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We propose a novel methodology for stochastic trajectory optimization which is based on merging the theory of spectral expansions with Differential Dynamic Programming. Specifically, we employ polynomial chaos expansions to handle parametric uncertainties and utilize the Karhunen-Loéve transformation to represent stochastic forces. This allows us to build a generic framework and avoid relying on restrictive...
For deterministic nonlinear dynamical systems, approximate dynamic programming based on Pontryagin's maximum principle provides a systematic way to solve optimal control problems. However, in the presence of noise, this approach becomes cumbersome. Hence, in current optimal control solution methodologies noise effect is typically ignored in the adjoint equations. Alternatively, in the Hamilton-Jacobi...
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