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Safe Control for Nonlinear Systems With Stochastic Uncertainty via Risk Control Barrier Functions

Singletary, Andrew and Ahmadi, Mohamadreza and Ames, Aaron D. (2022) Safe Control for Nonlinear Systems With Stochastic Uncertainty via Risk Control Barrier Functions. IEEE Control Systems Letters, 7 . pp. 349-354. ISSN 2475-1456. doi:10.1109/lcsys.2022.3187458.

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Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for enforcing safety related set-theoretic properties, such as forward invariance and reachability, of nonlinear dynamical systems. In this letter, we extend this rich framework to nonlinear discrete-time systems subject to stochastic uncertainty and propose a framework for assuring risk-sensitive safety in terms of coherent risk measures. To this end, we introduce risk control barrier functions (RCBFs), which are compositions of barrier functions and dynamic, coherent risk measures. We show that the existence of such barrier functions implies invariance in a coherent risk sense. Furthermore, we formulate conditions based on finite-time RCBFs to guarantee finite-time reachability to a desired set in the coherent risk. Conditions for risk-sensitive safety and finite-time reachability of sets composed of Boolean compositions of multiple RCBF are also formulated. We show the efficacy of the proposed method through its application to a cart-pole system in a safety-critical scenario.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Singletary, Andrew0000-0001-6635-4256
Ahmadi, Mohamadreza0000-0003-1447-3012
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2022 IEEE. Manuscript received 21 March 2022; revised 20 May 2022; accepted 11 June 2022. Date of publication 30 June 2022; date of current version 18 July 2022. This work was supported in part by AeroVironment and in part by NSF CPS under Award 1932091. Recommended by Senior Editor L. Zhang
Group:Center for Autonomous Systems and Technologies (CAST)
Funding AgencyGrant Number
Subject Keywords:Uncertain systems; Stochastic systems
Record Number:CaltechAUTHORS:20220707-315696000
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Official Citation:A. Singletary, M. Ahmadi and A. D. Ames, "Safe Control for Nonlinear Systems With Stochastic Uncertainty via Risk Control Barrier Functions," in IEEE Control Systems Letters, vol. 7, pp. 349-354, 2023, doi: 10.1109/LCSYS.2022.3187458
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115363
Deposited By: George Porter
Deposited On:07 Jul 2022 22:31
Last Modified:27 Jul 2022 17:18

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