access icon free Constrained robust model predictive control embedded with a new data-driven technique

© The Institution of Engineering and Technology
Received 22/11/2019, Accepted 28/07/2020, Revised 14/04/2020, Published 14/08/2020

In the control field, the adaptive model predictive control (AMPC) has the capability of taking effective control actions on unknown-but-bounded time-independent or slowly time-varying systems coupling with constraints. In essence, AMPC estimates the uncertain parameters or uncertainty set online by utilising historian data to extract model information. The model estimation procedure imposes some specific conditions on data and these extra conditions have restricted its practical use. To overcome these problems, a new data-driven control methodology is presented that integrates the data-driven concept into robust model predictive control (RMPC) architecture for unknown-but-bounded time-independent or slowly time-varying plant. The key novelty is to employ historian data to derive control policy and make a prediction in replacement with the complicated procedure of utilising data to estimate model parameters. A data-driven RMPC algorithm is developed within the robust model predictive control framework with the fulfilment of recursive feasibility and stability. The authors display the highlights of the data-driven model predictive control controller through two simulation examples. The resulting controller is verified to reduce conservativeness and increase the closed-loop performance of the system.

Inspec keywords: predictive control; closed loop systems; robust control; uncertain systems; time-varying systems; control system synthesis

Other keywords: historian data; data-driven technique; AMPC; model estimation procedure; constrained robust model predictive control; robust model predictive control framework; data-driven control methodology; adaptive model predictive control; data-driven concept; control policy; data-driven RMPC algorithm; utilising data; data-driven model predictive control controller; time-varying plant; control field; model information; robust model predictive control architecture; unknown-but-bounded time-independent; time-varying systems; model parameters; effective control actions

Subjects: Optimal control; Stability in control theory; Control system analysis and synthesis methods; Other topics in statistics

References

    1. 1)
      • 37. Hou, Z., Jin, S.: ‘Model free adaptive control: theory and applications’ (CRC Press, Boca Raton, Florida, USA, 2013).
    2. 2)
      • 6. Kouvaritakis, B., Rossiter, J.A., Schuurmans, J.: ‘Efficient robust predictive control’, IEEE Trans. Autom. Control, 2000, 45, (8), pp. 1545–1549.
    3. 3)
      • 18. Kim, T.H., Sugie, T.: ‘Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties’, Int. J. Control, 2008, 81, (1), pp. 62–73.
    4. 4)
      • 5. Franze, G., Mattei, M., Ollìo, L., et al: ‘A norm-bounded robust MPC strategy with partial state measurements’, IFAC Proc. Vol., 2014, 47, (3), pp. 7449–7454.
    5. 5)
      • 17. Fukushima, H., Kim, T.H., Sugie, T.: ‘Adaptive model predictive control for a class of constrained linear systems based on the comparison model’, Automatica, 2007, 43, (2), pp. 301–308.
    6. 6)
      • 30. da Ponte-Caun, R., Assunção, E., Minhoto-Teixeira, M.C., et al: ‘LQR-LMI control applied to convex-bounded domains’, Cogent Eng., 2018, 5, (1), p. 1457206.
    7. 7)
      • 14. Grammatico, S., Zhang, X., Margellos, K., et al: ‘A scenario approach for non-convex control design’, IEEE Trans. Autom. Control, 2015, 61, (2), pp. 334–345.
    8. 8)
      • 22. DeHaan, D., Guay, M.: ‘Adaptive robust mpc: a minimally-conservative approach’. Proc. Conf. on American Control Conf., New York, NY, 2007, pp. 3937–3942.
    9. 9)
      • 29. Lei, T., Hou, Z.: ‘Perimeter control for two-region urban traffic system based on model free adaptive predictive control with constraints’, IFAC-PapersOnLine, 2019, 52, (6), pp. 25–30.
    10. 10)
      • 16. Kim, T.H., Sugie, T.: ‘Discrete-time adaptive model predictive control based on comparison model’, IFAC Proc. Vol., 2005, 38, (1), pp. 562–567.
    11. 11)
      • 10. Ghasemi, M.S., Afzalian, A.A.: ‘Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbances’, Nonlinear Anal., Hybrid Syst., 2017, 26, pp. 86–100.
    12. 12)
      • 35. Wan, Z., Kothare, M.V.: ‘Efficient scheduled stabilizing output feedback model predictive control for constrained nonlinear systems’, IEEE Trans. Autom. Control, 2004, 49, (7), pp. 1172–1177.
    13. 13)
      • 9. Li, D., Xi, Y., Zheng, P.: ‘Constrained robust feedback model predictive control for uncertain systems with polytopic description’, Int. J. Control, 2009, 82, (7), pp. 1267–1274.
    14. 14)
      • 8. Lee, S., Park, J.H.: ‘Robust model predictive control for norm-bounded uncertain systems using new parameter dependent terminal weighting matrix’, Chaos Solitons Fractals, 2008, 38, (1), pp. 199–208.
    15. 15)
      • 19. Mayne, D.Q., Michalska, H.: ‘Adaptive receding horizon control for constrained nonlinear systems’. Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, USA, 1993, pp. 1286–1291.
    16. 16)
      • 13. Lorenzen, M., Cannon, M., Allgöwer, F.: ‘Robust MPC with recursive model update’, Automatica, 2019, 103, pp. 461–471.
    17. 17)
      • 15. Zhang, X., Grammatico, S., Schildbach, G., et al: ‘On the sample size of random convex programs with structured dependence on the uncertainty’, Automatica, 2015, 60, pp. 182–188.
    18. 18)
      • 38. Löfberg, J.: ‘‘Minimax approaches to robust model predictive control’, vol. 812 (Linköping University Electronic Press, Linköping, Sweden, 2003).
    19. 19)
      • 4. Casavola, A., Famularo, D., Franzé, G.: ‘Robust constrained predictive control of uncertain norm-bounded linear systems’, Automatica, 2004, 40, (11), pp. 1865–1876.
    20. 20)
      • 32. Saltık, M.B., Özkan, L., Ludlage, J.H.A., et al: ‘An outlook on robust model predictive control algorithms: reflections on performance and computational aspects’, J. Process Control, 2018, 61, pp. 77–102.
    21. 21)
      • 23. Aswani, A., Gonzalez, H., Sastry, S.S., et al: ‘Provably safe and robust learning-based model predictive control’, Automatica, 2013, 49, (5), pp. 1216–1226.
    22. 22)
      • 25. Wang, X., Sun, Y., Deng, K.: ‘Adaptive model predictive control of uncertain constrained systems’. Proc. Conf. on American Control Conf., Portland, OR, 2014, pp. 2857–2862.
    23. 23)
      • 12. Mayne, D.Q.: ‘Model predictive control: recent developments and future promise’, Automatica, 2014, 50, (12), pp. 2967–2986.
    24. 24)
      • 31. Boyd, S., El-Ghaoui, L., Feron, E., et al: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, PA, 1994, 1st edn.).
    25. 25)
      • 24. Manzano, J.M., Limon, D., de la Peña, D.M., et al: ‘Robust data-based model predictive control for nonlinear constrained systems’, IFAC-PapersOnLine, 2018, 51, (20), pp. 505–510.
    26. 26)
      • 27. Hou, Z., Chi, R., Gao, H.: ‘An overview of dynamic-linearization-based data-driven control and applications’, IEEE Trans. Ind. Electron., 2016, 64, (5), pp. 4076–4090.
    27. 27)
      • 34. Yang, L., Li, D., Lu, J., et al: ‘Robust MPC for constrained uncertain systems with data-driven improvement’. Proc. 37th Chinese Control Conf., Wuhan, 2018, pp. 3623–3628.
    28. 28)
      • 1. Xi, Y., Li, D., Lin, S.: ‘Model predictive control: status and challenges’, Acta Autom. Sin., 2013, 39, (3), pp. 222–236.
    29. 29)
      • 11. Yang, Y., Ding, B., Xu, Z., et al: ‘Tube-based output feedback model predictive control of polytopic uncertain system with bounded disturbances’, J. Franklin Inst., 2019, 356, (15), pp. 7990–8011.
    30. 30)
      • 28. Hou, Z., Liu, S., Yin, C.: ‘Local learning-based model-free adaptive predictive control for adjustment of oxygen concentration in syngas manufacturing industry’, IET Control Theory Applic., 2016, 10, (12), pp. 1384–1394.
    31. 31)
      • 36. Ding, B., Xie, L., Cai, W.: ‘Robust MPC for polytopic uncertain systems with time-varying delays’, Int. J. Control, 2008, 81, (8), pp. 1239–1252.
    32. 32)
      • 7. Li, J., Li, D., Xi, Y., et al: ‘Output-feedback model predictive control for stochastic systems with multiplicative and additive uncertainty’, Int. J. Robust Nonlinear Control, 2018, 28, (1), pp. 86–102.
    33. 33)
      • 26. Heertjes, M.F., Van der Velden, B., Oomen, T.: ‘Constrained iterative feedback tuning for robust control of a wafer stage system’, IEEE Trans. Control Syst. Technol., 2015, 24, (1), pp. 56–66.
    34. 34)
      • 33. 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.
    35. 35)
      • 2. Kothare, M.V., Balakrishnan, V., Morari, M.: ‘Robust constrained model predictive control using linear matrix inequalities’, Automatica, 1996, 32, (10), pp. 1361–1379.
    36. 36)
      • 3. Lu, Y., Arkun, Y.: ‘Quasi-min–max MPC algorithms for LPV systems’, Automatica, 2000, 36, (4), pp. 527–540.
    37. 37)
      • 20. Marafioti, G., Bitmead, R.R., Hovd, M.: ‘Persistently exciting model predictive control’, Int. J. Adapt. Control Signal Process., 2014, 28, (6), pp. 536–552.
    38. 38)
      • 21. Adetola, V., DeHaan, D., Guay, M.: ‘Adaptive model predictive control for constrained nonlinear systems’, Syst. Control Lett., 2009, 58, (5), pp. 320–326.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2019.1349
Loading

Related content

content/journals/10.1049/iet-cta.2019.1349
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading