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Local Stability and Convergence Analysis of Neural Network Controllers with Error Integral Inputs

Fu, X., Li, S., Wunsch, D. C. and Alonso, E. ORCID: 0000-0002-3306-695X (2021). Local Stability and Convergence Analysis of Neural Network Controllers with Error Integral Inputs. IEEE Transactions on Neural Networks and Learning Systems,


This paper investigates the local stability and convergence for a class of neural network controllers with error integral as inputs for reference tracking. It is proved that if the neural network controllers only have error terms as inputs, the control system has a non-zero steady-state error for any constant reference except for one special point. It is proved that adding error integral to the inputs of the neural network controller is one sufficient way to remove steady-state error for any constant reference. Due to the nonlinearity of the neural network controllers, the neural network control systems are linearized at the equilibrium points. It is proved that if all the eigenvalues of the linearized neural network control systems have negative real parts, local asymptotic stability and local exponential convergence are guaranteed. Two case studies were explored to verify the theoretical proofs: a single-layer neural network controller in a one-dimensional system and a four-layer neural network controller in a two-dimensional system applied in renewable energy integration. Simulations have demonstrated that when neural network controllers and corresponding Generalized Proportional-Integral controllers have the same eigenvalues, all control systems exhibit almost the same transient responses in a small enough neighborhood of their respective equilibrium points.

Publication Type: Article
Additional Information: © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publisher Keywords: Neural Network Controller, Error Integral, Steady-State Error, Local Asymptotic Stability, Local Exponential Convergence, Generalized PI controller
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
Departments: School of Mathematics, Computer Science & Engineering > Computer Science
Date available in CRO: 17 Sep 2021 14:45
Date deposited: 17 September 2021
Date of acceptance: 17 September 2021
Text - Accepted Version
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