Download or read book Numerical Solution of the Infinite Dimensional LQR Problem and the Associated Differential Riccati Equations written by Hermann Mena and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The numerical analysis of linear quadratic regulator design problems for parabolic partial differential equations requires solving large-scale Riccati equations. In the finite time horizon case, the differential Riccati equation (DRE) arises. Typically, the coefficient matrices of the resulting DRE have a given structure, e.g., sparse, symmetric or low rank. Moreover, in most control problems, fast and slow modes arepresent. This implies that the associated DRE will be fairly stiff. Therefore, implicit schemes have to be used to solve such DREs numerically. In this paper we derive efficient numerical methods for solving DREs capable of exploiting this structure, which are based on a matrix-valued implementation of the BDF and Rosenbrock methods. We show that these methods are particularly suitable for large-scale problems by working only on low-rank factors of the solutions. Step size and order control strategies can also be implemented based only on information contained in the solution factors. Finally, we briefly show that within a Galerkin projection framework the solutions of the finite-dimensional DREs converge in the strong operator topology to the solutions of the infinite-dimensional DREs. The performance of each of these methods is tested in numerical experiments.
Download or read book A Note on the Regularity of Solutions of Infinite Dimensional Riccati Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-09 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement. Burns, John A. and King, Belinda B. Unspecified Center NASA-CR-194898, NAS 1.26:194898, ICASE-94-20, AD-A280357 NAS1-19480; RTOP 505-90-52-01...
Download or read book A Note on the Regularity of Solutions of Infinite Dimensional Riccati Equations written by John A. Burns and published by . This book was released on 1994 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Large Scale Linear Time Varying Control Systems and related Differential Matrix Equations written by Norman Lang and published by Logos Verlag Berlin GmbH. This book was released on 2018 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the linear-quadratic optimal control and model order reduction (MOR) of large-scale linear time-varying (LTV) control systems. In the first two parts, particular attention is paid to a tracking-type finite-time optimal control problem with application to an inverse heat conduction problem and the balanced truncation (BT) MOR method for LTV systems. In both fields of application the efficient solution of differential matrix equations (DMEs) is of major importance. The third and largest part deals with the application of implicit time integration methods to these matrix-valued ordinary differential equations. In this context, in particular, the rather new class of peer methods is introduced. Further, for the efficient solution of large-scale DMEs, in practice low-rank solution strategies are inevitable. Here, low-rank time integrators, based on a symmetric indefinte factored representation of the right hand sides and the solution approximations of the DMEs, are presented. In contrast to the classical low-rank Cholesky-type factorization, this avoids complex arithmetic and tricky implementations and algorithms. Both low-rank approaches are compared for numerous implicit time integration methods.
Download or read book Equations Involving Malliavin Calculus Operators written by Tijana Levajković and published by Springer. This book was released on 2017-08-31 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introduced in terms of chaos expansions. The main properties of the operators, which are known in the literature for the square integrable processes, are proven using the chaos expansion approach and extended for generalized and test stochastic processes. Chapter 3, Equations involving Malliavin Calculus operators, is devoted to the study of several types of stochastic differential equations that involve the operators of Malliavin calculus, introduced in the previous chapter. Fractional versions of these operators are also discussed. Finally, in Chapter 4, Applications and Numerical Approximations are discussed. Specifically, we consider the stochastic linear quadratic optimal control problem with different forms of noise disturbances, operator differential algebraic equations arising in fluid dynamics, stationary equations and fractional versions of the equations studied – applications never covered in the extant literature. Moreover, numerical validations of the method are provided for specific problems."
Download or read book Numerical Analysis and Its Applications written by Ivan Dimov and published by Springer. This book was released on 2017-04-11 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016. The 90 revised papers presented were carefully reviewed and selected from 98 submissions. The conference offers a wide range of the following topics: Numerical Modeling; Numerical Stochastics; Numerical Approx-imation and Computational Geometry; Numerical Linear Algebra and Numer-ical Solution of Transcendental Equations; Numerical Methods for Differential Equations; High Performance Scientific Computing; and also special topics such as Novel methods in computational finance based on the FP7 Marie Curie Action,Project Multi-ITN STRIKE - Novel Methods in Compu-tational Finance, Grant Agreement Number 304617; Advanced numerical and applied studies of fractional differential equations.
Download or read book Chandrasekhar Equations for Infinite Dimensional Systems Part 2 Unbounded Input and Output Case written by and published by . This book was released on 1987 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. This paper considers the linear time invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and establish the existence, uniqueness, and regularity results of their solutions established. Keywords: Chandrasekhar equations; Unbounded operators; Boundary control problems.
Download or read book Numerical Control Part B written by Emmanuel Trélat and published by Elsevier. This book was released on 2023-02-20 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control
Download or read book Computational Science and Its Applications ICCSA 2017 written by Osvaldo Gervasi and published by Springer. This book was released on 2017-07-03 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: The six-volume set LNCS 10404-10409 constitutes the refereed proceedings of the 17th International Conference on Computational Science and Its Applications, ICCSA 2017, held in Trieste, Italy, in July 2017. The 313 full papers and 12 short papers included in the 6-volume proceedings set were carefully reviewed and selected from 1052 submissions. Apart from the general tracks, ICCSA 2017 included 43 international workshops in various areas of computational sciences, ranging from computational science technologies to specific areas of computational sciences, such as computer graphics and virtual reality. Furthermore, this year ICCSA 2017 hosted the XIV International Workshop On Quantum Reactive Scattering. The program also featured 3 keynote speeches and 4 tutorials.
Download or read book A Numerical Algorithm for Optimal Feedback Gains in High Dimensional LQR Problems written by H. T. Banks and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors a hybrid method for computing the feedback gains in linear quadratic regulator (LQR) problems. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of our proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented. (Author).
Download or read book Generalized Functions and Fourier Analysis written by Michael Oberguggenberger and published by Birkhäuser. This book was released on 2017-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Download or read book Chandrasekhar Equations for Infinite Dimensional Systems written by Kazufumi Ito and published by . This book was released on 1987 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systems with Delays written by A. V. Kim and published by John Wiley & Sons. This book was released on 2015-07-23 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of the book is to present new constructive methods of delay differential equation (DDE) theory and to give readers practical tools for analysis, control design and simulating of linear systems with delays. Referred to as “systems with delays” in this volume, this class of differential equations is also called delay differential equations (DDE), time-delay systems, hereditary systems, and functional differential equations. Delay differential equations are widely used for describing and modeling various processes and systems in different applied problems At present there are effective control and numerical methods and corresponding software for analysis and simulating different classes of ordinary differential equations (ODE) and partial differential equations (PDE). There are many applications for these types of equations, because of this progress, but there are not as many methodologies in systems with delays that are easily applicable for the engineer or applied mathematician. there are no methods of finding solutions in explicit forms, and there is an absence of generally available general-purpose software packages for simulating such systems. Systems with Delays fills this void and provides easily applicable methods for engineers, mathematicians, and scientists to work with delay differential equations in their operations and research.
Download or read book The Riccati Equation written by Sergio Bittanti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computation and Control II written by Kenneth L. Bowers and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers delivered by the partici pants at the second Conference on Computation and Control held at Mon tana State University in Bozeman, Montana from August 1-7, 1990. The conference, as well as this proceedings, attests to the vitality and cohesion between the control theorist and the numerical analyst that was adver tised by the first Conference on Computation and Control in 1988. The proceedings of that initial conference was published by Birkhiiuser Boston as the first volume of this same series entitled Computation and Control, Proceedings of the Bozeman Conference, Bozeman, Montana, 1988. Control theory and numerical analysis are both, by their very nature, interdisciplinary subjects as evidenced by their interaction with other fields of mathematics and engineering. While it is clear that new control or es timation algorithms and new feedback design methodologies will need to be implemented computationally, it is likewise clear that new problems in computational mathematics arise when implementing a new generation of control algorithms. For these reasons, computational mathematics is mov ing to the forefront in recent developments in modern control theory and conversely control theory and its applications continue to be a fertile area for computationalists. This volume contains a representative cross section of the interdisciplinary blend of analytic and numerical techniques that of ten occur between advanced control design and practical numerical solution of lumped and distributed parameter systems.
Download or read book NASA Workshop on Distributed Parameter Modeling and Control of Flexible Aerospace Systems written by and published by . This book was released on 1994 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:
