Handbook of numerical analysis: Volume 24 Numerical control: Part B
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| Format: | Buch |
| Sprache: | Englisch |
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Amsterdam
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[2023]
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| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034123434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xviii, 644 Seiten Illustrationen, Diagramme |
| ISBN: | 9780323850605 |
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| 245 | 1 | 0 | |a Handbook of numerical analysis |n Volume 24 |p Numerical control: Part B |c general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
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Datensatz im Suchindex
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| adam_text | Contents Contributors Preface 1. xv xvii Optimal design problems through the homogenization method Juan Casado-Diaz, Manuel Luna-Laynez, and Faustino Maestre 1 introduction 2 Statement of the problem and relaxed formulation 3 Discrete formulation and convergence 4 A numerical algorithm 5 Some numerical experiments Acknowledgments References 2. 2 5 14 18 22 26 26 Structure-preserving numerical schemes for Hamiltonian dynamics Philippe Chartier and Erwan Faou 1 Overview 1.1 Definition 1.2 Examples 1.3 Lattice dynamics and PDEs 2 Classical properties of Hamiltonian systems 2.1 First integrals and symplectic transformations 2.2 Theorem of Poincaré 2.3 Action-angle variables 2.4 The Toda lattice and the use of Lax pairs 2.5 Perturbation theory 3 Symplectic numerical schemes for nonstiff systems 3.1 Splitting methods 3.2 Composition methods 3.3 Runge-Kutta methods 4 Backward analysis, stiff systems and numerical resonances 30 30 31 34 35 35 37 39 40 43 44 45 47 48 53
The case of splitting and theBaker-Campbell-Hausdorff formula 4.2 Numerical resonances 4.3 Space discretization 4.4 Time discretization andnumerical resonances References 4.1 3. 53 54 55 56 57 Relaxation methods for optimal switching control of PDE-dynamical systems Falk Μ. Hante 1 Why switching control? 2 Unconstrained switching 2.1 Partial outer convexification (РОС) and the vanishing integrality gap 64 3 Constrained switching 3.1 Combinatorial integral approximation with constraints 3.2 Penalty-ADM techniques 4 Conclusions and open problems Acknowledgments References 4. 62 63 70 71 72 74 74 74 Feedback control of time-dependent nonlinear PDFs with applications in fluid dynamics Peter Benner and Michael Hinze 1 introduction: feedback control of time-dependent PDEs 1.1 Riccati-based feedback control 1.2 Model predictive control for PDEs 1.3 Other developments in feedbackcontrol 1.4 The MPC concept 2 Feedback control in fluid dynamics 2.1 Instantaneous rolling horizon control of theNavier-Stokes systems 2.2 Preliminaries 2.3 Rolling horizon optimization problem 2.4 Instantaneous rolling horizon control 2.5 Rolling horizon control of the Navier-Stokes system 2.6 Numerical validation of instantaneousand classical rolling horizon control 3 Feedback control of nonlinear PDEs via Riccati equations 3.1 Introduction 3.2 The coupled flow problem 3.3 Projection method 3.4 Numerical example 4 Conclusions and outlook References 78 79 81 83 84 87 88 90 91 93 98 103 109 109 110 1T3 118 123 124
5. Computation of invariant sets for complex systems Benoît Legat and Raphael Μ. Jungers 1 Introduction 1.1 Notation 2 Set programming formulations for the control of complex systems 2.1 Numerical implementation 2.2 Set programs 2.3 Applications 3 Template-independent set programming 3.1 Invariance inclusions 3.2 Strong invariance inclusions 3.3 Controlled invariance inclusions for convex bodies 3.4 Fixed point reformulation of set programs 4 Four numerical templates 4.1 Polyhedra 4.2 Ellipsoids 4.3 Piecewise semi-ellipsoids 4.4 Basic semialgebraic sets 5 Comparison of performance forconvex bodies 6 Conclusion Appendix A Convex sets: geometry and computation A.1 Properties of set-valued maps A.2 Functional representation of convex sets A.3 Operations preserving convexity A.4 Polyhedral computation A.5 Ellipsoids References 6. 132 133 133 133 134 137 140 140 141 142 145 146 147 152 152 156 159 162 163 163 164 167 171 176 180 Nonlocal balance laws - an overview over recent results Alexander Keimer and Lukas Pflug 1 Introduction 1.1 Chronological literature review 1.2 Nonlocal conservation laws in applications 1.3 Applications in applied sciences 2 Existence uniqueness of solutions 2.1 Transforming the dynamics into a fixed-point problem 2.2 Method of characteristics and a fixed-point setup 2.3 Existence on finite time horizon/maximum principle 3 Related models - extensions 3.1 Multi-d case 3.2 Spatially discontinuous flux 3.3 Delay 3.4 Bounded domain cases 184 185 188 188 191 191 193 194 195 196 196 199 201
3.5 Control 4 Approximating local entropy solutions by solutions of nonlocal conservation laws orthe singular limit problem 5 A numerical scheme withoutdissipation 6 Open problems Acknowledgments References 7. 203 203 208 210 212 212 Nonoverlapping domain decomposition and virtual controls for optimal control problems of p-type on metric graphs Günter Leugering 1 Introduction 218 1.1 Main goals and descriptionof the content 219 1.2 Modeling of gas flow in a single pipe 222 1.3 Network modeling 224 2 Optimal control problems 225 2.1 Problem formulation 225 2.2 Time discretization 227 2.3 Instantaneous control 231 3 Nonoverlapping domain decomposition: the concept of virtual controls 235 3.1 DDM and virtual controls: an introduction 236 3.2 The Lions-Pironneau method for the p-Laplacian on graphs 237 3.3 The method by P.L. Lions for the p-Laplacian on a graph 242 4 Domain decomposition for the static optima) control problem 247 5 Time-domain decomposition 252 6 Concluding remarks and open problems 256 References 257 8. Filtration techniques for the uniform controllability of semidiscrete hyperbolic equations Sorin Міси and Ionel Rovența 1 2 3 4 Introduction Problem of moments and biorthogonals Semidiscrete hyperboliccontrolproblems A case study: finite elements for the one dimensional wave equation 4.1 The product 4.2 A multiplier 4.3 The biorthogonal sequence 4.4 Uniform cotrollability results 5 Numerical experiments References 262 263 267 272 275 277 282 285 291 295
9. Discrete-time formulations as time discretization strategies in data assimilation Philippe Moirea u 1 Introduction 298 2 Least squares estimation and associated discretization for linear parabolic cases 301 2.1 The functional framework 301 2.2 Data assimilation via optimal control 302 2.3 Discretization of the variational strategy 305 2.4 The discrete time Kalman filter as a time discretization of the Kalman-Bucy filter 309 2.5 Link with stochastic filtering 310 2.6 Alternative strategies for large dimensional discretized systems 311 3 Luenberger observer strategies and discretization for linear hyperbolic cases 314 3.1 Optimal control strategy formalism for hyperbolic problems 315 3.2 Luenberger observers as an optimal filtering alternative 316 3.3 Time discretization: from observability conditions to numerical analysis 317 3.4 Coupling Luenberger observers with optimal filtering 322 4 Least squares estimation and associated discretization for nonlinear models 326 4.1 The Mortensen observer 327 4.2 Discretization of the Mortensen filter 329 4.3 Approximated optimal approaches and discretization 331 5 Conclusion 334 References 335 10. Approximation of exact controls for semilinear wave and heat equations through space-time methods Arnaud Münch 1 Introduction 2 The wave equation 2.1 Controllability results for the linear wave equation 2.2 Controllability results for a semilinear wave equation 2.3 Construction of a convergent sequence of state-control pairs for the semilinear system (5): a least-squares approach 2.4 Numerical approximation of exact controls for the wave
equation 349 2.5Numerical illustrations 3 The heat equation 3.1 Controllability results for the linear heat equation 342 343 343 345 346 356 360 360
Controllability results for the semilinear heat equation Construction of two sequences converging to a controlled pair for (24) 364 3.4 Numerical approximation of exact controls for the heat equation 368 3.5 Numericalillustrations 4 Perspectives References 3,2 3.3 362 369 371 372 11. Computational approaches for extremal geometric eigenvalue problems Chiu-Yen Kao, Braxton Osting, and Edouard Oudet 1 Introduction 378 2 Maximizing Laplace-Beltrami eigenvalues on closed surfaces 379 2.1 Maximizing Laplace-Beltrami eigenvalues on flat tori 380 2.2 Conformal Laplace-Beltrami eigenvalues 383 2.3 Topological Laplace-Beltrami eigenvalues 386 2.4 Maximizing Laplace-Beltrami eigenvalues on embedded surfaces 388 3 Maximizing Steklov eigenvalues on compact surfaces with boundary 393 3.1 Uniformization of multiply connected domains 394 3.2 Computational methods 395 3.3 Optimality conditions and free boundary minimal surfaces 397 3.4 Numerical solutions of the extremal Steklov eigenvalue problem and the corresponding free boundary minimal surfaces 399 4 Discussion and future directions 402 4.1 Future directions: spectral geometry 402 4.2 Future directions: computational methods 403 Acknowledgments 403 References 403 12. Unbalanced Optimal Transport, from theory to numerics Thibault Séjourné, Gabriel Peyré, and François-Xavier Vialard 1 Introduction 1.1 Distributions and positive measures in data sciences 2 φ-divergences, MMD and Optimal Transport 2.1 ¡^-divergences 2.2 Maximum mean discrepancies 2.3 Balanced Optimal Transport 3 Unbalanced Optimal Transport 3.1 Static formulation 408 408
411 411 413 417 422 423
3.2 Dynamic formulation 3.3 Conic formulation 3.4 Discussion and synthesis on (JOT formulations 4 Entropie regularization 4.1 Sinkhorn algorithm 4.2 Popular settings, closed forms andnumerical illustrations 4.3 Translation invariant Sinkhorn 4.4 Sinkhorn divergences 4.5 Sample complexity 5 Gromov-Wassersteindistances 5.1 Comparing balanced metric measure spaces 5.2 Unbalanced Gromov-Wasserstein 6 Conclusion References 425 427 432 434 434 440 442 446 450 452 452 456 462 463 13. Numerics and control of conservation laws Michael Herty and Stefan Ulbrich 1 Introduction 2 Notation and variational calculus 2.1 Scalar case 2.2 System s case 3 Numerical analysis 3.1 First-order finite-volume schemes 3.2 Scalar case 3.3 Higher-order finite-volume andLagragian schemes 3.4 Relaxation schemes 3.5 Wave-front tracking schemes 3.6 Automatic differentiation 4 Outlook Acknowledgments References 474 476 478 486 490 491 493 498 501 503 503 504 505 505 14. Extensions of ADMM for separable convex optimization problems with linear equality or inequality constraints Bingsheng He, Shengjie Xu, and Xiaoming Yuan 1 Introduction 2 Variational inequality characterization 3 Prototypical algorithmic framework 3.1 Algorithmic framework 3.2 Global convergence 3.3 Convergence rate 3.4 Remarks 4 Primal-dual extension of the ADMM (3) for the model (8) 4.1 Algorithm 512 516 518 519 519 522 526 527 527
4.2 Specification of the prototypical algorithmic framework (15) 529 4.3 Convergence 531 5 Dual-primal extension of ADMM (3) for the model (8) 533 5.1 Algorithm 533 5.2 Specification of the prototypical algorithmic framework (15) 533 5.3 Convergence 536 6 Extensions to multiple-block separable convex optimization problems with linear equality or inequality constraints 537 6.1 VI characterization 538 6.2 Prototypical algorithmic framework for VI(69) 539 6.3 Roadmap for convergence analysis 540 6.4 Some useful matrices 541 7 Primal-dual extension of the ADMM (3) for the model (67) 541 7.1 Algorithm 541 7.2 Specification of the prototypical algorithmicframework (71) 542 7.3 Convergence 545 8 Dual-primal extension of the ADMM (3) for the model (67) 546 8.1 Algorithm 546 8.2 Specification of the prototypical algorithmicframework (71) 547 8.3 Convergence 550 9 Panorama 551 10 Conclusions 553 References 555 15. An algorithmic guide for finite-dimensional optimal control problems Jean-Baptiste Caillau, Roberto Ferretti, Emmanuel Trélat, and Hasnaa Zidani 1 Introduction and statement of the problem 1.1 Brief overview 1.2 Formulation of the optimal control problem 1.3 Examples 2 Direct methods: nonlinear programming 2.1 Principle 2.2 Practical numerical implementation 2.3 Variants 2.4 Goddard problem by a direct approach 3 Indirect approaches: the shooting method 3.1 Pontryagin maximum principle 3.2 Shooting method 3.3 Turnpike property 3.4 Solving the Zermelo problem by the shooting method 560 560 562 565 567 567 568 568 569 571 571 574 578 581
3.5 Solving the Goddard problem by the shooting method 4 Hamilton-Jacobi-Bellmanapproach 4.1 Unconstrained Bolza control problems 4.2 Other unconstrained control problems and their HJB formulation 4.3 Constrained Bolza problems 4.4 Relationship between HJB and PMP 4.5 Numerical methods for HJB 4.6 Numerical examples 5 Optimistic planning algorithms References Index 584 587 589 592 597 601 602 610 616 623 627
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| title | Handbook of numerical analysis |
| title_auth | Handbook of numerical analysis |
| title_exact_search | Handbook of numerical analysis |
| title_full | Handbook of numerical analysis Volume 24 Numerical control: Part B general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_fullStr | Handbook of numerical analysis Volume 24 Numerical control: Part B general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_full_unstemmed | Handbook of numerical analysis Volume 24 Numerical control: Part B general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_short | Handbook of numerical analysis |
| title_sort | handbook of numerical analysis numerical control part b |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik Aufsatzsammlung |
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