Dynamic Optimization using Hermite Chaos

F.S. Hover and M.S.Triantafyllou (USA)


Polynomial chaos, dynamic optimization, Maximum Prin ciple.


The polynomial chaos of Wiener provides a framework for the statistical analysis of dynamical systems, with compu tational 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 fam ily of optimal trajectories parameterized with a small num ber of random variables.

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