Minimization of the Functionals. Necessary Conditions of the Functional Extremum. Minimization of the Functionals. Stationary Systems. Linear Stationary Systems. Weak Nonlinear Stationary Systems. Strong Nonlinear Stationary Systems. Stationary Systems with the Coefficient Control. Stationary Systems with Nonlinear Control. Evolutional Systems. First Order Linear Evolutional Systems. First Order Nonlinear Evolutional Systems. Second Order Evolutional Systems. Navier – Stokes equations. Additions. Optimal Control Problems with the Different State Equations. Optimal Control Problems with Different Controls. Optimal Control Problems with the Different State Functionals. Optimal Control Problems with Different Constraints. Appendix. Differentiation, Optimization and Categories Theory. Elementary Conterexamples of the Optimization Control Theory.
Simon Serovajsky is a Professor of Differential Equations and Control Theory at al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of Modelling, Optimisation and Optimal Control Theory as well as a long list of high-quality publications in learned journals.
"The book under review provides an inspired presentation of the
tools offered by mathematical analysis and its derivatives" such as
variational calculus and optimal control theory in solving extremal
problems [...] This clearly written book will be useful for
researches as well as students willing to enter in the
field."-Gheorghe Anicul□aesei, Zentralblatt MATH"This book provides
an inspired presentation of tools offered by mathematical analysis
and used in variational calculus of variations and optimal control
theory, for solving extremal problems. This clearly written book
will be useful for researchers as well as students interested in
entering the field.The main topics considered in the monograph are
as follows: Part I: Minimization of Functionals: necessary
conditions of extremum for functionals; Part II: Stationary
Systems: linear stationary systems, weakly nonlinear stationary
systems, strongly non-linear stationary systems, stationary systems
with the coefficient control, stationary systems with nonlinear
control; Part III: Evolutional Systems: first-order linear
evo-lutional systems, first-order nonlinear evolutional systems,
second-order evolutional systems, Navier-Stokes equations; Part IV:
Addition: functors of the differentiation.
In the last part, the author interprets differentiation by using
category theory and in particular proposes a concept of extended
derivation of an operator. By means of this notion, necessary
conditions of optimality are obtained."-Angelo Favini -
Mathematical Reviews Clippings - November 2018
|
Ask a Question About this Product More... |
|
