Skip to content

Convex Co-Design of Control Barrier Functions and State Feedback Controllers for Linear Systems with Input Constraints

Authors: Han Wang, Kostas Margellos, Antonis Papachristodoulou, Claudio De Persis

Published: 2024 (Journal Paper)

Source: IEEE Transactions on Automatic Control

Algorithm: CBF/controller co-design

arXiv: 2403.11763

DOI: 10.1109/TAC.2025.3638061

Summary

Formulates joint CBF and linear feedback-controller synthesis for linear systems as a semidefinite program, including input constraints and mixed-relative-degree safe sets. The useful idea is treating safe-set certificate design and controller design as one convex co-design problem.

Abstract

We study the problem of co-designing control barrier functions (CBF) and linear state feedback controllers for continuous-time linear systems. We achieve this by means of a single semi-definite optimization program. Our formulation can handle mixed-relative degree problems without requiring an explicit safe controller. Different L-norm based input limitations can be introduced as convex constraints in the proposed program. We demonstrate our results on an omni-directional car numerical example.

Primary

Paper ora.ox.ac.uk

Standard

arXiv Abstract 2403.11763 arXiv PDF 2403.11763 arXiv HTML 2403.11763 DOI 10.1109/TAC.2025.3638061

Tags

  • Control barrier functions

  • Safety

  • Sum-of-squares programming

  • Semidefinite programming

  • Input constraints

  • Linear systems