最优控制的计算方法

1、2021/8/612021/8/62最优控制的计算方法最优控制的计算方法2021/8/63最优控制的计算方法最优控制的计算方法 2021/8/64最优控制的计算方法最优控制的计算方法0UH),(),(min*tUXHtUXHUHXXH2021/8/652021/8/661、梯度法、梯度法0KgKKXKUKUH)()KKHgU2021/8/671、梯度法、梯度法KKKgKKKKgUU1)()()(1KKKUJUJUJ1 KKKg2021/8/681、梯度法、梯度法uxx210)0(x1022)(21dtuxJ0) 1 (0uxuxH222)(21xxxH22021/8/691、梯度法、梯度法0)

2、(0tu101c0)(0tudtxdx2ctx111010)()(0ttxtx(0)10 x2021/8/6101、梯度法、梯度法)(0tx0) 1 (00201( )1 (1 10 ) /121(1)02tt121/)101 (1 21)()()(2001tuHtutu1K00()( )HtuuuH2021/8/6111、梯度法、梯度法01)(1tu最优值)(0tuut10和最优值)(tx)(0txxt)(tx)(1tu2021/8/6121、梯度法、梯度法2021/8/613),(,)(2121nTTnaaaaxxxXQXXQXXT),(CXaQXXXFT),(21)(2021/8/614

3、2、共轭梯度法、共轭梯度法0),(QYXQYXTKP, 2, 1, 0KKPKKKKPXX1,0,1,2,KPK 2021/8/6152、共轭梯度法、共轭梯度法QKPK1KP1KKKKPgP0),(1KKQPP00Pg ),(),(0111KKKKKKQPPgQPP),(),(111KKKKKQPPQPgK),(),(111KKKKKQPPQPg2021/8/6162、共轭梯度法、共轭梯度法jixx ,2()()1, ijF XQi jnx x QXXQXXT),(CXaQXXXFT),(21)(，21211),(),(KKKKKKKgggggg2021/8/6172、共轭梯度法、共轭梯度法K

4、KKKPXX1212KKKgg00KKXFg)(001,gPPgPKKKK2021/8/6182、共轭梯度法、共轭梯度法KtutuKKuHuHtggK)()()()()()(tgKfttKKTKKKtgdttgtgtgtg02)()()()(),(2021/8/6192、共轭梯度法、共轭梯度法)(),(0tutuK)(0tX0tft)(tXK)(ftft0t)(tKkuuKuHg)(212)()(tgtgKKK001KKKKPgP00gP 2021/8/6202、共轭梯度法、共轭梯度法1 KK)()()(1KKKuJuJuJKKKKKKPuJPuJ0minKKKKPtutu)()(12021/

5、8/6212、共轭梯度法、共轭梯度法)(tuJ) 1 (2xJ 21)0(11xux 0)0(21)1 (2212xuuxux 2220( )Htcx )1 (211uxH212121)1(uuxuuH2021/8/6222、共轭梯度法、共轭梯度法11(1)(1)0u 1)(2t22(1)11(1)Jcx0) 1 () 1 () 1 (111xJx0)(0tu1, 0221121xxx1)(,21)(,21)(010201ttttxtx111(0)2xux22121(1)(0)02xu xuux2021/8/6232、共轭梯度法、共轭梯度法02212100)()()(uxuHtgttx2512

6、11020102012500tgP)25()()(00001tPtutu1u)25()(01ttx01002215515( )1() ( )()()2222x ttx ttt111(0)2xux22121(1)(0)02xu xuux2( )1t11(1)(1)0u 2021/8/6242、共轭梯度法、共轭梯度法210151( )()222tx tt)82581512138()()41526(2)(2342023012tttttttttx2000022232002551515( )1()()()()2222222115131525()() ()2242448tx tttttttttt )25(

7、)(01ttx11(0)2x2(0)0 x01002215515( )1()( )()()2222x ttx ttt1( )x t2021/8/6252、共轭梯度法、共轭梯度法2002)(2497124921) 1 ( xJ01297124900J097490)25(9749)(1ttu)25(97491 1t9711945119449)(211ttt1)(12t2( )1t11(1)(1)0u 2021/8/6262、共轭梯度法、共轭梯度法12212111)()()(uxuHtg97229748t210210220211194192)25()97229748()()(dttdtttgtg22

8、20111194901619418816)25(19419297229748tttPgP2021/8/6272、共轭梯度法、共轭梯度法)194901619418816()25(9749)()(2211112ttPtutu2( )u t) 1)()()(),(22212221tttxtx和1196194123)(2 ttu)() 1 (12fxJ2021/8/6282、共轭梯度法、共轭梯度法110,nPPPnngP)()(2tutu0)()(2221212uxuH2021/8/6290),(UtUXH),(tXUU),(tXUUnRtY2)( )( )( )TY tX ttHXXH2021/8/

9、6301、边界迭代法、边界迭代法), 1()(qitxfi), 1()(nqitfi),(tYgY )(ftfft)(Tnqqtttxtxt)()(),(),()(112021/8/6311、边界迭代法、边界迭代法)(0t)(0t)()(0ttf)(0tX)(0t)(tY)(tZ)(ft)(0t)()(0ttf)(0t)(ftf)()(00ttTnn)()()()()(0000tttttTf0 ( )t2021/8/6321、边界迭代法、边界迭代法0()( )ifjtt )()(0000)()()(ttjfiTjjttZt)()()()()(1000ffTttttt)(0t2021/8/633

10、1、边界迭代法、边界迭代法10)(0tK)(fKt)(0tK)()()()()(10001fKfKTKKttttt)(0tK)(01tK)()(fKftt2021/8/6341、边界迭代法、边界迭代法0uH),(tXuu)()(fkftt)(0t)(0tK)(0tXftt 到0)(),(ttXKK)(fKt)(01tK1 KKT2021/8/6351、边界迭代法、边界迭代法)(0t)(0t)(ft)(ft)()()()()(0000tttttTf2021/8/6361、边界迭代法、边界迭代法)(tu)(uJ1 . 00221)()(duuxuJ5)0(121xxx 5)0(414. 04 .

11、1232212xuxxxx ) 1 . 0(1x) 1 . 0(2x0) 1 . 0() 1 . 0(21)(0201tt（和)(1ft)(2ft2021/8/6371、边界迭代法、边界迭代法2021/8/63800)(XtXfft)(TYX),(tYgY )(tYK)(tYK1KY1 , 0)()(),(11KYYYgtYgYKKKKK2021/8/6392、拟线性化法、拟线性化法njXtXtYjjKj2 , 1)()(0001nnnjttYjffjfKj2, 2, 1)()(1)(),()(11KKKKKKYYgtYgYYgY)()(11tYtAYKKKKKKYgtA)()(11(, )() ()KKKKKgYg YtYYY1( )( ) (1, 2, , 2 )KKiiiYtYtin)(),()(KKKKYYgtYgt2021/8/6402、拟线性化法、拟线性化法)(tuJ1022)(21dtuxJ2(0)10 xxux u )()(21222uxuxH0uuH(0)10 x(1)0(1)X212( , )2gxxYg Y tgxx 2021/8/6412、拟线性化法、拟线性化法)(),()(KKKKYYgtYgtKKKKKKKKKKxxxxxx212122)(