本論文應用動態規劃法(dynamic programming)
分析飛機之最省燃料爬升軌跡。與傳統分析上將時間格點化不同的是，本研究中係將運動方程式的狀態變數在其限制區域內格點化。每一格點與其相鄰格點間之軌跡與燃料消耗，則以與參數最佳化法(parametric optimization method)分析之。在獲得每一格點與其相鄰格點間之燃料消耗後，動態規劃法則用以搜尋由起始點至終端點以最省燃料法所經的格點，連結這些格點即得全域性的最佳軌跡。最後，本論文以一數值例題之分析與模擬，更進一步驗證所提出之理論。

In this thesis, the minimum-fuel climb trajectories for an aircraft is studied by using the dynamic programming method.In contrast to the conventional analysis in which the time is discretized,the state variables of the equations of motion are discretized within their
constrained state space in this study.The trajectories and the fuel consumptions from each point to all of its neighbor points are analyzed by using the parametric optimization method.
After obtaining the fuel consumptions from all points to all of their neighbor points,the dynamic programming method is used to search for the points through which the fuel consumption is globally minimum.Finally, the analysis and simulation are conducted for a given numerical example to further validate the proposed theory.

[1] Connor, M. A.,"Optimization of a Lateral Turn at Constant Height,"
AIAA Journal, Vol.~5, No.~2, Feb.~1967, pp.~335--338.
[2] Bryson, A. E. and Lele, M. L."Minimum Fuel Lateral Turns at Constant
Altitude,"AIAA Journal, Vol.~7, No.~3 March 1969, pp.~559--560.
[3] Hedrick, J. K. and Bryson, A. E. Jr.,"Three-Dimensional,
Minimum Fuel Turns for a Supersonic Aircraft,"Journal of Aircraft,
Vol.~9, No.~3, March 1972, pp.~223--229.
[4] Vinh, N. X.,"Minimum Fuel Rocket Maneuvers in Horizontal Flight,"
AIAA Journal, Vol.~11, No.~2, Feb.~1973, pp.~165--169.
[5] Vinh, N. X.,Optimal Trajectory in Atmospherical Flight,
Elevier Scientific, Amsterdam, 1981.
[6] Burrows, J. W.,"Fuel Optimal Trajectory Computation,"
Journal of Aircraft, Vol.~19, No.~4, Apr.~1982, pp.~324--329.
[7] Kreindler, E. and Neuman, F.,
"Minimum Fuel Horizontal Flight Paths in the Terminal Area,"
Journal of Guidance and Control,
Vol.~5, No.~5, Sept.--Oct. 1982, pp.~490--497.
[8] Burrows, J. W.,"Fuel-Optimal Aircraft Trajectories with Fixed
Arrival Times,"Journal of Guidance and Control,
Vol.~6, No.~1, Jan.--Feb. 1983, pp.~14--19.
[9] Neuman, F.,"Minimum-Fuel, Three-Dimensional Flight Paths for Jet
Transport,"Journal of Guidance and Control,
Vol.~8, No.~5, Sept.--Oct. 1985, pp.~650--657.
[10] Sorensen, J. A. and Waters, M. H.,
"Airborne Method to Minimum Fuel with Fixed Time-of-Arrival
Constraints,"Journal of Guidance and Control,
Vol.~4, No.~3, May--June 1981, pp.~348--349.
[11] Bryson, A. E., Jr., and Ho, Y.C.,
Applied Optimal Control, Hemisphere Publishing Co.,
New York, U.S.A., 1975.
[12] Bousson, K.,"Single Gridpoint Dynamic Programming for
Trajectory Optimization,"AIAA-2005-5902,
AIAA Atmospheric Flight Mechanics
Conference and Exhibit, San Francisco, California, Aug. 15-18,2005
[13] Bertsekas, D. P.,
Dynamic Programming and Optimal Control, Vol. I,
Athena Scientific, Belmont, MA, U.S.A., 2000.
[14] U.S. Standard Atmosphere, 1976,
National Oceanic and Atmospheric Administration, NASA,
U.S. Air Force, Washington, DC, U.S.A., 1976.
[15] Bryson, A. E., Jr., Desai, M. N., and Hoffman, W. C.,
"Energy-State Approximation in Performance Optimization
of Supersonic Aircraft,"Journal of Aircraft,
Vol.~6, No.~6, November--December 1969, pp.~481--488.