Control of higher-dimensional PDEs : flatness and backstepping designs / / Thomas Meurer

• Record Nr.: UNINA9910437768003321
• Autore: Meurer Thomas
• Pubbl/distr/stampa: Heidelberg ; ; New York, : Springer, c2013
• ISBN: 9786613924520; 9781283612074; 1283612070; 9783642300158; 3642300154
• Edizione: [1st ed. 2013.]
• Descrizione fisica: 1 online resource (372 p.)
• Collana: Communications and control engineering
• Disciplina: 500
• Soggetti: Distributed parameter systems; Nonlinear control theory; Differential equations, Partial
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Model equations for multi–agent networks -- Model equations for flexible structures with piezoelectric actuation -- Mathematical problem formulation -- Spectral approach for time–invariant systems with general spatial domain -- Formal integration approach for time varying systems -- Backstepping for linear diffusion–convection–reaction systems with varying parameters on 1–dimensional domains -- Backstepping for linear diffusion–convection–reaction systems with varying parameters on parallelepiped domains.
• Sommario/riassunto: This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and ; experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.