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Nonlinear H Infinity Control Hamiltonian Systems And Hamilton Jacobi Equations
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Book Synopsis Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations by : M.D.S. Aliyu
Download or read book Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations written by M.D.S. Aliyu and published by CRC Press. This book was released on 2017-12-19 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.
Book Synopsis Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations by : S. Aliyu
Download or read book Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations written by S. Aliyu and published by CRC Press. This book was released on 2017-03-29 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of nonlinear H� control theory for both continuous-time and discrete-time systems, Nonlinear H�-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H�-control, nonlinear H � -filtering, mixed H2/ H�-nonlinear control and filtering, nonlinear H�-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H�-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H�-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.
Book Synopsis Approximation of Hamilton-Jacobi Equations Arising in Nonlinear H [infinity] Control Problems by : Fabio Camilli
Download or read book Approximation of Hamilton-Jacobi Equations Arising in Nonlinear H [infinity] Control Problems written by Fabio Camilli and published by . This book was released on 1995 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear H2/H-Infinity Constrained Feedback Control by : Murad Abu-Khalaf
Download or read book Nonlinear H2/H-Infinity Constrained Feedback Control written by Murad Abu-Khalaf and published by Springer Science & Business Media. This book was released on 2006-08-02 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides techniques to produce robust, stable and useable solutions to problems of H-infinity and H2 control in high-performance, non-linear systems for the first time. The book is of importance to control designers working in a variety of industrial systems. Case studies are given and the design of nonlinear control systems of the same caliber as those obtained in recent years using linear optimal and bounded-norm designs is explained.
Book Synopsis Numerical Solutions of the Hamilton-Jacobi Equations Arising in Nonlinear H[infinity] and Optimal Control by : Jerry Markman
Download or read book Numerical Solutions of the Hamilton-Jacobi Equations Arising in Nonlinear H[infinity] and Optimal Control written by Jerry Markman and published by . This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extending H-infinity Control to Nonlinear Systems by : J. William Helton
Download or read book Extending H-infinity Control to Nonlinear Systems written by J. William Helton and published by SIAM. This book was released on 1999-01-01 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: H-infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems to meet certain objectives. H-infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-infinity control problem.
Book Synopsis L2-Gain and Passivity Techniques in Nonlinear Control by : Arjan van der Schaft
Download or read book L2-Gain and Passivity Techniques in Nonlinear Control written by Arjan van der Schaft and published by Springer. This book was released on 2016-12-04 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with a geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization. · L2-Gain and Passivity Techniques in Nonlinear Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find: · updated and extended coverage of dissipative systems theory · substantial new material regarding converse passivity theorems and incremental/shifted passivity · coverage of recent developments on networks of passive systems with examples · a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics · updated treatment of all-pass factorization of nonlinear systems The book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.
Book Synopsis On the Hamilton-Jacobi Equation of Nonlinear H[infinity] Optimal Control by : A. J. van der Schaft
Download or read book On the Hamilton-Jacobi Equation of Nonlinear H[infinity] Optimal Control written by A. J. van der Schaft and published by . This book was released on 1990 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hamilton-Jacobi-Bellman Equations by : Dante Kalise
Download or read book Hamilton-Jacobi-Bellman Equations written by Dante Kalise and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
Book Synopsis On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities by : Guy Barles
Download or read book On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities written by Guy Barles and published by Springer Nature. This book was released on 2024-01-30 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the most recent developments in the study of Hamilton-Jacobi Equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text. After an initial section that provides a “toolbox” containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text – such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization – and several key open problems are presented. This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi Equations, network problems, or scalar conservation laws.
Author :William M. McEneaney Publisher :Springer Science & Business Media ISBN 13 :9780817635343 Total Pages :268 pages Book Rating :4.6/5 (353 download)
Book Synopsis Max-Plus Methods for Nonlinear Control and Estimation by : William M. McEneaney
Download or read book Max-Plus Methods for Nonlinear Control and Estimation written by William M. McEneaney and published by Springer Science & Business Media. This book was released on 2006 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton–Jacobi–Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches. Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 1460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Hamilton-Jacobi Equations, Viscosity Solutions and Asymptotics of Hamiltonian Systems by : Diogo Aguiar Gomes
Download or read book Hamilton-Jacobi Equations, Viscosity Solutions and Asymptotics of Hamiltonian Systems written by Diogo Aguiar Gomes and published by . This book was released on 2000 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by : Yves Achdou
Download or read book Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Book Synopsis Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by : Martino Bardi
Download or read book Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2008-01-11 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.
Book Synopsis Nearly Integrable Infinite-Dimensional Hamiltonian Systems by : Sergej B. Kuksin
Download or read book Nearly Integrable Infinite-Dimensional Hamiltonian Systems written by Sergej B. Kuksin and published by Springer. This book was released on 2006-11-15 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.
Book Synopsis Nonlinear H2/H-inifnity Constrained Feedback Control by : Murad Abu-Khalaf
Download or read book Nonlinear H2/H-inifnity Constrained Feedback Control written by Murad Abu-Khalaf and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this research, practical methods for the design of H2 and Hinfinity optimal state feedback controllers for constrained input systems are proposed. The dynamic programming principle is used along with special quasi-norms to derive the structure of both the saturated H2 and Hinfinity optimal controllers in feedback strategy form. The resulting Hamilton-Jacobi-Bellman (HJB) and Hamilton-Jacobi-Isaacs (HJI) equations are derived respectively. It is shown that introducing quasi-norms on the constrained input in the performance functional allows unconstrained minimization of the Hamiltonian of the corresponding optimal control problem. Moreover, it is shown how to obtain nearly optimal minimum-time and constrained state controllers by modifying the performance functional of the optimization problem. Policy iterations on the constrained input for both the H 2 and Hinfinity cases are studied. It is shown that the resulting sequence of Lyapunov functions in the H2 case, cost functions in the H infinity case, converge uniformly to the value function of the associated optimal control problem that solves the corresponding Hamilton-Jacobi equation. The relation between policy iterations for the zero-sum game appearing in the Hinfinity optimal control and the theory of dissipative systems is studied. It is shown that policy iterations on the disturbance player solve the nonlinear bounded real lemma problem of the associated closed loop system. Moreover, the relation between the domain of validity of the game value function and the corresponding L2-gain is addressed through policy iterations. Neural networks are used along with the least-squares method to solve for the linear in the unknown differential equations resulting from policy iterations on the saturated control in the H2 case, and the saturated control and the disturbance in the H infinity case. The result is a neural network constrained feedback controller that has been tuned a priori offline with the training set selected using Monte Carlo methods from a prescribed region of the state space which falls within the region of asymptotic stability of an initial stabilizing control used to start the policy iterations. Finally, the obtained algorithms are applied to different examples including the Nonlinear Benchmark Problem to reveal the power of the proposed method.
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