Control barrier functions for stochastic systems

Control Barrier Functions (CBFs) aim to ensure safety by constraining the control input at each time step so that system state remains within a desired safe region. This paper presents framework for CBFs in stochastic systems presence of Gaussian process and measurement noise. We first consider case where is known step, present reciprocal zero CBF constructions guarantee with probability 1. extend our results high relative degree both general special linear dynamics affine constraints. then develop incomplete information environments, which must be estimated using sensors are corrupted prove proposed ensures 1 when estimate given bound true state, can achieved an Extended Kalman Filter or noise sufficiently small. propose policies combine these Lyapunov order jointly stability. Our validated via numerical study on multi-agent collision avoidance scenario.