Mathematical Theory of Optimal Processes, The

by L.S. Pontryagin

The physical processes which take place in technology are, as a rule, controllable, i.e., they can be realized by various means depending on the will of man. In this connection, there arises the question of finding the very best (in one sense or another) or, as is said, the optimal control of the process. For example, one can speak about optimality in the sense of rapidity of action, i.e., about achieving the aim of the process in the shortest time; about achieving this aim with a minimum expenditure of energy, etc. Mathematically formulated, these are problems in the calculus of variations, which in fact owes its origin to these problems. However, the solution of a whole range of variational problems, which are important in contemporary technology, is outside the classical calculus of variations. The solution presented here of a considerable number of such non-classical variational problems is due to the collective authors of this book. In its essential features, this solution is unified in one general mathematical method, which we call the maximum principle. It should be noted that all the fundamental necessary conditions in the classical calculus of variations (with ordinary derivatives) follow from the maximum principl

Hardcover

Published January 1, 1964

About the author

Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтря́гин) was a Soviet mathematician.