Download or read book Singular Linear quadratic Zero sum Differential Games and H infinity Symbol Control Problems written by Valery Y. Glizer and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the analysis and solution of singular differential games and singular H [infinity symbol] control problems in both finite- and infinite-horizon settings. Expanding on the authors previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and H [infinity symbol] control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic H [infinity symbol] control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections. Singular Linear-Quadratic Zero-Sum Differential Games and H [infinity symbol] Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these areas.
Download or read book Singular Linear Quadratic Zero Sum Differential Games and H Control Problems written by Valery Y. Glizer and published by Springer Nature. This book was released on 2022-08-29 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors’ previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections. Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area
Download or read book The Singular Zero sum Differential Game with Stability Using H infinity Control Theory written by A. A. Stoorvogel and published by . This book was released on 1989 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book H infinity Optimal Control and Related written by Basar and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major concentrated activities of the past decade in control theory has been the development of the so-called "HOO-optimal control theory," which addresses the issue of worst-case controller design for linear plants subject to unknown additive disturbances, including problems of disturbance attenuation, model matching, and tracking. The mathematical OO symbol "H " stands for the Hardy space of all complex-valued functions of a complex variable, which are analytic and bounded in the open right half complex plane. For a linear (continuous-time, time-invariant) plant, oo the H norm of the transfer matrix is the maximum of its largest singular value over all frequencies. OO Controller design problems where the H norm plays an important role were initially formulated by George Zames in the early 1980's, in the context of sensitivity reduction in linear plants, with the design problem posed as a mathematical optimization problem using an (HOO) operator norm. Thus formulated originally in the frequency domain, the main tools used during the early phases of research on this class of problems have been operator and approximation theory, spectral factorization, and (Youla) parametrization, leading initially to rather complicated (high-dimensional) OO optimal or near-optimal (under the H norm) controllers.
Download or read book Differential Games A Concise Introduction written by Jiongmin Yong and published by World Scientific. This book was released on 2014-12-05 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses a small volume to present the most basic results for deterministic two-person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two-person games. For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games.The book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. Researchers in some other related areas, such as engineering, social science, etc. will also find the book useful.
Download or read book Stochastic and Differential Games written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.
Download or read book Linear quadratic singular Stochastic Differential Games and Applications written by Jodi Dianetti and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.
Download or read book Nonlinear Zero sum Differential Game Analysis by Singular Perturbation Methods written by and published by . This book was released on 1982 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singular Differential Game Numerical Technique and Closed Loop Guidance and Control Strategies written by Kamran Forouhar and published by . This book was released on 1982 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report a class of linear quadratic pursuit-evasion games with bounds on the pursuer's control has been defined. In this problem the pursuer's control appears linearly in the Hamiltonian and singular arcs may occur in the solution. A sufficient condition for the existence of a saddle point for this class of problems is derived. An indirect numerical technique has been proposed to generate a rapid and accurate solution to a class of problems with linear state equations in which singular arcs occur. Then, by linearization this technique is extended to solve a class of problems with non-linear state equations. By modifying this technique a second approach has been obtained that can solve a broader class of singular problems with linear state equations. The effect of the deviation of one player from the saddle point strategy on the performance index and the opponent's strategy has been studied for a two person zero-sum differential game with perfect information. An inverse system technique is used to determine the opponent's strategy by periodically measuring the state or the output of the system. Then, the proposed technique for singular problems is applied periodically to generate an approximate closed loop solution (which takes into consideration the deviation of the opponent from the saddle point trajectory) to achieve better performance than simply following the optimal open loop solution. A numerical example is presented to illustrate the efficiency of the proposed algorithm, and, comparisons have been made between the results of the open loop and closed loop solutions.
Download or read book Differential Games written by Raimo P. Hämäläinen and published by Springer. This book was released on 1991 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Zero Sum Differential Game Analysis by Singular Perturbation Methods written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-14 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane. Sinar, J. and Farber, N. Ames Research Center NASA-TM-84271, NAS 1.15:84271, A-8998 RTOP 505-34-11-11-00...
Download or read book Differential Games written by Joseph Lewin and published by Springer. This book was released on 1994 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential games theory is the most appropriate discipline for the modelling and analysis of real life conflict problems. The theory of differential games is here treated with an emphasis on the construction of solutions to actual problems with singular surfaces. The reader is provided with the knowledge necessary to put the theory of differential games into practice.
Download or read book The H infinity Control Problem written by Anton Stoorvogel and published by . This book was released on 1992 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory and Application of Differential Games written by NATO Advanced Study Institute Staff and published by Springer Science & Business Media. This book was released on 1975-02-01 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ~irst international con~erence on differential games was held at Amherst, Massachusetts, in September 1969. A second meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new theoretical results and applications, especially in economic problems, were presented. The present volume consists o~ the lectures presented at a N.A.T.O. Advanced Study Institute on the "Theory and Applications of Differential Games" held at the University of Warwick, Coventry, England, from 27th August to 6th September, 1974. The main contributions during the first week consisted of a survey of two person zero sum differential games by L. D. Berkovitz and four integrated lectures by R. J. Elliott and N. J. Kalton, who have made important contributions to the concept of "value" of a differential game. Applications were featured during the second week and included tactical air games, pursuit and evasion problems, as well as computational aspects. A closing lecture with historical perspectives was given by Rufus Issacs, the recognised pioneer of differential games theory.
Download or read book On Some Further Properties of Nonzero sum Differential Games written by Alan Wilbor Starr and published by . This book was released on 1968 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general nonzero-sum differential game has N players, each controlling a different set of inputs to a single nonlinear dynamic system and each trying to minimize a different performance criterion. Several interesting new phenomena arise in these general games which are absent in the two best-known special cases (the optimal control problem and the two person zero-sum differential game). This paper considers some of the difficulties which arise in attempting to generalize ideas which are well-known in optimal control theory, such as the 'principle of optimality' and the relation between 'open-loop' and 'closed-loop' controls. Two types of 'solutions' are discussed: the 'Nash equilibrium' and the 'noninferior set.' Some simple multistage discrete (bimatrix) games are used to illustrate phenomena which also arise in the continuous formulation. (Author).
Download or read book Differential Games and Control Theory Iii written by Pan-Tai Liu and published by CRC Press. This book was released on 2020-12-18 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the Third Kingston Conference on Differential Games and Control Theory held at the University of Rhode Island June 5-8, 1978. It deals with deterministic systems and stochastic systems, and is helpful for the researchers in applied mathematics.
Download or read book Nonzero sum Differential Games Concepts and Models written by Alan W. Starr and published by . This book was released on 1969 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general class of differential games, where the N players try to minimize different cost criteria by controlling inputs to a single dynamic system, is investigated as an extension of optimal control theory. Dropping the usual zero-sum assumption makes it possible to model a more realistic class of competitive situations where mutual interest is important. The nonzero-sum formulation has several interesting analytic and conceptual features not found in zero-sum differential games. It is no longer obvious what should be demanded of a 'solution, ' and three types of solution concepts are discussed: Nash equilibrium, minimax, and noninferior (or Pareto optimal) strategies. For one special case, the 'linear-quadratic' differential game, all of these solutions can be computed exactly by solving sets of coupled ordinary matrix differential equations. Some simple examples are solved, and series of more difficult but more realistic nonzero-sum differential game situations are presented (but not solved) for models of economic oligopoly, advertising policy, labor-management negotiations, and international trade. (Author).
