四个俐题 例6.7考虑受控方程二阶李导数x1=x1 解:设∫ (x)=x1 元(x)=[ 则有 L22四个例题 例6.4考虑受控方程 解： 设 则有 1 2 2 2 1 1 2 1 (1 ) x x x x x x u y x  = = − + − + = 2 2 1 1 1 2 , ( ) (1 ) x f x x x x x     = =   − + −     2 2 2 1 1 2 ( ) 1 0 (1 ) f x L x x x x x     = =     − + − 例6.5 考虑受控方程 解： 设 则有 附注：高阶李导数 函数的高阶李导数由以下递推形式定义 k阶李导数为 约定：零阶李导数为 1 1 2 2 1 x x x x u y x = = + = 1 1 2 , ( ) x f x x x    = =       1 1 2 f ( ) 1 0 x L x x x    = =     ( ) 1   − = k f f k Lf L L ( ) 1 1   − − = k g f k Lg Lf L L  =  0 Lf 例6.6 考虑受控方程二阶李导数\ 解: 设 则有 1 2 2 2 1 1 2 1 (1 ) x x x x x x u y x  = = − + − + = 2 2 1 1 1 2 , ( ) (1 ) x f x x x x x     = =     − + −   2 2 2 1 1 2 ( ) 1 0 (1 ) f x L x x x x x     = =     − + −   2 2 2 2 1 1 2 1 1 2 ( ) 0 1 (1 ) (1 ) f x L x x x x x x x      = = − + −     − + − 例6.7考虑受控方程二阶李导数 解： 设 则有 1 1 2 2 1 x x x x u y x = = + = 1 1 2 , ( ) x f x x x    = =       1 1 2 f ( ) 1 0 x L x x x    = =       2 1 1 2 f ( ) 1 0 x L x x x    = =    