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This paper studies the well-posedness and regularity of safe stabilizingoptimization-based controllers for control-affine systems in the presence ofmodel uncertainty. When the system dynamics contain unknown parameters, afinite set of samples can be used to formulate distributionally robust versionsof control barrier function and control Lyapunov function constraints. Controlsynthesis with such distributionally robust constraints can be achieved bysolving a (convex) second-order cone program (SOCP). We provide one necessaryand two sufficient conditions to check the feasibility of such optimizationproblems, characterize their computational complexity and numerically show thatthey are significantly faster to check than direct use of SOCP solvers.Finally, we also analyze the regularity of the resulting control laws.

Feasibility Analysis and Regularity Characterization of Distributionally Robust Safe Stabilizing Controllers