Any order approximate solution of the state equation for an affine nonlinear system
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摘要: 針對典型的仿射非線性系統,采用常微分方程理論對其進行求解.首先將系統在平衡點附近進行展開,求得其齊次方程的解,然后利用常數變易法將非線性微分方程變為等價的第二類非線性Volterra積分方程.采用逐次逼近法,求得任意階近似解,并證明解的收斂性.Abstract: 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.
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