions on the model errors in terms of a Gaussian process prior, we use an underlying Lyapunov function in order to determine a region in which an equilibrium point is asymptotically stable with high probability. Moreover, we provide an algorithm to actively and safely explore the state space in order to expand the ROA estimate. We demonstrate the effectiveness of this method in simulation.

Proc. of the Conference on Decision and Control (CDC) 2016 (extended version), 7 pages, code and experiment documentation available at https://github.com/befelix/lyapunov-learning

Cited by in corpus (9)

• Online learning-based Model Predictive Control with Gaussian Process Models and Stability Guarantees
• Barrier-Certified Adaptive Reinforcement Learning with Applications to Brushbot Navigation
• Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems
• Barrier Functions in Cascaded Controller: Safe Quadrotor Control
• Personalized Optimization with User's Feedback
• Learning a Low-dimensional Representation of a Safe Region for Safe Reinforcement Learning on Dynamical Systems
• Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes
• Deep Learning for Robotic Mass Transport Cloaking
• A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability