guidance, flight mechanics and trajectory optimization

TABIE OF CONTENTS
SECTION PAGE
1.0
2.0
STATEMENT OF THE PROBLEM. . . . . . . . . . . . . . . . . . . 1
STATE OF THE ART. . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Development of Dynamic Programming ..........
2.2 Fundamental Concepts and Applications. ........
2.2.1 Simple Multi-Stage Decision Problem. .....
2.2.2 Simple Applications to Calculus of Variations.
2.2.2.1 Shortest Distance Problem ......
2.2.2.2 Variational Problem with a
Movable Boundary. ..........
2.2.2.3 Simple Guidance Problem .......
2.2.3 Maximum Minimum Problem. ...........
2.2.4 Equipment Replacement Problem. ........
2.3 Computational Considerations .............
2.3.1 Merits of Dynamic Programming over
Conventional Analysis. ............
2.3.1.1 Relative Extrema. ..........
2.3.1.2 Constraints .............
2.3.1.3 Continuity. .............
2.3.2 Dynamic Programming versus Straightforward
Combinational Search .............
2.3.3 Difficulties Encountered in Dynamic
Programming. .................
2.3.3.1 Curse of Dimensionality .......
2.3.3.2 Stability and Sensitivity ......
2.4 Limiting Process in Dynamic Programming. .......
2.4.1 Recursive Equation for the Problem of Lagrange
2.4.2 Recursive Equation in Limiting Form. .....
2.4.3 An Example Problem ..............
2.4.4 Additional Properties of the Optimal Solution.
2.4.5 Lagrange Problem with Variable End Points. ..
2.4.6 N-Dimensional Lagrange Problem ........
2.4.7 Discussion of the Problem of Lagrange. ....
2.4.8 The Problem of Bolza .............
2.4.9 Bellman Equation for the Bolza Problem ....
2.4.10 Linear Problem with Quadratic Cost ......
2.4.11 Dynamic Programming and the Pontryagin
Maximum Principle. ..............
2.4.12 Some Limitations on the Development of
the Bellman Equation .............
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