Bayesian Learning-Based Adaptive Control for Safety Critical Systems

Abstract

Deep learning has enjoyed much recent success, and applying state-of-the-art model learning methods to controls is an exciting prospect. However, there is a strong reluctance to use these methods on safety-critical systems, which have constraints on safety, stability, and real-time performance. We propose a framework which satisfies these constraints while allowing the use of deep neural networks for learning model uncertainties. Central to our method is the use of Bayesian model learning, which provides an avenue for maintaining appropriate degrees of caution in the face of the unknown. In the proposed approach, we develop an adaptive control framework leveraging the theory of stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control Barrier Functions) along with tractable Bayesian model learning via Gaussian Processes or Bayesian neural networks. Under reasonable assumptions, we guarantee stability and safety while adapting to unknown dynamics with probability 1. We demonstrate this architecture for high-speed terrestrial mobility targeting potential applications in safety-critical high-speed Mars rover missions.

arXiv commentCorrected an error in section II, where previously the problem was introduced in a non-stochastic setting and wrongly assumed the solution to an ODE with Gaussian distributed parametric uncertainty was equivalent to an SDE with a learned diffusion term. See Lew, T et al. "On the Problem of Reformulating Systems with Uncertain Dynamics as a Stochastic Differential Equation"

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• Probabilistic Safety Constraints for Learned High Relative Degree System Dynamics
• NeBula: Quest for Robotic Autonomy in Challenging Environments; TEAM CoSTAR at the DARPA Subterranean Challenge
• Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties
• Safe Learning-Based Feedback Linearization Tracking Control for Nonlinear System with Event-Triggered Model Update
• Adaptive Meta-Learning for Identification of Rover-Terrain Dynamics
• An Addendum to NeBula: Towards Extending TEAM CoSTAR's Solution to Larger Scale Environments
• High-Relative Degree Stochastic Control Lyapunov and Barrier Functions
• Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safety
• A Safe Control Architecture Based on a Model Predictive Control Supervisor for Autonomous Driving
• Safe Learning MPC with Limited Model Knowledge and Data
• Robust Safety-Critical Control for Dynamic Robotics
• Limits of Probabilistic Safety Guarantees when Considering Human Uncertainty
• Adaptive Safety Margin Estimation for Safe Real-Time Replanning under Time-Varying Disturbance
• On the Problem of Reformulating Systems with Uncertain Dynamics as a Stochastic Differential Equation
• Safe Control of Quadruped in Varying Dynamics via Safety Index Adaptation
• The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networks
• Combining Control Barrier Functions and Behavior Trees for Multi-Agent Underwater Coverage Missions