Conjugate direction methods for optimal control
Conjugate direction methods for optimal control
复制标题
最优控制的共轭方向方法
DOI：
10.1109/tac.1970.1099440
复制
发表时间：
1970
影响因子：
6.8
通讯作者：
L. Lasdon
中科院分区：
文献类型：
--
作者：
L. Lasdon
这种对应关系扩展了两个算法的无约束最小化的Rn，大卫的方法和投影梯度算法，最优控制问题。两者都只需要被最小化的函数的值和梯度;两者都通过用二进算子在负梯度上操作来找到当前搜索方向;并且两者都在应用于二次函数时生成共轭方向。为了计算迭代i的搜索方向，Davidon算法需要存储在过去和当前周期中生成的2 i + 2个函数。投影梯度法只需要i + 2。这两种方法都降低了每一步被最小化的泛函的值。存储需求将要求定期重新启动这两种方法。然而，最近的计算结果表明，这可能会提高收敛速度。
This correspondence extends two algorithms for unconstrained minimization in Rn, Davidon's method and a projected gradient algorithm, to optimal control problems. Both require only the value and gradient of the functional being minimized; both find the current search direction by operating on the negative gradient with a dyadic operator; and both generate conjugate directions when applied to a quadratic functional. To compute the direction of search at iteration i , the Davidon algorithm requires that 2i + 2 functions, generated in past and current cycles, be stored. The projected gradient method requires only i + 2 . Both decrease the value of the functional being minimized at each step. The storage demands will require that both methods be restarted periodically. However, recent computational results indicate that this may improve the rate of convergence.