作　　者： ; ; ;

机构地区： 北京印刷学院信息与机电工程学院

出　　处： 《北京科技大学学报》 2008年第6期690-693,共4页

摘　　要： 针对典型的仿射非线性系统,采用常微分方程理论对其进行求解.首先将系统在平衡点附近进行展开,求得其齐次方程的解,然后利用常数变易法将非线性微分方程变为等价的第二类非线性Volterra积分方程.采用逐次逼近法,求得任意阶近似解,并证明解的收敛性. The state equation of an typical affine nonlinear system was solved with the ordinary differential equation theory. By utilizing the expansion expression of equilibrium point of the system, the homogeneous equation＇s solution was obtained, and then the nonlinear differential equation was equivalent to its nonlinear Volterra＇s integral equation of the second kind by the constant variation method. Any order approximate solution of the equation was presented, and its convergence was mathematically proved by the successive approximation method.

关 键 词： 非线性系统 状态方程 常微分方程 积分方程 逐次逼近法 近似解

领　　域： [自动化与计算机技术] [自动化与计算机技术]