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The two major themes of this book are risk-sensitive control and path-integral or Hamiltonian formulation. It covers risk-sensitive certainty-equivalence principles, the consequent extension of the conventional LQG treatment and the path-integral formulation.
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
This workshop on stochastic theory and adaptive control assembled many of the leading researchers on stochastic control and stochastic adaptive control to increase scientific exchange and cooperative research between these two subfields of stochastic analysis. The papers included in the proceedings include survey and research. They describe both theoretical results and applications of adaptive control. There are theoretical results in identification, filtering, control, adaptive control and various other related topics. Some applications to manufacturing systems, queues, networks, medicine and other topics are gien.
A collection of 22 papers devoted to questions of optimal control theory and differential games, providing an overview of current trends of research in the area of control systems. Numerous optimization methods are covered as well as necessary and sufficient conditions for optimality."
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.
Optimal control and differential games continue to attract strong interest from researchers interested in dynamical problems and models in management science. This volume explores the application of these methodologies to new as well as to classical decision problems in management sciences and economics. In Part I, optimal control and dynamical systems approaches are used to analyze problems in areas such as monetary policy, pollution control, relationship marketing, drug control, debt financing, and ethical behavior. In Part II differential games are applied to problems such as oligopolistic competition, common resource management, spillovers in foreign direct investments, marketing channels, incentive strategies, and the computation of Markov perfect Nash equilibria. Optimal Control and Differential Games is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in management science.
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
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.