Convex Chance Constrained Predictive Control without Sampling

In this paper we consider finite-horizon predictive control of dynamic systems subject to stochastic uncertainty; such uncertainty arises due to exogenous disturbances, modeling errors, and sensor noise. Stochastic robustness is typically defined using chance constraints, which require that the probability of state constraints being violated is below a prescribed value. Prior work showed that in the case of linear system dynamics, Gaussian noise and convex state constraints, optimal chanceconstrained predictive control results in a convex optimization problem. Solving this problem in practice, however, requires the evaluation of multivariate Gaussian densities through sampling, which is time-consuming and inaccurate. We propose a new approach to chance-constrained predictive control that does not require the evaluation of multivariate densities. We use a new bounding approach to ensure that chance constraints are satisfied, while showing empirically that the conservatism introduced is small. This is in contrast to prior bounding approaches that are extremely conservative. Furthermore we show that the resulting optimization is convex, and hence amenable to online control design.