Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more.
1. 1 Introduction - p. page2 2. 2 Finite Element approximation of the fractional Laplace operator - p. 4 3. 3 Interior controllability properties of the fractional heat equation - p. 12 4. 4 Exterior controllability properties of the fractional heat equation - p. 26 5. 5 Simultaneous control of parameter-dependent fractional heat equations - p. 33 6. 6 Conclusion and open problems - p. 44 7. Acknowledgements - p. 47 8. References - p. 54 9. Chapter 2: Modeling, control, and numerics of gas networks - p. 59 10. Chapter 3: Optimal control, numerics, and applications of fractional PDEs - p. 87 11. Chapter 4: Optimal control of PDEs and FE-approximation - p. 115 12. Abstract - p. 115 13. Introduction - p. 116 14. 1 The L2 framework - p. 117 15. 2 Controlling with measures - p. 146 16. 3 Related topics - p. 155 17. References - p. 158 18. Chapter 5: Numerical solution of multi-objective optimal control and hierarchic controllability problems - p. 165 19. Abstract - p. 165 20. 1 Introduction - p. 166 21. 2 Bi-objective control problems for heat and wave equations - p. 168 22. 3 Stackelberg strategies and hierarchical control problems - p. page183 23. 4 Additional comments and conclusions - p. 196 24. References - p. page197 25. Chapter 6: Numerics for stochastic distributed parameter control systems: a finite transposition method - p. 201 26. Abstract - p. 201 27. 1 Introduction - p. 202 28. 2 Dual equations for stochastic distributed parameter control problems - p. 203 29. 3 The space of finite transposition - p. 209 30. 4 Finite transposition method for backward stochastic evolution equations - p. 214 31. 5 Numerical method for optimal controls - p. 226 32. References - p. 230 33. Chapter 7: Numerical solutions of stochastic control problems: Markov chain approximation methods - p. 233 34. Abstract - p. 233 35. 1 Stochastic control problems - p. 234 36. 2 Methods of Markov chain approximation - p. 238 37. 3 Application to insurance - p. 247 38. 4 Application to mathematical biology - p. 255 39. 5 Final remarks - p. 262 40. References - p. 262 41. Chapter 8: Control of parameter dependent systems - p. 265 42. Abstract - p. 265 43. 1 Introduction - p. 266 44. 2 Parameter invariant controls - p. 269 45. 3 Parameter dependent controls - p. 284 46. 4 Conclusion - p. 298 47. Acknowledgements - p. page300 48. References - p. 303 49. Chapter 9: Space-time POD-Galerkin approach for parametric flow control - p. 307 50. Chapter 10: Moments and convex optimization for analysis and control of nonlinear PDEs - p. 339 51. Chapter 11: Turnpike properties in optimal control: An overview of discrete-time and continuous-time results - p. 367 52. Chapter 12: Some challenging optimization problems for logistic diffusive equations and their numerical modeling - p. 401 53. Chapter 13: Gradient flows and nonlinear power methods for the computation of nonlinear eigenfunctions - p. 427 54. Abstract - p. 427 55. 1 Introduction - p. 428 56. 2 Convex analysis and nonlinear eigenvalue problems - p. page432 57. 3 Gradient flows and decrease of Rayleigh quotients - p. 434 58. 4 Flows for solving nonlinear eigenproblems - p. 438 59. 5 Nonlinear power methods for homogeneous functionals - p. 444 60. 6 Γ-convergence implies convergence of ground states - p. 449 61. 7 Applications - p. 453 62. Appendices - p. 457 63. References - p. 462 64. Chapter 14: Dynamic Programming versus supervised learning: Optimal fishing quotas - p. 467 65. Abstract - p. 467 66. 1 Introduction - p. 468 67. 2 A model problem - p. page469 68. 3 Brute force solution of the non-dynamic control problem by Monte-Carlo - p. 473 69. 4 Solution of the non-dynamic control problem by supervised learning - p. 475 70. 5 Bellman's Stochastic Dynamic Programming for the dynamic problem - p. 478 71. 6 Solution with the Hamilton-Jacobi-Bellman partial differential equations - p. 481 72. 7 Solution with the Kolmogorov equation - p. 485 73. 8 Solution by Itô calculus - p. 489 74. 9 Limit with vanishing volatility - p. 492 75. 10 Conclusion - p. 492 76. Acknowledgements - p. 493 77. References - p. page497 78. Chapter 15: Data-driven modeling and control of large-scale dynamical systems in the Loewner framework: Methodology and applications - p. 499 79. Chapter 16: Machine learning and control theory - p. 531 80. Index - p. 558
Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more.
1. 1 Introduction - p. page2 2. 2 Finite Element approximation of the fractional Laplace operator - p. 4 3. 3 Interior controllability properties of the fractional heat equation - p. 12 4. 4 Exterior controllability properties of the fractional heat equation - p. 26 5. 5 Simultaneous control of parameter-dependent fractional heat equations - p. 33 6. 6 Conclusion and open problems - p. 44 7. Acknowledgements - p. 47 8. References - p. 54 9. Chapter 2: Modeling, control, and numerics of gas networks - p. 59 10. Chapter 3: Optimal control, numerics, and applications of fractional PDEs - p. 87 11. Chapter 4: Optimal control of PDEs and FE-approximation - p. 115 12. Abstract - p. 115 13. Introduction - p. 116 14. 1 The L2 framework - p. 117 15. 2 Controlling with measures - p. 146 16. 3 Related topics - p. 155 17. References - p. 158 18. Chapter 5: Numerical solution of multi-objective optimal control and hierarchic controllability problems - p. 165 19. Abstract - p. 165 20. 1 Introduction - p. 166 21. 2 Bi-objective control problems for heat and wave equations - p. 168 22. 3 Stackelberg strategies and hierarchical control problems - p. page183 23. 4 Additional comments and conclusions - p. 196 24. References - p. page197 25. Chapter 6: Numerics for stochastic distributed parameter control systems: a finite transposition method - p. 201 26. Abstract - p. 201 27. 1 Introduction - p. 202 28. 2 Dual equations for stochastic distributed parameter control problems - p. 203 29. 3 The space of finite transposition - p. 209 30. 4 Finite transposition method for backward stochastic evolution equations - p. 214 31. 5 Numerical method for optimal controls - p. 226 32. References - p. 230 33. Chapter 7: Numerical solutions of stochastic control problems: Markov chain approximation methods - p. 233 34. Abstract - p. 233 35. 1 Stochastic control problems - p. 234 36. 2 Methods of Markov chain approximation - p. 238 37. 3 Application to insurance - p. 247 38. 4 Application to mathematical biology - p. 255 39. 5 Final remarks - p. 262 40. References - p. 262 41. Chapter 8: Control of parameter dependent systems - p. 265 42. Abstract - p. 265 43. 1 Introduction - p. 266 44. 2 Parameter invariant controls - p. 269 45. 3 Parameter dependent controls - p. 284 46. 4 Conclusion - p. 298 47. Acknowledgements - p. page300 48. References - p. 303 49. Chapter 9: Space-time POD-Galerkin approach for parametric flow control - p. 307 50. Chapter 10: Moments and convex optimization for analysis and control of nonlinear PDEs - p. 339 51. Chapter 11: Turnpike properties in optimal control: An overview of discrete-time and continuous-time results - p. 367 52. Chapter 12: Some challenging optimization problems for logistic diffusive equations and their numerical modeling - p. 401 53. Chapter 13: Gradient flows and nonlinear power methods for the computation of nonlinear eigenfunctions - p. 427 54. Abstract - p. 427 55. 1 Introduction - p. 428 56. 2 Convex analysis and nonlinear eigenvalue problems - p. page432 57. 3 Gradient flows and decrease of Rayleigh quotients - p. 434 58. 4 Flows for solving nonlinear eigenproblems - p. 438 59. 5 Nonlinear power methods for homogeneous functionals - p. 444 60. 6 Γ-convergence implies convergence of ground states - p. 449 61. 7 Applications - p. 453 62. Appendices - p. 457 63. References - p. 462 64. Chapter 14: Dynamic Programming versus supervised learning: Optimal fishing quotas - p. 467 65. Abstract - p. 467 66. 1 Introduction - p. 468 67. 2 A model problem - p. page469 68. 3 Brute force solution of the non-dynamic control problem by Monte-Carlo - p. 473 69. 4 Solution of the non-dynamic control problem by supervised learning - p. 475 70. 5 Bellman's Stochastic Dynamic Programming for the dynamic problem - p. 478 71. 6 Solution with the Hamilton-Jacobi-Bellman partial differential equations - p. 481 72. 7 Solution with the Kolmogorov equation - p. 485 73. 8 Solution by Itô calculus - p. 489 74. 9 Limit with vanishing volatility - p. 492 75. 10 Conclusion - p. 492 76. Acknowledgements - p. 493 77. References - p. page497 78. Chapter 15: Data-driven modeling and control of large-scale dynamical systems in the Loewner framework: Methodology and applications - p. 499 79. Chapter 16: Machine learning and control theory - p. 531 80. Index - p. 558
