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Author: S. S. Sritharan
Publisher: SIAM
ISBN: 9781611971415
Category : Technology & Engineering
Languages : en
Pages : 210
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Book Description
Author: S. S. Sritharan
Publisher: SIAM
ISBN: 9781611971415
Category : Technology & Engineering
Languages : en
Pages : 210
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Book Description
Author: Akbar Sahrapour
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The present research is concerned with the application of optimal control theory to time-dependent viscous flows. Some specific designs of artificial hearts are described briefly, followed by a review on common hemodynamic problems created by artificial hearts and heart valves. Some mathematical models for certain types of artificial hearts are formulated. Optimal control theory has been applied to some of these models to obtain the necessary conditions of optimality. The optimization problem consists of determining the optimal control policy in order to minimize the value of an appropriate cost functional, which accounts for differences from a desired flow rate and the mean squared shear stresses and vorticity. The necessary conditions of optimality include the Navier-Stokes equations, the associated adjoint equations and an inequality. For the purpose of the numerical solution of the governing equations, a numerical code has been developed, which solves the Navier-Stokes and the corresponding adjoint equations by the Finite Element Method with penalty function formulation. The Navier-Stokes and the adjoint equations were solved iteratively. Each system of equations was solved separately but the two systems were iteratively coupled in the control problem context. At the end of each iteration a new control was computed using the inequality, and the process was repeated until convergence was achieved. Numerical solution of the optimization algorithm was achieved for a two-dimensional model with an initial velocity distribution as the control variable, and a two-dimensional model with a time-dependent boundary velocity applied at some part of the boundary as the control. The latter case was further extended to an approximate three-dimensional model of an artificial heart. In all cases, it was observed that, in the absence of shear stress and vorticity in the cost functional, the desired flow rate was almost achieved, while including these parameters resulted in a decreased optimal flow rate but with smoother velocity distributions. In the case of two- and three-dimensional boundary control, it was found that, when the stress and vorticity levels were minimized, the optimization algorithm could successfully rearrange the flow distribution, smoothen the sharp gradients and remove the vortices that would occur otherwise in the velocity field. This study demonstrates that optimal control of flow systems is practical and can be used as a design tool.
Author: Max D. Gunzburger
Publisher: SIAM
ISBN: 089871527X
Category : Science
Languages : en
Pages : 273
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Book Description
Introduces several approaches for solving flow control and optimization problems through the use of modern methods.
Author: Jason L. Speyer
Publisher: SIAM
ISBN: 0898716942
Category : Mathematics
Languages : en
Pages : 316
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Book Description
A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.
Author: Toyoki Matsuzawa
Publisher:
ISBN:
Category :
Languages : en
Pages : 398
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Book Description
Author: Xungjing Li
Publisher: Springer Science & Business Media
ISBN: 1461242606
Category : Mathematics
Languages : en
Pages : 462
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Book Description
Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.
Author: A. V. Fursikov
Publisher: American Mathematical Soc.
ISBN: 9780821897904
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This volume presents the analysis of optimal control problems for systems described by partial differential equations. The book offers simple and clear exposition of main results in this area. The methods proposed by the author cover cases where the controlled system corresponds to well-posed or ill-posed boundary value problems, which can be linear or nonlinear. The uniqueness problem for the solution of nonlinear optimal control problems is analyzed in various settings. Solutions of several previously unsolved problems are given. In addition, general methods are applied to the study of two problems connected with optimal control of fluid flows described by the Navier-Stokes equations.
Author: W. Desch
Publisher: Springer Science & Business Media
ISBN: 9783764358358
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.
Author: Juan Carlos de los Reyes
Publisher:
ISBN:
Category :
Languages : en
Pages : 254
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Book Description
Author: Mohamed Gad-el-Hak
Publisher: Cambridge University Press
ISBN: 0521770068
Category : Science
Languages : en
Pages : 445
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Book Description
A thorough treatment of the basics of flow control and flow control practices.
