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Convex Co-Design of Control Barrier Function and Safe Feedback Controller Under Input Constraints
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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.
Forward citations
Cited by 3 Pith papers
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Synthesis of safety certificates for discrete-time uncertain systems via convex optimization
The paper derives SDPs that co-design quadratic control barrier functions and linear feedback controllers, certifying worst-case or probabilistic safety for discrete-time uncertain linear systems.
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Synthesis of Discrete-time Control Barrier Functions for Polynomial Systems Based on Sum-of-Squares Programming
A discrete-time control barrier function and a polynomial control policy are synthesized jointly for polynomial systems via an iterative sum-of-squares program that bypasses the bilinear terms blocking earlier approaches.
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Opt-ODENet: A Neural ODE Framework with Differentiable QP Layers for Safe and Stable Control Design (longer version)
Opt-ODENet learns safe, stable state-feedback controllers by backpropagating a CLF-based loss through a neural ODE and a differentiable CBF-QP layer, and it learns the CBF class-K parameter during training.
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