Contents

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Acknowledgments IX
4. Contents XI
5. List of Tables XV
6. List of Figures XVII
7. Part I: Calculus of variations
8. 1 The brachistochrone 1
9. 2 Euler–Lagrange equation 11
10. 3 Dido and transversality 21
11. 4 Extremals versus minimizers 29
12. 5 Second-derivative test 32
13. 6 Strong second-derivative test 38
14. 7 Integral constraints 47
15. Part II: Optimal control
16. 8 Discrete-time optimal control 55
17. 9 Continuous-time optimal control 63
18. 10 Multistate optimal control 69
19. 11 Nanosatellite 75
20. 12 Real-eigenvalue systems 80
21. 13 Controllability 83
22. 14 Complex-eigenvalue systems 89
23. 15 Controllability (complex eigenvalues) 91
24. 16 Control to target curve 97
25. 17 Singular controls 102
26. 18 Energy-optimal control 106
27. 19 Time & energy optimal control 109
28. A Invitation to research 117
29. B Solutions 121
30. Bibliography 155
31. Index 157