Evaluating integration approaches to robust process optimization and control using chance constrained programming

This contribution concerns robust optimization and control of nonlinear steady-state and dynamic processes under uncertain disturbances or parameters. We use chance constrained programming to solve such stochastic optimization and control problems. While steady-state processes always possess time-independent uncertain parameters, in dynamic processes there may be both time-independent and time-dependent uncertain parameters. For problems with time-dependent uncertain parameters these parameters will be discretized in the time horizon and thus the total number of uncertain variables to be treated will be high, which leads to difficulties to compute probabilities and their gradients. A new approach to an efficient computation is developed by using the sparse grid technique with which CPU-time can be significantly reduced. Two application examples from process engineering are taken to demonstrate the effectiveness of our computational framework. The performance of sparse grid integration is verified through numerical experiments in comparison to Monte-Carlo and Quasi-Monte-Carlo techniques.