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Stability --- Distributed parameter systems

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Estimation theory --- Distributed parameter systems --- Control theory

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Distributed parameter systems. --- Green's functions. --- Transfer functions. --- Transfer functions --- Distributed parameter systems

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The behaviour of systems occurring in real life is often modelled by partial differential equations. This book investigates how a user or observer can influence the behaviour of such systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically, these methods being validated by the results of numerical experiments. In Part I of the book the authors discuss the mathematics and numerics relating to the controllability of systems modelled by linear and non-linear diffusion equations; Part II is dedicated to the controllability of vibrating systems, typical ones being those modelled by linear wave equations; finally, Part III covers flow control for systems governed by the Navier-Stokes equations modelling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of use to more advanced practitioners.

Control theory --- Distributed parameter systems --- Differential equations, Partial --- Numerical solutions --- Control theory. --- Distributed parameter systems. --- Systems, Distributed parameter --- Engineering systems --- System analysis --- Numerical analysis --- Dynamics --- Machine theory --- Numerical solutions. --- Differential equations, Partial - Numerical solutions

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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.

Algebraic varieties -- Classification theory. --- Distributed parameter systems --- Differential equations, Partial --- Nonlinear control theory --- Mechanical Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mechanical Engineering - General --- Distributed parameter systems. --- Nonlinear control theory. --- Differential equations, Partial. --- Partial differential equations --- Systems, Distributed parameter --- Engineering. --- System theory. --- Control engineering. --- Control. --- Systems Theory, Control. --- Control theory --- Engineering systems --- System analysis --- Nonlinear theories --- Systems theory. --- Control and Systems Theory. --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy