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In this paper, pursuit-evasion scenarios in a stochastic flow field involving one pursuer and one evader are analyzed. Using a forward reachability set-based approach and the associated level set equations, nominal solutions of the players are generated. The dynamical system is linearized along the nominal solution to formulate a chance-constrained, linear-quadratic stochastic dynamic game. Assuming an affine disturbance feedback structure, the proposed game is solved using the standard Gauss-Seidel iterative scheme. Numerical simulations demonstrate the proposed approach for realistic flow fields.
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This paper addresses trajectory optimization for hypersonic vehicles under atmospheric and aerodynamic uncertainties using techniques from desensitized optimal control (DOC), wherein open-loop optimal controls are obtained by minimizing the sum of the standard objective function and a first-order penalty on trajectory variations due to parametric uncertainty. The proposed approach is demonstrated via numerical simulations of a minimum-final-time Earth reentry trajectory for an X-33 vehicle with an uncertain atmospheric scale height and drag coefficient. Monte Carlo simulations indicate that dispersions in the final position footprint and the final energy can be significantly reduced without closed-loop control and with little tradeoff in the performance metric set for the trajectory.more » « less
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