Safe and Stable Control Synthesis for Uncertain System Models via Distributionally Robust Optimization

TL;DR

This paper develops a distributionally robust control synthesis method that ensures safety and stability for uncertain systems, using a finite data set of model samples and reformulating the problem as a second-order cone program for efficient online control.

Contribution

It introduces a novel distributionally robust chance-constrained control framework based on finite samples, improving safety and stability guarantees under uncertainty.

Findings

Outperforms baseline quadratic programming approach in safety and stability.

Efficient SOCP reformulation enables real-time control implementation.

Demonstrates effectiveness in an adaptive cruise control example.

Abstract

This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF), respectively. To take model uncertainty into account, robust and chance formulations of the constraints are commonly considered. However, this requires known error bounds or a known distribution for the model uncertainty, and the resulting formulations may suffer from over-conservatism or over-confidence. In this paper, we assume that only a finite set of model parametric uncertainty samples is available and formulate a distributionally robust chance-constrained program (DRCCP) for control synthesis with CBF safety and CLF stability guarantees. To facilitate efficient computation of control inputs during online execution, we present a reformulation of the DRCCP as a second-order cone program (SOCP). Our formulation is evaluated in an adaptive cruise control example in comparison to 1) a baseline CLF-CBF quadratic programming approach, 2) a robust approach that assumes known error bounds of the system uncertainty, and 3) a chance-constrained approach that assumes a known Gaussian Process distribution of the uncertainty.