Quadrature-based scenario tree generation for Nonlinear Model Predictive Control - Leidereiter, Conrad; Potschka, Andreas; Bock, Hans Georg (IFAC-PapersOnLine, 2014)
A relatively recent approach for robust Nonlinear Model Predictive Control (NMPC) is based on scenario trees with a so-called recourse formulation. This approach is of interest, because it is less conservative than worst-case robustification approaches. A major challenge when using scenario trees for robust NMPC is the large number of scenarios, which grows exponentially. This exponential growth quickly becomes a bottleneck for the computational costs, which need to stay within bounds that permit real-time applicability. We present how to generate scenarios based on a quadrature rule for the expectation value of an arbitrary economic objective function. The use of sparse grids for the quadrature of the high-dimensional stochastic integrals yields a drastically smaller number of scenarios than the tensor grid approaches used so far. We compare the performance of several robust NMPC approaches for a distillation column with three normally distributed uncertain parameters within a simulated Monte-Carlo controller testbed.
Available online 25 April 2016
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