Geodesic
A tracking controller design with preview action for a class of nonlinear Lur'e systems with time-varying delays and external disturbances
Kybernetika, Tome 57 (2021) no. 1, pp. 78-101
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In this paper, the tracking control problem for a class of discrete-time nonlinear Lur'e systems with time-varying delays and external disturbances is studied via a preview control method. First, a novel translation approach is introduced to construct the augmented error system for Lur'e systems. The output tracking problem is thereby transformed into a guaranteed cost $H_\infty$ controller design problem. To produce an integral control action that can eliminate the static error, a discrete integrator is included. Next, a memory state feedback controller is developed, and the sufficient conditions for asymptotic stability and guaranteed cost $H_\infty$ performance of the closed-loop system are established by applying a suitable Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique. Based on this, the tracking control scheme with preview action for the original system is presented. Finally, the effectiveness of our proposed control method is illustrated via a numerical example.
In this paper, the tracking control problem for a class of discrete-time nonlinear Lur'e systems with time-varying delays and external disturbances is studied via a preview control method. First, a novel translation approach is introduced to construct the augmented error system for Lur'e systems. The output tracking problem is thereby transformed into a guaranteed cost $H_\infty$ controller design problem. To produce an integral control action that can eliminate the static error, a discrete integrator is included. Next, a memory state feedback controller is developed, and the sufficient conditions for asymptotic stability and guaranteed cost $H_\infty$ performance of the closed-loop system are established by applying a suitable Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique. Based on this, the tracking control scheme with preview action for the original system is presented. Finally, the effectiveness of our proposed control method is illustrated via a numerical example.
DOI : 10.14736/kyb-2021-1-0078
Classification : 93Cxx, 93Dxx
Keywords: tracking control; preview control; nonlinear Lur'e system; linear matrix inequality 
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Yu, Xiao; Liao, Fucheng. A tracking controller design with preview action for a class of nonlinear Lur'e systems with time-varying delays and external disturbances. Kybernetika, Tome 57 (2021) no. 1, pp. 78-101. doi: 10.14736/kyb-2021-1-0078

[1] Açikmeşe, B., Corless, M.: Stability analysis with quadratic Lyapunov functions: Some necessary and sufficient multiplier conditions. Systems Control Lett. 57 (2008), 1, 78-94. | DOI | MR

[2] Birla, N., Swarup, A.: Optimal preview control: A review. Optim. Control Appl. Meth. 36(2015), 2, 241-268. | DOI | MR

[3] Boyd, S., Ghaoui, L. E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, 1994. | DOI | MR | Zbl

[4] Cao, J., Sivasamy, R., Rakkiyappan, R.: Sampled-data $H_\infty$ synchronization of chaotic Lur'e systems with time delay. Circuits Syst. Signal Process. 35 (2016), 3, 811-835. | DOI | MR

[5] Chen, J., Park, J. H.: New versions of Bessel-Legendre inequality and their applications to systems with time-varying delay. Appl. Math. Comput. 375 (2020), 15, 125060. | DOI | MR

[6] Chua, L., Yang, L.: Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35 (1988), 10, 1257-1272. | DOI | MR

[7] Delellis, P., Bernardo, M. di, Garofalo, F.: Adaptive pinning control of networks of circuits and systems in Lur'e form. IEEE Trans. Circuits Syst. -I: Reg. Papers 60 (2013), 11, 3033-3042. | DOI

[8] Guzelis, C., Chua, L.: Stability analysis of generalized celluar neural networks. Int. J. Circuit Theory Appl. 21 (1993), 1, 1-33. | DOI

[9] Gyurkovics, E.: Guaranteed cost control of discrete-time uncertain systems with both state and input delays. Int. J. Control 89 (2016), 10, 2073-2082. | DOI | MR

[10] Huang, H., Feng, G., Cao, J.: Exponential synchronization of chaotic Lur'e systems with delayed feedback control. Nonlinear Dyn. 57 (2009), 441-453. | DOI | MR

[11] Katayama, T., Hirono, T.: Design of an optimal servomechanism with preview action and its dual problem. Int. J. Control 45 (1987), 2, 407-420. | DOI

[12] Katayama, T., Ohki, T., Inoue, T., Kato, T.: Design of an optimal controller for a discrete-time system subject to previewable demand. Int. J. Control 41 (1985), 3, 677-699. | DOI | MR

[13] Khalil, H. K.: Nonlinear Systems. Prentice Hall: Upper Saddle River, New Jersey, 2002. | Zbl

[14] Kim, K. K. K., Braatz, R. D.: Observer-based output feedback control of discrete-time Lur's systems with sector-bounded and slope-restricted nonlinearities. Int. J. Robust Nonlinear Control 24 (2014), 16, 2458-2472. | DOI | MR

[15] Kim, K. K. K., Braatz, R. D.: Robust static and fixed-order dynamic output feedback control of discrete-time parametric uncertain Lur's systems: Sequential SDP relaxation approaches. Optim. Control Appl. Meth. 38 (2017), 1, 36-58. | DOI | MR

[16] Kojima, A.: $H_\infty$ controller design for preview and delayed systems. IEEE Trans. Autom. Control 60 (2015), 2, 404-419. | DOI | MR

[17] Lee, T. H., Park, J. H.: Improved criteria for sampled-data synchronization of chaotic Lur'e systems using two new approaches. Nonlinear Anal. Hybrid Syst.24 (2017), 132-145. | DOI | MR

[18] Li, C., Chen, L., Aihara, K.: Synchronization of coupled nonidentical genetic oscillators. Phys. Biol. 3 (2006), 1, 37-44. | DOI

[19] Li, Z., Duan, Z., Chen, G.: Global synchronised regions of linearly coupled Lur'e systems. Int. J. Control 84 (2011), 2, 216-227. | DOI | MR

[20] Liao, F., Cao, M., Hu, Z., An, P.: Design of an optimal preview controller for linear discrete-time causal descriptor systems. Int. J. Control 85 (2012), 10, 1616-1624. | DOI | MR

[21] Liao, F., Ren, Z., Tomizuka, M., Wu, J.: Preview control for impulse-free continuous-time descriptor systems. Int. J. Control 88 (2015), 6, 1142-1149. | DOI | MR

[22] Liu, Y., Lee, S.M.: Synchronization of chaotic Lur'e systems using sampled-data PD control. Nonlinear Dyn. 85 (2016), 2, 981-992. | DOI | MR

[23] Liu, Y., Lee, S. M.: Synchronization criteria of chaotic Lur'e systems with delayed feedback PD control. Neurocomputing 189 (2016), 66-71. | DOI

[24] Liu, M., Li, Z.: Robust consensus of Lur'e networks with uncertain communications. IET Control Theory Appl. 11 (2017), 6, 877-882. | DOI | MR

[25] Liu, W., Wang, Y.: Robust observer-based absolute stabilization for Lur'e singularly perturbed systems with state delay. ISA Trans. 65 (2016), 1-8. | DOI | MR

[26] Madan, R. N.: Chua's Circuit: A Paradigm for Chaos. World Scientific, 1993. | DOI | MR

[27] Matsumoto, T.: A chaotic attractor from Chua's circuit. IEEE Trans. Circuits Syst. CAS 31 (1984), 12, 1055-1058. | DOI | MR

[28] Nasiri, A., Nguang, S. K., Swain, A., Almakhles, D. J.: Robust output feedback controller design of discrete-time Takagi-Sugeno fuzzy systems: a non-monotonic Lyapunov approach. IET Control Theory Appl. 10 (2016), 5, 545-553. | DOI | MR

[29] Park, J. H., Ji, D. H., Won, S. C., Lee, S. M., Choi, S. J.: $H_\infty$ control of Lur'e systems with sector and slope restricted nonlinearities. Phys. Lett. A 373 (2009), 41, 3734-3740. | DOI | MR

[30] Park, J. H., Lee, T. H., Liu, Y., Chen, J.: Dynamic Systems with Time Delays: Stability and Control. Springer-Nature, 2019. | DOI | MR

[31] Sheridan, T. B.: Three models of preview control. IEEE Trans. on Human Factors in Electronics HFE 7 (1966), 2, 91-102. | DOI

[32] Song, Q., Liu, F., Cao, J., Lu, J.: Some simple criteria for pinning a Lur'e network with directed topology. IET Control Theory Appl. 8 (2014), 2, 131-138. | DOI | MR

[33] Takaba, K.: Robust servomechanism with preview action for polytopic uncertain systems. Int. J. Robust Nonlinear Control 10 (2000), 2, 101-111. | DOI | MR

[34] Tang, Z., Park, J. H., Wang, Y., Zheng, W. X.: Synchronization on Lur'e cluster networks with proportional delay: impulsive effects method. IEEE Trans. Syst., Man, Cybern., Syst. 2019. | DOI

[35] Tomizuka, M., Rosenthal, D. E.: On the optimal digital state vector feedback controller with integral and preview actions. ASME J. Dyn. Sys. Meas. Control 101 (1979), 2, 172-178. | DOI

[36] Tsuchiya, T., Egami, T.: Digital Preview and Predictive Control. Beijing Science and Technology, Beijing, 1994.

[37] Xia, J., Park, J. H., Lee, T. H., Zhang, B.: $H_\infty$ tracking of uncertain stochastic time-delay systems: memory state-feedback controller design. Appl. Math. Comput. 249 (2014), 356-370. | MR

[38] Yin, C., Zhong, S., Liu, X.: Novel delay-dependent stabilization criterion for Lur'e systems with sector-restricted nonlinearities and external disturbances via PD feedback approach. J. Optim. Theory Appl. 151 (2011), 1, 81-99. | DOI | MR

[39] Yu, X., Li, L.: Trajectory tracking control with preview action for a class of continuous-time Lur'e-type nonlinear systems. Adv. Differ. Equ. 293 (2020), 1-17. | DOI | MR

[40] Yu, X., Liao, F.: Preview tracking control for discrete-time nonlinear Lur'e systems with sector-bounded nonlinearities. Trans. Inst. Meas. Control 41 (2019), 10, 2726-2737. | DOI

[41] Zhang, F., Trentelman, H. L., Feng, G., Scherpen, J. M. A.: Absolute stabilization of Lur'e systems via dynamic output feedback. Eur. J. Control 44(2018), 15-26. | DOI | MR

[42] Zhao, Y., Duan, Z., Wen, G.: Robust consensus tracking of multi-agent systems with uncertain Lur'e-type non-linear dynamics. IET Control Theory Appl. 7 (2013), 9, 1249-1260. | DOI | MR

[43] Zhen, Z.: Research development in preview control theory and applications. Acta Autom. Sin. 42 (2016), 2, 172-188.

[44] Zhu, X., Zhang, H., Xi, J.: Robust speed synchronization control for clutchless automated manual transmission systems in electric vehicles. Proc. IMechE. Part D: J. Automobile Engineering 229 (2015), 4, 424-436. | DOI

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