Abstract
Application of a dynamic programming method to the problem of aircraft control during take-off in a windshear is considered. A simplified four-dimensional model of the aircraft dynamics is used, and stable numerical algorithms for solving Hamilton–Jacobi–Bellman–Isaacs equations arising from differential games with state constraints are utilized for the design of feedback controls.
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References
Botkin N, Kein V, Patsko V, Turova V, Zarkh M (1993) Differential games and aircraft control problems in the presence of wind disturbances. Izv Ross Akad Nauk, Tekhn Kibernet 1:68–76, translated as J Comput Syst Sci Int 32(3):110–117 (1994)
Botkin N, Hoffmann KH, Mayer N, Turova V (2011a) Approximation schemes for solving disturbed control problems with non-terminal time and state constraints. Analysis 31:355–379
Botkin N, Hoffmann KH, Turova V (2011b) Stable numerical schemes for solving Hamilton–Jacobi–Bellman–Isaacs equations. SIAM J Sci Comp 33(2):992–1007
Chen Y, Pandey S (1989) Robust control strategy for take-off performance in a windshear. Optim Control Appl Methods 10(1):65–79
Krasovskii N, Subbotin A (1974) Positional differential games. Nauka, Moscow, in Russian
Krasovskii N, Subbotin A (1988) Game-theoretical control problems. Springer, New York
Leitmann G, Pandey S (1990) Aircraft control under conditions of windshear. In: Leondes C (ed) Control and dynamic systems, vol 34. Academic Press, New York, pp 1–79
Leitmann G, Pandey S (1991) Aircraft control for flight in an uncertain environment: Takeoff in windshear. J Optim Theory Appl 70(1):25–55
Leitmann G, Pandey S, Ryan E (1993) Adaptive control of aircraft in windshear. Int J Robust Nonlinear Control 3:133–153
Miele A, Wang T, Melvin W (1986a) Guidance strategies for near-optimum take-off performance in a windshear. J Optim Theory Appl 50(1):1–47
Miele A, Wang T, Melvin W (1986b) Optimal take-off trajectories in the presence of windshear. J Optim Theory Appl 49(1):1–45
Mößner B, Reif U (2009) Error bounds for polynomial tensor product interpolation. Computing 86(2–3):185–197
Subbotin A (1995) Generalized solutions of first order PDEs: The dynamical optimization perspective. Birkhäuser, Boston
Subbotin A, Chentsov A (1981) Optimization of guaranteed result in control problems. Nauka, Moscow, in Russian
Turova V (1991) Take-off control in a windshear. Tech. Rep., Preprint of the Inst Math Mech, Ekaterinburg
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The authors are grateful to anonymous reviewer for his constructive and helpful comments.
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Botkin, N.D., Turova, V.L. (2013). Dynamic Programming Approach to Aircraft Control in a Windshear. In: Křivan, V., Zaccour, G. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 13. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-02690-9_3
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DOI: https://doi.org/10.1007/978-3-319-02690-9_3
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