Stochastic Model Predictive Control with Probabilistic Control Barrier Functions and Smooth Sample-based Approximation

Addressing chance constraints in stochastic model predictive control (MPC) poses a significant challenge, especially in investigating recursive feasibility in the closed-loop system. We propose a novel stochastic MPC for nonlinear systems subject to stochastic uncertainties. We incorporate probabilistic control barrier functions (PCBFs) in the proposed stochastic MPC formulation. A notable merit of employing PCBFs in stochastic MPC is the alleviation from dependence on parameterization with a feedback control law. Furthermore, we present a smooth sample-based approximation approach to the stochastic MPC, which enhances the tractability of the proposed stochastic MPC formulation. Finally, we provide a numerical example to exhibit the efficacy of the proposed stochastic MPC.