Second order partial differential equations in Hilbert spaces / / Giuseppe Da Prato, Jerzy Zabczyk [[electronic resource]]

• Record Nr.: UNINA9910782937403321
• Autore: Da Prato Giuseppe
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2002
• ISBN: 1-107-11991-X; 1-280-42958-5; 9786610429585; 0-511-17727-5; 0-511-15823-8; 0-511-32567-3; 0-511-54321-2; 0-511-04995-1
• Descrizione fisica: 1 online resource (xvi, 379 pages) : digital, PDF file(s)
• Collana: London Mathematical Society lecture note series ; ; 293
• Disciplina: 515/.353
• Soggetti: Differential equations, Partial; Hilbert space
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references (p. 358-375) and index.
• Nota di contenuto: Theory in Spaces of Continuous Functions -- Gaussian measures -- Introduction and preliminaries -- Definition and first properties of Gaussian measures -- Measures in metric spaces -- Gaussian measures -- Computation of some Gaussian integrals -- The reproducing kernel -- Absolute continuity of Gaussian measures -- Equivalence of product measures in R[superscript [infinity] -- The Cameron-Martin formula -- The Feldman-Hajek theorem -- Brownian motion -- Spaces of continuous functions -- Preliminary results -- Approximation of continuous functions -- Interpolation spaces -- Interpolation between UC[subscript b](H) and UC[superscript 1 subscript b](H) -- Interpolatory estimates -- Additional interpolation results -- The heat equation -- Strict solutions -- Regularity of generalized solutions -- Q-derivatives -- Q-derivatives of generalized solutions -- Comments on the Gross Laplacian -- The heat semigroup and its generator -- Poisson's equation -- Existence and uniqueness ; results -- Regularity of solutions -- The equation [Delta subscript Q]u = g -- The Liouville theorem -- Elliptic equations with variable coefficients -- Small perturbations -- Large perturbations -- Ornstein-Uhlenbeck equations -- Existence and uniqueness of strict solutions -- Classical solutions -- The Ornstein-Uhlenbeck semigroup -- [pi]-Convergence -- Properties of the [pi]-semigroup (R[subscript t]) -- The infinitesimal generator -- Elliptic equations -- Schauder estimates -- The Liouville theorem -- Perturbation results for parabolic equations.
• Sommario/riassunto: Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.

Adaptive Dynamic Programming with Applications in Optimal Control / / by Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li

• Record Nr.: UNINA9910158672003321
• Autore: Liu Derong
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
• Edizione: [1st ed. 2017.]
• Descrizione fisica: 1 online resource (XXX, 594 p. 203 illus., 175 illus. in color.)
• Collana: Advances in Industrial Control, , 1430-9491
• Disciplina: 670.427
• Soggetti: Automatic control; Computational intelligence; Statistical physics; Control and Systems Theory; Computational Intelligence; Applications of Nonlinear Dynamics and Chaos Theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: History of Adaptive Dynamic Programming -- Part I: Continuous-Time Systems -- Optimal Control of Continuous-Time Affine Nonlinear Systems -- Optimal Control of Nonaffine Continuous-Time Systems -- Robust and Guaranteed Cost Control of Continuous-Time Nonlinear Systems -- Decentralized Stabilization and Control of Nonlinear Interconnected Systems -- Online Synchronous Optimal Learnign Algorithms for Multiplayer Nonzero-Sum Games with Unknown Dynamics -- Part II: Discrete-Time Systems -- Value Iteration Adaptive Dynamic Programming for Discrete-Time Nonlinear Systems -- Finite Approximation Error-Based Value Iteration for Adaptive Dynamic Programming -- Policy Iteration for Optimal Control of Discrete-Time Nonlinear Systems -- Generalized Policy Iteration Adaptive Dynamic Programming for Discrete-Time Nonlinear Systems -- Error-Bound Analysis of Adaptive Dynamic Programming Algorithms for Solving Undiscounted Optimal Control Problems -- Part III: Applications -- Adaptive Dynamic Programming for Renewable Energy Scheduling and Battery Management in Smart Homes -- Adaptive Dynamic ; Programming for Optimal Tracking Control of a Coal Gasification Process -- Data-Driven Neuro-Optimal Temperature Control of Water–Gas Shift Reaction.
• Sommario/riassunto: This book covers the most recent developments in adaptive dynamic programming (ADP). The text begins with a thorough background review of ADP making sure that readers are sufficiently familiar with the fundamentals. In the core of the book, the authors address first discrete- and then continuous-time systems. Coverage of discrete-time systems starts with a more general form of value iteration to demonstrate its convergence, optimality, and stability with complete and thorough theoretical analysis. A more realistic form of value iteration is studied where value function approximations are assumed to have finite errors. Adaptive Dynamic Programming also details another avenue of the ADP approach: policy iteration. Both basic and generalized forms of policy-iteration-based ADP are studied with complete and thorough theoretical analysis in terms of convergence, optimality, stability, and error bounds. Among continuous-time systems, the control of affine and nonaffine nonlinear systems is studied using the ADP approach which is then extended to other branches of control theory including decentralized control, robust and guaranteed cost control, and game theory. In the last part of the book the real-world significance of ADP theory is presented, focusing on three application examples developed from the authors’ work: • renewable energy scheduling for smart power grids; • coal gasification processes; and • water–gas shift reactions. Researchers studying intelligent control methods and practitioners looking to apply them in the chemical-process and power-supply industries will find much to interest them in this thorough treatment of an advanced approach to control. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.