Some Questions In The Theory Of Oscillations And The Theory Of Optimal Control
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Some Questions in the Theory of Oscillations and the Theory of Optimal Control by R. V. Gamkrelidze Pdf
This book contains two fundamental papers. The first is, in essence, a short monograph devoted to the theory of periodic motions in singularly perturbed systems. The second deals with structural properties of the solutions of a system having infinitely many switchings on a finite time interval to Hamiltonian systems with discontinuous right-hand side.
Optimal Control of Mechanical Oscillations by Agnessa Kovaleva Pdf
This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory. All theoretical propositions are illustrated by examples with exact mechanical context. An appendix covers the necessary mathematical prerequisites.
Mathematical Theory of Optimal Processes by L.S. Pontryagin Pdf
The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.
Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.
Introduction to Optimal Control Theory by Jack Macki,Aaron Strauss Pdf
This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].
Counterexamples in Optimal Control Theory by S. I︠A︡ Serovaĭskiĭ Pdf
This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.
Principles of Optimal Control Theory by R. Gamkrelidze Pdf
In the late 1950's, the group of Soviet mathematicians consisting of L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko made fundamental contributions to optimal control theory. Much of their work was collected in their monograph, The Mathematical Theory of Optimal Processes. Subsequently, Professor Gamkrelidze made further important contributions to the theory of necessary conditions for problems of optimal control and general optimization problems. In the present monograph, Professor Gamkrelidze presents his current view of the fundamentals of optimal control theory. It is intended for use in a one-semester graduate course or advanced undergraduate course. We are now making these ideas available in English to all those interested in optimal control theory. West Lafayette, Indiana, USA Leonard D. Berkovitz Translation Editor Vll Preface This book is based on lectures I gave at the Tbilisi State University during the fall of 1974. It contains, in essence, the principles of general control theory and proofs of the maximum principle and basic existence theorems of optimal control theory. Although the proofs of the basic theorems presented here are far from being the shortest, I think they are fully justified from the conceptual view point. In any case, the notions we introduce and the methods developed have one unquestionable advantage -they are constantly used throughout control theory, and not only for the proofs of the theorems presented in this book.
Introduction to Control of Oscillations and Chaos by Aleksandr L?vovich Fradkov,Alexander Yu. Pogromsky Pdf
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
Optimal Control Systems by AA Fel'Dbaum by Anonim Pdf
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Among the finest achievements in modern mathematics are two of L.S. Pontryagin's most notable contributions: Pontryagin duality and his general theory of characters of a locally compact commutative group. This book, the first in a four-volume set, contains the most important papers of this eminent mathematician, those which have influenced many generations of mathematicians worldwide. They chronicle the development of his work in many areas, from his early efforts in homology groups, duality theorems, and dimension theory to his later achievements in homotopic topology and optimal control theory. On 3 September 1983 Lev Semenovich Pontryagin was seventy-five. To mark this important event in the life of this outstanding contemporary mathematician we are beginning the publication of his scientific works in four volumes, according to a decision taken by the Mathematics Division of the USSR Academy of Sciences. The first volume contains the most important mathematical papers of L. S. Pontryagin and also includes a bibliography of his basic scientific works, the second is his well-known monograph Topological Groups, the third comprises two monographs, Foundations of Algebraic Topology and Smooth Manifolds and Their Applications in Homotopy Theory, and the fourth is a revised edition of The Mathematical Theory of Optimal Processes by L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko.