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Event-Triggered Sliding Mode Control Strategies for a Class of Nonlinear Uncertain Systems

  • Antonella Ferrara
  • Michele CucuzzellaEmail author
Chapter

Abstract

This chapter presents novel Sliding Mode Control (SMC) strategies of Event-Triggered (ET) type for a class of nonlinear systems affected by uncertainties and external disturbances. By virtue of its ET nature, the proposed control strategies are particularly appropriate for Networked Control Systems (NCSs), i.e., feedback systems including communication networks. The objective of the proposed control schemes is indeed to reduce the number of data transmissions over the communication network, in order to avoid problems typically due to the network congestion such as jitter and packet loss. In particular, an ET-SMC scheme and an ET Second Order SMC (ET-SOSMC) scheme are designed for a class of nonlinear uncertain NCSs, guaranteeing satisfactory performance of the controlled system even in presence of delayed transmissions. The proposed control schemes are theoretically analyzed in this chapter, showing their capability of enforcing the robust ultimate boundedness of the sliding variable associated with the controlled system, and also of its first time derivative in case of ET-SOSMC. Moreover, in order to guarantee the avoidance of the notorious Zeno behaviour, the existence of a lower bound for the time elapsed between consecutive triggering events is proven.

References

  1. 1.
    Alur, R., Arzen, K.E., Baillieul, J., Henzinger, T., Hristu-Varsakelis, D., Levine, W.S.: Handbook of Networked and Embedded Control Systems. Springer Science & Business Media. Birkhäuser, Boston (2007)Google Scholar
  2. 2.
    Ames, A.D., Tabuada, P., Sastry, S.: On the stability of zeno equilibria. In: International Workshop on Hybrid Systems: Computation and Control, pp. 34–48. Springer, Berlin (2006)Google Scholar
  3. 3.
    Aström, K.J.: Event based control. In: Analysis and Design of Nonlinear Control Systems, pp. 127–147. Springer, Berlin (2008)Google Scholar
  4. 4.
    Bartolini, G., Ferrara, A., Usai, E.: Output tracking control of uncertain nonlinear second-order systems. Automatica 33(12), 2203–2212 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bartolini, G., Ferrara, A., Pisano, A., Usai, E.: Adaptive reduction of the control effort in chattering-free sliding-mode control of uncertain nonlinear systems. Appl. Math. Comput. Sci. 8(1), 51–71 (1998)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Bartolini, G., Ferrara, A., Usai, E.: Chattering avoidance by second-order sliding mode control. IEEE Trans. Autom. Control 43(2), 241–246 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bartolini, G., Ferrara, A., Usai, E.: On boundary layer dimension reduction in sliding mode control of siso uncertain nonlinear systems. In: Proceedings of the 1998 IEEE International Conference on Control Applications, 1998, vol. 1, pp. 242–247. IEEE (1998)Google Scholar
  8. 8.
    Bartolini, G., Ferrara, A., Levant, A., Usai, E.: On second order sliding mode controllers. Variable Structure Systems. Sliding Mode and Nonlinear Control, pp. 329–350. Springer, Berlin (1999)Google Scholar
  9. 9.
    Bartolini, G., Ferrara, A., Usai, E., Utkin, V.I.: On multi-input chattering-free second-order sliding mode control. IEEE Trans. Autom. Control 45(9), 1711–1717 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Behera, A.K., Bandyopadhyay, B.: Event based sliding mode control with quantized measurement. In: 2015 International Workshop on Recent Advances in Sliding Modes (RASM), pp. 1–6. IEEE (2015)Google Scholar
  11. 11.
    Behera, A.K., Bandyopadhyay, B.: Event-triggered sliding mode control for a class of nonlinear systems. Int. J. Control 89(9), 1916–1931 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Behera, A.K., Bandyopadhyay, B., Xavier, N., Kamal, S.: Event-triggered sliding mode control for robust stabilization of linear multivariable systems. In: Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics, pp. 155–175. Springer, Berlin (2015)Google Scholar
  13. 13.
    Boiko, I.M.: Analysis of chattering in sliding mode control systems with continuous boundary layer approximation of discontinuous control. In: American Control Conference (ACC), 2011, pp. 757–762. IEEE (2011)Google Scholar
  14. 14.
    Boiko, I., Fridman, L., Pisano, A., Usai, E.: Analysis of chattering in systems with second-order sliding modes. IEEE Trans. Autom. Control 52(11), 2085–2102 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Buttazzo, G., Cervin, A.: Comparative assessment and evaluation of jitter control methods. In: Proceedings of the 15th conference on Real-Time and Network Systems, pp. 163–172 (2007)Google Scholar
  16. 16.
    Cucuzzella, M., Incremona, G.P., Ferrara, A.: Design of robust higher order sliding mode control for microgrids. IEEE J. Emerg. Sel. Top. Circuits Syst. 5(3), 393–401 (2015)Google Scholar
  17. 17.
    Cucuzzella, M., Incremona, G.P., Ferrara, A.: Master-slave second order sliding mode control for microgrids. In: American Control Conference (ACC), 2015, pp. 5188–5193. IEEE (2015)Google Scholar
  18. 18.
    Cucuzzella, M., Incremona, G.P., Ferrara, A.: Third order sliding mode voltage control in microgrids. In: 2015 European Control Conference (ECC), pp. 2384–2389. IEEE (2015)Google Scholar
  19. 19.
    Cucuzzella, M., Ferrara, A.: Event-triggered second order sliding mode control of nonlinear uncertain systems. In: 2016 European Control Conference (ECC), pp. 295–300. IEEE (2016)Google Scholar
  20. 20.
    Cucuzzella, M., Incremona, G.P., Ferrara, A.: Event-triggered sliding mode control algorithms for a class of uncertain nonlinear systems: experimental assessment. In: American Control Conference (ACC), 2016, pp. 6549–6554. IEEE (2016)Google Scholar
  21. 21.
    Cucuzzella, M., Incremona, G.P., Guastalli, M., Ferrara, A.: Sliding mode control for maximum power point tracking of photovoltaic inverters in microgrids. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 7294–7299. IEEE (2016)Google Scholar
  22. 22.
    Cucuzzella, M., Rosti, S., Cavallo, A., Ferrara, A.: Decentralized sliding mode voltage control in DC microgrids. In: Proceedings of the American Control Conference (2017)Google Scholar
  23. 23.
    Cucuzzella, M., Trip, S., De Persis, C., Ferrara, A.: Distributed second order sliding modes for optimal load frequency control. In: Proceeding of the American Control Conference (2017)Google Scholar
  24. 24.
    Demirel, B., Gupta, V., Johansson, M.: On the trade-off between control performance and communication cost for event-triggered control over lossy networks. In: 2013 European Control Conference (ECC), pp. 1168–1174. IEEE (2013)Google Scholar
  25. 25.
    Dinuzzo, F., Ferrara, A.: Finite-time output stabilization with second order sliding modes. Automatica 45(9), 2169–2171 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Dinuzzo, F., Ferrara, A.: Higher order sliding mode controllers with optimal reaching. IEEE Trans. Autom. Control 54(9), 2126–2136 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. CRC Press, Boca Raton (1998)zbMATHGoogle Scholar
  28. 28.
    Ferrara, A., Incremona, G.P., Magni, L.: Model-based event-triggered robust MPC/ISM. In: 2014 European Control Conference (ECC), pp. 2931–2936. IEEE (2014)Google Scholar
  29. 29.
    Ferrara, A., Sacone, S., Siri, S.: Event-triggered strategies for the networked control of freeway traffic systems. In: 2014 European Control Conference (ECC), pp. 2594–2599. IEEE (2014)Google Scholar
  30. 30.
    Ferrara, A., Sacone, S., Siri, S.: Design of networked freeway traffic controllers based on event-triggered control concepts. International Journal of Robust and Nonlinear Control (2015)Google Scholar
  31. 31.
    Ferrara, A., Sacone, S., Siri, S.: Event-triggered model predictive schemes for freeway traffic control. Trans. Res. Part C: Emerg. Technol. 58, 554–567 (2015)CrossRefGoogle Scholar
  32. 32.
    Ferrara, A., Sacone, S., Siri, S.: Model-based event-triggered control for freeway traffic systems. In: 2015 International Conference on Event-based Control, Communication, and Signal Processing (EBCCSP), pp. 1–6. IEEE (2015)Google Scholar
  33. 33.
    Fridman, L.: The problem of Chattering: an Averaging Approach. Variable Structure Systems, Sliding Mode and Nonlinear Control, pp. 363–386. Berlin, Berlin (1999)Google Scholar
  34. 34.
    Fridman, L., Levant, A.: Higher order sliding modes. Sliding Mode Control Eng. 11, 53–102 (2002)Google Scholar
  35. 35.
    Garcia, E., Antsaklis, P.J.: Model-based event-triggered control with time-varying network delays. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 1650–1655. IEEE (2011)Google Scholar
  36. 36.
    Gupta, R.A., Chow, M.Y.: Networked control system: overview and research trends. IEEE Trans. Ind. Electron. 57(7), 2527–2535 (2010)CrossRefGoogle Scholar
  37. 37.
    Heemels, W., Sandee, J., Van Den Bosch, P.: Analysis of event-driven controllers for linear systems. Int. J. Control 81(4), 571–590 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Heemels, W., Johansson, K.H., Tabuada, P.: An introduction to event-triggered and self-triggered control. In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), pp. 3270–3285. IEEE (2012)Google Scholar
  39. 39.
    Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)CrossRefGoogle Scholar
  40. 40.
    Incremona, G.P., Cucuzzella, M., Ferrara, A.: Adaptive suboptimal second-order sliding mode control for microgrids. Int. J. Control 89(9), 1849–1867 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Incremona, G.P., Ferrara, A.: Adaptive model-based event-triggered sliding mode control. Int. J. Adapt. Control Signal Process. 30(8–10), 1099–1117 (2016)MathSciNetzbMATHGoogle Scholar
  42. 42.
    Incremona, G.P., Cucuzzella, M., Magni, L., Ferrara, A.: MPC with sliding mode control for the energy management system of microgrids. In: Proceedings of the 20th IFAC World Congress IFAC, 7658–7663 (2017)Google Scholar
  43. 43.
    Johansson, K.H., Lygeros, J., Sastry, S., Egerstedt, M.: Simulation of zeno hybrid automata. In: Proceedings of the 38th IEEE Conference on Decision and Control, 1999, vol. 4, pp. 3538–3543. IEEE (1999)Google Scholar
  44. 44.
    Ke-You, Y., Li-Hua, X.: Survey of recent progress in networked control systems. Acta Autom. Sin. 39(2), 101–117 (2013)MathSciNetGoogle Scholar
  45. 45.
    Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River (1996)Google Scholar
  46. 46.
    La Salle, J., Lefschetz, S.: Stability by Liapunov’s Direct Method with Applications by Joseph L Salle and Solomon Lefschetz, vol. 4. Elsevier, Academic Press, New York (2012)Google Scholar
  47. 47.
    Liu, G.P., Xia, Y., Chen, J., Rees, D., Hu, W.: Networked predictive control of systems with random network delays in both forward and feedback channels. IEEE Trans. Ind. Electron. 54(3), 1282–1297 (2007)CrossRefGoogle Scholar
  48. 48.
    Luck, R., Ray, A.: An observer-based compensator for distributed delays. Automatica 26(5), 903–908 (1990)CrossRefzbMATHGoogle Scholar
  49. 49.
    Mazo, M., Tabuada, P.: On event-triggered and self-triggered control over sensor/actuator networks. In: CDC 2008. 47th IEEE Conference on Decision and Control, 2008, pp. 435–440. IEEE (2008)Google Scholar
  50. 50.
    Montestruque, L.A., Antsaklis, P.: Stability of model-based networked control systems with time-varying transmission times. IEEE Trans. Autom. Control 49(9), 1562–1572 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Nilsson, J., Bernhardsson, B.: Analysis of real-time control systems with time delays. In: Proceedings of the 35th IEEE Conference on Decision and Control, 1996, vol. 3, pp. 3173–3178. IEEE (1996)Google Scholar
  52. 52.
    Rubagotti, M., Ferrara, A.: Second order sliding mode control of a perturbed double integrator with state constraints. In: American Control Conference (ACC), 2010, pp. 985–990. IEEE (2010)Google Scholar
  53. 53.
    Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Tallapragada, P., Chopra, N.: Decentralized event-triggering for control of nonlinear systems. IEEE Trans. Autom. Control 59(12), 3312–3324 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Tanelli, M., Ferrara, A.: Enhancing robustness and performance via switched second order sliding mode control. IEEE Trans. Autom. Control 58(4), 962–974 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Utkin, V.: Sliding mode control in discrete-time and difference systems. Variable Structure and Lyapunov Control, pp. 87–107. Springer, UK (1994)Google Scholar
  57. 57.
    Trip, S., Cucuzzella, M., Ferrara, A., De Persis, C.: An energy function based design of second order sliding modes for automatic generation control. In: Proceedings of the 20th IFAC World Congress IFAC, 1211–12123 (2017)Google Scholar
  58. 58.
    Utkin, V.I.: Sliding Modes in Control and Optimization. Springer Science & Business Media, Berlin (2013)Google Scholar
  59. 59.
    Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-mechanical Systems, vol. 34. CRC Press, London (2009)CrossRefGoogle Scholar
  60. 60.
    Wang, F.-Y., Liu, D.: Networked Control Systems: Theory and Applications. Springer, London (2008)CrossRefGoogle Scholar
  61. 61.
    Yu, H., Antsaklis, P.J.: Event-triggered real-time scheduling for stabilization of passive and output feedback passive systems. In: American Control Conference (ACC), 2011, pp. 1674–1679. IEEE (2011)Google Scholar
  62. 62.
    Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control Syst. 21(1), 84–99 (2001)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Industriale e dell’InformazioneUniversity of PaviaPaviaItaly

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