Mathematical Programming and Control Theory

Released on by B. D. Craven
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  • Mathematical Programming and Control Theory Book Detail

  • Author : B. D. Craven
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Science
  • Pages : 173
  • ISBN 13 : 9400957963
  • File Size : 66,66 MB
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Mathematical Programming and Control Theory by B. D. Craven PDF Summary

Book Description: In a mathematical programming problem, an optimum (maxi mum or minimum) of a function is sought, subject to con straints on the values of the variables. In the quarter century since G. B. Dantzig introduced the simplex method for linear programming, many real-world problems have been modelled in mathematical programming terms. Such problems often arise in economic planning - such as scheduling industrial production or transportation - but various other problems, such as the optimal control of an interplanetary rocket, are of similar kind. Often the problems involve nonlinear func tions, and so need methods more general than linear pro gramming. This book presents a unified theory of nonlinear mathe matical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e. g. a continuous curve (i. e. infinitely many variables). The underlying ideas of vector space, convex cone, and separating hyperplane are the same, whether the dimension is finite or infinite; and infinite dimension makes very little difference to the proofs. Duality theory - the various nonlinear generaliz ations of the well-known duality theorem of linear program ming - is found relevant also to optimal control, and the , PREFACE Pontryagin theory for optimal control also illuminates finite dimensional problems. The theory is simplified, and its applicability extended, by using the geometric concept of convex cones, in place of coordinate inequalities.

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Mathematical Control Theory

Mathematical Control Theory

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In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both l

Mathematical Control Theory

Mathematical Control Theory

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Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engine