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

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New Perspectives and Applications of Modern Control Theory

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.

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References

  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. 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. Aström, K.J.: Event based control. In: Analysis and Design of Nonlinear Control Systems, pp. 127–147. Springer, Berlin (2008)

    Google Scholar 

  4. Bartolini, G., Ferrara, A., Usai, E.: Output tracking control of uncertain nonlinear second-order systems. Automatica 33(12), 2203–2212 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  6. Bartolini, G., Ferrara, A., Usai, E.: Chattering avoidance by second-order sliding mode control. IEEE Trans. Autom. Control 43(2), 241–246 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Behera, A.K., Bandyopadhyay, B.: Event-triggered sliding mode control for a class of nonlinear systems. Int. J. Control 89(9), 1916–1931 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Dinuzzo, F., Ferrara, A.: Finite-time output stabilization with second order sliding modes. Automatica 45(9), 2169–2171 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Dinuzzo, F., Ferrara, A.: Higher order sliding mode controllers with optimal reaching. IEEE Trans. Autom. Control 54(9), 2126–2136 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. CRC Press, Boca Raton (1998)

    MATH  Google Scholar 

  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. 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. 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. 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)

    Article  Google Scholar 

  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. 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. Fridman, L., Levant, A.: Higher order sliding modes. Sliding Mode Control Eng. 11, 53–102 (2002)

    Google Scholar 

  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. Gupta, R.A., Chow, M.Y.: Networked control system: overview and research trends. IEEE Trans. Ind. Electron. 57(7), 2527–2535 (2010)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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. 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. Ke-You, Y., Li-Hua, X.: Survey of recent progress in networked control systems. Acta Autom. Sin. 39(2), 101–117 (2013)

    MathSciNet  Google Scholar 

  45. Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River (1996)

    Google Scholar 

  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. 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)

    Article  Google Scholar 

  48. Luck, R., Ray, A.: An observer-based compensator for distributed delays. Automatica 26(5), 903–908 (1990)

    Article  MATH  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  54. Tallapragada, P., Chopra, N.: Decentralized event-triggering for control of nonlinear systems. IEEE Trans. Autom. Control 59(12), 3312–3324 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer Science & Business Media, Berlin (2013)

    Google Scholar 

  59. Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-mechanical Systems, vol. 34. CRC Press, London (2009)

    Book  Google Scholar 

  60. Wang, F.-Y., Liu, D.: Networked Control Systems: Theory and Applications. Springer, London (2008)

    Book  Google Scholar 

  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. Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control Syst. 21(1), 84–99 (2001)

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, Via Ferrata 5, 27100, Pavia, Italy

    Antonella Ferrara & Michele Cucuzzella

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  1. Antonella Ferrara
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  2. Michele Cucuzzella
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Correspondence to Michele Cucuzzella .

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Editors and Affiliations

  1. Centro de Investigaciones Económicas, Administrativas y Sociales, Instituto Politécnico Nacional, Mexico city, Mexico

    Julio B. Clempner

  2. Department of Automatic Control, Center for Research and Advanced Studies, Mexico city, Mexico

    Wen Yu

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Ferrara, A., Cucuzzella, M. (2018). Event-Triggered Sliding Mode Control Strategies for a Class of Nonlinear Uncertain Systems. In: Clempner, J., Yu, W. (eds) New Perspectives and Applications of Modern Control Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-62464-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-62464-8_16

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