Regular Paper

International Journal of Control, Automation and Systems 2022; 20(9): 3045-3052

Published online August 27, 2022

https://doi.org/10.1007/s12555-021-0230-x

© The International Journal of Control, Automation, and Systems

A Continuous Finite-time Neural Network with Bias Noises for Convex Quadratic Bilevel Programming Problem

Peng Miao* and Fan Yang

Zhengzhou University of Science & Technology

Abstract

A continuous finite-time neural network with bias noises is proposed to solve the convex quadratic bilevel programming problem in this paper. In order to solve the convex quadratic bilevel programming problem, it is transformed into a nonlinear programming problem based on the Kaeush-Kuhn-Tucker conditions. Then, a neural network is designed to solve this problem. Compared with the existing networks, the designed network contains biased noise. Furthermore, it is proved that the proposed neural network can converge to the equilibrium point in finite time and it is Lyapunov stable. Moreover, the robustness performance of the present neural network against bias noises is discussed and the effect is very good. At the same time, the upper bound of the steady-state error is estimated. Lastly, two numerical examples show the effectiveness of the proposed methods.

Keywords Bias noises, convex quadratic bilevel programming problem, finite-time, robustness.

Article

Regular Paper

International Journal of Control, Automation and Systems 2022; 20(9): 3045-3052

Published online September 1, 2022 https://doi.org/10.1007/s12555-021-0230-x

Copyright © The International Journal of Control, Automation, and Systems.

A Continuous Finite-time Neural Network with Bias Noises for Convex Quadratic Bilevel Programming Problem

Peng Miao* and Fan Yang

Zhengzhou University of Science & Technology

Abstract

A continuous finite-time neural network with bias noises is proposed to solve the convex quadratic bilevel programming problem in this paper. In order to solve the convex quadratic bilevel programming problem, it is transformed into a nonlinear programming problem based on the Kaeush-Kuhn-Tucker conditions. Then, a neural network is designed to solve this problem. Compared with the existing networks, the designed network contains biased noise. Furthermore, it is proved that the proposed neural network can converge to the equilibrium point in finite time and it is Lyapunov stable. Moreover, the robustness performance of the present neural network against bias noises is discussed and the effect is very good. At the same time, the upper bound of the steady-state error is estimated. Lastly, two numerical examples show the effectiveness of the proposed methods.

Keywords: Bias noises, convex quadratic bilevel programming problem, finite-time, robustness.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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