By Arjan van der Schaft
This commonplace textual content provides a unified therapy of passivity and L2-gain concept for nonlinear country area structures, preceded by means of a compact therapy of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis among passivity and L2-gain thought is equipped through the idea of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear balance and stabilization are mentioned from this viewpoint. the relationship between L2-gain and passivity through scattering is detailed.
Feedback equivalence to a passive method and ensuing stabilization concepts are discussed. The passivity suggestions are enriched through a generalised Hamiltonian formalism, emphasising the shut kinfolk with actual modeling and regulate by way of interconnection, and leading to novel keep watch over methodologies going past passivity.
The power of L2-gain strategies in nonlinear control, including a thought of all-pass factorizations of nonlinear structures, and of parametrization of stabilizing controllers, is established. The nonlinear H-infinity optimum keep watch over challenge is additionally handled and the e-book concludes with a geometric research of the answer units of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization.
· L2-Gain and Passivity ideas in Nonlinear Control (third version) is punctiliously up to date, revised, reorganized and accelerated. one of the alterations, readers will find:
· updated and prolonged insurance of dissipative platforms theory
· substantial new fabric relating to speak passivity theorems and incremental/shifted passivity · coverage of contemporary advancements on networks of passive structures with examples
· a thoroughly overhauled and succinct creation to modeling and regulate of port-Hamiltonian platforms, by way of an exposition of port-Hamiltonian formula of actual community dynamics
· updated remedy of all-pass factorization of nonlinear systems
The e-book offers graduate scholars and researchers in structures and keep watch over with a compact presentation of a primary and swiftly constructing region of nonlinear regulate thought, illustrated via a huge variety of suitable examples stemming from varied software areas.