Output-Feedback Safe Control of Discrete-Time Stochastic Systems with Chance Constraints

TL;DR

This paper presents a new output-feedback control barrier function framework for ensuring safety in discrete-time stochastic systems with noisy measurements, balancing real-time computation and safety guarantees.

Contribution

It introduces an expectation-based CBF approach that explicitly accounts for estimation uncertainty and provides a tractable safety filter for real-time control.

Findings

The proposed safety filter achieves fast online computation.

It reliably enforces safety despite process noise and measurement uncertainty.

Numerical simulations validate the effectiveness of the approach.

Abstract

In this paper, we investigate safety-critical control problem of discrete-time stochastic systems with incomplete information, where safety constraints must be enforced using state estimates obtained from noisy measurements. We develop an output-feedback control barrier function (CBF) framework based on an expectation-based discrete-time barrier condition that explicitly incorporates estimation uncertainty through the evolving belief over the state. To enable real-time implementation, we derive deterministic sufficient conditions that conservatively enforce the expectation-based CBF by bounding the expectation with computable functions of the belief statistics using Jensen inequalities. The resulting safety filter is formulated as a tractable optimization problem compatible with standard online controllers. Numerical simulations demonstrate that the proposed output-feedback approach achieves fast online computation while providing reliable safety performance in the presence of process noise and measurement uncertainty.