Конструирование Решений В Некоторых Дифференциальных Играх С Фазовыми Ограничениями

Григорьева, С. В.; Пахотинских, Василий Юрьевич; Pakhotinskikh, Vasilii Yur'evich; Успенский, А. А.; Ушаков, В. Н.

doi:10.4213/sm1284

Cited by 6 publications

(1 citation statement)

References 1 publication

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“…При этом узлы сплайнов находятся экстремальным сдвигом (см. [7,8]). Приводятся результаты моделирования задачи быстродействия с различной геометрией краевого условия.…”

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Construction of the function of the best result for the system with simple dynamic

Успенский¹,

Lebedev²

2008

Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki

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Предложены аналитические и численные алгоритмы построения функции оптимального результата и ее множеств Лебега для задачи управления по быстродействию с круговой индикатрисой скоростей. Выделены и изучены многообразия, на которых функция оптимального результата теряет гладкость.Ключевые слова: функция оптимального результата, минимаксное решение, биссектриса, евклидово расстояние.

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Construction of the function of the best result for the system with simple dynamic

Успенский¹,

Lebedev²

2008

Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki

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Computation of Value Functions in Nonlinear Differential Games with State Constraints

Botkin

Hoffmann

Mayer

et al. 2013

IFIP Advances in Information and Communication Technology

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Part 4: Stabilization, Feedback, and Model Predictive ControlInternational audienceFinite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented

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Aircraft Control During Cruise Flight in Windshear Conditions: Viability Approach

et al. 2017

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This paper addresses the analysis of aircraft control capabilities during the cruise phase (flying at the established level with practically constant configuration and speed) in the presence of windshears. The study uses a point-mass aircraft model describing flight in a vertical plane. The problem is formulated as a differential game against wind disturbances. The first player, autopilot, controls the angle of attack and the power setting, whereas the second player, wind, produces dangerous gusts. The state variables of the model are subjected to constraints expressing aircraft safety conditions. Namely, the altitude, path inclination, and velocity are constrained. Viability theory is used to find the so-called viability kernel, the maximal subset of the state constraint where the aircraft trajectories can remain arbitrary long if the first player utilizes an appropriate feedback control, and the second player generates any admissible disturbances. The computations are based on grid methods developed by the authors and implemented on a multiprocessor computer system.

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Конструирование Решений В Некоторых Дифференциальных Играх С Фазовыми Ограничениями

Cited by 6 publications

References 1 publication

Construction of the function of the best result for the system with simple dynamic

Construction of the function of the best result for the system with simple dynamic

Computation of Value Functions in Nonlinear Differential Games with State Constraints

Aircraft Control During Cruise Flight in Windshear Conditions: Viability Approach

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