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.