Appendix E. Basic Parabolic PDEs and Their Exact Solutions

Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface ix
4. Chapter One. Introduction 1
5. PART I. Nonadaptive Controllers
6. Chapter Two. State Feedback 13
7. Chapter Three. Closed-Form Controllers 35
8. Chapter Four. Observers 55
9. Chapter Five. Output Feedback 63
10. Chapter Six. Control of Complex-Valued PDEs 73
11. PART II. Adaptive Schemes
12. Chapter Seven. Systematization of Approaches to Adaptive Boundary Stabilization of PDEs 111
13. Chapter Eight. Lyapunov-Based Designs 125
14. Chapter Nine. Certainty Equivalence Design with Passive Identifiers 150
15. Chapter Ten. Certainty Equivalence Design with Swapping Identifiers 166
16. Chapter Eleven. State Feedback for PDEs with Spatially Varying Coefficients 176
17. Chapter Twelve. Closed-Form Adaptive Output-Feedback Controllers 198
18. Chapter Thirteen. Output Feedback for PDEs with Spatially Varying Coefficients 226
19. Chapter Fourteen. Inverse Optimal Control 261
20. Appendix A. Adaptive Backstepping for Nonlinear ODEs—The Basics 277
21. Appendix B. Poincaré and Agmon Inequalities 305
22. Appendix C. Bessel Functions 307
23. Appendix D. Barbalat’s and Other Lemmas for Proving Adaptive Regulation 310
24. Appendix E. Basic Parabolic PDEs and Their Exact Solutions 313
25. References 317
26. Index 327