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Dynamic Optimization Using Hermite Chaos
(Proc. IASTED Control Applications Conference 2005 (refereed))
Hover, Franz S. and Michael S. Triantafyllou
(Proc. IASTED Control Applications Conference 2005 (refereed))
Hover, Franz S. and Michael S. Triantafyllou
Abstract
The polynomial chaos of Wiener provides a framework for the statistical analysis of dynamical systems, with computational cost far superior to Monte Carlo simulations. We show that the gradient method for dynamic optimization (the Maximum Principle) can be applied in a stochastic sense using Hermite chaos, giving rise to the complete family of optimal trajectories parameterized with a small number of random variables.
