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Controllability Stabilization And The Regulator Problem For Random Differential Systems
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Book Synopsis Controllability, Stabilization, and the Regulator Problem for Random by : Russell Johnson
Download or read book Controllability, Stabilization, and the Regulator Problem for Random written by Russell Johnson and published by Oxford University Press, USA. This book was released on 2014-09-11 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Controllability, Stabilization, and the Regulator Problem for Random Differential Systems by : Russell Johnson
Download or read book Controllability, Stabilization, and the Regulator Problem for Random Differential Systems written by Russell Johnson and published by American Mathematical Soc.. This book was released on 1998 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control by : Russell Johnson
Download or read book Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control written by Russell Johnson and published by Springer. This book was released on 2016-03-25 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem by : Lawrence C. Evans
Download or read book Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem written by Lawrence C. Evans and published by American Mathematical Soc.. This book was released on 1999 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 $- \mathrm{div}(\vert DU_p\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1,-\mathrm{div}(aDu)=f^+-f^-$ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f^+$ and $f^-$.
Book Synopsis Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications by : Shlomo Strelitz
Download or read book Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications written by Shlomo Strelitz and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics are built for the solutions $y_j(x, \lambda)$, $y_j DEGREES{(k)}(0, \lambda)=\delta_{j\, n-k}$, $0\le j, k+1\le n$ of the equation $L(y)=\lambda p(x)y, \quad x\in [0,1], $ where $L(y)$ is a linear differential operator of whatever order $n\ge 2$ and $p(x)$ is assumed to possess a finite number of turning points. The established asymptotics are afterwards applied to the study of: 1) the existence of infinite eigenvalue sequences for various multipoint boundary problems posed on $L(y)=\lambda p(x)y, \quad x\in [0,1], $, especially as $n=2$ and $n=3$ (let us be aware that the same method can be successfully applied on many occasions in case $n>3$ too) and 2) asymptotical distribution of the corresponding eigenvalue sequences on the
Book Synopsis The Riemann Problem for the Transportation Equations in Gas Dynamics by : Wancheng Sheng
Download or read book The Riemann Problem for the Transportation Equations in Gas Dynamics written by Wancheng Sheng and published by American Mathematical Soc.. This book was released on 1999 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 have 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.
Download or read book Dynamical Systems written by S.-N. Chow and published by Springer. This book was released on 2003-12-15 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The C.I.M.E. session on Dynamical Systems, held in Cetraro (Italy), June 19-26, 2000, focused on the latest developments in several important areas in dynamical systems, with full development and historical context. The lectures of Chow and Mallet-Paret focus on the area of lattice differential systems, the lectures of Conto and Galleotti treat the classical problem of classification of orbits for two-dimensional autonomous systems with polynomial right sides, the lectures of Nussbaum focus on applications of fixed point theorems to the problem of limiting profiles for the solutions of singular perturbations of delay differential equations, and the lectures of Johnson and Mantellini deal with the existence of periodic and quasi-periodic orbits to non-autonomous systems. The volume will be of interest to researchers and graduate students working in these areas.
Book Synopsis Well-Posedness of the Cauchy Problem for n Xn Systems of Conservation Laws by : Alberto Bressan
Download or read book Well-Posedness of the Cauchy Problem for n Xn Systems of Conservation Laws written by Alberto Bressan and published by American Mathematical Soc.. This book was released on 2000 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Book Synopsis Recent Advances in Delay Differential and Difference Equations by : Ferenc Hartung
Download or read book Recent Advances in Delay Differential and Difference Equations written by Ferenc Hartung and published by Springer. This book was released on 2014-08-22 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.
Book Synopsis Control and Relaxation over the Circle by : Bruce Hughes
Download or read book Control and Relaxation over the Circle written by Bruce Hughes and published by American Mathematical Soc.. This book was released on 2000 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work formulates and proves a geometric version of the fundamental theorem of algebraic K-theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the fundamental theorem of lower algebraic K-theory. The main new innovation is a geometrically defined nil space.
Book Synopsis Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by : Donald J. Estep
Download or read book Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations written by Donald J. Estep and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Dynamics of Control by : Fritz Colonius
Download or read book The Dynamics of Control written by Fritz Colonius and published by Springer Science & Business Media. This book was released on 2000-04-20 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.
Book Synopsis Matching of Orbital Integrals on GL(4) and GSp(2) by : Yuval Zvi Flicker
Download or read book Matching of Orbital Integrals on GL(4) and GSp(2) written by Yuval Zvi Flicker and published by American Mathematical Soc.. This book was released on 1999 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group $Sp(2)$. These orbital integrals are compared with those on $GL(4)$, twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form $H\backslash G/K$--where H is a subgroup containing the centralizer--plays a key role.
Book Synopsis Invariants Under Tori of Rings of Differential Operators and Related Topics by : Ian Malcolm Musson
Download or read book Invariants Under Tori of Rings of Differential Operators and Related Topics written by Ian Malcolm Musson and published by American Mathematical Soc.. This book was released on 1998 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X)^G$ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k^r\times (k^*)^s$. They give a precise description of the primitive ideals in $D(X)^G$ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X)^G$. The latter are of the form $B^x=D(X)^G/({\mathfrak g}-\chi({\mathfrak g}))$ where ${\mathfrak g}=\textnormal{Lie}(G)$, $\chi\in {\mathfrak g}^\ast$ and ${\mathfrak g}-\chi({\mathfrak g})$ is the set of all $v-\chi(v)$ with $v\in {\mathfrak g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X[LAMBDA]!/G)$ is a simple ring.
Book Synopsis Algebraic and Strong Splittings of Extensions of Banach Algebras by : William G. Bade
Download or read book Algebraic and Strong Splittings of Extensions of Banach Algebras written by William G. Bade and published by American Mathematical Soc.. This book was released on 1999 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\ 0\rightarrow I\rightarrow\frak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\frak A$ is a Banach algebra and $I$ is a closed ideal in $\frak A$. The extension splits algebraically (respectively, splits strongly) if there is a homomorphism (respectively, continuous homomorphism) $\theta\: A\rightarrow\frak A$ such that $\pi\circ\theta$ is the identity on $A$. Consider first for which Banach algebras $A$ it is true that every extension of $A$ in a particular class of extensions splits, either algebraically or strongly, and second for which Banach algebras it is true that every extension of $A$ in a particular class which splits algebraically also splits strongly. These questions are closely related to the question when the algebra $\frak A$ has a (strong) Wedderburn decomposition. The main technique for resolving these questions involves the Banach cohomology group $\cal H2(A,E)$ for a Banach $A$-bimodule $E$, and related cohomology groups. Later chapters are particularly concerned with the case where the ideal $I$ is finite-dimensional. Results are obtained for many of the standard Banach algebras $A$.
Book Synopsis Cutting Brownian Paths by : Richard F. Bass
Download or read book Cutting Brownian Paths written by Richard F. Bass and published by American Mathematical Soc.. This book was released on 1999 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? In this volume, the authors provide a solution, discuss related works, and present a number of open problems.
Book Synopsis Splitting Theorems for Certain Equivariant Spectra by : L. Gaunce Lewis
Download or read book Splitting Theorems for Certain Equivariant Spectra written by L. Gaunce Lewis and published by American Mathematical Soc.. This book was released on 2000 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $G$ be a compact Lie group, $\Pi$ be a normal subgroup of $G$, $\mathcal G=G/\Pi$, $X$ be a $\mathcal G$-space and $Y$ be a $G$-space. There are a number of results in the literature giving a direct sum decomposition of the group $[\Sigma^\infty X,\Sigma^\infty Y]_G$ of equivariant stable homotopy classes of maps from $X$ to $Y$. Here, these results are extended to a decomposition of the group $[B,C]_G$ of equivariant stable homotopy classes of maps from an arbitrary finite $\mathcal G$-CW sptrum $B$ to any $G$-spectrum $C$ carrying a geometric splitting (a new type of structure introduced here). Any naive $G$-spectrum, and any spectrum derived from such by a change of universe functor, carries a geometric splitting. Our decomposition of $[B,C]_G$ is a consequence of the fact that, if $C$ is geometrically split and $(\mathfrak F',\mathfrak F)$ is any reasonable pair of families of subgroups of $G$, then there is a splitting of the cofibre sequence $(E\mathfrak F_+ \wedge C)^\Pi \longrightarrow (E\mathfrak F'_+ \wedge C)^\Pi \longrightarrow (E(\mathfrak F', \mathfrak F) \wedge C)^\Pi$ constructed from the universal spaces for the families. Both the decomposition of the group $[B,C]_G$ and the splitting of the cofibre sequence are proven here not just for complete $G$-universes, but for arbitrary $G$-universes. Various technical results about incomplete $G$-universes that should be of independent interest are also included in this paper. These include versions of the Adams and Wirthmuller isomorphisms for incomplete universes. Also included is a vanishing theorem for the fixed-point spectrum $(E(\mathfrak F',\mathfrak F) \wedge C)^\Pi$ which gives computational force to the intuition that what really matters about a $G$-universe $U$ is which orbits $G/H$ embed as $G$-spaces in $U$.
