The solution of nonlinear optimization is usually encountered in many fields of scientific researches and engineering applications, which spawns a large number of corresponding algorithms to cope with it. Besides, with developments of modern cybernetics technology, it imperatively requires some advanced numerical algorithms to solve online dynamic nonlinear optimization (ODNO). Nevertheless, the major existing algorithms are limited to the static nonlinear optimization models, few works considering the dynamic ones, let alone tolerating noise. For the abovementioned reasons, this paper proposes a modified Newton integration (MNI) algorithm for ODNO with strong robustness and high-accuracy computing solution, which can effectively suppress the influence caused by noise components. In addition, the correlative theoretical analyses and mathematical proofs on convergence and robustness of the MNI algorithm are carried out, which indicates that computing solutions of the proposed MNI algorithm can globally converge to relative small value in the presence of various noise or zero noise conditions. Finally, to illustrate the advantages and feasibilities of the proposed MNI algorithm for ODNO problems, four numerical simulation examples and an application to robot manipulator motion generation are performed.

非线性优化的解决方案通常在科学研究和工程应用的许多领域中遇到，这就产生了许多相应的算法来应对。此外，随着现代控制论技术的发展，迫切需要一些先进的数值算法来求解在线动态非线性优化（ODNO）。尽管如此，现有的主要算法仅限于静态非线性优化模型，很少考虑动态算法，更不用说容忍噪声了。由于上述原因，本文提出了一种针对ODNO的改进牛顿积分（MNI）算法，该算法具有很强的鲁棒性和高精度的计算解决方案，可以有效地抑制噪声分量的影响。此外，对MNI算法的收敛性和鲁棒性进行了相关的理论分析和数学证明，表明所提出的MNI算法的计算方案可以在各种噪声或零噪声条件下全局收敛到较小的数值。最后，为了说明所提出的MNI算法解决ODNO问题的优点和可行性，进行了四个数值模拟示例并将其应用于机器人操纵器运动生成。