A Duality-Based Optimization Formulation of Safe Control Design with State Uncertainties
For control engineers dealing with real-world safety-critical systems, this provides a less conservative approach to handle state uncertainty in control barrier functions.
This work addresses safety-critical control under state estimation uncertainty by formulating a robust safety filter that directly analyzes the image of the set of possible states under Control Barrier Function dynamics. Using duality, they derive a tractable reformulation that is less conservative than existing methods, as demonstrated in simulations.
State estimation uncertainty is prevalent in real-world applications, hindering the application of safety-critical control. Existing methods address this by strengthening a Control Barrier Function (CBF) condition either to handle actuation errors induced by state uncertainty, or to enforce stricter, more conservative sufficient conditions. In this work, we take a more direct approach and formulate a robust safety filter by analyzing the image of the set of all possible states under the CBF dynamics. We first prove that convexifying this image set does not change the set of possible inputs. Then, by leveraging duality, we propose an equivalent and tractable reformulation for cases where this convex hull can be expressed as a polytope or ellipsoid. Simulation results show the approach in this paper to be less conservative than existing alternatives.