Numerical Control: Part A
View on ScienceDirect

Numerical Control: Part A

1st Edition - February 15, 2022

Write a review

  • Editors: Emmanuel Trélat, Enrique Zuazua
  • eBook ISBN: 9780323853392
  • Hardcover ISBN: 9780323850599

Purchase options

Purchase options
DRM-free (PDF, EPub)
eBook Format Help
Available
Sales tax will be calculated at check-out

Institutional Subscription

Support CenterReturns & Refunds
Free Global Shipping
No minimum order

Description

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.

Key Features

  • Provides the authority and expertise of leading contributors from an international board of authors
  • Presents the latest release in the Handbook of Numerical Analysis series
  • Updated release includes the latest information on Numerical Control

Readership

Mathematically trained research scientists and engineers with basic knowledge in numerical control systems

Table of Contents

  • Cover image
  • Title page
  • Table of Contents
  • Copyright
  • Dedication
  • Contributors
  • Preface
  • Chapter 1: Control and numerical approximation of fractional diffusion equations
  • Abstract
  • 1. Introduction
  • 2. Finite Element approximation of the fractional Laplace operator
  • 3. Interior controllability properties of the fractional heat equation
  • 4. Exterior controllability properties of the fractional heat equation
  • 5. Simultaneous control of parameter-dependent fractional heat equations
  • 6. Conclusion and open problems
  • Acknowledgements
  • Appendix A. Fractional order Sobolev spaces and the fractional Laplacian
  • Appendix B. The fractional Laplace operator with exterior conditions
  • References
  • Chapter 2: Modeling, control, and numerics of gas networks
  • Abstract
  • 1. Introduction
  • 2. Modeling of gas flow
  • 3. Well-posedness of mathematical models for fixed control action
  • 4. Control and controllability
  • 5. Uncertainty quantification
  • 6. Numerical methods for simulation and control
  • 7. Open problems
  • References
  • Chapter 3: Optimal control, numerics, and applications of fractional PDEs
  • Abstract
  • 1. Introduction and applications of fractional operators
  • 2. Two fractional operators and their properties
  • 3. Fractional diffusion equation: analysis and numerical approximation
  • 4. Exterior optimal control of fractional parabolic PDEs with control constraints
  • 5. Distributed optimal control of fractional PDEs with state and control constraints
  • 6. Fractional deep neural networks – FDNNs
  • 7. Some open problems
  • Acknowledgements
  • References
  • Chapter 4: Optimal control of PDEs and FE-approximation
  • Abstract
  • Introduction
  • 1. The L2 framework
  • 2. Controlling with measures
  • 3. Related topics
  • References
  • Chapter 5: Numerical solution of multi-objective optimal control and hierarchic controllability problems
  • Abstract
  • 1. Introduction
  • 2. Bi-objective control problems for heat and wave equations
  • 3. Stackelberg strategies and hierarchical control problems
  • 4. Additional comments and conclusions
  • References
  • Chapter 6: Numerics for stochastic distributed parameter control systems: a finite transposition method
  • Abstract
  • 1. Introduction
  • 2. Dual equations for stochastic distributed parameter control problems
  • 3. The space of finite transposition
  • 4. Finite transposition method for backward stochastic evolution equations
  • 5. Numerical method for optimal controls
  • References
  • Chapter 7: Numerical solutions of stochastic control problems: Markov chain approximation methods
  • Abstract
  • 1. Stochastic control problems
  • 2. Methods of Markov chain approximation
  • 3. Application to insurance
  • 4. Application to mathematical biology
  • 5. Final remarks
  • References
  • Chapter 8: Control of parameter dependent systems
  • Abstract
  • 1. Introduction
  • 2. Parameter invariant controls
  • 3. Parameter dependent controls
  • 4. Conclusion
  • Acknowledgements
  • Appendix A. Proof of technical results related to Section 2
  • References
  • Chapter 9: Space-time POD-Galerkin approach for parametric flow control
  • Abstract
  • 1. Motivations and historical background
  • 2. Introduction
  • 3. Nonlinear time dependent parametrized optimal flow control problems
  • 4. ROMs for nonlinear space-time OCP(μ)s
  • 5. Application to shallow waters equations
  • 6. Conclusions
  • Acknowledgements
  • References
  • Chapter 10: Moments and convex optimization for analysis and control of nonlinear PDEs
  • Abstract
  • 1. Introduction
  • 2. Problem statement (analysis)
  • 3. Occupation measures for nonlinear PDEs
  • 4. Computable bounds using SDP relaxations
  • 5. Problem statement (control)
  • 6. Linear representation (control)
  • 7. Control design using SDP relaxations
  • 8. Higher-order PDEs
  • 9. Numerical examples
  • 10. Conclusion
  • Acknowledgements
  • References
  • Chapter 11: Turnpike properties in optimal control
  • Abstract
  • 1. Introduction and historical origins
  • 2. Definition and taxonomy of turnpike properties
  • 3. Generating mechanisms
  • 4. Exploitation of turnpikes in numerics and receding-horizon control
  • 5. Topics not discussed and open problems
  • Acknowledgement
  • References
  • Chapter 12: Some challenging optimization problems for logistic diffusive equations and their numerical modeling
  • Abstract
  • 1. Introduction and bio-mathematical background
  • 2. Optimal eigenvalue problem
  • 3. Maximizing the total population size
  • 4. Generalization and perspectives
  • References
  • Chapter 13: Gradient flows and nonlinear power methods for the computation of nonlinear eigenfunctions
  • Abstract
  • 1. Introduction
  • 2. Convex analysis and nonlinear eigenvalue problems
  • 3. Gradient flows and decrease of Rayleigh quotients
  • 4. Flows for solving nonlinear eigenproblems
  • 5. Nonlinear power methods for homogeneous functionals
  • 6. Γ-convergence implies convergence of ground states
  • 7. Applications
  • Appendices
  • Appendix A. Exact reconstruction time
  • Appendix B. Extinction time
  • Appendix C. Remaining proofs
  • References
  • Chapter 14: Dynamic Programming versus supervised learning
  • Abstract
  • 1. Introduction
  • 2. A model problem
  • 3. Brute force solution of the non-dynamic control problem by Monte-Carlo
  • 4. Solution of the non-dynamic control problem by supervised learning
  • 5. Bellman's Stochastic Dynamic Programming for the dynamic problem
  • 6. Solution with the Hamilton-Jacobi-Bellman partial differential equations
  • 7. Solution with the Kolmogorov equation
  • 8. Solution by Itô calculus
  • 9. Limit with vanishing volatility
  • 10. Conclusion
  • Acknowledgements
  • Appendix A. A model with fishing quota
  • Appendix B. Reformulation
  • Appendix C. An analytical solution for a similar problem
  • References
  • Chapter 15: Data-driven modeling and control of large-scale dynamical systems in the Loewner framework
  • Abstract
  • 1. Introduction: data-driven modeling and control
  • 2. The Loewner framework for data-driven modeling: an overview
  • 3. Model reduction examples (large-scale systems)
  • 4. Control in the Loewner framework
  • 5. Summary and conclusions
  • References
  • Chapter 16: Machine learning and control theory
  • Abstract
  • 1. Introduction
  • 2. Reinforcement learning
  • 3. Control theory and deep learning
  • 4. Stochastic gradient descent and control theory
  • 5. Machine learning approach of stochastic control problems
  • 6. Focus on the deterministic case
  • 7. Convergence results
  • 8. Numerical results
  • Acknowledgement
  • References
  • Index

Product details

  • No. of pages: 594
  • Language: English
  • Copyright: © North Holland 2022
  • Published: February 15, 2022
  • Imprint: North Holland
  • eBook ISBN: 9780323853392
  • Hardcover ISBN: 9780323850599

About the Serial Volume Editors

Emmanuel Trélat

Emmanuel Trelat works at Sorbonne Universite in Laboratoire Jacques-Louis Lions, CNRS, Inria, equipe CAGE, Paris, France.

Affiliations and Expertise

Sorbonne Universite, Laboratoire Jacques-Louis Lions, CNRS, Inria, équipe CAGE, Paris, France

Enrique Zuazua

Enrique Zuazua works in the Department of Mathematics at Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen in Germany.

Affiliations and Expertise

Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

Ratings and Reviews

Write a review

There are currently no reviews for "Numerical Control: Part A"