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Singular Arcs in the Optimal Evasion Against a Proportional Navigation Vehicle

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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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Authors and Affiliations

  1. Applied Mechanics and Control Department, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

    O. Yu. Cherkasov (Senior Researcher) & A.G. Yakushev

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  1. O. Yu. Cherkasov
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  2. A.G. Yakushev
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Cherkasov, O.Y., Yakushev, A. Singular Arcs in the Optimal Evasion Against a Proportional Navigation Vehicle. Journal of Optimization Theory and Applications 113, 211–226 (2002). https://doi.org/10.1023/A:1014869623415

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