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A Series Solution Framework For Finite Time Optimal Feedback Control H Infinity Control And Games
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Book Synopsis A Series Solution Framework for Finite-time Optimal Feedback Control, H-infinity Control and Games by : Rajnish Sharma
Download or read book A Series Solution Framework for Finite-time Optimal Feedback Control, H-infinity Control and Games written by Rajnish Sharma and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bolza-form of the finite-time constrained optimal control problem leads to the Hamilton-Jacobi-Bellman (HJB) equation with terminal boundary conditions and tobe- determined parameters. In general, it is a formidable task to obtain analytical and/or numerical solutions to the HJB equation. This dissertation presents two novel polynomial expansion methodologies for solving optimal feedback control problems for a class of polynomial nonlinear dynamical systems with terminal constraints. The first approach uses the concept of higher-order series expansion methods. Specifically, the Series Solution Method (SSM) utilizes a polynomial series expansion of the cost-to-go function with time-dependent coefficient gains that operate on the state variables and constraint Lagrange multipliers. A significant accomplishment of the dissertation is that the new approach allows for a systematic procedure to generate optimal feedback control laws that exactly satisfy various types of nonlinear terminal constraints. The second approach, based on modified Galerkin techniques for the solution of terminally constrained optimal control problems, is also developed in this dissertation. Depending on the time-interval, nonlinearity of the system, and the terminal constraints, the accuracy and the domain of convergence of the algorithm can be related to the order of truncation of the functional form of the optimal cost function. In order to limit the order of the expansion and still retain improved midcourse performance, a waypoint scheme is developed. The waypoint scheme has the dual advantages of reducing computational efforts and gain-storage requirements. This is especially true for autonomous systems. To illustrate the theoretical developments, several aerospace application-oriented examples are presented, including a minimum-fuel orbit transfer problem. Finally, the series solution method is applied to the solution of a class of partial differential equations that arise in robust control and differential games. Generally, these problems lead to the Hamilton-Jacobi-Isaacs (HJI) equation. A method is presented that allows this partial differential equation to be solved using the structured series solution approach. A detailed investigation, with several numerical examples, is presented on the Nash and Pareto-optimal nonlinear feedback solutions with a general terminal payoff. Other significant applications are also discussed for one-dimensional problems with control inequality constraints and parametric optimization.
Book Synopsis H-Infinity Optimal Control and Related Minimax Design Problems by : Tamer Başar
Download or read book H-Infinity Optimal Control and Related Minimax Design Problems written by Tamer Başar and published by Springer Science & Business Media. This book was released on 2008-01-21 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. Based mostly on recent work by the authors, the book is written on a good mathematical level. Many results in it are original.
Book Synopsis Finite Horizon H [infinity] and Related Control Problems by : M. Bala Subrahmanyam
Download or read book Finite Horizon H [infinity] and Related Control Problems written by M. Bala Subrahmanyam and published by . This book was released on 1995-01-01 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal H-infinity Controller Design and Strong Stabilization for Time-delay and Mimo Systems by : Suat Gümüşsoy
Download or read book Optimal H-infinity Controller Design and Strong Stabilization for Time-delay and Mimo Systems written by Suat Gümüşsoy and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this dissertation, the problems of optimal H-infinity controller design and strong stabilization for time-delay systems are studied. First, the optimal H-infinity controller design problem is considered for time-delay plants with finitely many unstable zeros and infinitely many unstable poles. It is shown that this problem is the dual version of the same problem for the plants with finitely many unstable poles and infinitely many unstable zeros, that is solved by the so-called Skew-Toeplitz approach. The optimal H-infinity controller is obtained by a simple data transformation. Next, the solution of the optimal H-infinity controller design problem is given for plants with finitely many unstable poles or unstable zeros by using duality and the Skew-Toeplitz approach. Necessary and sufficient conditions on time-delay systems are determined for applicability of the Skew-Toeplitz method to find optimal H-infinity controllers. Internal unstable pole-zero cancellations are eliminated and finite impulse response structure of the optimal H-infinity controller is obtained. The problem of strong stabilization is studied for time delay and MIMO finite dimensional systems. An indirect approach to design a stable controller achieving a desired H-infinity performance level for time delay systems is given. This approach is based on stabilization of H-infinity controller by another H-infinity controller in the feedback loop. In another approach, when the optimal controller is unstable (with infinitely or finitely many unstable poles), two methods are given based on a search algorithm to find a stable suboptimal controller. In this approach, the main idea is to search for a free parameter which comes from the parameterization of suboptimal H-infinity controller, such that it results in a stable H-infinity controller. Finally, the strong stabilization problem and stable H-infinity controller design for finite dimensional multi-input multi-output linear time invariant systems are studied. It is shown that if a certain linear matrix inequality condition has a solution then a stable controller, whose order is the same as the order of the generalized plant, can be constructed. This result is applied to design stable H-infinity controller with the order twice of the order of the generalized plant.
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 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles by : Draguna L. Vrabie
Download or read book Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles written by Draguna L. Vrabie and published by IET. This book was released on 2013 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews developments in the following fields: optimal adaptive control; online differential games; reinforcement learning principles; and dynamic feedback control systems.
Book Synopsis Feedback Systems by : Karl Johan Åström
Download or read book Feedback Systems written by Karl Johan Åström and published by Princeton University Press. This book was released on 2021-02-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory
Book Synopsis Industrial Mathematics and Statistics by : J. C. Misra
Download or read book Industrial Mathematics and Statistics written by J. C. Misra and published by Alpha Science Int'l Ltd.. This book was released on 2003 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume introduces educational units dealing with important topics in Industrial Mathematics and Statistics.
Book Synopsis International Aerospace Abstracts by :
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1998 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Learning and Approximate Dynamic Programming by : Jennie Si
Download or read book Handbook of Learning and Approximate Dynamic Programming written by Jennie Si and published by John Wiley & Sons. This book was released on 2004-08-02 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete resource to Approximate Dynamic Programming (ADP), including on-line simulation code Provides a tutorial that readers can use to start implementing the learning algorithms provided in the book Includes ideas, directions, and recent results on current research issues and addresses applications where ADP has been successfully implemented The contributors are leading researchers in the field
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Indefinite-Quadratic Estimation and Control by : Babak Hassibi
Download or read book Indefinite-Quadratic Estimation and Control written by Babak Hassibi and published by SIAM. This book was released on 1999-01-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified mathematical framework for a wide range of problems in estimation and control.
Book Synopsis Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE by : Nizar Touzi
Download or read book Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE written by Nizar Touzi and published by Springer Science & Business Media. This book was released on 2012-09-25 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Book Synopsis Adaptive Optimal Control by : Robert R. Bitmead
Download or read book Adaptive Optimal Control written by Robert R. Bitmead and published by . This book was released on 1990 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Book Synopsis H∞-Optimal Control and Related Minimax Design Problems by : Tamer Başar
Download or read book H∞-Optimal Control and Related Minimax Design Problems written by Tamer Başar and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. The book can be used for a second or third year graduate level course in the subject, and researchers working in the area will find the book useful as a standard reference. Based mostly on recent work of the authors, the book is written on a good mathematical level. Many results in it are original, interesting, and inspirational. The topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with important theoretical developments in applied mathematics and control.
Book Synopsis Optimal Control Theory with Applications in Economics by : Thomas A. Weber
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
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