L2-Gain and passivity techniques in nonlinear control

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Bibliographic Details
Author / Creator:	Schaft, A. J. van der.
Edition:	3rd ed.
Imprint:	Cham : Springer, 2016.
Description:	1 online resource (334 pages)
Language:	English
Series:	Communications and Control Engineering Communications and control engineering.
Subject:	Feedback control systems. Nonlinear control theory. Feedback control systems. Nonlinear control theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11269947

Hidden Bibliographic Details
ISBN:	9783319499925 3319499920 9783319499918 3319499912
Notes:	Print version record.
Summary:	This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with a geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization. · L2-Gain and Passivity Techniques in Nonlinear Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find: · updated and extended coverage of dissipative systems theory · substantial new material regarding converse passivity theorems and incremental/shifted passivity <· coverage of recent developments on networks of passive systems with examples · a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics · updated treatment of all-pass factorization of nonlinear systems The book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.
Other form:	Print version: Van der Schaft, Arjan. L2-Gain and Passivity Techniques in Nonlinear Control. Cham : Springer International Publishing, ©2016 9783319499918

Table of Contents:

Preface; Preface to the First Edition; Preface to the Second Edition; Contents; Introduction; 1 Nonlinear Input-Output Stability; 1.1 Input
Output Maps on Extended Lq-Spaces; 1.2 Lq-Stability and Lq-Gain; Closed-Loop Stability; 1.3 Input
Output Maps from State Space Models; 1.4 Notes for Chapter 1; 2 Small-Gain and Passivity for Input
Output Maps; 2.1 The Small-Gain Theorem; 2.2 Passivity and the Passivity Theorems; 2.3 Loop Transformations; 2.4 Scattering and the Relation Between Passivity and L2-Gain; 2.5 Notes for Chapter2; 3 Dissipative Systems Theory; 3.1 Dissipative Systems
3.2 Stability of Dissipative Systems3.3 Interconnections of Dissipative Systems; 3.4 Scattering of State Space Systems; 3.5 Dissipativity and the Return Difference Inequality; 3.6 Notes for Chapter3; 4 Passive State Space Systems; 4.1 Characterization of Passive State Space Systems; 4.2 Stability and Stabilization of Passive Systems; 4.3 The Passivity Theorems Revisited; 4.4 Network Interconnection of Passive Systems; 4.5 Passivity of Euler
Lagrange Equations; 4.6 Passivity of Second-Order Systems and Riemannian Geometry; 4.7 Incremental and Shifted Passivity; 4.8 Notes for Chapter 4
5 Passivity by Feedback5.1 Feedback Equivalence to a Passive System; 5.2 Stabilization of Cascaded Systems; 5.3 Stabilization by Backstepping; 5.4 Notes for Chapter5; 6 Port-Hamiltonian Systems; 6.1 Input-State-Output Port-Hamiltonian Systems; 6.2 Mechanical Systems; 6.3 Port-Hamiltonian Models of Electromechanical Systems; 6.4 Properties of Port-Hamiltonian Systems; 6.5 Shifted Passivity of Port-Hamiltonian Systems; 6.6 Dirac Structures; 6.7 Port-Hamiltonian DAE Systems; 6.8 Port-Hamiltonian Network Dynamics; 6.9 Scattering of Port-Hamiltonian Systems; 6.10 Notes for Chapter 6
7 Control of Port-Hamiltonian Systems7.1 Stabilization by Interconnection; 7.2 Passivity-Based Control; 7.3 Control by Energy-Routing; 7.4 Notes for Chapter 7; 8 L2-Gain and the Small-Gain Theorem; 8.1 L2-Gain of State Space Systems; 8.2 The Small-Gain Theorem Revisited; 8.3 Network Version of the Small-Gain Theorem; 8.4 L2-Gain as Response to Periodic Input Functions; 8.5 Relationships with IIS- and iIIS-Stability; 8.6 Notes for Chapter8; 9 Factorizations of Nonlinear Systems; 9.1 Stable Kernel and Image Representations; 9.2 L2-Gain Perturbation Models
9.3 Stable Kernel Representations and Parametrization of Stabilizing Controllers9.4 All-Pass Factorizations; 9.5 Notes for Chapter9; Nonlinear H∞ Control; 10.1 State Feedback calHinfty Control; 10.2 Output Feedback calHinfty Control; 10.3 Notes for Chapter 10; Hamilton-Jacobi Inequalities ; 11.1 Solvability of Hamilton
Jacobi Inequalities; 11.2 An Aside on Optimal Control; 11.3 Dissipativity of a Nonlinear System and Its Linearization; 11.4 calHinfty Control of a Nonlinear System and Its Linearization; 11.5 Notes for Chapter11; References; Index

L2-Gain and passivity techniques in nonlinear control

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