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Bounding Stochastic Safety: Leveraging Freedman’s Inequality with Discrete-Time Control Barrier Functions, Extended Proofs

Ryan K. Cosner, Preston Culbertson, and Aaron D. Ames The authors are with the Department of Mechanical and Civil Engineering at the California Institute of Technology, Pasadena, CA 91125, USA. {rkcosner, pbulbert, ames}@caltech.edu This work was supported by BP and NSF CPS Award #1932091.

I Proof for Lemma 1

II Proof for Theorem 1 (RSS + cc-martingales)

II-A RSS Proof

II-B Steinhardt Proof

III Proof for Theorem 4

IV Proof of proposition 6

V Proof of Corollary 1