Download e-book for iPad: 41st IEEE Conference on Decision and Control, Tutorial by Blas M. Vinagre, YangQuan Chen (Eds.)

By Blas M. Vinagre, YangQuan Chen (Eds.)

Show description

Read or Download 41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes PDF

Best calculus books

Get Malliavin Calculus for Lévy Processes with Applications to PDF

Whereas the unique works on Malliavin calculus aimed to review the smoothness of densities of suggestions to stochastic differential equations, this publication has one other target. It portrays an important and cutting edge purposes in stochastic regulate and finance, similar to hedging in entire and incomplete markets, optimisation within the presence of uneven info and in addition pricing and sensitivity research.

A Course in Multivariable Calculus and Analysis - download pdf or read online

This self-contained textbook offers an intensive exposition of multivariable calculus. it may be seen as a sequel to the one-variable calculus textual content, A direction in Calculus and actual research, released within the similar sequence. The emphasis is on correlating normal innovations and result of multivariable calculus with their opposite numbers in one-variable calculus.

Read e-book online A First Course on Complex Functions PDF

This booklet may be of curiosity to undergraduates taking classes on advanced services.

New PDF release: Mathematics for Engineers II: Calculus and Linear Algebra

"Mathematics for Engineers II" gehort zu einer vierbandigen Reihe und gibt eine Einfuhrung in die Mathematik fur Undergraduates, die ein Bachelor-Studium im Bereich Ingenieurwissenschaften aufgenommen haben. In Band II wird der klassische Calculus castle- und in die Grundlagen der Linearen Algebra eingefuhrt.

Additional info for 41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes

Example text

4 . n, 2 + , + . , + ,@ + 2 .  ! ===== .  . ===== +55,  , {+3, @ +w,{+3, Lw lv fohdu wkdw wkh Plwwdj0Oh"hu ixqfwlrq khuh kdv wkh uroo ri wkh h{srqhqwldo ixqfwlrq iru wkh lqwhjhu rughu v|vwhpv1 Wkh zhoo nqrzq h{srqhqwldo pdwul{/ h|> lv mxvw d sduwlfxodu fdvh ri wkh jhqhudol}hg h{srqhqwldo pdwul{/ Hk +Dw , > zklfk fdq eh fdoohg Plwwdj0Oh"hu pdwul{ ixqfwlrq1 LY1 Frqwuroodelolw| dqg revhuydelolw| iru v|vwhpv ri frqphvxudwh rughu Wkh frqwuroodelolw| dqg revhuydelolw| frqglwlrqv iru frqphvxudwh rughu v|vwhpv fdq eh vhhq lq ^5` zlwkrxw ghprqvwudwlrq1 Khuh wkh ghprqvwudwlrqv duh jlyhq iroorzlqj d phwkrg vlplodu wr wkh rqh xvhg iru lqwhjhu rughu v|vwhpv +vhh/ h1j1/ ^6`/ ^7`, D1 Frqwuroodelolw| Wr rewdlq wkh frqwurodelwlw| frqglwlrq wkh qh{w ghqlwlrq zloo eh wdnhq lqwr dffrxqw= Ghqlwlrq 6= Lw lv vdlg wkdw d v|vwhp lv frqwuroodeoh li lw lv srvvleoh wr vwdeolvk d qrq0uhvwulfwhg frqwuro yhfwru zklfk fdq ohdg wkh v|vwhp iurp d lqlwldo vwdwh/ {+wf,> wr dqrwkhu qdo vwdwh/ {+wu ,>lq d qlwh wlph wf  w  ws 1 Dv lw kdv ehhq ghgxfhg/ wkh vroxwlrq ri wkh vwdwh htxdwlrq fdq eh zulwwhq dv iroorzv ] | +w   ,Ex+ ,g > +56, zlwk +w, @ H +Dw , = Lw fdq eh vxsrvhg wkdw wkh ghvluhg qdo vwdwh lv {+wu , @ 3/ lw lv/ wkh ruljlq ri wkh vwdwh0vsdfh1 Grlqj vr/ dqg wdnlqj lqwr dffrxqw wkdw iru d vwdwh wudqvlwlrq pdwul{ wkh qh{w uhodwlrqv duh ixooohg +vhh/ h1j1/ ^6`,= {+w, @ +w  wf ,{+wf , .

Therefore, we will pursue a different way. Instead of beginning by a definition of differintegration, let us invert the problem and take the LT as the starting point, not only for the differentiation, but also for integration - differintegration. Essentially, we intend to prolong the sequence: ... , s ... 1) in order to include other kinds of exponents: rational or, generally, real (or even complex numbers). It is immediate to see that there are two forms of obtaining the extension, depending on the choice done for region of convergence for the LT: the left and right half-planes.

To this integral, with the term (-1)p omitted, we give the name of Liouville fractional integral. In other papers, Liouville went ahead with the development of ideas concerning this theme, having presented a generalisation of the notion of incremental ratio to define a fractional derivative. This idea was recovered, later, by Grünwald (1867) and Letnikov (1868). 1) for the fractional integral. Holmgren (1865/66) and Letnikov (1868/74) discussed that problem when looking for the solution of differential equations, putting in a correct statement the fractional differentiation as inverse operation of the fractional integration.

Download PDF sample

41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes by Blas M. Vinagre, YangQuan Chen (Eds.)


by Paul
4.3

Rated 4.99 of 5 – based on 25 votes