Efficient stochastic model predictive control based on polynomial chaos expansions for embedded applications

Assuming the probability distributions of the uncertainties to be known, we use polynomial chaos theory to propagate the uncertainty through the dynamics of a linear system in order to obtain explicit expressions of the mean and variance of the future states. These expressions can then be used to formulate an stochastic MPC problem with chance constraints. We formulate the described method as a tractable optimization problem that can be solved very efficiently using fast optimization methods which are suitable for embedded applications. The methods are validated considering an uncertain aircraft system. The resulting optimization problems are verified on a low-cost microcontroller underlining the real-time feasibility and the potential of the approach.