Abstract
This paper studies the problem of guaranteed cost anti-windup stabilization of discrete delayed cellular neural networks. Saturation degree function is initially presented and the convex hull theory is applied to handle the saturated terms of discrete delayed cellular neural networks. Accordingly, after choosing a common quadratic performance function, the paper designs a guaranteed cost stabilization controller in the absence of input saturation on the basis of Lyapunov–Krasovskii theorem and linear matrix inequality formulation. Then a static state feedback anti-windup compensation is derived, which guarantee a guaranteed cost and the estimation of the asymptotic stability region for the closed-loop system. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed design technique.
Similar content being viewed by others
References
Wu F, Wang J, Fang X et al (2007) New developments in anti-windup control. Control Instrum Chem Ind 34(2):1–6
Xian J, Hong C, Ke W (2012) Dynamic anti-windup design for missile overload control system. Appl Mech Mater 236–237:273–277
Tingshu H, Teelb AR, Zaccarianc L (2008) Anti-windup synthesis for linear control systems with input saturation: achieving regional, nonlinear performance. Automatica 44(2):512–519
Mulder EF, Tiwari PY, Kothare MV (2009) Simultaneous linear anti-windup controller synthesis using multiobjective convex optimization. Automatica 45(1):805–811
Wang Q, Wang Y, Peng C, et al (2011) Two-step anti-windup control of helicopter. J Beijing Univ Aeronaut Astronaut 37(7):888–894, 900
Wu X, Lin Z (2014) Dynamic anti-windup design for anticipatory activation: enlargement of the domain of attraction. Sci China 1:164–177
Wu X, Lin Z (2014) Dynamic anti-windup design in anticipation of actuator saturation. Int J Robust Nonlinear Control 24(2):295–312
Biannic JM, Tarbouriech S (2009) Optimization and implementation of dynamic anti-windup compensators with multiple saturations in flight control systems. Control Eng Pract 17:703–713
Yan L, He H, Xiong P. (2014) Static anti-windup scheme for state linearizable nonlinear control systems with saturating inputs. In: Proceedings of the 33rd Chinese Control Conference, 7: 1783–1787
Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35(10):1257–1272
Sahin UA, Bayat C, Ucan ON (2011) Application of cellular neural network (CNN) to the prediction of missing air pollutant data. Atmos Res 101(1–2):314–326
Wang S, Fu D, Xu M et al (2007) Advanced fuzzy cellular neural network: application to CT liver images. Artif Intell Med 39(1):65–77
Ren X, Liao X, Xiong Y (2011) New image encryption algorithm based on cellular neural network. J Comput Appl 6:1528–1530
Jamrozik W (2014) Cellular neural networks for welding arc thermograms segmentation. Infrared Phys Technol 66:18–28
Sakthivel R, Anbuvithya R, Mathiyalagan K, Prakash P (2015) Combined \(H_{\infty }\) and passivity state estimation of memristive neural networks with random gain fluctuations. Neurocomputing 168:1111–1120
Mathiyalagan K, Su H, Shi P, Sakthivel R (2015) Exponential \(H_{\infty }\) filtering for discrete-time switched neural networks with random delays. IEEE Trans cybern 45:676–687
Mathiyalagan K, Sakthivel R, Anthoni SM (2011) New stability and stabilization criteria for fuzzy neural networks with various activation functions. Phys Scr 84:015007–015018
Chandrasekar A, Rakkiyappan R, Rihan FA, Lakshmanan S (2014) Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control. Neurocomputing 133:385–398
Balasubramaniam P, Lakshmanan S, Manivannan A (2012) Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays. Chaos Solitons Fractals 45(4):483–495
Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park JH, Jung HY (2013) Effects of leakage time-varying delays in Markovian jump neural networks with impulse control. Neurocomputing 121:365–378
Chang SSL, Peng TKC (1972) Adaptive guaranteed cost control of systems with uncertain parameters. IEEE Trans Autom Control 17(4):474–483
Kang Q, Wang W (2010) Guaranteed cost control for T-S fuzzy systems with time-varying delays. Control Theory Technol 8(4):413–417
Xie JS, Fan BQ, Lee YS, Yang J (2007) Guaranteed cost controller design of networked control systems with state delay. Acta Autom Sin 33(2):170–174
Yu L, Gao F (2001) Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays. J Frankl Inst 338:101–110
He H, Yan L, Tu J (2013) Guaranteed cost stabilization of cellular neural networks with time-varying delay. Asian J Control 15:1224–1227
He H, Yan L, Tu J (2012) Guaranteed cost stabilization of time-varying delay cellular neural networks via Riccati inequality approach. Neural Process Lett 35:151–158
Jiang M, He H, Xiong P (2015) Anti-windup for time-varying delayed cellular neural networks subject to input saturation. In: Fifth international conference on intelligent control and information processing, 18–20 Aug 2014, Dalian, Liaoning, China, pp 485–491
Gomes da Silva JM, Jr Tarbouriech S (2005) Anti-windup design with guaranteed regions of stability: an LMI- based approach. IEEE Trans Autom Control 50:106–111
Acknowledgements
The authors acknowledge the support of the National Natural Science Foundation of China (Grant No. 61374003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Some results from this paper were presented at \(5{\mathrm{th}}\) International Conference on Intelligent Control and Information Processing, ICICIP 2014.
Rights and permissions
About this article
Cite this article
He, H., Xu, W. & Jiang, M. Guaranteed Cost Anti-windup Stabilization of Discrete Delayed Cellular Neural Networks. Neural Process Lett 46, 343–354 (2017). https://doi.org/10.1007/s11063-017-9583-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-017-9583-9