The article considers the problem of pursuit and evasion for objects whose dynamics is described by the isotropic rocket model, as well as the problem in which the escapee, in addition to evading the pursuer, needs to intercept a moving target. A method for constructing optimal attacking and escaping trajectories based on the generalized Hopf formula for the minimax solution of the Cauchy problem for the Hamilton–Jacobi equation is proposed. Analytical expressions for the Hamiltonian and optimal controls of the attacker and the escapee are obtained. Algorithms for constructing trajectories for the pursuit-evasion task and for the task with a moving target are presented.
Keywords: pursuit-evasion problem, Hamilton–Jacobi equation, Hopf formula, isotropic rocket
Received May 11, 2026
Revised June 15, 2026
Accepted June 22, 2026
Funding Agency: This work was supported by the youth scientific schools of the Institute of Control Sciences of the Russian Academy of Sciences (ICS RAS), project “Methods and algorithms for information processing and trajectory planning of controlled mobile objects”.
Alina Muratovna Mayer, V.A.Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia, e-mail: mayer@ipu.ru
Andrey Alexeevich Galyaev, Dr. Eng. Sci., V.A.Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, 117997 Russia, e-mail: galaev@ipu.ru
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Cite this article as: A.M. Mayer, A.A. Galyaev. Construction of evasion and interception trajectories in isotropic missile games based on the generalized Hopf formula. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 3, pp. 159–175.
