SlideShare a Scribd company logo
1 of 8
Download to read offline
! #$
               ""            %         & '* #
                                        '(
                                         )          (
                                                    )* +       * ,
                                                                $
* -
 )                                                  *+
                                               * ('
                                                  ""             ..
                                                                  "
/ ,' +0          ! # $%
                  ""             " 1 2( #
                                  + '*   )        + * ,)
                                                       $ *
             ,)    )                             / %  ' $( (
                                                      $     +)
     ) 3      ,+    4             5                + + 6 ! #$
                                                   ,            ""
- ( )) 7
      *                  % &
                          8 '         8
                         ,9$ + + & 5 -+ 6 ! # $
                          + ,         4    1              ""
 ( )*
 ) 7"
  *                 ! # $9$,' , %
                      ""             "              *,
                                                     "      &'
                                                             '
    :                                    %            -+        ,+
 $ $ ! # $9$
          ""
             ;     : 8%
                      8"                     -+       '
                                                      :, :
,: * , %   9         /       + + )!
                             ,        1 3"           ) < 8 +0&
         '1 &
          &     '        ' )'*" " ,
                             " )
                              $            " ' $      " 8 ' 1
                                                            ,+
                  ( %
                  )*                ;      : " 8 '$ "$ $+ + '
                                            8      ,
 $( '': '
  + $ + $,
  *"                                    : +
                                         ,              : -
                                                         , ,
* 6=
 " '  $          % ! #$ )
                     "" 3
       6= %
        '
        $          ) &' :
                    3 ',  :                      ) ,
                                                  3       " 8 +0
% ! #$ +
    ""                   " 8 ):  3            :            *- '
                                                            "     $
        :    &$
              '        ,:      6 = 4%
                                '
                                $             "           5%
           -+ -*+; > 6 = % ") ?
                    & ''   $          '(
                                      $                            1
    :% % % ! # $ 23 ' ,'
     +          "" )            & '       + 6= -
                                               '
                                               $         & , '%
                                                          : 1'!$
                                                               (
*          :% % % ! # $%
            +          ""                        -+     9$
! " #"                       ,$+)

       8 ( ,)
         ) -%
          &                          -+

                         x   f t , x , x t0   x0
9$&x dx dt
   '        t ,x                                ,   n
                                                        * =$
                                                         "
                                             -& +f t , x ) ?
                                              %'          3@ +        t * )
                                                                         " 3
" &# &
 )       '       !                x D   n
                                               -, ' # $ x t; x0 $(': '
                                                  +! ""           +$ + $,
     & 1 ' ",+) '
        & + - 1                     )' & ! # $ ,
                                      $ ' ""
                                          $             +
           vt   f t ,v t                      x f t, x = $      -&+
                                                                 %',      %
?@         " v t :- $+- 2 & 1' 6 $
                       +                1 )              ?@     " vt & + 6
                                                                      -
                                                                      '
           & & - ", ''
            1            +: $           $                       D vt   :"
                   D vt   f t , v t * ' ! # $%
                                     " $ ""                 1
                                                            ' % & "$
                                                            ,+
                                            $ %             ) ,
                                                             -+

         AB v t ) ?
           6     3@                                       -&t *,
                                                            ' "
                                                                         vt   h vt
                                                D vt            lim                           vt
                                                               h     0         h
         CB6
                      1
                        vt         h       vt       g t,h ,              h    (0 , b ]   *"        im g t , h   g0 t
                      h                                                                        h    0

           *,
           "
                                                                     D vt           g0 t


                                                '

                                                         x      f t , x , x t0           x0

()"#*f    t, x       !+,- *                 *
                                            . / t 0 !+ ! # & #*
                                                              /                                     x   1       #      t    0 0 #
x    J           /    [t 0 , T )              2!+    ) !+ / #*)                                                            #* & " x t
                                                                                                                            %
         )0     / x t J, t                              [t 0 , T )
          1 )/ v t !+,- *                                 * 34
                                                          . *                      # ) $                                        )

                                                        D vt             f t , v t , v t0          x0

()"#*v t         J,      t [t0 , T )        0 ' )            vt          x t , t [t 0 , T )

                 ( (                            "#

                 : % & 1'
                        :
                        1                                   6 :% % % ! # $
                                                               +      ""      ) :
                                                                               @ +  /
9$                                     u    f t ,u ,      u t0 u0     ' # $ $( * '': '
                                                                      ! " + " $ + $,
                                                                       "
         6 )) % -
             31                             1
                                            '

                     ) ' ,)
                      " *
                       $                        +$
                                                9               ?@            vt     hxt
8                  vt        46 '
                                                           5                         % *
                                                                                      , "                                               )
                                                                                                                                        (
                                       D vt              D hxt                 f t , v t , v t0                v0
                      ! # $%
                       ""
                                                            ut        f t , u t , u t0                 u0
        4 )' :
           "$                 $ $ % % CB 3:
                                        )      $ $& 5
                                                  %
                          $! "
                            "      & 1 * ) ' ) ,)
                                      A " " 3 *
                                           $
                                                             vt        hxt            ut

+) '
 - 1   " ,' ) ' &
              $ '$                                                              :% % %
                                                                                 +                                                 / * )3
,$+ +) '
     - 1

                     :% % % ! # $%
                      +      ""                                                                   "

                                                   x     f x           1 x2 x , x 0                    a

              vt      x2 t                         vt       )?
                                                            3@                                -* :
                                                                                                " '+                       :

                     vt        2x t x t                2x2 t        2x4 t            2x2 t             4            , x4 t
                                                                                                                    +          0            5

    :    vt           :"
                                                               vt           2v t , v 0                a2
    ut        ) ! # $%
               3" "
                                                                  u         2u , u 0              a2
        )                  % -
                                          u t          1                t
                                                         du           2 dt               ut            a 2e   2t
                                          a2           u                0


    1         " ,' ) ' &
                     $ '$
                                                             vt        x2 t       a 2e   2t


    ) ,! # $
     - +" "               xt         :-
                                      +                     &: t
                                                              +            0   * ' %:
                                                                                " %
                                                  xt            vt      e ta,            t        0                                                 '


                &'                                             ,$+ '3
                                                                   1
                                                                   )                         * * ,) - /! # $
                                                                                                $ *     ""                                      6
-              ) 9$                            :
               x t      dx                t                                                   x t      1        x                  t
                                              dt       *$             , $
                                                                      + $+ -                                       dx                  dt
               a     x 1 x2               0                                                   a        x      1 x2                 0

                                 x t
              1                                                        x                 1 x2                          x       1 a2
    ln x        ln 1 x 2                      t             1    ln             ln                            ln                                t
              2                  a
                                                                       a                 1 a2                        1 x2       a
x                ae    t
                                                                                                                          e ta
                                                   $         " C & % *, ( -
                                                                  1  " )                                             xt
                 1 x2               1 a2                                                                                  1 a2
                  e ta
/        2+
          ,                 2
                                    eta
                   1 a




                   :% % % ! # $%
                    +      ""                                                                     "
                                                                       sin t
                                                        x        x           , x0                 2
                                                                       1 x2

              vt           x2 t         )?
                                        3@                                  -* '
                                                                              " :+                        :
                                                                                             2 x t sin t
                                              vt        2x t x t                2x2 t
                                                                                              1 x2 t
                                    2
                       xt       1         0             x2 t         2x t        1 0
                                                        x2 t 1 2x t
                                                         2x t
                                                               1
                                                        1 x2 t
    0    sin t         1   : "
                            8
                            (                                 -
                                                            2 x t sin t
                                                                                  sin t           1
                                                             1 x2 t
    :    vt            :"
                                                        vt           2v t        1, v 0           4
    ut        ) ! # $%
               3" "
                                                        ut           2u t         1, u 0              4
        )                  % -
                                                                                                          u t
                                    u t         1                       t             1
                                                   du                       dt          n 2u 1                       t
                                    4         2u 1                     0              2                   4
                                                                                                                2t
                                                        2u t 1                                        1 7e
                                               n                                 2t     ut
                                                           7                                            2
    1         " ,' ) ' &
                     $ '$
                                                                                             2t
                                                                                  1 7e
                                                            vt        x2 t
                                                                                    2
    ) ,! # $
     - +" "            xt           :-
                                     +                      &: t
                                                              +             0    * ' %:
                                                                                  " %
                                                                                        2t
                                                                                 1 7e
                                                   xt            vt                          ,        t   0                      '
                                                                                   2
8
                                                                                 1
                                                            x1                       x1     tanh x1                   tanh x 2
                                                                                 1
                                                           x2                        x2       tanh x1                 tanh x 2

9$& *
   ' "        ) ::& , (
               3+ ' + $
                                                                                                                                                    1
      *      2 +r
              ,                           x12           2
                                                       x2                        :"                                                       r             r       2 2

                             x1 x1         x2 x 2                    1                                                      x1                                   x1
                 r                                                                   xT f x            9$&x
                                                                                                          '                          *"          f x
                                  x  2
                                     1         x   2
                                                   2                 x x T                                                 x2                                    x2
                             1            1
                                              xT x              x1 tanh x1                         x1 tanh x2                    x2 tanh x1                     x2 tanh x1
                             r
                                 1                 x1           x2                                          x1        x2
                                      r                                  tanh x1                                            tanh x2
                                                           r                                                     r
                                 1             x1          x2                                          x1        x2
                                     r                               tanh x1                                           tanh x2
                                                       r                                                    r
     8
                                                                     2
                 x1          x2                 x1              x2                    x12          2
                                                                                                  x2 2 x1 x2                             2 x1 x2
                                                                                                                             1                              2
                         r                              r                                          r2                                      r2
4     , x1
      +      x2
                     2
                              0                2 x1 x2               x12              2
                                                                                     x2       r2   5
    &   $,
        '
                                                                             2
                 x1          x2                        x1 x2                              x12        2
                                                                                                    x2 2 x1 x2                                2 x1 x2
                                                                                                                                     1                          2
                      r                                  r                                           r2                                         r2
                                          ex           e    x
*"           tanh x                                                  1
                                          ex           e    x


                             1
     1       r                   r        2 2                                                                                                                                '


     9$   $ " ,' ) ' & *
                   $ '$                                                                     2 ++ % % ! # $
                                                                                             ,:%      ""                                                :"
                                                                             t                                                   t
                                                xt          2
                                                                     e                x0      2
                                                                                                       2 2            1 e

                                                                 1
                                                   r                  r          2 2              9$& r
                                                                                                     '                     x12        2
                                                                                                                                     x2            xt       2


     ut   ) ! # $%
           3" "
                                                                                          1
                                                                             u                u 2 2

      )              % -
1                                         1
                                                                    ut         2 2                                ut   2 2
     u t         du              t
                                                                                                                                 t
                                     dt                 n                                        t                           e
     u0    1                    0                               1                                             1
                u 2 2                                               u0        2 2                                 u0   2 2

                                                                    t                                 t
                                                      ut        e        u0        2 2       1 e
 1         " ,' ) ' &
                  $ '$
                                                                    t                                 t
                                         rt           ut        e        u0        2 2       1 e

) ,! # $
 - +" "             xt         :-
                                +                     &: t
                                                        +                0    * ' %:
                                                                               " %
                                      xt          2
                                                       e    t
                                                                x0        2
                                                                                   2 2       1 e      t
                                                                                                                                             '



     AB         x          n
                               ),
                               3                       ) = * $:
                                                          (    "                       n                  $                          %   x
                9$
                                                            p                      p 1 p
                                          x   p
                                                       x1                     xn           , 1       p!

     *"
                                                                x            max xi
                                                                               i

     CB , $+ ' 2 +
             1 ,          & 8 1 $( (C
                           '        + )  & '9
                                          '$,$   $(
                                                  +
        % % % ! # $9$ " ,' ) ' &
               ""            $ '$    " (
                                       )        "
         ' 9$ ) ' ,) r x t 2 / ' % % r 4% % x 5 )
         $,     " *
                 $                %              3
     ) & (
      @ ' "     %
                ' %% x t



                 :% % % ! # $%
                  +      ""                                                                       "

                                     x        f t,x                 1 x 2 x et ,                 x0           a

           vt       x2 t       /:+                              9$           vt       2x t x t
                                     2x2 t            2x4 t             2 x t et           2v t       2 v t et
         6 $ " ,' ) ' &
          )           $ '
                        $                                                                                        -
                                                                                                                 1
                                                                                                                 ' *+          &-
                                                                                                                                '
1 +$
 -+       :    : ,'1
                   "      ,) + v t
                          *                                                                                   xt     8 ' , v t -+
                                                                                                                      ' +
                                                                                                                       1         '
   & x 04
     '        , ? x t ' &x 0 5
              +           '
       1       % vt     8 )C 8
                            3   :
                                '
8' xt "0
 'A(
 &
   : +   % vt     9$
d                          xt xt                                                                   xt t
                  vt                  x2 t                                                  x t 1 x2 t                              e,        x"0
                              dt                          xt                                                                     xt
          1 x2 t         1         -,
                                    +                    x t 1 x2 t                                      xt              *"      vt          vt    et
 8'xt
  'C(
  &              0
                  vt      h        vt               xt             h        1           t h
           '                                                                                     f        ,x             d
                             h                                h             h           t

                                                                       1    t h
                                                    f t ,0                              #f           ,x                  f t, x t      $d
                                                                       h    t

                                                                       1        t h
                                                    f t ,0                                  f        ,x                  f t, x t      d
                                                                       h    t

                     f t, x t       )?
                                    3@                             +                        t            :                                  & %0        ' % 0 /&
                                                                                                                                                        '
6        t !'    *, f , x
                 "                                      f t, x t            !&
    1           &: 0 ! h ! '
                  +                                 -
                                               1    t h
                                                              f        ,x                       f t, x t d                    !&
                                               h    t

*         2+
           ,
                                                    1     t h
                                               im                  f     ,x                          f t, x t d                    0
                                           h   0    h     t

    1   % D
         ,                vt           f t ,0                 et            xt                   0
    )1 8
    &C '
        &: t
          +                  [t 0 , t1 )                '
                                                    D vt                    vt                   et , v 0                    a
    ut    ) ! # $%
           3" "
                                                         ut                 u et , u 0                                   a
     " ,' ) ' & -
            $ '$
                                    vt              ut             et a             1
                                                                                    2       et       e       t
                                                                                                                     ,       t [0, t1 )
% % % v t ):
           3+                                                 & 0:+ t1 * v t ' )
                                                                        "    : 3
                                                                              +                                                                         t1
  1 ! # $%
     ""                                                       :-
                                                               +    &: t 0 * ' % :
                                                                       +    " %

                                                xt                et a          1
                                                                                2       et           e   t
                                                                                                                 ,       t 0                                       '


        & , ' - " ,' ) ' &
         : 1              $ '$                 )+- /0 0)3 5
                                                *,. *1 2 * 4
                                                  +         *
6 86 6 ;) *9=. @ BE ?2E;=@ ) *9=. @ B5= -IH5E @. *K
 7 9: 7< /0 ; > AD9 *75E/ < /0 ; > A),9. J)5. + /0 *
            ,7 ? C F
                .        * G8
                           ;      ,7 ? H9; G ; /
                                       .     < ; *
L 9M + 0 O 8 P94 = 7K @ *. E R0 ) : @ 1 9U *< /0,7 > AC E5
 MF E. N 8 1 Q . 6 ; M /0 R N *< ) = O 0? K 7 ) *9=. @ BD 4
        1    D 4      / S57Q G
                             /     :T    G
                                         7        ; ? .     *
7 > A 7:O 0 R ) = . E)K1 7 > A T
 . @ B ;@1 Q ) : J @ 7 +-V . @ B*
  ? 6 T G 6 S
   .         < S..      9. ? 6
                             .                 H- E;0W)E)
                                                D 75H/ * @R
                                                    * : ;
90;U U R)0.)+- /0 *57 9: 7L 9MH-*=
4U) 7 Q **X Y*,. *K46 86 6 ;MF ED7Q
  G 7G G
  7 .<        * +       *                          ," D " *
                                                     " "
Z [               Q. N. **X J *D*9/ *7;= #K U . < 9R/
                   SS *
                   @ R 5<)0 ]H-/7 <0-7 " 0K @U/T@
                   ;L -
                      7     / ^       *;      7 ;7 G 8
                                                     E
< /0 =. @ B0D < < QENR H-/^ E ` *=-<K 8 b . @ 76 4@
 ) *9; > A. 2@ N > -L6. D *CQ B KQQE *0 _ _ / < ;7 0
    ,7 ? + 8 ; D * -E _
        .            9        1 S* Y @ / . - 8
                               a ;

            " ,' ) ' & *
                   $ '$                 2 +"# $%
                                         ,! "

                               x         1 x 2 x3
  :"
                                        x0
                     xt                               ,    t   0
                                                  2
                                   1 2t x 0


       9$   $ " ,' ) ' & *
                     $ '$                         2 +"# $%
                                                   ,! "
                                                  2 x2
                              x1        x1             2
                                                 1 x2
                                                  2 x1
                              x2        x2
                                                 1 x12
  :"
                                    t                          t
                     xt   2
                               e        x0   2
                                                      2 1 e




   !"
"# c d e
       ec              f    g h i                                  j( l
                                                                    k         d   mm e
"# c n e
      eo      k
              e       p he !
                         ei !    "#
                                  $                                       %        % &'   %
   ( % j[q ro
           (          g    l mmf
                               e


) , /) 2 .E= =,) )) .  ]1 = *Qs4=TT0)4U/
 * - *1 *7 A N @R @ J *0 a C *T*=/090;M
 + .0-     Q 9 M G // a
             D ;                 ,    7
                                       G
4 2=/0< 0) *= *@ 4. MR 27 9MA 8 R
 3 TT0) *:BKT EM9 C CE 0^)/ -. >
              Q E Q     ?     * 0
"3        t
          u e

4 7 4.E= =,) )) 0) 6 4m vm mwmxy : < 7 ) 0 E 2>;;B1
 5 8 *7 A M @R 7
 +
 69     Q9 NG . 8
           D   ;     9            ;0 7 Q @ B
                                    =    ?     ?@A
C)X . 6 T D 6- {f ) -<) 4 . ) Q B X . T= 0 6;M ;>
    . < < @ =+D w K N. *@ R T= 0 my . . ) Q B T4 7/
       > < z 1yf    8
                    5* 4      .           . O      )
                                                   5
9: J>/ ) m { 0+E;8 E w v{ m K Um y m|mf
6 8/ Q e m 7 ; G m| yx m{ 0
   ;5)          F H            7

More Related Content

What's hot

Mantovani Gruppo 2003 Insieme Per La Ricerca Milano 21 Settembre
Mantovani Gruppo 2003 Insieme Per La Ricerca  Milano 21 SettembreMantovani Gruppo 2003 Insieme Per La Ricerca  Milano 21 Settembre
Mantovani Gruppo 2003 Insieme Per La Ricerca Milano 21 SettembreScienzainrete
 
Italo calvino as cidades invisíveis
Italo calvino   as cidades invisíveisItalo calvino   as cidades invisíveis
Italo calvino as cidades invisíveismorrosemcensura
 
Italo calvino-as-cidades-invisiveis-rev
Italo calvino-as-cidades-invisiveis-revItalo calvino-as-cidades-invisiveis-rev
Italo calvino-as-cidades-invisiveis-revArtetudo
 
Fascículo alfa
Fascículo alfaFascículo alfa
Fascículo alfaSkepper63
 
การบันทึกและออกจากโปรแกรมMspowerpoint
การบันทึกและออกจากโปรแกรมMspowerpointการบันทึกและออกจากโปรแกรมMspowerpoint
การบันทึกและออกจากโปรแกรมMspowerpointเทวัญ ภูพานทอง
 
4th Quarter 2009 Results
4th Quarter 2009 Results4th Quarter 2009 Results
4th Quarter 2009 ResultsAES Eletropaulo
 
Transició democràcia i autonomia
Transició democràcia i autonomiaTransició democràcia i autonomia
Transició democràcia i autonomiaEduard Costa
 
Pdf Tema 15: Transició, democràcia i autonomia
Pdf Tema 15: Transició, democràcia i autonomiaPdf Tema 15: Transició, democràcia i autonomia
Pdf Tema 15: Transició, democràcia i autonomiariberamontserrat
 

What's hot (17)

Mantovani Gruppo 2003 Insieme Per La Ricerca Milano 21 Settembre
Mantovani Gruppo 2003 Insieme Per La Ricerca  Milano 21 SettembreMantovani Gruppo 2003 Insieme Per La Ricerca  Milano 21 Settembre
Mantovani Gruppo 2003 Insieme Per La Ricerca Milano 21 Settembre
 
Italo calvino as cidades invisíveis
Italo calvino   as cidades invisíveisItalo calvino   as cidades invisíveis
Italo calvino as cidades invisíveis
 
Italo calvino-as-cidades-invisiveis-rev
Italo calvino-as-cidades-invisiveis-revItalo calvino-as-cidades-invisiveis-rev
Italo calvino-as-cidades-invisiveis-rev
 
Fascículo alfa
Fascículo alfaFascículo alfa
Fascículo alfa
 
Minishell
MinishellMinishell
Minishell
 
การบันทึกและออกจากโปรแกรมMspowerpoint
การบันทึกและออกจากโปรแกรมMspowerpointการบันทึกและออกจากโปรแกรมMspowerpoint
การบันทึกและออกจากโปรแกรมMspowerpoint
 
With enter
With enterWith enter
With enter
 
2012 kalpataru
2012 kalpataru2012 kalpataru
2012 kalpataru
 
Innovation injection
Innovation injectionInnovation injection
Innovation injection
 
Ratsaravolana s3
Ratsaravolana s3Ratsaravolana s3
Ratsaravolana s3
 
Scarica pdf
Scarica pdfScarica pdf
Scarica pdf
 
20091181
2009118120091181
20091181
 
4th Quarter 2009 Results
4th Quarter 2009 Results4th Quarter 2009 Results
4th Quarter 2009 Results
 
Scarica pdf
Scarica pdfScarica pdf
Scarica pdf
 
Burocratas
BurocratasBurocratas
Burocratas
 
Transició democràcia i autonomia
Transició democràcia i autonomiaTransició democràcia i autonomia
Transició democràcia i autonomia
 
Pdf Tema 15: Transició, democràcia i autonomia
Pdf Tema 15: Transició, democràcia i autonomiaPdf Tema 15: Transició, democràcia i autonomia
Pdf Tema 15: Transició, democràcia i autonomia
 

More from อิทธิเดช มูลมั่งมี

Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์
Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์
Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์อิทธิเดช มูลมั่งมี
 
เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์
เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์
เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์อิทธิเดช มูลมั่งมี
 

More from อิทธิเดช มูลมั่งมี (20)

Peaking phenomenon
Peaking phenomenonPeaking phenomenon
Peaking phenomenon
 
Constructive nonlinear smc
Constructive nonlinear smcConstructive nonlinear smc
Constructive nonlinear smc
 
A contribution to the control of the non holonomic integrator including drift...
A contribution to the control of the non holonomic integrator including drift...A contribution to the control of the non holonomic integrator including drift...
A contribution to the control of the non holonomic integrator including drift...
 
วารสารคณิตศาสตร์ ฉบับพิเศษ
วารสารคณิตศาสตร์ ฉบับพิเศษวารสารคณิตศาสตร์ ฉบับพิเศษ
วารสารคณิตศาสตร์ ฉบับพิเศษ
 
Sliding Mode Control Stability (Jan 19, 2013)
Sliding Mode Control Stability (Jan 19, 2013)Sliding Mode Control Stability (Jan 19, 2013)
Sliding Mode Control Stability (Jan 19, 2013)
 
Stabilization of Inertia Wheel Pendulum using Multiple Sliding Surface Contro...
Stabilization of Inertia Wheel Pendulum using Multiple Sliding Surface Contro...Stabilization of Inertia Wheel Pendulum using Multiple Sliding Surface Contro...
Stabilization of Inertia Wheel Pendulum using Multiple Sliding Surface Contro...
 
In–Cylinder Air Estimation on Diesel Dual Fuel Engine Using Kalman Filter
In–Cylinder Air Estimation on Diesel Dual Fuel Engine Using Kalman FilterIn–Cylinder Air Estimation on Diesel Dual Fuel Engine Using Kalman Filter
In–Cylinder Air Estimation on Diesel Dual Fuel Engine Using Kalman Filter
 
Sliding Mode Control of Air-Path in Diesel Dual-Fuel Engine
Sliding Mode Control of Air-Path in Diesel Dual-Fuel EngineSliding Mode Control of Air-Path in Diesel Dual-Fuel Engine
Sliding Mode Control of Air-Path in Diesel Dual-Fuel Engine
 
Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์
Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์
Tricks ทางคณิตศาสตร์กับการแก้ปัญหาฟิสิกส์
 
Sliding mode control (revised march, 2012)
Sliding mode control (revised march, 2012)Sliding mode control (revised march, 2012)
Sliding mode control (revised march, 2012)
 
Robust and quadratic stabilization of tora system via dsc technique
Robust and quadratic stabilization of tora system via dsc techniqueRobust and quadratic stabilization of tora system via dsc technique
Robust and quadratic stabilization of tora system via dsc technique
 
Lyapunov stability 1
Lyapunov  stability 1Lyapunov  stability 1
Lyapunov stability 1
 
Lyapunov stability 2
Lyapunov stability 2Lyapunov stability 2
Lyapunov stability 2
 
Sliding mode control (revised march, 2012)
Sliding mode control (revised march, 2012)Sliding mode control (revised march, 2012)
Sliding mode control (revised march, 2012)
 
Calculus of variation ตอนที่ 2
Calculus of variation ตอนที่ 2Calculus of variation ตอนที่ 2
Calculus of variation ตอนที่ 2
 
Calculus of variation ตอนที่ 3 (จบ)
Calculus of variation ตอนที่ 3 (จบ)Calculus of variation ตอนที่ 3 (จบ)
Calculus of variation ตอนที่ 3 (จบ)
 
เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์
เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์
เรขาคณิตของการเคลื่อนที่แบบโปรเจกไตล์
 
สมการการแปลงพิกัด
สมการการแปลงพิกัดสมการการแปลงพิกัด
สมการการแปลงพิกัด
 
เรขาคณิตของการสะท้อนของแสง
เรขาคณิตของการสะท้อนของแสงเรขาคณิตของการสะท้อนของแสง
เรขาคณิตของการสะท้อนของแสง
 
Multilinear mapping and its application to determinants
Multilinear mapping and its application to determinantsMultilinear mapping and its application to determinants
Multilinear mapping and its application to determinants
 

Recently uploaded

Bahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali AzmiBahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali Azmibookbahareshariat
 
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...Nguyen Thanh Tu Collection
 
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...Nguyen Thanh Tu Collection
 
Bahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali AzmiBahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali Azmibookbahareshariat
 
Bahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali AzmiBahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali Azmibookbahareshariat
 
مختصر علم احكام القرآن فقه القرآن وفق منهج العرض
مختصر علم احكام القرآن فقه القرآن وفق منهج العرضمختصر علم احكام القرآن فقه القرآن وفق منهج العرض
مختصر علم احكام القرآن فقه القرآن وفق منهج العرضأنور غني الموسوي
 
FAIL REKOD PENGAJARAN.pptx fail rekod pengajaran
FAIL REKOD PENGAJARAN.pptx fail rekod pengajaranFAIL REKOD PENGAJARAN.pptx fail rekod pengajaran
FAIL REKOD PENGAJARAN.pptx fail rekod pengajaransekolah233
 

Recently uploaded (9)

Bahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali AzmiBahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 1 By SadurshSharia Mufti Amjad Ali Azmi
 
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
 
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
 
Energy drink .
Energy drink                           .Energy drink                           .
Energy drink .
 
LAR MARIA MÃE DE ÁFRICA .
LAR MARIA MÃE DE ÁFRICA                 .LAR MARIA MÃE DE ÁFRICA                 .
LAR MARIA MÃE DE ÁFRICA .
 
Bahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali AzmiBahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 4 By SadurshSharia Mufti Amjad Ali Azmi
 
Bahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali AzmiBahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali Azmi
Bahare Shariat Jild 2 By SadurshSharia Mufti Amjad Ali Azmi
 
مختصر علم احكام القرآن فقه القرآن وفق منهج العرض
مختصر علم احكام القرآن فقه القرآن وفق منهج العرضمختصر علم احكام القرآن فقه القرآن وفق منهج العرض
مختصر علم احكام القرآن فقه القرآن وفق منهج العرض
 
FAIL REKOD PENGAJARAN.pptx fail rekod pengajaran
FAIL REKOD PENGAJARAN.pptx fail rekod pengajaranFAIL REKOD PENGAJARAN.pptx fail rekod pengajaran
FAIL REKOD PENGAJARAN.pptx fail rekod pengajaran
 

Comparison Principle

  •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x f t , x , x t0 x0
  • 2. 9$&x dx dt ' t ,x , n * =$ " -& +f t , x ) ? %' 3@ + t * ) " 3 " &# & ) ' ! x D n -, ' # $ x t; x0 $(': ' +! "" +$ + $, & 1 ' ",+) ' & + - 1 )' & ! # $ , $ ' "" $ + vt f t ,v t x f t, x = $ -&+ %', % ?@ " v t :- $+- 2 & 1' 6 $ + 1 ) ?@ " vt & + 6 - ' & & - ", '' 1 +: $ $ D vt :" D vt f t , v t * ' ! # $% " $ "" 1 ' % & "$ ,+ $ % ) , -+ AB v t ) ? 6 3@ -&t *, ' " vt h vt D vt lim vt h 0 h CB6 1 vt h vt g t,h , h (0 , b ] *" im g t , h g0 t h h 0 *, " D vt g0 t ' x f t , x , x t0 x0 ()"#*f t, x !+,- * * . / t 0 !+ ! # & #* / x 1 # t 0 0 # x J / [t 0 , T ) 2!+ ) !+ / #*) #* & " x t % )0 / x t J, t [t 0 , T ) 1 )/ v t !+,- * * 34 . * # ) $ ) D vt f t , v t , v t0 x0 ()"#*v t J, t [t0 , T ) 0 ' ) vt x t , t [t 0 , T ) ( ( "# : % & 1' : 1 6 :% % % ! # $ + "" ) : @ + / 9$ u f t ,u , u t0 u0 ' # $ $( * '': ' ! " + " $ + $, " 6 )) % - 31 1 ' ) ' ,) " * $ +$ 9 ?@ vt hxt
  • 3. 8 vt 46 ' 5 % * , " ) ( D vt D hxt f t , v t , v t0 v0 ! # $% "" ut f t , u t , u t0 u0 4 )' : "$ $ $ % % CB 3: ) $ $& 5 % $! " " & 1 * ) ' ) ,) A " " 3 * $ vt hxt ut +) ' - 1 " ,' ) ' & $ '$ :% % % + / * )3 ,$+ +) ' - 1 :% % % ! # $% + "" " x f x 1 x2 x , x 0 a vt x2 t vt )? 3@ -* : " '+ : vt 2x t x t 2x2 t 2x4 t 2x2 t 4 , x4 t + 0 5 : vt :" vt 2v t , v 0 a2 ut ) ! # $% 3" " u 2u , u 0 a2 ) % - u t 1 t du 2 dt ut a 2e 2t a2 u 0 1 " ,' ) ' & $ '$ vt x2 t a 2e 2t ) ,! # $ - +" " xt :- + &: t + 0 * ' %: " % xt vt e ta, t 0 ' &' ,$+ '3 1 ) * * ,) - /! # $ $ * "" 6 - ) 9$ : x t dx t x t 1 x t dt *$ , $ + $+ - dx dt a x 1 x2 0 a x 1 x2 0 x t 1 x 1 x2 x 1 a2 ln x ln 1 x 2 t 1 ln ln ln t 2 a a 1 a2 1 x2 a
  • 4. x ae t e ta $ " C & % *, ( - 1 " ) xt 1 x2 1 a2 1 a2 e ta / 2+ , 2 eta 1 a :% % % ! # $% + "" " sin t x x , x0 2 1 x2 vt x2 t )? 3@ -* ' " :+ : 2 x t sin t vt 2x t x t 2x2 t 1 x2 t 2 xt 1 0 x2 t 2x t 1 0 x2 t 1 2x t 2x t 1 1 x2 t 0 sin t 1 : " 8 ( - 2 x t sin t sin t 1 1 x2 t : vt :" vt 2v t 1, v 0 4 ut ) ! # $% 3" " ut 2u t 1, u 0 4 ) % - u t u t 1 t 1 du dt n 2u 1 t 4 2u 1 0 2 4 2t 2u t 1 1 7e n 2t ut 7 2 1 " ,' ) ' & $ '$ 2t 1 7e vt x2 t 2 ) ,! # $ - +" " xt :- + &: t + 0 * ' %: " % 2t 1 7e xt vt , t 0 ' 2
  • 5. 8 1 x1 x1 tanh x1 tanh x 2 1 x2 x2 tanh x1 tanh x 2 9$& * ' " ) ::& , ( 3+ ' + $ 1 * 2 +r , x12 2 x2 :" r r 2 2 x1 x1 x2 x 2 1 x1 x1 r xT f x 9$&x ' *" f x x 2 1 x 2 2 x x T x2 x2 1 1 xT x x1 tanh x1 x1 tanh x2 x2 tanh x1 x2 tanh x1 r 1 x1 x2 x1 x2 r tanh x1 tanh x2 r r 1 x1 x2 x1 x2 r tanh x1 tanh x2 r r 8 2 x1 x2 x1 x2 x12 2 x2 2 x1 x2 2 x1 x2 1 2 r r r2 r2 4 , x1 + x2 2 0 2 x1 x2 x12 2 x2 r2 5 & $, ' 2 x1 x2 x1 x2 x12 2 x2 2 x1 x2 2 x1 x2 1 2 r r r2 r2 ex e x *" tanh x 1 ex e x 1 1 r r 2 2 ' 9$ $ " ,' ) ' & * $ '$ 2 ++ % % ! # $ ,:% "" :" t t xt 2 e x0 2 2 2 1 e 1 r r 2 2 9$& r ' x12 2 x2 xt 2 ut ) ! # $% 3" " 1 u u 2 2 ) % -
  • 6. 1 1 ut 2 2 ut 2 2 u t du t t dt n t e u0 1 0 1 1 u 2 2 u0 2 2 u0 2 2 t t ut e u0 2 2 1 e 1 " ,' ) ' & $ '$ t t rt ut e u0 2 2 1 e ) ,! # $ - +" " xt :- + &: t + 0 * ' %: " % xt 2 e t x0 2 2 2 1 e t ' AB x n ), 3 ) = * $: ( " n $ % x 9$ p p 1 p x p x1 xn , 1 p! *" x max xi i CB , $+ ' 2 + 1 , & 8 1 $( (C ' + ) & '9 '$,$ $( + % % % ! # $9$ " ,' ) ' & "" $ '$ " ( ) " ' 9$ ) ' ,) r x t 2 / ' % % r 4% % x 5 ) $, " * $ % 3 ) & ( @ ' " % ' %% x t :% % % ! # $% + "" " x f t,x 1 x 2 x et , x0 a vt x2 t /:+ 9$ vt 2x t x t 2x2 t 2x4 t 2 x t et 2v t 2 v t et 6 $ " ,' ) ' & ) $ ' $ - 1 ' *+ &- ' 1 +$ -+ : : ,'1 " ,) + v t * xt 8 ' , v t -+ ' + 1 ' & x 04 ' , ? x t ' &x 0 5 + ' 1 % vt 8 )C 8 3 : ' 8' xt "0 'A( & : + % vt 9$
  • 7. d xt xt xt t vt x2 t x t 1 x2 t e, x"0 dt xt xt 1 x2 t 1 -, + x t 1 x2 t xt *" vt vt et 8'xt 'C( & 0 vt h vt xt h 1 t h ' f ,x d h h h t 1 t h f t ,0 #f ,x f t, x t $d h t 1 t h f t ,0 f ,x f t, x t d h t f t, x t )? 3@ + t : & %0 ' % 0 /& ' 6 t !' *, f , x " f t, x t !& 1 &: 0 ! h ! ' + - 1 t h f ,x f t, x t d !& h t * 2+ , 1 t h im f ,x f t, x t d 0 h 0 h t 1 % D , vt f t ,0 et xt 0 )1 8 &C ' &: t + [t 0 , t1 ) ' D vt vt et , v 0 a ut ) ! # $% 3" " ut u et , u 0 a " ,' ) ' & - $ '$ vt ut et a 1 2 et e t , t [0, t1 ) % % % v t ): 3+ & 0:+ t1 * v t ' ) " : 3 + t1 1 ! # $% "" :- + &: t 0 * ' % : + " % xt et a 1 2 et e t , t 0 ' & , ' - " ,' ) ' & : 1 $ '$ )+- /0 0)3 5 *,. *1 2 * 4 + * 6 86 6 ;) *9=. @ BE ?2E;=@ ) *9=. @ B5= -IH5E @. *K 7 9: 7< /0 ; > AD9 *75E/ < /0 ; > A),9. J)5. + /0 * ,7 ? C F . * G8 ; ,7 ? H9; G ; / . < ; * L 9M + 0 O 8 P94 = 7K @ *. E R0 ) : @ 1 9U *< /0,7 > AC E5 MF E. N 8 1 Q . 6 ; M /0 R N *< ) = O 0? K 7 ) *9=. @ BD 4 1 D 4 / S57Q G / :T G 7 ; ? . * 7 > A 7:O 0 R ) = . E)K1 7 > A T . @ B ;@1 Q ) : J @ 7 +-V . @ B* ? 6 T G 6 S . < S.. 9. ? 6 . H- E;0W)E) D 75H/ * @R * : ; 90;U U R)0.)+- /0 *57 9: 7L 9MH-*= 4U) 7 Q **X Y*,. *K46 86 6 ;MF ED7Q G 7G G 7 .< * + * ," D " * " "
  • 8. Z [ Q. N. **X J *D*9/ *7;= #K U . < 9R/ SS * @ R 5<)0 ]H-/7 <0-7 " 0K @U/T@ ;L - 7 / ^ *; 7 ;7 G 8 E < /0 =. @ B0D < < QENR H-/^ E ` *=-<K 8 b . @ 76 4@ ) *9; > A. 2@ N > -L6. D *CQ B KQQE *0 _ _ / < ;7 0 ,7 ? + 8 ; D * -E _ . 9 1 S* Y @ / . - 8 a ; " ,' ) ' & * $ '$ 2 +"# $% ,! " x 1 x 2 x3 :" x0 xt , t 0 2 1 2t x 0 9$ $ " ,' ) ' & * $ '$ 2 +"# $% ,! " 2 x2 x1 x1 2 1 x2 2 x1 x2 x2 1 x12 :" t t xt 2 e x0 2 2 1 e !" "# c d e ec f g h i j( l k d mm e "# c n e eo k e p he ! ei ! "# $ % % &' % ( % j[q ro ( g l mmf e ) , /) 2 .E= =,) )) . ]1 = *Qs4=TT0)4U/ * - *1 *7 A N @R @ J *0 a C *T*=/090;M + .0- Q 9 M G // a D ; , 7 G 4 2=/0< 0) *= *@ 4. MR 27 9MA 8 R 3 TT0) *:BKT EM9 C CE 0^)/ -. > Q E Q ? * 0 "3 t u e 4 7 4.E= =,) )) 0) 6 4m vm mwmxy : < 7 ) 0 E 2>;;B1 5 8 *7 A M @R 7 + 69 Q9 NG . 8 D ; 9 ;0 7 Q @ B = ? ?@A C)X . 6 T D 6- {f ) -<) 4 . ) Q B X . T= 0 6;M ;> . < < @ =+D w K N. *@ R T= 0 my . . ) Q B T4 7/ > < z 1yf 8 5* 4 . . O ) 5 9: J>/ ) m { 0+E;8 E w v{ m K Um y m|mf 6 8/ Q e m 7 ; G m| yx m{ 0 ;5) F H 7