Monte Rey Methods for Unscented Optimization

Unscented optimization offers a simple approach for solving stochastic programming problems. Optimization problems with uncertainty appear in nearly all aspects of guidance and control: air-traffic control, missile guidance, mission planning, pilot modeling etc. The uncertain parameters in many of these problems have a boundary defined by the laws of physics. Some of the strategies used in the selection of sigma points for unscented optimization may not lie in the support of the distribution. The alternative of using cubature points with nonnegative weights is limited by the curse of dimensionality. Monte Carlo sampling is very simple, but it generates a large scale optimization problem. The new idea of Monte Rey sampling provides a balance between simplicity, accuracy and scalability. These ideas are used in this paper to develop an unscented approach for risk-cost management. Results for a sample chance-constrained problem demonstrate a reduction in risk by over a factor of three when compared to deterministic optimization.

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