Some aspects of the mathematical theory of control processes

by Richard Ernest Bellman, Irving Leonard Glicksberg, Oliver Alfred Gross


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A presentation of (1) various representative mathematical problems that arise in the modern theory of the control of economic, industrial, engineering, and military systems, and (2) the types of mathematical theories and techniques that can be used to treat these problems. These problems are variational in the sense that the aim is to maximize or minimize some function which is being used as a criterion of the performance of the system under consideration. What distinguishes these problems form those encountered in the classical calculus of variations is the presence of constraints of physical origin, the consideration of random effects, or, alternatively, the introduction of the theory of games, and finally, the emphasis on computational solution. An attempt is make to indicate the new types of mathematical problems that have arisen from the more realistic description of old problems and from the pressure of new problems, and to illustrate the applicability of a wide variety of mathematical tools to their solution. 263 pp.

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