Control Barrier Functions With Real-Time Gaussian Process Modeling

TL;DR

This paper introduces a real-time Gaussian process-based method for ensuring system safety through control barrier functions, effectively handling nonparametric uncertainty with efficient updates and guaranteed constraint satisfaction.

Contribution

It develops a recursive, computationally efficient GP update method with an error bound, integrated into CBFs for real-time safety guarantees in uncertain systems.

Findings

Real-time GP updates reduce computational complexity from O(p^3) to O(p^2).

The approach guarantees satisfaction of state constraints.

The method effectively manages nonparametric uncertainty in control systems.

Abstract

We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real time as it is obtained and select old data is removed from the model. This update process helps improve the model estimate while keeping the model size (memory required) and computational complexity fixed. We present a recursive formulation for the model update, which reduces time complexity of the update from O(p3) to O(p2), where p is the number of data used. The GP model includes a computable upper bound on the model error. Together, the model and upper bound are used to construct a control-barrier-function (CBF) constraint that guarantees state constraints are satisfied.