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.