Abstract A possible approach to an air-to-air combat problem consists in considering it as a zero-sum game between two aircrafts on a fixed time-interval. When one is looking for an open-loop solution, this leads to solving a certain optimal control problem, governed by ordinary differential equations : the state equations are the nonlinear equations describing the flight-mechanics ; the cost function -either final or integral- is evaluated by the relative positions of the aircrafts ; the control variables -pilots' actions- and state variables -aircrafts' positions- are subject to nonlinear constraints, depending on the characteristics of the aircrafts. We demonstrate that open-loop solutions to the minimax problem thus obtained, can be computed by projected gradient algorithms, using either saddle-point methods (Arrow-Hurwicz) or methods for nonsmooth optimization (Uzawa-like). The above methodology is illustrated by numerical simulation of some tri-dimensional combats, for various configurations. We present and analyze the results (sensivity of the solution to the choice of the objective function, to initial conditions, to the time-length of the game).
Gradient type optimization methods to solve differential games applied to tri-dimensional air-to-air combats
1980-01-01
20 pages
Article/Chapter (Book)
Electronic Resource
English
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