LEADER 04453nam 2200685Ia 450 001 9910437768003321 005 20200520144314.0 010 $a9786613924520 010 $a9781283612074 010 $a1283612070 010 $a9783642300158 010 $a3642300154 024 7 $a10.1007/978-3-642-30015-8 035 $a(CKB)2560000000090955 035 $a(EBL)973112 035 $a(OCoLC)809767624 035 $a(SSID)ssj0000740733 035 $a(PQKBManifestationID)11411165 035 $a(PQKBTitleCode)TC0000740733 035 $a(PQKBWorkID)10700991 035 $a(PQKB)11468850 035 $a(DE-He213)978-3-642-30015-8 035 $a(MiAaPQ)EBC973112 035 $a(PPN)168315742 035 $a(EXLCZ)992560000000090955 100 $a20120409d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aControl of higher-dimensional PDEs $eflatness and backstepping designs /$fThomas Meurer 205 $a1st ed. 2013. 210 $aHeidelberg ;$aNew York $cSpringer$dc2013 215 $a1 online resource (372 p.) 225 0$aCommunications and control engineering 300 $aDescription based upon print version of record. 311 08$a9783642435096 311 08$a3642435092 311 08$a9783642300141 311 08$a3642300146 320 $aIncludes bibliographical references and index. 327 $aModel 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. 330 $aThis monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs ? Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs. 410 0$aCommunications and Control Engineering,$x0178-5354 606 $aDistributed parameter systems 606 $aNonlinear control theory 606 $aDifferential equations, Partial 615 0$aDistributed parameter systems. 615 0$aNonlinear control theory. 615 0$aDifferential equations, Partial. 676 $a500 700 $aMeurer$b Thomas$01058416 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437768003321 996 $aControl of higher-dimensional PDEs$94190489 997 $aUNINA