A Fast Algorithm for Stochastic Model Predictive Control with Probabilistic Constraints

A fast suboptimal algorithm for finite horizon stochastic linear-quadratic control under probabilistic constraints is presented. This type of control problem is solved repeatedly in stochastic model predictive control. Under the assumption of affine state feedback, the control problem is converted to an equivalent deterministic problem using the mean and covariance matrix as the state. An interior point method is proposed to solve this optimization problem, where the step direction can be quickly computed via a Riccati difference equation. On a two state, two constraint numerical example in this paper, the algorithm is over 200 times faster than a convex formulation that uses a general purpose solver when the time horizon is 25.