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Optimal Control of Systems Governed by Partial Differential Equations (Grundelhren Der Mathematishen Wissenschaften : Vol 170)

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Optimal Control of Systems Governed by Partial Differential Equations (Grundelhren Der Mathematishen Wissenschaften : Vol 170) image
ISBN-10:

0387051155

ISBN-13:

9780387051154

Author(s): Jacques-Louis Lions
Released: Mar 01, 1971
Publisher: Springer, Verlag
Format: Hardcover, 275 pages
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Description:

1. The development of a theory of optimal control (deterministic) requires the following initial data: (i) a control u belonging to some set ilIi ad (the set of 'admissible controls') which is at our disposition, (ii) for a given control u, the state y(u) of the system which is to be controlled is given by the solution of an equation (*) Ay(u)=given function ofu where A is an operator (assumed known) which specifies the system to be controlled (A is the 'model' of the system), (iii) the observation z(u) which is a function of y(u) (assumed to be known exactly; we consider only deterministic problems in this book), (iv) the "cost function" J(u) ("economic function") which is defined in terms of a numerical function z-+

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