L2-Gain and Passivity Techniques in Nonlinear Control

Beschreibung

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 techniquesin 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

·         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

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.

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 techniquesin 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

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.

Autor*in

Arjan van der Schaft

Themen in »L2-Gain and Passivity Techniques in Nonlinear Control«

Hamilton–Jacobi Inequalities Nonlinear Control Passive Systems Small-gain Theorem Input–Output Stability Port-Hamiltonian Systems Physical Network Dynamics Nonlinear Minimum-Phase Nonlinear H-infinity Control

Stimmen zu »L2-Gain and Passivity Techniques in Nonlinear Control«

“The book presents a well written and systematically organized text focused on a unified treatment of classical input-output stability theory and recent results in nonlinear robust and passivity-based control. … The book will be useful to advanced graduate students, researchers and applied mathematicians interested in this emerging area.” (Lubomír Bakule, zbMath 1410.93004, 2019)
“This text is sure to continue to be one of the go-to references for nonlinear control researchers and practitioners interested in both the classical and modern interpretations and applications of L2-gain and passivity methods for nonlinear systems.” (James Richard Forbes, IEEE Control Systems Magazine, December, 2017)

()

Details

Link teilen