Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free State-dependent intermittent control of non-linear systems

  • Author(s): Qingzhi Wang 1 ; Yong He 2, 3 ; Guanzheng Tan 1 ; Min Wu 2, 3
    • View affiliations
    • Affiliations: 1: School of Information Science and Engineering, Central South University, Changsha 410083, People's Republic of China ;
      2: Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, People's Republic of China ;
      3: School of Automation, China University of Geosciences, Wuhan 430074, People's Republic of China
  • Source: Volume 11, Issue 12, 11 August 2017, p. 1884 – 1893
    DOI:  10.1049/iet-cta.2016.1385 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 02/11/2016, Accepted 31/03/2017, Revised 17/03/2017, Published 04/04/2017

State-dependent intermittent control is presented to investigate the exponential stabilisation issue for a class of non-linear systems. The so-called state-dependent intermittent control means that whether control signals are imposed on a plant or not is related to system dynamics. Based on the concept, the mathematical description of a state-dependent intermittent controller is initially introduced. Then, in the framework of it, the globally exponential stability is analysed in detail for the deduced state-dependent intermittent control system with the pre-given state-dependent regions. It is worth mentioning that parameters in the pre-given state-dependent regions are tunable, which makes it flexible to design. Furthermore, a state-dependent intermittent controller can be designed for the concerned non-linear system according to the established exponential stabilisation criterion. Here, the designed state-dependent intermittent controller can not only avoid chattering effectively but also control switching frequency by adjusting values of parameters in the pre-given state-dependent regions. Finally, two examples are given to show the effectiveness and superiority of the proposed method.

Inspec keywords: nonlinear control systems; asymptotic stability; control system synthesis

Other keywords: nonlinear systems; deduced state-dependent intermittent control system; switching frequency; exponential stabilisation; control signals; system dynamics; globally exponential stability

Subjects: Stability in control theory; Control system analysis and synthesis methods; Nonlinear control systems

References

    1. 1)
      • 21. Hu, C., Yu, J., Jiang, H.J., et al: ‘Exponential synchronization for reaction-diffusion networks with mixed delays in terms of p-norm via intermittent driving’, IEEE Trans. Neural Netw., 2012, 31, pp. 1–11.
    2. 2)
      • 8. Huang, T.W., Li, C.D., Yu, W.W., et al: ‘Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback’, Nonlinearity, 2009, 22, (2), pp. 569–584.
    3. 3)
      • 25. Yang, F., Mei, J., Wu, Z.: ‘Finite-time synchronization of neural networks with discrete and distributed delays via periodically intermittent memory feedback control’, IET Control Theory Applic., 2016, 10, (14), pp. 1630–1640.
    4. 4)
      • 28. Zhu, H.B., Cui, B.T.: ‘Stabilization and synchronization of chaotic systems via intermittent control’, Commun. Nonlinear Sci. Numer. Simul., 2010, 15, (11), pp. 3577–3586.
    5. 5)
      • 14. Hu, C., Yu, J., Jiang, H.J., et al: ‘Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control’, Nonlinearity, 2010, 23, (10), pp. 2369–2391.
    6. 6)
      • 3. Wang, Q.Z., He, Y., Tan, G.Z., et al: ‘Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method’, Appl. Math. Comput., 2017, 293, pp. 438–447.
    7. 7)
      • 15. Liu, C., Li, C.D., Duan, S.K.: ‘Stabilization of oscillating neural networks with time-delay by periodically intermittent control’, Int. J. Control Autom. Syst., 2011, 9, (6), pp. 1074–1079.
    8. 8)
      • 6. Huang, T.W., Li, C.D.: ‘Chaotic synchronization by the intermittent feedback method’, J. Comput. Appl. Math., 2010, 234, (4), pp. 1097–1104.
    9. 9)
      • 13. Yuan, K., Cao, J.D., Fei, S.M.: ‘Synchronization of coupled networks with mixed delays by intermittent control’, IMA J. Appl. Math., 2012, 2012, p. 927609.
    10. 10)
      • 31. Petersen, I.R., Hollot, C.V.: ‘A Riccati equation to the stabilization of uncertain linear systems’, Automatica, 1986, 22, (4), pp. 397–411.
    11. 11)
      • 9. Wang, Y.J., Hao, J.N., Zuo, Z.Q.: ‘A new method for exponential synchronization of chaotic delayed systems via intermittent control’, Mod. Phys. Lett. A, 2010, 374, (19), pp. 2024–2029.
    12. 12)
      • 26. Liang, Y., Wang, X.Y.: ‘Synchronization in complex networks with non-delay and delay couplings via intermittent control with two switched periods’, Phys. A Stat. Mech. Appl., 2014, 395, pp. 434–444.
    13. 13)
      • 32. Liberzon, D.: ‘Switching in systems and control’ (Springer Science and Business Media, 2012).
    14. 14)
      • 4. Huang, J.J., Li, C.D., Huang, T.W., et al: ‘Lag quasi-synchronization of coupled delayed systems with parameter mismatch by periodically intermittent control’, Nonlinear Dyn., 2013, 71, (3), pp. 469–478.
    15. 15)
      • 33. Lin, H., Antsaklis, P.J.: ‘Stability and stabilizability of switched linear systems: a survey of recent results’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 308–322.
    16. 16)
      • 27. Li, Y., Li, C.D.: ‘Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period’, Neurocomputing, 2016, 173, pp. 1341–1347.
    17. 17)
      • 7. Lee, S.H., Kapila, V., Porfiri, M., et al: ‘Master-slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators’, Commun. Nonlinear Sci. Numer. Simul., 2010, 15, (12), pp. 4100–4113.
    18. 18)
      • 29. Song, Q.K., Huang, T.W.: ‘Stabilization and synchronization of chaotic systems with mixed time-varying delays via intermittent control with non-fixed both control period and control width’, Neurocomputing, 2015, 154, pp. 61–69.
    19. 19)
      • 24. Wang, Y.J., Hao, J.N., Zuo, Z.Q.: ‘Exponential synchronization of master-slave Lur'e systems via intermittent time-delay feedback control’, Commun. Theor. Phys., 2010, 54, (4), pp. 679–686.
    20. 20)
      • 11. Cai, S.M., Hao, J.J., Liu, Z.R.: ‘Exponential synchronization of chaotic systems with time-varying delays and parameter mismatches via intermittent control’, Chaos, 2011, 21, (2), p. 023112.
    21. 21)
      • 12. Pan, L.J., Cao, J.D.: ‘Stochastic quasi-synchronization for delayed dynamical networks via periodically intermittent control’, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, (3), pp. 1332–1343.
    22. 22)
      • 5. Chen, W.H., Zhong, J.C., Zheng, W.X.: ‘Delay-independent stabilization of a class of time-delay systems via periodically intermittent control’, Automatica, 2016, 71, pp. 89–97.
    23. 23)
      • 35. Wang, M., Zhao, J.: ‘Quadratic stabilization of a class of switched nonlinear systems via single Lyapunov function’, Nonlinear Anal. Hybrid Syst., 2010, 4, (1), pp. 44–53.
    24. 24)
      • 20. Zhao, M., Zhang, H.G., Wang, Z.L., et al: ‘Synchronization between two general complex networks with time-delay by adaptive periodically intermittent pinning control’, Neurocomputing, 2014, 144, pp. 215–221.
    25. 25)
      • 34. Pettersson, S., Lennartson, B.: ‘Stabilization of hybrid systems using a min-projection strategy’, Am. Control Conf., 2001, 1, pp. 223–228.
    26. 26)
      • 22. Wang, J.Y., Feng, J.W., Xu, C., et al: ‘Exponential synchronization of stochastic perturbed complex networks with time-varying delays via periodically intermittent pinning’, Commun. Nonlinear Sci. Numer. Simul., 2013, 18, (11), pp. 3146–3157.
    27. 27)
      • 19. Li, Y., Li, C.D.: ‘Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period’, Neurocomputing, 2016, 173, (3), pp. 1341–1347.
    28. 28)
      • 23. Hu, C., Yu, J., Jiang, H., et al: ‘Exponential synchronization of complex networks with finite distributed delays coupling’, IEEE Trans. Neural Netw., 2011, 22, (12), pp. 1999–2010.
    29. 29)
      • 16. Zhang, Z.M., He, Y., Zhang, C.K., et al: ‘Exponential stabilization of neural networks with time-varying delay by periodically intermittent control’, Neurocomputing, 2016, 207, pp. 469–475.
    30. 30)
      • 1. Żochowski, M.: ‘Intermittent dynamical control’, Phys. D Nonlinear Phenomena, 2000, 145, (3), pp. 181–190.
    31. 31)
      • 18. Huang, J.J., Li, C.D., Han, Q.: ‘Stabilization of delayed chaotic neural networks by periodically intermittent control’, Circuits Syst. Signal Process., 2009, 28, (4), pp. 567–579.
    32. 32)
      • 17. Zhang, W., Huang, J.J., Wei, P.C.: ‘Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control’, Appl. Math. Model., 2011, 35, (2), pp. 612–620.
    33. 33)
      • 2. Li, C.D., Feng, G., Liao, X.F.: ‘Stabilization of nonlinear systems via periodically intermittent control’, IEEE Trans. Circuits Syst. II Express Briefs, 2007, 54, (11), pp. 1019–1023.
    34. 34)
      • 10. Cai, S.M., Hao, L.L., He, Q.B., et al: ‘New results on synchronization of chaotic systems with time-varying delays via intermittent control’, Nonlinear Dyn., 2012, 67, (1), pp. 393–402.
    35. 35)
      • 30. Wang, Q.Z., He, Y., Tan, G.Z., et al: ‘Stabilization of linear systems via state-dependent intermittent control’. Proc. of the 35th Chinese Control Conf., 2016, pp. 1556–1561.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.1385
Loading

Related content

content/journals/10.1049/iet-cta.2016.1385
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address