Stochastic nonlinear model predictive control based on progressive density simplification

Increasing demand for Nonlinear Model Predictive Control with the ability to handle highly noise-corrupted systems has recently given rise to stochastic control approaches. Besides providing high-quality results within a noisy environment, these approaches have one problem in common, namely a high computational demand and, as a consequence, generally a short prediction horizon. In this paper, we propose to reduce the computational complexity of prediction and value function evaluation within the control horizon by simplifying the system progressively down to the deterministic case. Approximation of occurring probability densities by a specific representation, the deterministic Dirac mixture density, with a decreasing resolution (i.e., approximation quality) leads via natural decomposition to a point estimate and thus, can be treated in a deterministic manner. Hence, calculation of the remaining time steps requires considerably less computation time.