Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs

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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 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. 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.

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.

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Goal The aim of this workshop is to give an introductory overview and some basic concepts on recent control strategies developed for distributed parameters systems. This workshop focusses on three main control design strategies: flatness-based motion planning, tracking and observation, Backstepping and energy shaping.

The theoretical development will be illustrated on a set of physical examples such as transmission lines, beam equations, shallow water equations, Burgers equations or reaction-transport diffusion problems including chemical processes, diffusion equation, population dynamics, etc.

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Synopsis Open physical distributed parameter systems governed by partial differential equations PDEs are more and more often encountered in modern engineering applications. It is the case for example for applications involving fluids, elasticity, plasmas, and other spatially distributed phenomena modeled by PDEs. The system theoretical formulation of such phenomena, their analysis and control are of high theoretical and practical interest.

This interest, even for industrial applications, has been strengthened by the recent computational and technological progresses.

Control Of Higher Dimensional Pdes : Flatness And Backstepping Designs

From the control point of view, many results have been proposed the last 20 years for the asymptotic or exponential stabilization of PDE systems. Even if the literature on this topic is quite prolific, only few contributions attempt to deal with achievable performances and system oriented control design. The aim of this workshop is to present some of these control design techniques and to highlight recent trends as well as open research questions.

The first one is the flatness-based motion planning. It addresses the determination of the input trajectories so that the system states or outputs, respectively, follow certain prescribed paths. For solving the motion planning problem for distributed parameter systems differential flatness has in the last years evolved into a design systematics that is applicable to rather large system classes, see, e.

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Depending on the type of PDE, the dimension and shape of the spatial domain and the location of the control inputs the used techniques utilize, e. In addition to theoretical results the available experimental results obtained for flexible structures or thermal processes clearly indicate the applicability of flatness-based motion planning for PDEs. The second control technique that is presented in this workshop is backstepping.