Tuesday, September 16, 2014, 10:00 - 12:00
Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany
ANNOUNCEMENT: The talk will be followed by an interactive discussion round, where all participants will have the chance to briefly present highlights of their work and contribute to an extended discussion on topics in robust optimal control
The objective of the talk is to show how to solve nonlinear optimal control problems with uncertain parameters and uncertain initial conditions using the Polynomial Chaos method that is based on a series expansion of each influenced variable. We identify the Galerkin-projection approach as particularly suitable for optimization problems as it allows to employ existing software to solve only one larger deterministic problem in place of the original uncertain one. The transformation using symbolic computation is fast and exact. We demonstrate the functionality on a simple continuous charge batch reactor model. Besides the nonlinearity, the curse of dimensionality is the reason for the increased size of the new system, which may result in numerical challenges and sometimes a failure to converge. It appears in an exponential blow-up of additional terms in dependence of the truncation order of the series, and therefore accuracy, or in dependence of the number of uncertain parameters. We investigate this problem and identify possible approaches to deal with it.