Neural approximations for optimal control and decision. (2020)

• Record Type: Book
• Further Information: Note: Riccardo Zoppoli, Marcello Sanguineti, Giorgio Gnecco, Thomas Parisini.
• Other Names: Zoppoli, Riccardo; Sanguineti, Marcello; Gnecco, Giorgio; Parisini, Thomas
• Contents: Intro -- Preface -- Contents -- 1 The Basic Infinite-Dimensional or Functional Optimization Problem -- 1.1 General Comments on Infinite-Dimensional or Functional Optimization -- 1.1.1 IDO and FDO Problems -- 1.1.2 From the Ritz Method to the Extended Ritz Method (ERIM) -- 1.1.3 Approximation of Functions -- 1.1.4 From Function Approximation to Approximate Infinite-Dimensional Optimization -- 1.1.5 Relationships with Parametrized Control Approaches -- 1.2 Contents and Structure of the Book -- 1.3 Infinite-Dimensional Optimization -- 1.3.1 Statement of the Problem 1.3.2 Finite-Dimensional Versus Infinite-Dimensional Optimization -- 1.4 General Conventions and Assumptions -- 1.4.1 Existence and Uniqueness of Minimizers -- 1.4.2 Other Definitions, Conventions, and Assumptions -- 1.5 Examples of Infinite-Dimensional Optimization Problems -- 1.5.1 A Deterministic Continuous-Time Optimal Control Problem -- 1.5.2 A Continuous-Time Network Flow Problem -- 1.5.3 A T-Stage Stochastic Optimal Control Problem -- 1.5.4 An Optimal Estimation Problem -- 1.5.5 A Static Team Optimal Control Problem -- References 2 From Functional Optimization to Nonlinear Programming by the Extended Ritz Method -- 2.1 Fixed-Structure Parametrized (FSP) Functions -- 2.2 The Sequence of Nonlinear Programming Problems Obtained by FSP Functions of Increasing Complexity -- 2.2.1 The Case of Problem P -- 2.2.2 The Case of Problem PM -- 2.3 Solution of the Nonlinear Programming Problem Pn -- 2.4 Optimizing FSP Functions -- 2.5 Polynomially Complex Optimizing FSP Functions -- 2.5.1 The Growth of the Dimension d -- 2.5.2 Polynomial and Exponential Growths of the Model Complexity n with the Dimension d -- 2.6 Approximating Sets 2.7 Polynomially Complex Approximating Sequences of Sets -- 2.7.1 The Worst-Case Error of Approximation of Functions -- 2.7.2 Polynomial and Exponential Growth of the Model Complexity n with the Dimension d -- 2.8 Connections Between Approximating Sequences and Optimizing Sequences -- 2.8.1 From mathcalSd-Approximating Sequences of Sets to Pd-Optimizing Sequences of FSP Functions -- 2.8.2 From Pd-Optimizing Sequences of FSP Functions to Polynomially Complex Pd-Optimizing Sequences of FSP Functions -- 2.8.3 Final Remarks -- 2.9 Notes on the Practical Application of the ERIM -- References 3 Some Families of FSP Functions and Their Properties -- 3.1 Linear Combinations of Fixed-Basis Functions -- 3.2 One-Hidden-Layer Networks -- 3.2.1 The Structure of OHL Networks -- 3.2.2 A More Abstract View -- 3.2.3 Tensor-Product, Ridge, and Radial Constructions -- 3.3 Multi-Hidden-Layer Networks -- 3.4 Terminology -- 3.5 Kernel Smoothing Models -- 3.6 Density Properties -- 3.6.1 mathscrC- and mathscrLp-Density Properties -- 3.6.2 The Case of Ridge OHL Networks -- 3.6.3 The Case of Radial OHL Networks -- 3.6.4 Multiple Hidden Layers and Multiple Outputs
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (532 pages)
• Subjects: 629.8/312; Control theory -- Mathematical models; Mathematical optimization; Control theory -- Mathematical models; Mathematical optimization; Electronic books
• Languages: English
• ISBNs: 9783030296933; 3030296938
• Related ISBNs: 9783030296919
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.