Skip to main content

Constrained Sliding-Mode Control: A Survey

  • Chapter
  • First Online:
Variable-Structure Systems and Sliding-Mode Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 271))

Abstract

In this chapter, the robust control of input and state-constrained nonlinear systems is discussed from the perspective of sliding-mode control. The proposals currently available in the literature are summarized and some of them are briefly discussed, in particular cases providing also commented examples.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Springer Science & Business Media, Berlin (2001)

    Book  MATH  Google Scholar 

  2. Åström, K.J., Hägglund, T.: PID Controllers: Theory, Design, and Tuning, vol. 2. Instrument Society of America Research Triangle Park, NC (1995)

    Google Scholar 

  3. Åström, K.J., Hägglund, T., Astrom, K.J.: Advanced PID Control, vol. 461. ISA-The Instrumentation Systems, and Automation Society Research Triangle (2006)

    Google Scholar 

  4. Goodwin, G., Seron, M.M., De Doná, J.A.: Constrained control and estimation: an optimisation approach. Springer Science & Business Media, Berlin (2006)

    MATH  Google Scholar 

  5. Bak, M.: Control of systems with constraints. Ph.D. thesis, Technical University of Denmark, Department of Automation (2000)

    Google Scholar 

  6. Clarke, D., Scattolini, R.: Constrained receding-horizon predictive control. In: IEE Proceedings D (Control Theory and Applications), vol. 138, pp. 347–354. IET (1991)

    Google Scholar 

  7. Maciejowski, J.M.: Predictive Control with Constraints. Pearson Education, London (2002)

    MATH  Google Scholar 

  8. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.: Constrained model predictive control: stability and optimality. Automatica 36(6), 789–814 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Qin, S.J., Badgwell, T.A.: A survey of industrial model predictive control technology. Control Eng. Pract. 11(7), 733–764 (2003)

    Article  Google Scholar 

  10. Garcia, C.E., Prett, D.M., Morari, M.: Model predictive control: theory and practice-a survey. Automatica 25(3), 335–348 (1989)

    Article  MATH  Google Scholar 

  11. Muske, K.R., Rawlings, J.B.: Model predictive control with linear models. AIChE J. 39(2), 262–287 (1993)

    Article  Google Scholar 

  12. Mayne, D.Q.: Model predictive control: recent developments and future promise. Automatica 50(12), 2967–2986 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rawlings, J.B., Muske, K.R.: The stability of constrained receding horizon control. IEEE Trans. Autom. Control 38(10), 1512–1516 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Freeman, R., Kokotovic, P.V.: Robust Nonlinear Control Design: State-Space and Lyapunov Techniques. Springer Science & Business Media, Berlin (2008)

    MATH  Google Scholar 

  15. Hansen, L., Sargent, T.J.: Robust control and model uncertainty. Am. Econ. Rev. 91(2), 60–66 (2001)

    Article  Google Scholar 

  16. Wang, Y., Xie, L., De Souza, C.E.: Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19(2), 139–149 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhou, K., Doyle, J.C.: Essentials of Robust Control, vol. 104. Prentice Hall, Upper Saddle River (1998)

    MATH  Google Scholar 

  18. Bemporad, A., Morari, M.: Robust model predictive control: a survey. In: Robustness in Identification and Control, pp. 207–226. Springer, Berlin (1999)

    Google Scholar 

  19. Edwards, C., Fossas, E., Fridman, L.: Advances in Variable Structure and Sliding Mode Control. Birkh strä user, Basel (2008)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  21. Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Birkhäuser, Basel (2014)

    Book  Google Scholar 

  22. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (1992)

    Book  MATH  Google Scholar 

  23. Garcia-Gabin, W., Camacho, E.F.: Sliding mode model based predictive control for non minimum phase systems. In: 2003 European Control Conference (ECC), pp. 904–909 (2003)

    Google Scholar 

  24. Incremona, G.P., Ferrara, A., Magni, L.: Hierarchical model predictive/sliding mode control of nonlinear constrained uncertain systems. IFAC-PapersOnLine 48(23), 102–109 (2015)

    Article  Google Scholar 

  25. Raimondo, D., Rubagotti, M., Jones, C., Magni, L., Ferrara, A., Morari, M.: Multirate sliding mode disturbance compensation for model predictive control. Int. J, Robust Nonlinear Control (2014)

    MATH  Google Scholar 

  26. Rubagotti, M., Raimondo, D.M., Ferrara, A., Magni, L.: Robust model predictive control with integral sliding mode in continuous-time sampled-data nonlinear systems. IEEE Trans. Autom. Control 56(3), 556–570 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. Incremona, G.P., Ferrara, A., Magni, L.: Asynchronous networked MPC with ISM for uncertain nonlinear systems. IEEE Trans. Autom. Control 62(9), 4305–4317 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  28. Steinberger, M., Castillo, I., Horn, M., Fridman, L.: Model predictive output integral sliding mode control. In: 2016 14th International Workshop on Variable Structure Systems (VSS), pp. 228–233 (2016)

    Google Scholar 

  29. Corradini, M., Orlando, G.: Linear unstable plants with saturating actuators: Robust stabilization by a time varying sliding surface. Automatica 43(1), 88–94 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Corradini, M.L., Cristofaro, A., Orlando, G.: On the robust stabilization of discrete-time SISO plants with saturating actuators. In: 2008 47th IEEE Conference on Decision and Control, pp. 1599–1604 (2008)

    Google Scholar 

  31. Corradini, M.L., Cristofaro, A., Orlando, G.: Robust stabilization of multi input plants with saturating actuators. IEEE Trans. Autom. Control 55(2), 419–425 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  32. Corradini, M.L., Orlando, G.: A result on the robust stabilization of MIMO plants with saturating actuators. In: 2007 46th IEEE Conference on Decision and Control, pp. 548–553 (2007)

    Google Scholar 

  33. Fulwani, D., Bandyopadhyay, B.: Design of Sliding Mode Controller with Actuator Saturation, pp. 207–219. Springer, Berlin (2013)

    Google Scholar 

  34. Ma, Z., Sun, G., Li, Z.: Dynamic adaptive saturated sliding mode control for deployment of tethered satellite system. Aerosp. Sci. Technol. 66, 355–365 (2017)

    Article  Google Scholar 

  35. Torchani, B., Sellami, A., M’hiri, R., Garcia, G.: Comparative analysis of the saturated sliding mode and lqr controllers applied to an inverted pendulum. In: 2011 International Conference on Communications, Computing and Control Applications (CCCA), pp. 1–6 (2011)

    Google Scholar 

  36. Wang, S., Gao, Y., Liu, J., Wu, L.: Saturated sliding mode control with limited magnitude and rate. IET Control Theory Appl. 12(8), 1075–1085 (2018)

    Article  MathSciNet  Google Scholar 

  37. Xiao, B., Hu, Q., Zhang, Y.: Adaptive sliding mode fault tolerant attitude tracking control for flexible spacecraft under actuator saturation. IEEE Trans. Control Syst. Technol. 20(6), 1605–1612 (2012)

    Article  Google Scholar 

  38. Oliveira, C.M.R., Aguiar, M.L., Monteiro, J.R.B.A., Pereira, W.C.A., Paula, G.T., Almeida, T.E.P.: Vector control of induction motor using an integral sliding mode controller with anti-windup. J. Control Autom. Electr. Syst. 27(2), 169–178 (2016)

    Article  Google Scholar 

  39. Shi, X.J., Zhao, H.C., Xu, K.W.: Dynamic anti-windup design for missile overload control system. In: Advanced Technology for Manufacturing Systems and Industry. Applied Mechanics and Materials, vol. 236, pp. 273–277. Trans Tech Publications, Stafa (2012)

    Article  Google Scholar 

  40. Yokoyama, M., Kim, G.N., Tsuchiya, M.: Integral sliding mode control with anti-windup compensation and its application to a power assist system. J. Vib. Control 16(4), 503–512 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  41. Slotine, J.J., Sastry, S.S.: Tracking control of non-linear systems using sliding surfaces with application to robot manipulators. In: 1983 American Control Conference, pp. 132–135 (1983). https://doi.org/10.23919/ACC.1983.4788090

  42. Seshagiri, S., Khalil, H.K.: On introducing integral action in sliding mode control. In: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, vol. 2, pp. 1473–1478 (2002). https://doi.org/10.1109/CDC.2002.1184727

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

    Google Scholar 

  44. Levant, A.: Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence. IEEE Trans. Autom. Control 46(9), 1447–1451 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  45. Levant, A.: Quasi-continuous high-order sliding-mode controllers. In: 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475), vol. 5, pp. 4605–4610. IEEE (2003)

    Google Scholar 

  46. Bartolini, G., Ferrara, A., Levant, A., Usai, E.: On Second Order Sliding Mode Controllers, pp. 329–350. Springer, London (1999)

    Google Scholar 

  47. 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 

  48. Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control. 58(6), 1247–1263 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  49. Ferrara, A., Rubagotti, M.: A sub-optimal second order sliding mode controller for systems with saturating actuators. IEEE Trans. Autom. Control 54(5), 1082–1087 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  50. Castillo, I., Steinberger, M., Fridman, L., Moreno, J., Horn, M.: Saturated super-twisting algorithm based on perturbation estimator. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 7325–7328 (2016)

    Google Scholar 

  51. Castillo, I., Steinberger, M., Fridman, L., Moreno, J.A., Horn, M.: Saturated super-twisting algorithm: Lyapunov based approach. In: 2016 14th International Workshop on Variable Structure Systems (VSS), pp. 269–273 (2016)

    Google Scholar 

  52. Golkani, M.A., Koch, S., Reichhartinger, M., Horn, M.: A novel saturated super-twisting algorithm. Syst. Control Lett. 119, 52–56 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  53. Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  54. Levant, A.: Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control 76(9–10), 924–941 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  55. Seeber, R., Horn, M.: Guaranteeing disturbance rejection and control signal continuity for the saturated super-twisting algorithm. IEEE Control Syst. Lett. (2019). https://doi.org/10.1109/LCSYS.2019.2917054

    Article  Google Scholar 

  56. Ferrara, A., Rubagotti, M.: A sub-optimal second order sliding mode controller for systems with saturating actuators. In: 2008 American Control Conference, pp. 4715–4720 (2008)

    Google Scholar 

  57. 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 

  58. Khalil, H.K.: Noninear Systems. Prentice-Hall, New Jersey (1996)

    Google Scholar 

  59. Innocenti, M., Falorni, M.: State constrained sliding mode controllers. In: Proceedings of the 1998 American Control Conference, vol. 1, pp. 104–108 (1998)

    Google Scholar 

  60. Fan, Q.Y., Yang, G.H.: Nearly optimal sliding mode fault-tolerant control for affine nonlinear systems with state constraints. Neurocomputing 216, 78–88 (2016). https://doi.org/10.1016/j.neucom.2016.06.063

    Article  Google Scholar 

  61. Pietrala, M., Jaskuła, M., Leśniewski, P., Bartoszewicz, A.: Sliding mode control of discrete time dynamical systems with state constraints. In: Trends in Advanced Intelligent Control, Optimization and Automation, pp. 4–13 (2017)

    Google Scholar 

  62. Ding, S., Mei, K., Li, S.: A new second-order sliding mode and its application to nonlinear constrained systems. IEEE Trans. Autom. Control 64, 2545–2552 (2018). https://doi.org/10.1109/TAC.2018.2867163

    Article  MathSciNet  MATH  Google Scholar 

  63. Rubagotti, M., Ferrara, A.: Second order sliding mode control of a perturbed double integrator with state constraints. In: Proceedings of the 2010 American Control Conference, pp. 985–990 (2010)

    Google Scholar 

  64. Ferrara, A., Incremona, G.P., Rubagotti, M.: Third order sliding mode control with box state constraints. In: 53rd IEEE Conference on Decision and Control, pp. 4727–4732 (2014)

    Google Scholar 

  65. 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 

  66. Tanizawa, H., Ohta, Y.: Sliding mode control under state and control constraints. In: 2007 IEEE International Conference on Control Applications, pp. 1173–1178 (2007)

    Google Scholar 

  67. Incremona, G.P., Rubagotti, M., Ferrara, A.: Sliding mode control of constrained nonlinear systems. IEEE Trans. Autom. Control 9286(c), 1 (2016)

    Google Scholar 

  68. Zambelli, M., Ferrara, A.: Linearization-based integral sliding mode control for a class of constrained nonlinear systems. In: 2018 15th International Workshop on Variable Structure Systems (VSS), pp. 402–407 (2018)

    Google Scholar 

  69. Utkin, V., Shi, J.: Integral sliding mode in systems operating under uncertainty conditions. In: Proceedings of 35th IEEE Conference on Decision and Control, vol. 4, pp. 4591–4596 (1996)

    Google Scholar 

  70. Rubagotti, M., Estrada, A., Castanos, F., Ferrara, A., Fridman, L.: Integral sliding mode control for nonlinear systems with matched and unmatched perturbations. IEEE Trans. Autom. Control 56(11), 2699–2704 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  71. Kiencke, U., Nielsen, L.: Automotive Control Systems - For Engine, Driveline, and Vehicle. Springer, Berlin (2005)

    Book  Google Scholar 

  72. Genta, G.: Motor Vehicle Dynamics - Modeling and Simulation. World Scientific, Singapore (1993)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Massimo Zambelli .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zambelli, M., Ferrara, A. (2020). Constrained Sliding-Mode Control: A Survey. In: Steinberger, M., Horn, M., Fridman, L. (eds) Variable-Structure Systems and Sliding-Mode Control. Studies in Systems, Decision and Control, vol 271. Springer, Cham. https://doi.org/10.1007/978-3-030-36621-6_5

Download citation

Publish with us

Policies and ethics