EAN: 9783319497808

OPTIMAL CONTROL - LEONID ASCHEPKOV DMITRIY DOLG...

This book is based on lectures from a one-year course at the Far Eastern Federal University
(Vladivostok  Russia) as well as on workshops on optimal control offered to students at various
mathematical departments at the university level. The main themes of the theory of linear and
nonlinear systems are considered  including the basic problem of establishing the necessary and
sufficient conditions of optimal processes.In the first part of the course  the theory of
linear control systems is constructed on the basis of the separation theorem and the concept of
a reachability set. The authors prove the closure of a reachability set in the class of
piecewise continuous controls  and the problems of controllability  observability 
identification  performance and terminal control are also considered. The second part of the
course is devoted to nonlinear control systems. Using the method of variations and the Lagrange
multipliers rule of nonlinear problems  the authors prove the Pontryagin maximum principle for
problems with mobile ends of trajectories. Further exercises and a large number of additional
tasks are provided for use as practical training in order for the reader to consolidate the
theoretical material.

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