access icon free Robust model predictive control with sliding mode for constrained non-linear systems

© The Institution of Engineering and Technology
Received 07/12/2019, Accepted 17/08/2020, Revised 01/08/2020, Published 07/09/2020

This study proposes a tractable robust non-linear model predictive control for constrained continuous-time uncertain systems with stability guarantees. First, a sampled-data model predictive control for the nominal system is designed to provide a desired performance. Then, a sliding mode control is designed to recover the nominal performance for the uncertain system. The sampled-data model predictive control that is solved online includes the initial state of the model employed in the problem as a decision variable. By merging sampled-data model predictive control and sliding mode control in between samples, the effect of the uncertainty, which is matched with the input, is reduced efficiently. The computational complexity of the proposed robust model predictive control is the same as for the model predictive control while the input and state constraints satisfaction and asymptotic stability of the closed-loop system are achieved. To illustrate the effectiveness of the proposed approach, the controller is applied to a vehicle platooning system.

Inspec keywords: uncertain systems; variable structure systems; closed loop systems; asymptotic stability; discrete time systems; continuous time systems; linear systems; predictive control; nonlinear control systems; control system synthesis; stability; robust control

Other keywords: nonlinear model predictive control; constrained continuous-time uncertain systems; robust model predictive control; sliding mode control; sampled-data model predictive control; nonlinear systems

Subjects: Control system analysis and synthesis methods; Nonlinear control systems; Optimal control; Multivariable control systems; Discrete control systems; Stability in control theory; Linear control systems

References

    1. 1)
      • 39. Kianfar, R., Falcone, P., Fredriksson, J.: ‘A receding horizon approach to string stable cooperative adaptive cruise control’. 2011 14th Int. IEEE Conf. on Intelligent Transportation Systems, Washington, DC, USA, 2011, pp. 734–739.
    2. 2)
      • 34. Khalil, H.K.: ‘Nonlinear systems’ (Prentice-Hall, New Jersey, 2002, 3rd edn.).
    3. 3)
      • 12. Fesharaki, S.J., Kamali, M., Sheikholeslam, F.: ‘Adaptive tube-based model predictive control for linear systems with parametric uncertainty’, IET Control Theory Appl., 2017, 11, (17), pp. 2947–2953.
    4. 4)
      • 36. Slotine, J.J.E., Li, W.: ‘Applied nonlinear control’ (Prentice-Hall, New Jersey, 1991).
    5. 5)
      • 38. Sheikholeslam, S., Desoer, C.A.: ‘Longitudinal control of a platoon of vehicles with no communication of lead vehicle information: a system level study’, IEEE Trans. Veh. Technol., 1993, 42, (4), pp. 546–554.
    6. 6)
      • 20. Magni, L., Scattolini, R.: ‘Model predictive control of continuous-time nonlinear systems with piecewise constant control’, IEEE Trans. Autom. Control, 2004, 49, (6), pp. 900–906.
    7. 7)
      • 22. Lopez, B.T., Slotine, J.J.E., How, J.P.: ‘Robust collision avoidance via sliding control’. IEEE Int. Conf. on Robotics and Automation, Brisbane, 2018, pp. 2962–2969.
    8. 8)
      • 19. Rubagotti, M., Raimondo, D.M., Ferrara, A., et al: ‘Robust model predictive control with integral sliding mode in continuous-time sampled-data nonlinear systems’, IEEE Trans. Autom. Constrol, 2011, 56, (3), pp. 556–570.
    9. 9)
      • 3. Grüne, L., Pannek, J.: ‘Nonlinear model predictive control’ (Springer International Publishing, London, UK, 2017, 2nd edn.).
    10. 10)
      • 32. Findeisen, R., Imsland, L., Allgöwer, F., et al: ‘State and output feedback nonlinear model predictive control: an overview’, Eur. J. Control, 2003, 9, (2-3), pp. 190–206.
    11. 11)
      • 31. Findeisen, R., Raff, T., Allgöwer, F.: ‘Sampled-data nonlinear model predictive control for constrained continuous time systems’, in Tarbouriech, S., Garcia, G., Glattfelder, A.H. ‘Advanced strategies in control systems with input and output constraints’. Lecture Notes in Control and Information Sciences (Springer, Berlin, Heidelberg, 2007).
    12. 12)
      • 10. Mayne, D.Q., Raković, S.V., Findeisen, R., et al: ‘Robust output feedback model predictive control of constrained linear systems: time varying case’, Automatica, 2009, 45, (9), pp. 2082–2087.
    13. 13)
      • 14. Rakovic, S.V., Teel, D.Q.M.A., Astolfi, A.: ‘Simple robust control invariant tubes for some classes of nonlinear’. IEEE Conf. on Decision and Control, San Diego, 2006, pp. 6397–6402.
    14. 14)
      • 24. Cannon, M., Raković, S.V.: ‘Robust tubes in nonlinear model predictive control’. IFAC Symp. on Nonlinear Control Systems 1, Bologna, 2010, pp. 208–213.
    15. 15)
      • 35. Moulay, E., Perruquetti, W.: ‘Finite time stability and stabilization of a class of continuous systems’, Math. Anal. Appl., 2006, 323, (2), pp. 1430–1443.
    16. 16)
      • 33. Kögel, M., Findeisen, R.: ‘Discrete-time robust model predictive control for continuous-time nonlinear systems’. 2015 American Control Conf., Chicago, IL, USA, 2015, pp. 924–930.
    17. 17)
      • 4. Gonzalez, A.H., Odloak, D.: ‘Robust model predictive controller with output feedback and target tracking’, IET Control Theory Appl., 2010, 4, (8), pp. 1377–1390.
    18. 18)
      • 17. Singh, S., Slotine, J.J.E., Pavone, M.: ‘Robust online motion planning via contraction theory and convex optimization’. Int. Conf. on Robotics and Automation, Singapore, 2017, pp. 5883–5890.
    19. 19)
      • 7. Lopez, B.T., Howl, J.P., Slotine, J.J.E.: ‘Dynamic tube mpc for nonlinear systems’. 2019 American Control Conf., Philadelphia, PA, USA, 2019, pp. 789–814.
    20. 20)
      • 11. Rawlings, J.B., Mayne, D.Q.: ‘Model predictive control: theory and design’ (Nob Hill Publishing, USA, 2016, 2nd edn.).
    21. 21)
      • 30. Fontes, F.A.C.C.: ‘A general framework to design stabilizing nonlinear model predictive controllers’, Syst. Control Lett., 2001, 42, (2), pp. 127–143.
    22. 22)
      • 25. Kianfar, R., Falcone, P., Fredriksson, J.: ‘A control matching-based predictive approach to string stable vehicle platooning’, IFAC Proc. Vol., 2014, 47, (3), pp. 10700–10705. 19th IFAC World Congress.
    23. 23)
      • 18. Koehler, J., Soloperto, R., Muller, M.A., et al: ‘A computationally efficient robust model predictive control framework for uncertain nonlinear systems’, IEEE Trans. Autom. Control, 2020, pp. 1–1.
    24. 24)
      • 13. Abbas, H.S., Männel, G., né Hoffmann, C.H., et al: ‘Tube-based model predictive control for linear parameter-varying systems with bounded rate of parameter variation’, Automatica, 2019, 107, pp. 21–28.
    25. 25)
      • 23. Chen, H., Allgöwer, F.: ‘A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability’, Automatica, 1998, 34, (10), pp. 1205–1217.
    26. 26)
      • 26. Naus, G.J.L., Ploeg, J., de Molengraft, M.J.G.V., et al: ‘Design and implementation of parameterized adaptive cruise control: an explicit model predictive control approach’, Control Eng. Pract., 2010, 18, (8), pp. 882–892.
    27. 27)
      • 8. Mayne, D.Q., Seron, M.M., Raković, S.V.: ‘Robust model predictive control of constrained linear systems with bounded disturbances’, Automatica, 2005, 41, (2), pp. 219–224.
    28. 28)
      • 2. Mayne, D.Q.: ‘Model predictive control: recent developments and future promise’, Automatica, 2014, 50, (12), pp. 2967–2986.
    29. 29)
      • 29. Bardi, M., Capuzzo-Dolcetta, I.: ‘Optimal control and viscosity solutions of Hamilton–Jacobi-Bellman equations’ (Birkhäuser, Switzerland, 1997).
    30. 30)
      • 37. Angeli, D., Sontag, E., Wang, Y.: ‘A characterization of integral input-to-state stability’, IEEE Trans. Autom. Constrol, 2000, 45, (6), pp. 1082–1097.
    31. 31)
      • 15. Mayne, D.Q., Kerrigan, E.C., Wyk, E.J.V., et al: ‘Tube-based robust nonlinear model predictive control’, Int. J. Robust Nonlinear Control, 2011, 21, (11), pp. 1341–1353.
    32. 32)
      • 28. Magdici, S., Althoff, M.: ‘Adaptive cruise control with safety guarantees for autonomous vehicles’. 20th IFAC World Congress, Brisbane, 2017, pp. 5774–5781.
    33. 33)
      • 5. Ramirez, D.R., Alamo, T., Camacho, E.F.: ‘Min-max MPC based on a computationally efficient upper bound of the worst case cost’, J. Process Control, 2006, 16, (5), pp. 511–519.
    34. 34)
      • 21. Incremona, G., Ferrara, A., Magni, L.: ‘MPC for robot manipulators with integral sliding modes generation’, IEEE/ASME Trans. Mechateronics, 2017, 22, (3), pp. 1299–1307.
    35. 35)
      • 16. Falugi, P., Mayne, D.Q.: ‘Getting robustness against unstructured uncertainty: a tube-based MPC approach’, IEEE Trans. Autom. Control, 2014, 59, (5), pp. 1290–1295.
    36. 36)
      • 1. Mayne, D.Q., Rawlings, J.B., Rao, C.V., et al: ‘Constrained model predictive control: stability and optimality’, Automatica, 2000, 36, (6), pp. 789–814.
    37. 37)
      • 27. Corona, D., Schutter, B.D.: ‘IEEE Transactions on Control Systems Technology’.
    38. 38)
      • 6. Gonzalez, R., Fiacchini, M., Alamo, T., et al: ‘Online robust tube-based MPC for time-varying systems: a practical approach’, Int. J. Control, 2011, 84, (6), pp. 1157–1170.
    39. 39)
      • 9. Mayne, D.Q., Rakovic, S.V., Findeisen, R., et al: ‘Robust output feedback model predictive control of constrained linear systems’, Automatica, 2006, 42, (7), pp. 1217–1222.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2019.1357
Loading

Related content

content/journals/10.1049/iet-cta.2019.1357
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading