Download Control of Higher-Dimensional PDEs: Flatness and by Thomas Meurer PDF

By Thomas Meurer

This monograph offers new model-based layout equipment for trajectory making plans, suggestions stabilization, kingdom estimation, and monitoring keep watch over of distributed-parameter structures ruled by way of partial differential equations (PDEs). Flatness and backstepping ideas and their generalization to PDEs with higher-dimensional spatial area lie on the center of this treatise. This contains the improvement of systematic overdue lumping layout systems and the deduction of semi-numerical techniques utilizing compatible approximation equipment. Theoretical advancements are mixed with either simulation examples and experimental effects to bridge the distance among mathematical thought and keep watch over engineering perform within the swiftly evolving PDE keep watch over sector. The textual content is split into 5 elements that includes: - a literature survey of paradigms and keep an eye on layout equipment for PDE structures - the first precept mathematical modeling of purposes coming up in warmth and mass move, interconnected multi-agent platforms, and piezo-actuated clever elastic buildings - the generalization of flatness-based trajectory making plans and feedforward keep watch over to parabolic and biharmonic PDE platforms outlined on basic higher-dimensional domain names - an extension of the backstepping method of the suggestions keep watch over and observer layout for parabolic PDEs with parallelepiped area and spatially and time various parameters - the improvement of layout options to achieve exponentially stabilizing monitoring keep watch over - the review in simulations and experiments keep an eye on of Higher-Dimensional PDEs — Flatness and Backstepping Designs is a complicated learn monograph for graduate scholars in utilized arithmetic, keep an eye on conception, and comparable fields. The booklet could function a connection with fresh advancements for researchers and regulate engineers attracted to the research and keep watch over of platforms ruled through PDEs.

Show description

Read Online or Download Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs PDF

Best system theory books

Stochastic Differential Equations

This ebook offers an advent to the fundamental concept of stochastic calculus and its functions. Examples are given in the course of the textual content, that allows you to encourage and illustrate the speculation and convey its value for plenty of purposes in e. g. economics, biology and physics. the elemental concept of the presentation is to begin from a few easy effects (without proofs) of the simpler circumstances and advance the idea from there, and to pay attention to the proofs of the simpler case (which however are usually sufficiently common for plenty of reasons) in an effort to manage to achieve fast the components of the idea that is most vital for the functions.

Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering)

This can be a self-contained advent to algebraic keep watch over for nonlinear structures appropriate for researchers and graduate scholars. it's the first publication facing the linear-algebraic method of nonlinear keep watch over structures in the sort of exact and huge model. It offers a complementary method of the extra conventional differential geometry and bargains extra simply with a number of very important features of nonlinear structures.

Hyperbolic Chaos: A Physicist’s View

"Hyperbolic Chaos: A Physicist’s View” provides fresh development on uniformly hyperbolic attractors in dynamical structures from a actual instead of mathematical point of view (e. g. the Plykin attractor, the Smale – Williams solenoid). The structurally reliable attractors appear robust stochastic houses, yet are insensitive to version of features and parameters within the dynamical platforms.

Fundamentals of complex networks : models, structures, and dynamics

Complicated networks equivalent to the web, WWW, transportation networks, energy grids, organic neural networks, and clinical cooperation networks of every kind supply demanding situations for destiny technological improvement. • the 1st systematic presentation of dynamical evolving networks, with many updated functions and homework initiatives to augment examine• The authors are all very lively and famous within the quickly evolving box of complicated networks• advanced networks have gotten an more and more very important quarter of study• provided in a logical, positive type, from uncomplicated via to advanced, interpreting algorithms, via to build networks and learn demanding situations of the long run

Additional info for Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs

Example text

23) ν(z , t) t ˙ (x(z , t), uΩ (z , t), z, t). 23) can be introduced depending on the properties of the fluid: (i) For incompressible fluids with ∇ · v(z , t) = 0 and hence Dt ρ(z , t) = 0, the term p(z , t)∇ · v(z , t) is dropped. (ii) If the flow is isobaric, then Dt p(z, t) = 0. (iii) Given an ideal gas with pν = Rϑ, then ϑ(∂x ν)p /ν = ϑ(∂ϑ ν)p /ν = 1 can be directly deduced [3]. In addition, boundary and initial conditions have to be specified to completely establish the evolution of the temperature field.

In: Proc (CD–ROM) 17th IFAC World Congress, Seoul (KR), pp. 8743–8748 (2008) 152. : Linear and Nonlinear Waves. John Wiley & Sons, New York (1999) 153. : Beitr¨age zum Steuerungsentwurf f¨ur lineare, o¨ rtlich verteilte Systeme mit konzentrierten Stelleingriffen. Berichte aus der Steuerungs– und Regelungstechnik. Shaker–Verlag, Aachen (2007) 154. : On Spectrum and Riesz Basis Assignment of Infinite–Dimensional Linear Systems by Bounded Linear Feedbacks. SIAM J. Control Optim. 34(2), 521–541 (1996) 155.

Elsevier, New York (1969) 23. : Output Regulation for Linear Distributed Parameter Systems. IEEE Trans. Automat. Control 40(12), 2236–2252 (2000) 24. : An Algebra of Transfer Functions for Distributed Linear Time– Invariant Systems. IEEE Trans. Circuits Syst. 25(9), 651–662 (1978) 25. : An Introduction to Semilinear Evolution Equations. Clarendon Press, Oxford (1998) 26. : Thermal analysis of lithium-ion batteries. J. Electrochem. Soc. 143(9), 2708–2712 (1996) 27. : Nonlinear and Robust Control of PDE Systems.

Download PDF sample

Rated 4.86 of 5 – based on 40 votes