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Varying-parameter recurrent neural network, being a special kind of neural-dynamic methodology, has revealed powerful abilities to handle various time-varying problems, such as quadratic minimization (QM) and quadratic programming (QP) problems. In this paper, a novel power-type varying-parameter recurrent neural network (PT-VP-RNN) is proposed to solve the perturbed time-varying QM and QP problems. First, based on the generalization of time-varying QM and QP problems, the design process of the PT-VP-RNN is presented in detail. Second, the robustness performance of the proposed PT-VP-RNN is theoretically analyzed and proved. What is more, two numerical examples are simulated to illustrate the robustness convergence performance of PT-VP-RNN even in a large disturbance condition. Finally, two practical application examples (i.e., a robot tracking example and a venture investment example) further verify the effectiveness, accuracy, and widespread applicability of the proposed PT-VP-RNN.

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