Singular Arcs in the Optimal Evasion Against a Proportional Navigation Vehicle |
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Authors: | O. Yu. Cherkasov A.G. Yakushev |
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Affiliation: | (1) Applied Mechanics and Control Department, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia |
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Abstract: | The two-dimensional optimal evasion problem against a proportional navigation pursuer is analyzed using a nonlinear model. The velocities of both players have constant modulus, but change in direction. The problem is to determine the time-minimum trajectory (disengagement) or time-maximum trajectory (evasion) of the evader while moving from the assigned initial conditions to the final conditions. A maximum principle procedure allows one to reduce the optimal control problem to the phase portrait analysis of a system of two differential equations. The qualitative features of the optimal process are determined. |
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Keywords: | Optimal evasion proportional navigation singular arcs |
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