Control Barriers in Bayesian Learning of System Dynamics

TL;DR

This paper introduces a Bayesian learning framework using matrix variate Gaussian processes to model system dynamics online, ensuring safety through chance constraints on control Lyapunov and barrier functions, adaptable with a self-triggering mechanism.

Contribution

It develops a novel MVGP regression method for nonlinear control systems and integrates safety constraints into real-time control synthesis with a self-triggering approach.

Findings

Efficient covariance factorization for MVGP improves learning speed.

Probabilistic safety guarantees via CLF-CBF constraints.

Safe control policies synthesized through SOCP for systems with arbitrary relative degree.

Abstract

This paper 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 (SOCP). 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.