L2-Gain and Passivity Techniques in Nonlinear Control - van der Schaft, Arjan; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2017)
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 · 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.
Chapter 1: Input-Output Stability -- Chapter 2: Small-Gain and Passivity of Input-Output Maps -- Chapter 3: Dissipative Systems Theory -- Chapter 4: Passivity -- Chapter 5: Passivity by Feedback -- Chapter 6: Port-Hamiltonian Systems -- Chapter 7: Port-Hamiltonian Network Dynamics -- Chapter 8: L2-Gain and the Small Gain Theorem -- Chapter 9: Factorizations of Nonlinear Systems -- Chapter 10: Nonlinear H-infinity Control.-Chapter 11: Hamilton-Jacobi Inequalities.
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