Controllability Stabilization And The Regulator Problem For Random
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Controllability Stabilization And The Regulator Problem For Random
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Author : Russell Johnson
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-09-11
Controllability Stabilization And The Regulator Problem For Random written by Russell Johnson and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Control theory categories.
This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.
The Riemann Problem For The Transportation Equations In Gas Dynamics
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Author : Wancheng Sheng
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
The Riemann Problem For The Transportation Equations In Gas Dynamics written by Wancheng Sheng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically
Nonautonomous Linear Hamiltonian Systems Oscillation Spectral Theory And Control
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Author : Russell Johnson
language : en
Publisher: Springer
Release Date : 2016-03-25
Nonautonomous Linear Hamiltonian Systems Oscillation Spectral Theory And Control written by Russell Johnson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-25 with Mathematics categories.
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
Differential Equations Methods For The Monge Kantorovich Mass Transfer Problem
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Author : Lawrence C. Evans
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Differential Equations Methods For The Monge Kantorovich Mass Transfer Problem written by Lawrence C. Evans and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
In this volume, the authors demonstrate under some assumptions on $f $, $f $ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{ }=f dx$ onto $\mu =f dy$ can be constructed by studying the $p$-Laplacian equation $- \roman{div}(\vert DU_p\vert p-2}Du_p)=f -f $ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1, -\roman{div}(aDu)=f -f $ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f $ and $f $
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations
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Author : Donald J. Estep
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations written by Donald J. Estep and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
New Trends In Nonlinear Dynamics And Control And Their Applications
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Author : Wei Kang
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-16
New Trends In Nonlinear Dynamics And Control And Their Applications written by Wei Kang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-16 with Technology & Engineering categories.
A selection of papers exploring a wide spectrum of new trends in nonlinear dynamics and control, such as bifurcation control, state estimation and reconstruction, analysis of behavior and stabilities, dynamics of nonlinear neural network models, and numerical algorithms. The papers focus on new ideas and the latest developments in both theoretical and applied research topics of nonlinear control. Because many of the authors are leading researchers in their own fields, the papers presented in this volume reflect the state of the art in the areas of nonlinear dynamics and control. Many of the papers in this volume were first presented at the highly succesful ''Symposium on New Trends in Nonlinear Dynamics and Control, and Their Applications,'' held October 18-19, 2002, in Monterey, California.
Equivariant E Theory For C Algebras
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Author : Erik Guentner
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Equivariant E Theory For C Algebras written by Erik Guentner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space
Limit Theorems For Functionals Of Ergodic Markov Chains With General State Space
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Author : Xia Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Limit Theorems For Functionals Of Ergodic Markov Chains With General State Space written by Xia Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians working probability theory and statistics.
Caustics For Dissipative Semilinear Oscillations
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Author : Jean-Luc Joly
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Caustics For Dissipative Semilinear Oscillations written by Jean-Luc Joly and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in partial differential equations.
Inverse Invariant Theory And Steenrod Operations
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Inverse Invariant Theory And Steenrod Operations written by Mara D. Neusel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.