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Superior robustness of power-sum activation functions in Zhang neural networks for time-varying quadratic programs perturbed with large implementation errors

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Abstract

A special class of recurrent neural network termed Zhang neural network (ZNN) depicted in the implicit dynamics has recently been introduced for online solution of time-varying convex quadratic programming (QP) problems. Global exponential convergence of such a ZNN model is achieved theoretically in an error-free situation. This paper investigates the performance analysis of the perturbed ZNN model using a special type of activation functions (namely, power-sum activation functions) when solving the time-varying QP problems. Robustness analysis and simulation results demonstrate the superior characteristics of using power-sum activation functions in the context of large ZNN-implementation errors, compared with the case of using linear activation functions. Furthermore, the application to inverse kinematic control of a redundant robot arm also verifies the feasibility and effectiveness of the ZNN model for time-varying QP problems solving.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grants 61075121 and 60935001, and also by the Fundamental Research Funds for the Central Universities of China. In addition, the authors would like to thank the editors and anonymous reviewers sincerely for their constructive comments and suggestions which have really improved the presentation and quality of this paper very much.

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  1. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, 510006, China

    Yiwen Yang & Yunong Zhang

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  1. Yiwen Yang
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  2. Yunong Zhang
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Correspondence to Yunong Zhang.

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Yang, Y., Zhang, Y. Superior robustness of power-sum activation functions in Zhang neural networks for time-varying quadratic programs perturbed with large implementation errors. Neural Comput & Applic 22, 175–185 (2013). https://doi.org/10.1007/s00521-011-0692-5

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