Risk-Bounded Control with Kalman Filtering and Stochastic Barrier Functions

TL;DR

This paper develops a probabilistic safety control framework combining Kalman filtering and stochastic barrier functions to ensure finite-time system safety under uncertainties, demonstrated through highway lane-changing simulations.

Contribution

It introduces a novel method that integrates Kalman filtering with stochastic control barrier functions to bound failure probabilities in real-time control systems.

Findings

Control inputs can be derived as linear constraints for safety optimization.

The approach effectively bounds failure probabilities in simulation scenarios.

Method enables safe control with noisy measurements and uncertainties.

Abstract

In this paper, we study Stochastic Control Barrier Functions (SCBFs) to enable the design of probabilistic safe real-time controllers in presence of uncertainties and based on noisy measurements. Our goal is to design controllers that bound the probability of a system failure in finite-time to a given desired value. To that end, we first estimate the system states from the noisy measurements using an Extended Kalman filter, and compute confidence intervals on the filtering errors. Then, we account for filtering errors and derive sufficient conditions on the control input based on the estimated states to bound the probability that the real states of the system enter an unsafe region within a finite time interval. We show that these sufficient conditions are linear constraints on the control input, and, hence, they can be used in tractable optimization problems to achieve safety, in addition to other properties like reachability, and stability. Our approach is evaluated using a simulation of a lane-changing scenario on a highway with dense traffic.