Control Barriers in Bayesian Learning of System Dynamics

This article focuses on learning a model of system dynamics online, while satisfying safety constraints. Our objective is to avoid offline system identification or hand-specified models and allow a system to safely and autonomously estimate and adapt its own model during operation. Given streaming o...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 1; pp. 214 - 229
Main Authors: Dhiman, Vikas, Khojasteh, Mohammad Javad, Franceschetti, Massimo, Atanasov, Nikolay
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Bayes methods
Bayesian analysis
Control barrier function (CBF)
Control systems
Gaussian process
Gaussian processes
high relative-degree system safety
learning for dynamics and control
Liapunov functions
Machine learning
Nonlinear control
Nonlinear dynamical systems
Probabilistic logic
Safety
self-triggered safe control
Stability analysis
Statistical analysis
System dynamics
System identification
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article focuses on learning a model of system dynamics online, while satisfying safety constraints. Our objective is to avoid offline system identification or hand-specified models and allow a system to safely and autonomously estimate and adapt its own model during operation. Given streaming observations of the system state, we use Bayesian learning to obtain a distribution over the system dynamics. Specifically, we propose a new matrix variate Gaussian process (MVGP) regression approach with an efficient covariance factorization to learn the drift and input gain terms of a nonlinear control-affine system. The MVGP distribution is then used to optimize the system behavior and ensure safety with high probability, by specifying control Lyapunov function (CLF) and control barrier function (CBF) chance constraints. We show that a safe control policy can be synthesized for systems with arbitrary relative degree and probabilistic CLF-CBF constraints by solving a second-order cone program. Finally, we extend our design to a self-triggering formulation, adaptively determining the time at which a new control input needs to be applied in order to guarantee safety.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3137059