Risk-Aware Control of Discrete-Time Stochastic Systems: Integrating Kalman Filter and Worst-case CVaR in Control Barrier Functions

Abstract

This paper proposes control approaches for discrete-time linear systems subject to stochastic disturbances. It employs Kalman filter to estimate the mean and covariance of the state propagation, and the worst-case conditional value-at-risk (CVaR) to quantify the tail risk using the estimated mean and covariance. The quantified risk is then integrated into a control barrier function (CBF) to derive constraints for controller synthesis, addressing tail risks near safe set boundaries. Two optimization-based control methods are presented using the obtained constraints for half-space and ellipsoidal safe sets, respectively. The effectiveness of the obtained results is demonstrated using numerical simulations.

arXiv commentThis has been presented at IEEE Conference on Decision and Control 2024, pp. 2019-2024. Minor typos in equations (12) - (14) have been fixed