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