By Iu.P. Petrov (Eds.)

ISBN-10: 0125528507

ISBN-13: 9780125528504

Show description

Read or Download Variational Methods in Optimum Control Theory PDF

Similar robotics & automation books

New PDF release: Automating manufacturing systems with PLCs

A detailed exam of producing regulate platforms utilizing dependent layout equipment. issues contain ladder good judgment and different IEC 61131 criteria, wiring, communique, analog IO, based programming, and communications. Allen Bradley PLCs are used broadly throughout the e-book, however the formal layout tools are appropriate to such a lot different PLC manufacturers.

Download e-book for kindle: Direct-Drive Robots: Theory and Practice by Haruhiko Asada, Kamal Youcef-Toumi

This publication describes the layout inspiration and discusses the regulate matters relating to the functionality of a direct-drive robotic, in particular, a direct-drive mechanical arm able to sporting as much as 10 kilograms, at 10 meters according to moment, accelerating at five G (a unit of acceleration equivalent to the acceleration of gravity).

Download e-book for kindle: Afro-European Conference for Industrial Advancement: by Ajith Abraham, Pavel Krömer, Vaclav Snasel

This quantity comprises permitted papers offered at AECIA2014, the 1st foreign Afro-European convention for commercial development. the purpose of AECIA was once to assemble the most important specialists in addition to first-class younger researchers from Africa, Europe, and the remainder of the realm to disseminate newest effects from a variety of fields of engineering, details, and communique applied sciences.

Download PDF by Albert C. J. Luo: Analytical Routes to Chaos in Nonlinear Engineering

Nonlinear difficulties are of curiosity to engineers, physicists and mathematicians and lots of different scientists simply because such a lot structures are inherently nonlinear in nature. As nonlinear equations are tricky to resolve, nonlinear structures are in general approximated via linear equations. This works good as much as a few accuracy and a few variety for the enter values, yet a few attention-grabbing phenomena comparable to chaos and singularities are hidden by way of linearization and perturbation research.

Additional resources for Variational Methods in Optimum Control Theory

Sample text

Let us fix all functions except one, y, = y , ( x ) , say, to which we shall assign the increment 6y, ( x ) . Then the variation of the functional (18) will depend only on one function, and exactly as in Section 5, the Euler equation for the function y, ( x ) aF d aF ay, dxdy,‘ will follow from the condition 6J = 0. - 0. 28 11. ;y , = y,(x) to yield the extremum of the functional (18), it is necessary that the functions y,(x) satisfy a system of differential equations, Euler equations : Fyn- d Fyn* =0 .

In principle, z may be expressed in terms of y and x from the coupling equation (40), be substituted into the integral (39), and the minimum of the usual functional of one variable might be sought. However, such elimination of variables often leads to very complex computations, and it is more convenient to utilize another method of solution, such as the Lagrange method of undetermined multipliers. The following simple mnemonic rule (theorem) exists: In order to find the extremum of the functional J = l X 1 F ( x ;y ; y ’ ; z ; z’) dx xo under the condition q ( x ; y ; z ) = 0, (41) (42) it is necessary to introduce an intermediate function H =F + A ( x ) V ( X ; y ; z), (43) where A(x)is a function of x as yet unknown, and to seek the extremum of the functional J1 = [ XI J xo H dx (44) by customary methods.

A curve passing through the points A and B and yielding the minimum distance has been found. This curve may be only the extremal. In fact, if this curve is not the extremal, then another curve may be drawn between these same points A and B on which the value of the functional will be less. But the integral term in (3) vanishes for an extremal and 6J = Fy4x=xl 6y1 + ( F - y’Fy*)lx=xl 6x1 - F y ’ l x = x o 6Yo - ( F - Y f ~ y 4 x = x6x0 o ’ Since to the accuracy of higher-order infinitesimals 6yo = CP’ (46x0 ; 6 y , = +‘(x) 6x1, the condition for the extremum 6J = 0 may then be written as 6J = (Fy# + F - f F y , ) l x = x ,6x1 - (Fyq’ + F - yfFyt)~x=xo 6x0.

Download PDF sample

Variational Methods in Optimum Control Theory by Iu.P. Petrov (Eds.)


by Kevin
4.2

Rated 4.35 of 5 – based on 39 votes