Risk-Bounded Control Using Stochastic Barrier Functions

In this letter, we design real-time controllers that react to uncertainties with stochastic characteristics and bound the probability of a failure in finite-time to a given desired value. Stochastic control barrier functions are used to derive sufficient conditions on the control input that bound the probability that the states of the system enter an unsafe region within a finite time. These conditions are combined with reachability conditions and used in an optimization problem to find the required control actions that lead the system to a goal set. We illustrate our theoretical development using a simulation of a lane-changing scenario in a highway with dense traffic.

[1]  Huei Peng,et al.  Obstacle Avoidance for Low-Speed Autonomous Vehicles With Barrier Function , 2018, IEEE Transactions on Control Systems Technology.

[2]  Sriram Sankaranarayanan,et al.  Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances , 2020, 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC).

[3]  Aaron D. Ames,et al.  Input-to-State Safety With Control Barrier Functions , 2018, IEEE Control Systems Letters.

[4]  David D. Fan,et al.  Bayesian Learning-Based Adaptive Control for Safety Critical Systems , 2019, 2020 IEEE International Conference on Robotics and Automation (ICRA).

[5]  Majid Zamani,et al.  Temporal Logic Verification of Stochastic Systems Using Barrier Certificates , 2018, ATVA.

[6]  Andrew Clark,et al.  Control Barrier Functions for Complete and Incomplete Information Stochastic Systems , 2019, 2019 American Control Conference (ACC).

[7]  George J. Pappas,et al.  A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates , 2007, IEEE Transactions on Automatic Control.

[8]  Mrdjan Jankovic,et al.  Robust control barrier functions for constrained stabilization of nonlinear systems , 2018, Autom..

[9]  Marco Pavone,et al.  How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics , 2017, ISRR.

[10]  M. Buss,et al.  Stochastic reachable sets of interacting traffic participants , 2008, 2008 IEEE Intelligent Vehicles Symposium.

[11]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  Paulo Tabuada,et al.  Control barrier function based quadratic programs with application to adaptive cruise control , 2014, 53rd IEEE Conference on Decision and Control.

[13]  H. Kushner.  Stochastic Stability and Control , 2012 .

[14]  Debasish Ghose,et al.  High-Relative Degree Stochastic Control Lyapunov and Barrier Functions , 2020, ArXiv.

[15]  Matthias Althoff,et al.  Utilizing dependencies to obtain subsets of reachable sets , 2020, HSCC.

[16]  Samuel Coogan,et al.  A Barrier Function Approach to Finite-Time Stochastic System Verification and Control , 2019, Autom..

[17]  Magnus Egerstedt,et al.  Control of Multi-Agent Systems with Finite Time Control Barrier Certificates and Temporal Logic , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[18]  Paulo Tabuada,et al.  Robustness of Control Barrier Functions for Safety Critical Control , 2016, ADHS.

[19]  Massimo Franceschetti,et al.  Probabilistic Safety Constraints for Learned High Relative Degree System Dynamics , 2020, L4DC.

[20]  P. Olver.  Nonlinear Systems , 2013 .

[21]  Lydia Tapia,et al.  Hybrid Dynamic Moving Obstacle Avoidance Using a Stochastic Reachable Set-Based Potential Field , 2017, IEEE Transactions on Robotics.

[22]  Calin Belta,et al.  Decentralized merging control in traffic networks: a control barrier function approach , 2019, ICCPS.

[23]  George J. Pappas,et al.  Control Barrier Functions for Nonholonomic Systems under Risk Signal Temporal Logic Specifications , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).