Hybrid Solution of Stochastic Optimal Control Problems Using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms

摘要

Two numerical methods, Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithm, were combined to form a hybrid algorithm for solving nonlinear optimal control and optimal path planning problems with uncertain parameters. The algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a mission planning problem sponsored by USSTRATCOM. The mission planning scenario was constructed to find the path that minimizes the probability of being killed by lethal threats whose locations are uncertain to statistically quantify the effects those uncertainties have on the flight path solution, and to use the statistical properties to estimate the probability that the vehicle will be killed during mission execution. The results demonstrated that the method is able to effectively characterize how the optimal solution changes with uncertainty and that the results can be presented in a form that can be used by mission planners and aircrews to assess risks associated with a mission profile.