By Thomas Meurer
This monograph offers new model-based layout equipment for trajectory making plans, suggestions stabilization, country estimation, and monitoring regulate of distributed-parameter structures ruled through partial differential equations (PDEs). Flatness and backstepping concepts and their generalization to PDEs with higher-dimensional spatial area lie on the center of this treatise. This contains the advance of systematic overdue lumping layout methods and the deduction of semi-numerical methods utilizing compatible approximation tools. Theoretical advancements are mixed with either simulation examples and experimental effects to bridge the space among mathematical idea and keep watch over engineering perform within the swiftly evolving PDE regulate area.The textual content is split into 5 elements featuring:- a literature survey of paradigms and keep watch over layout tools for PDE structures- the 1st precept mathematical modeling of functions bobbing up in warmth and mass move, interconnected multi-agent platforms, and piezo-actuated clever elastic constructions- the generalization of flatness-based trajectory making plans and feedforward keep an eye on to parabolic and biharmonic PDE platforms outlined on normal higher-dimensional domain names- an extension of the backstepping method of the suggestions regulate and observer layout for parabolic PDEs with parallelepiped area and spatially and time various parameters- the advance of layout thoughts to achieve exponentially stabilizing monitoring keep watch over- the assessment in simulations and experimentsControl of Higher-Dimensional PDEs -- Flatness and Backstepping Designs is a sophisticated learn monograph for graduate scholars in utilized arithmetic, regulate thought, and comparable fields. The ebook may perhaps function a connection with contemporary advancements for researchers and keep an eye on engineers drawn to the research and keep an eye on of structures ruled by means of PDEs. learn more... half 1. advent and Survey -- advent -- half 2. Modeling and alertness Examples -- version Equations for Non-Convective and Convective warmth move -- version Equations for Multi-Agent Networks -- version Equations for versatile constructions with Piezoelectric Actuation -- Mathematical challenge formula -- half three. Trajectory making plans and Feedforward keep an eye on -- Spectral strategy for Time-Invariant structures with common Spatial area -- Formal Integration strategy for Time various structures with Parallelepiped Spatial area -- half four. suggestions Stabilization, Observer layout, and monitoring regulate -- Backstepping for Linear Diffusion-Convection-Reaction structures with various Parameters on 1-Dimensional domain names -- Backstepping for Linear Diffusion-Convection-Reaction platforms with various Parameters on Parallelepiped domain names
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Additional resources for Control of higher-dimensional PDEs : flatness and backstepping designs
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