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E-raamat: Counterexamples in Optimal Control Theory illustrated edition [De Gruyter e-raamatud]

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Counterexamples in Optimal Control Theory illustrated editionSuurem pilt
Teised raamatud teemal:
Wiley OnlineRohkem infot De Gruyter e-raamatute kohta
Raamatu kodulehekülg: http://dx.doi.org/10.1515/9783110915532
This book contains detailed analysis of a number of different problems in optimal control theory that can cause standard techniques to fail. The level of sophistication makes it appropriate for graduate students, which is not unexpected since it began life as a graduate course; but it could be useful to anyone who regularly makes use of techniques from optimal control theory. Although an introduction to the basic problems of the field is included, some background in the area will be helpful; specialists in this field, however, are likely to be familiar with this material. VSP is a subsidiary of Brill. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
Preface 1(4)
Introduction 5(14)
1. Problem formulation
5(2)
2. The maximum principle
7(4)
3. Example
11(3)
4. Approximate solution of the optimality conditions
14(4)
Summary
18(1)
Example
1. Insufficiency of the optimality conditions		 19(28)
1.1. Problem formulation
20(1)
1.2. The maximum principle
21(2)
1.3. Analysis of the optimality conditions
23(3)
1.4. Uniqueness of the optimal control
26(2)
1.5. Uniqueness of an optimal control in a specific example
28(3)
1.6. Further analysis of optimality conditions
31(2)
1.7. Sufficiency of the optimality conditions
33(3)
1.8. Sufficiency of the optimality conditions in a specific example
36(3)
1.9. Conclusion of the analysis of the optimality conditions
39(3)
Summary
42(5)
Example
2. The singular control		 47(18)
2.1. Problem formulation
47(1)
2.2. The maximum principle
48(1)
2.3. Analysis of the optimality conditions
49(4)
2.4. Nonoptimality of singular controls
53(3)
2.5. Uniqueness of singular controls
56(3)
2.6. The Kelly condition
59(3)
Summary
62(3)
Example
3. Nonexistence of optimal controls		 65(22)
3.1. Problem formulation
65(1)
3.2. The maximum principle
66(1)
3.3. Analysis of the optimality conditions
67(4)
3.4. Unsolvability of the optimization problem
71(4)
3.5. Existence of optimal controls
75(2)
3.6. The proof of the solvability of an optimization problem
77(3)
3.7. Conclusion of the analysis
80(5)
Summary
85(2)
Example
4. Nonexistence of optimal controls (Part 2)		 87(26)
4.1. Problem formulation
88(1)
4.2. The maximum principle for systems with fixed final state
89(2)
4.3. Approximate solution of the optimality conditions
91(2)
4.4. The optimality conditions for Problem 4
93(1)
4.5. Direct investigation of Problem 4
94(2)
4.6. Revising the problem analysis
96(2)
4.7. Problems with unbounded set of admissible controls
98(3)
4.8. The Cantor function
101(2)
4.9. Further analysis of the maximum condition
103(2)
4.10. Conclusion of the problem analysis
105(5)
Summary
110(3)
Example
5. Ill-posedness in the sense of Tikhonov		 113(14)
5.1. Problem formulation
114(1)
5.2. Solution of the problem
114(1)
5.3. Ill-posedness in the sense of Tikhonov
115(5)
5.4. Analysis of well-posedness in the sense of Tikhonov
120(1)
5.5. The well-posed optimization problem
121(2)
5.6. Regularization of optimal control problems
123(2)
Summary
125(2)
Example
6. Ill-posedness in the sense of Hadamard		 127(8)
6.1. Problem formulation
128(1)
6.2. Ill-posedness in the sense of Hadamard
128(2)
6.3. Well-posedness In the sense of Hadamard
130(1)
6.4. A well-posed optimization problem
131(1)
Summary
132(3)
Example
7. Insufficiency of the optimality conditions (Part 2)		 135(18)
7.1. Problem formulation
135(1)
7.2. The existence of an optimal control
136(3)
7.3. Necessary condition for an extremum
139(2)
7.4. Transformation of the optimality conditions
141(2)
7.5. Analysis of the boundary value problem
143(6)
7.6. The nonlinear heat conduction equation with infinitely many equilibrium states
149(1)
7.7. Conclusion of the analysis of the variational problem
150(2)
Summary
152(1)
Example
8. The Chafee-Infante problem		 153(12)
8.1. Problem formulation
153(1)
8.2. The necessary condition for an extremum
154(1)
8.3. Solvability of the Chafee-Infante problem
155(3)
8.4. The set of solutions of the Chafee-Infante problem
158(3)
8.5. Bifurcation points
161(2)
Summary
163(2)
Comments 165(2)
Conclusion 167(2)
Bibliography 169


Semen Ya. Serovaiskii, Al-Farabi Kazakh National University, Almaty, Kazakhstan.
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