Neural-model based robust H∞ controllers for discrete-time nonlinear systems: An BMI approach

Meiqin Liu; Gangfeng Yan; Shouguang Wang

doi:10.1109/ICSMC.2004.1401133

Neural-model based robust H_∞ controllers for discrete-time nonlinear systems: An BMI approach

Meiqin Liu
, Gangfeng Yan
, Shouguang Wang

Zhejiang University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this paper, a neural-model based robust H_∞ control design for a discrete-time nonlinear system is addressed. The design approach is to approximate the nonlinear system with a neural network with biases of which the activation functions satisfy the sector conditions. A novel neural network model named as standard neural network model (SNNM) with uncertainty is advanced for describing this class of approximating neural networks with biases. And a state-feedback control law is designed for the SNNM with real parametric uncertainty, such that L₂ gain of the closed-loop system is minimal. The approach is based on the robust L₂ gain (i.e. robust H _∞ performance) analysis of the Lur'e system using the common Lyapunov approach. The control design equations are shown to be a set of bilinear matrix inequalities (BMIs) which can be solved by an improved iterative algorithm. Finally, a detailed design procedure of the control law for the nonlinear system is provided.

Original language	English
Title of host publication	2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004
Pages	5876-5881
Number of pages	6
DOIs	https://doi.org/10.1109/ICSMC.2004.1401133
State	Published - 2004
Externally published	Yes
Event	2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004 - The Hague, Netherlands Duration: 10 Oct 2004 → 13 Oct 2004

Publication series

Name	Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
Volume	6
ISSN (Print)	1062-922X

Conference

Conference	2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004
Country/Territory	Netherlands
City	The Hague
Period	10/10/04 → 13/10/04

Keywords

Bilinear matrix inequality (BMI)
L gain
Linear differential inclusion (LDI)
Linear matrix inequality (LMI)
Nonlinear robust control
Real parametric uncertainty
Standard neural network model (SNNM)

Access to Document

10.1109/ICSMC.2004.1401133

Cite this

Liu, M., Yan, G., & Wang, S. (2004). Neural-model based robust H_∞ controllers for discrete-time nonlinear systems: An BMI approach. In 2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004 (pp. 5876-5881). (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics; Vol. 6). https://doi.org/10.1109/ICSMC.2004.1401133

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title = "Neural-model based robust H∞ controllers for discrete-time nonlinear systems: An BMI approach",

abstract = "In this paper, a neural-model based robust H∞ control design for a discrete-time nonlinear system is addressed. The design approach is to approximate the nonlinear system with a neural network with biases of which the activation functions satisfy the sector conditions. A novel neural network model named as standard neural network model (SNNM) with uncertainty is advanced for describing this class of approximating neural networks with biases. And a state-feedback control law is designed for the SNNM with real parametric uncertainty, such that L2 gain of the closed-loop system is minimal. The approach is based on the robust L2 gain (i.e. robust H ∞ performance) analysis of the Lur'e system using the common Lyapunov approach. The control design equations are shown to be a set of bilinear matrix inequalities (BMIs) which can be solved by an improved iterative algorithm. Finally, a detailed design procedure of the control law for the nonlinear system is provided.",

keywords = "Bilinear matrix inequality (BMI), L gain, Linear differential inclusion (LDI), Linear matrix inequality (LMI), Nonlinear robust control, Real parametric uncertainty, Standard neural network model (SNNM)",

author = "Meiqin Liu and Gangfeng Yan and Shouguang Wang",

year = "2004",

doi = "10.1109/ICSMC.2004.1401133",

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Liu, M, Yan, G & Wang, S 2004, Neural-model based robust H_∞ controllers for discrete-time nonlinear systems: An BMI approach. in 2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004. Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, vol. 6, pp. 5876-5881, 2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004, The Hague, Netherlands, 10/10/04. https://doi.org/10.1109/ICSMC.2004.1401133

Neural-model based robust H_∞ controllers for discrete-time nonlinear systems: An BMI approach. / Liu, Meiqin; Yan, Gangfeng; Wang, Shouguang.
2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004. 2004. p. 5876-5881 (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics; Vol. 6).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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