Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations

Nana Wang; Nan Xie

doi:doi:10.11648/j.aas.20200504.12

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Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations

Nana Wang, Nan Xie

Published in Advances in Applied Sciences (Volume 5, Issue 4)

Received: 10 October 2020 Accepted: 23 October 2020 Published: 4 November 2020

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Abstract

Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.

Published in	Advances in Applied Sciences (Volume 5, Issue 4)
DOI	10.11648/j.aas.20200504.12
Page(s)	103-111
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Reliable Control, Guaranteed Cost Control, Time-delay, Actuator Failure, LMI

References

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[4]	L. Yu, F. Gao, Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays [J]. Journal of the Franklin Institute, 2001, 338 (1): 101-110.
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[7]	Q. X. Zhu, K. H. Lu, Y. H. Zhu, S. S. Hu. The guaranteed-cost controller design for networked-control system with markov delay [J]. Aerospace Control, 2014, 32 (04): 3-7.
[8]	J. Song. Fault-Tolerant control of networked control systems with time-varying actuator fault [J]. Aerospace Control, 2016, 34 (05): 3-8.
[9]	X. Z. Liu. Research on fault toleran control of networked control systems [D]. Beijing institute of technology, 2016.
[10]	Q. Zhu, K. Lu, G. M. Xie, et al. Guaranteed cost fault-tolerant control for networked control systems with sensor faults [J]. Mathematical Problems in Engineering, 2015, 2015.
[11]	P. P. Yao, X. J. Fu. Reliable guaranteed cost control for a class of nonlinear uncertain time-delay systems [J]. Computing Technology and Automation, 2017, 36 (01): 1-5.
[12]	S. Deng, L. C. Yang. Reliable H∞ control design of discrete-time Takagi-Sugeno fuzzy systems with actuator faults [J]. Neurocomputing, 2016, 173 (3): 1784-1788.
[13]	J. S. Zhang, Y. W. Wang, J. W. Xiao, et al. Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure [J]. International Journal of Systems Science, 2016, 47 (4): 946-955.
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[16]	S. Q. Zou, H. Yan, L. Zhang. Reliable static output feedback guaranteed cost control for uncertain systems with time-delay [C]. In: Chinese Intelligent Automation Conference. Springer, Singapore, 2017, 458: 407-413.
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APA Style

Nana Wang, Nan Xie. (2020). Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Advances in Applied Sciences, 5(4), 103-111. https://doi.org/10.11648/j.aas.20200504.12

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ACS Style

Nana Wang; Nan Xie. Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Adv. Appl. Sci. 2020, 5(4), 103-111. doi: 10.11648/j.aas.20200504.12

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AMA Style

Nana Wang, Nan Xie. Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Adv Appl Sci. 2020;5(4):103-111. doi: 10.11648/j.aas.20200504.12

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@article{10.11648/j.aas.20200504.12,
  author = {Nana Wang and Nan Xie},
  title = {Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations},
  journal = {Advances in Applied Sciences},
  volume = {5},
  number = {4},
  pages = {103-111},
  doi = {10.11648/j.aas.20200504.12},
  url = {https://doi.org/10.11648/j.aas.20200504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20200504.12},
  abstract = {Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.},
 year = {2020}
}

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TY  - JOUR
T1  - Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations
AU  - Nana Wang
AU  - Nan Xie
Y1  - 2020/11/04
PY  - 2020
N1  - https://doi.org/10.11648/j.aas.20200504.12
DO  - 10.11648/j.aas.20200504.12
T2  - Advances in Applied Sciences
JF  - Advances in Applied Sciences
JO  - Advances in Applied Sciences
SP  - 103
EP  - 111
PB  - Science Publishing Group
SN  - 2575-1514
UR  - https://doi.org/10.11648/j.aas.20200504.12
AB  - Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.
VL  - 5
IS  - 4
ER  -

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Author Information

Nana Wang

College of Computer Science and Technology, Shandong University of Technology, Zibo, China
Nan Xie

College of Computer Science and Technology, Shandong University of Technology, Zibo, China

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APA Style

Nana Wang, Nan Xie. (2020). Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Advances in Applied Sciences, 5(4), 103-111. https://doi.org/10.11648/j.aas.20200504.12

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ACS Style

Nana Wang; Nan Xie. Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Adv. Appl. Sci. 2020, 5(4), 103-111. doi: 10.11648/j.aas.20200504.12

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AMA Style

Nana Wang, Nan Xie. Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Adv Appl Sci. 2020;5(4):103-111. doi: 10.11648/j.aas.20200504.12

Copy | Download

@article{10.11648/j.aas.20200504.12,
  author = {Nana Wang and Nan Xie},
  title = {Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations},
  journal = {Advances in Applied Sciences},
  volume = {5},
  number = {4},
  pages = {103-111},
  doi = {10.11648/j.aas.20200504.12},
  url = {https://doi.org/10.11648/j.aas.20200504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20200504.12},
  abstract = {Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations
AU  - Nana Wang
AU  - Nan Xie
Y1  - 2020/11/04
PY  - 2020
N1  - https://doi.org/10.11648/j.aas.20200504.12
DO  - 10.11648/j.aas.20200504.12
T2  - Advances in Applied Sciences
JF  - Advances in Applied Sciences
JO  - Advances in Applied Sciences
SP  - 103
EP  - 111
PB  - Science Publishing Group
SN  - 2575-1514
UR  - https://doi.org/10.11648/j.aas.20200504.12
AB  - Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.
VL  - 5
IS  - 4
ER  -

Copy | Download