Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

doi:10.21629/JSEE.2019.06.18

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (6): 1243-1251.doi: 10.21629/JSEE.2019.06.18

• Control Theory and Application • Previous Articles Next Articles

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

Sen WANG(), Xuhui BU*(), Jiaqi LIANG()

School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China

Received:2018-11-12 Online:2019-12-20 Published:2019-12-25
Contact: Xuhui BU E-mail:wangsmmm@126.com;buxuhui@gmail.com;1459485470@qq.com
About author:WANG Sen was born in 1994. He received his bachelor's degree in automation control from the School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China, in 2016. He is currently pursuing his master's degree in control science and engineering with the School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China. His current research interests include two-dimensional system theory, network control systems. E-mail: wangsmmm@126.com|BU Xuhui was born in 1981. received his bachelor's and master's degree in automation control from Henan Polytechnic University, Jiaozuo, China, in 2004 and 2007, respectively, and Ph.D. degree in control thoery and application from Beijing Jiaotong University, Beijing, China, in 2011. He is currently an associate professor in Henan Polytechnic University, Jiaozuo, China. He has authored over 50 peerreviewed journal papers and over 20 papers in prestigious conference proceedings. His research interests include data-driven control, iterative learning control, traffic control and networked system control. E-mail: buxuhui@gmail.com|LIANG Jiaqi was born in 1992. She is currently a doctor graduate student in mining control engineering, with Henan Polytechnic University, Jiaozuo, China. She received her bachelor's degree in computer science and technology from Henan University of Science and Technology and master's degree in control science and engineering from Henan Polytechnic University, in 2014 and 2018, respectively. Her research interests include iterative learning control, mulit-agent systems control. E-mail: 1459485470@qq.com
Supported by:
the National Natural Science Foundation of China(61573129);the National Natural Science Foundation of China(U1804147);the Innovative Scientists and Technicians Team of Henan Provincial High Education(20IRTSTHN019);the Innovative Scientists and Technicians Team of Henan Polytechnic University(T2019-2);the Innovative Scientists and Technicians Team of Henan Polytechnic University(T2017-1);This work was supported by the National Natural Science Foundation of China (61573129; U1804147), the Innovative Scientists and Technicians Team of Henan Provincial High Education (20IRTSTHN019), and the Innovative Scientists and Technicians Team of Henan Polytechnic University (T2019-2; T2017-1)

Abstract

Abstract:

An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional (2-D) discrete-time systems. Firstly, an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities. Then, according to the Lyapunov functional method, the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given. Furthermore, based on the sufficient conditions and the linear matrix inequality (LMI) technique, the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI. Finally, a numerical example is given to demonstrate that, under the proposed event-triggered robust guaranteed cost control, the closed-loop system is asymptotically stable and fewer communication resources are occupied.

CLC Number:

Sen WANG, Xuhui BU, Jiaqi LIANG. Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems[J]. Journal of Systems Engineering and Electronics, 2019, 30(6): 1243-1251.

Figures/Tables 10

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Table 1

References 25

1	LU M C, HSU C C, YU Y L. Image-based system for measuring objects on an oblique plane and its applications in 2-D localization. IEEE Sensors Journal, 2012, 12 (6): 2249- 2261. doi: 10.1109/JSEN.2012.2186438
2	AHN C K, SHI P, BASIN M V. Two-dimensional dissipative control and filtering for Roesser model. IEEE Trans. on Automatic Control, 2015, 60 (7): 1745- 1759. doi: 10.1109/TAC.2015.2398887
3	SONG H F, LIU J M, LIU B, et al. Two-dimensional materials for thermal management applications. Joule, 2018, 2 (3): 442- 463. doi: 10.1016/j.joule.2018.01.006
4	YE S X, WANG W Q. Stability analysis and stabilisation for a class of 2-D nonlinear discrete systems. International Journal of Systems Science, 2011, 42 (5): 839- 851. doi: 10.1080/00207721.2010.518255
5	HUANG S P, XIANG Z R. Delay-dependent robust H-infinity control for 2-D discrete nonlinear systems with state delays. Multidimensional Systems and Signal Processing, 2014, 25 (4): 775- 794. doi: 10.1007/s11045-013-0230-y
6	BU X H, WANG H Q, HOU Z S, et al. Stabilisation of a class of two-dimensional nonlinear systems with intermittent measurements. IET Control Theory and Applications, 2014, 8 (15): 1596- 1604. doi: 10.1049/iet-cta.2014.0170
7	BU X H, WANG H Q, HOU Z S, et al. H$\infty$ control for a class of 2-D nonlinear systems with intermittent measurements. Applied Mathematics and Computation, 2014, 247, 651- 662. doi: 10.1016/j.amc.2014.08.107
8	KOKIL P. An improved criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities. Circuits, Systems and Signal Processing, 2017, 36 (6): 2209- 2222. doi: 10.1007/s00034-016-0397-1
9	XU H, ZOU Y, LU J, et al. Robust control for a class of uncertain nonlinear two-dimensional systems with state delays. Journal of the Franklin Institute, 2005, 342 (7): 877- 891. doi: 10.1016/j.jfranklin.2005.07.003
10	KHALIL H K. Nonlinear systems. New Jersey: Prentice Hall, 2002.
11	DHAWAN A, KAR H. LMI-based criterion for the robust guaranteed cost control of 2-D systems described by the Fornasini-Marchesini second model. Signal Processing, 2007, 87 (3): 479- 488. doi: 10.1016/j.sigpro.2006.06.002
12	DHAWAN A, KAR H. An LMI approach to robust optimal guaranteed cost control of 2-D discrete systems described by the Roesser model. Signal Processing, 2010, 90 (9): 2648- 2654. doi: 10.1016/j.sigpro.2010.03.008
13	XU J M, YU L. Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model. Journal of the Franklin Institute, 2009, 346 (2): 159- 174. doi: 10.1016/j.jfranklin.2008.08.003
14	PENG D, GUAN X P, LONG C N. Robust output feedback guaranteed cost control for 2-D uncertain state-delayed systems. Asian Journal of Control, 2007, 9 (4): 470- 474.
15	ARZEN K E. A simple event-based PID controller. Proc. of 14th IFAC World Congress, 1999, 18, 423- 428.
16	ASTROM K J, BERNHARDSSON B. Comparison of periodic and event based sampling for first order stochastic systems. Proc. of the 14th IFAC World Congress, 1999: 301-306.
17	LUNZE J, LEHMANN D. A state-feedback approach to event-based control. Automatica, 2010, 46 (1): 211- 215. doi: 10.1016/j.automatica.2009.10.035
18	HEEMEL W, SANDEE J H, VAN D B. Analysis of event-driven controllers for linear systems. International Journal of Control, 2008, 81 (4): 571- 590. doi: 10.1080/00207170701506919
19	WANG X, LEMMON M D. Event-triggering in distributed networked control systems. IEEE Trans. on Automatic Control, 2011, 56 (3): 586- 601. doi: 10.1109/TAC.2010.2057951
20	YUE D, TIAN E, HAN Q L. A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. on Automatic Control, 2013, 58 (2): 475- 481. doi: 10.1109/TAC.2012.2206694
21	HU S, YIN X, ZHANG Y, et al. Event-triggered guaranteed cost control for uncertain discrete-time networked control systems with time-varying transmission delays. IET Control Theory and Applications, 2012, 6 (18): 2793- 2804. doi: 10.1049/iet-cta.2012.0036
22	YAN H C, ZHANG H, YANG F, et al. Event-triggered asynchronous guaranteed cost control for Markov jump discrete-time neural networks with distributed delay and channel fading. IEEE Trans. on Neural Networks and Learning Systems, 2018, 29(8): 3588-3598.
23	PENG C, HAN Q L. A novel event-triggered transmission scheme and L-2 control co-design for sampled-data control systems. IEEE Trans. on Automatic Control, 2013, 58(10): 2620-2626.
24	PENG C, YANG T C. Event-triggered communication and H$\infty $ control co-design for networked control systems. Automatica, 2013, 49 (5): 1326- 1332. doi: 10.1016/j.automatica.2013.01.038
25	BARMISH B R. Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. Journal of Optimization Theory and Applications, 1985, 46 (4): 399- 408. doi: 10.1007/BF00939145

$\gamma $	0	0.2	0.4	0.6	0.8
Nh	1 600	800	531	469	390
Nv	1 600	653	520	400	324
Rh	100%	50%	33.19%	29.31%	24.38%
Rv	100%	40.81%	32.5%	25%	20.25%

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 10

References 25

Related Articles 0

Recommended Articles

Metrics

Comments