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This book is on existence and necessary conditions, such as
Potryagin's maximum principle, for optimal control problems
described by ordinary and partial differential equations. These
necessary conditions are obtained from Kuhn-Tucker theorems for
nonlinear programming problems in infinite dimensional spaces. The
optimal control problems include control constraints, state
constraints and target conditions. Evolution partial differential
equations are studied using semigroup theory, abstract differential
equations in linear spaces, integral equations and interpolation
theory. Existence of optimal controls is established for arbitrary
control sets by means of a general theory of relaxed controls.
Applications include nonlinear systems described by partial
differential equations of hyperbolic and parabolic type and results
on convergence of suboptimal controls.
This volume deals with the Cauchy or initial value problem for
linear differential equations. It treats in detail some of the
applications of linear space methods to partial differential
equations, especially the equations of mathematical physics such as
the Maxwell, Schrodinger and Dirac equations. Background material
presented in the first chapter makes the book accessible to
mathematicians and physicists who are not specialists in this area
as well as to graduate students.
This volume deals with the Cauchy or initial value problem for
linear differential equations. It treats in detail some of the
applications of linear space methods to partial differential
equations, especially the equations of mathematical physics such as
the Maxwell, Schrodinger and Dirac equations. Background material
presented in the first chapter makes the book accessible to
mathematicians and physicists who are not specialists in this area
as well as to graduate students.
This text discusses existence and necessary conditions, such as
Potryagin's maximum principle, for optimal control problems
described by ordinary and partial differential equations. These
necessary conditions are obtained from KuhnTucker theorems for
nonlinear programming problems in infinite dimensional spaces. The
optimal control problems include control constraints, state
constraints and target conditions. Evolution partial differential
equations are studied using semigroup theory, abstract differential
equations in linear spaces, integral equations and interpolation
theory. Existence of optimal controls is established for arbitrary
control sets by means of a general theory of relaxed controls.
Applications include nonlinear systems described by partial
differential equations of hyperbolic and parabolic type and results
on convergence of suboptimal controls.
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