For the pursuit-evasion game of an interception missile (interceptor) pursuit an incoming ballistic missile (warhead), each missile was given a modest post launch capability to maneuver, differential model and solving method of the game was proposed. Firstly, we gave a mass-point dynamics model of the missile pursuit-evasion system. Secondly, based on differential game theory, we established the detailed differential game model of missile pursuit-evasion problem. The model took thrust angle as control variable and flight height, velocity, longitude as state variables, it also considered earth gravity and rotation effects. Thirdly, as differential game can hardly solved analytically, we gave numerical solving method that employed fourth degree Gauss-Lobatto quadrature rule to improve accuracy when compared with lower degree rules such as Simpson's rule, at the nodes and collocation points the values of the state and control were discrete to transform differential equations to algebraic equations. Fourthly, we gave the method able to transform a two-side differential game into a single objective problem. Experimental study verified the model and solving method proposed.
Key words
missile /
pursuit-evasion system /
differential game model /
collocation method
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References
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Footnotes
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Funding
Military Graduate Student Foundation of Army
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