摘要
对性能泛函求极值用欧拉(Euler)方程和横截条件,现有文献仅讨论性能泛函形式为J(x)=∫tft0L(x,x,t)dt,即状态量x最高为一阶导数的Euler方程和横截条件.用数学归纳法推导出状态变量x为高阶导数的性能泛函极值的必要条件,并以二阶导数为例,用Matlab进行了极值求解.
Euler equation and transversality condition are used to solve the extreme value for performancefunctional. However,only the form of performance functional J（x）=∫t0 t1L（x,x,t）dtdt is discussed by presentliteratures,which means that the Euler equation and transversality condition contain the first derivative of the state variable x. By mathematical induction, the Euler equation and transversality condition for the higher derivatives of the state variable x as the necessary conditions of the extreme value existing were deduced. Taking the second derivative as an example,the extreme value was resolved by using Matlab.
出处
《上海工程技术大学学报》
CAS
2012年第4期374-377,共4页
Journal of Shanghai University of Engineering Science
关键词
最优控制
积分型性能泛函
高阶导数
极值
数学归纳法
optimal control
integral type performance functional
higher derivative
extreme value
mathematical induction
