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Optimization of Stochastic Systems

  • 1st Edition
  • Volume 32
  • January 1, 1967
  • Masanao Aoki
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 3 9 - 1
Optimization of Stochastic Systems is an outgrowth of class notes of a graduate level seminar on optimization of stochastic systems. Most of the material in the book was taught for the first time during the 1965 Spring Semester while the author was visiting the Department of Electrical Engineering, University of California, Berkeley. The revised and expanded material was presented at the Department of Engineering, University of California, Los Angeles during the 1965 Fall Semester. The systems discussed in the book are mostly assumed to be of discrete-time type with continuous state variables taking values in some subsets of Euclidean spaces. There is another class of systems in which state variables are assumed to take on at most a denumerable number of values, i.e., these systems are of discrete-time discrete-space type. Although the problems associated with the latter class of systems are many and interesting, andalthough they are amenable to deep analysis on such topics as the limiting behaviors of state variables as time indexes increase to infinity, this class of systems is not included here, partly because there are many excellent books on the subjects and partly because inclusion of these materials would easily double the size of the book.

Introduction to the Mathematical Theory of Control Processes: Linear Equations and Quadratic Criteria v. 1

  • 1st Edition
  • Volume 40A
  • January 1, 1967
  • Bellman
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 4 7 - 6
This work discusses the theory of control processes. The extremely rapid growth of the theory, associated intimately with the continuing trend toward automation, makes it imperative that the courses of this nature rest upon a broad basis. The work discusses the fundamentals of the calculus of variations, dynamic programming, discrete control processes, use of the digital computer, and functional analysis. Introductory courses in control theory are essential for training the modern graduate student in pure and applied mathematics, engineering, mathematical physics, economics, biology, operations research, and related fields. The work also describes the dual approaches of the calculus of variations and dynamic programming in the scalar case and illustrates ways to tackle the multidimensional optimization problems.

Nonlinear Autonomous Oscillations: Analytical Theory

  • 1st Edition
  • Volume 34
  • January 1, 1967
  • Urabe
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 4 1 - 4
Nonlinear Autonomous Oscillations presents a self-contained and readable account for mathematicians, physicists, and engineers. This monograph is mainly concerned with the analytical theory of nonlinear autonomous oscillations, with the approach based mostly on the author’s work. After some introductory material, in Chapter 5 a moving orthogonal coordinate system along a closed orbit is introduced. In the next four chapters, stability theory and perturbation theory are systematically discussed for general autonomous systems by means of a moving coordinate system. In Chapter 10, the two-dimensional autonomous system is discussed in detail on the basis of results obtained in the preceding chapters. In Chapter 11, a numerical method for determining a periodic solution of the general nonlinear autonomous system is described. To illustrate this, the periodic solutions of the autonomous van der Pol equation for various values of thedamping coefficient are computed. Chapter 12, which is based on the work of the author and Sibuya, discusses the center of higher dimension. Chapter 13 discusses a particular inverse problem connected with the period of periodicsolutions of one interesting equation. There are, of course, many other topics of importance in the theory of nonlinear autonomous oscillations. These are, however, omitted in the present monograph because they are mainly topological rather than analytical and in order to keep the book from growing inordinately long.

Lectures on Functional Equations and Their Applications

  • 1st Edition
  • Volume 19
  • January 1, 1966
  • J. Aczél
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 2 5 - 4
Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

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