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Robust model predictive control: A survey

  • Part II Robust Control
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Robustness in identification and control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 245))

Abstract

This paper gives an overview of robustness in Model Predictive Control (MPC). After reviewing the basic concepts of MPC, we survey the uncertainty descriptions considered in the MPC literature, and the techniques proposed for robust constraint handling, stability, and performance. The key concept of “closedloop prediction” is discussed at length. The paper concludes with some comments on future research directions.

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References

  1. Allwright, J. C. (1994). On min-max model-based predictive control. In: Advances in Model-Based Predictive Control. pp. 415–426. Oxford Press Inc.,N. Y., New York.

    Google Scholar 

  2. Allwright, J.C. and G.C. Papavasiliou (1992). On linear programming and robust model-predictive control using impulse-responses. Systems & Control Letters 18, 159–164.

    Article  MATH  MathSciNet  Google Scholar 

  3. Badgwell, T. A. (1997). Robust model predictive control of stable linear systems. Int. J. Control 68(4), 797–818.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bemporad, A. (1998a). A predictive controller with artificial Lyapunov function for linear systems with input/state constraints. Automatica 34(10), 1255–1260.

    Article  MATH  MathSciNet  Google Scholar 

  5. Bemporad, A. (1998b). Reducing conservativeness in predictive control of constrained systems with disturbances. In: Proc. 37th IEEE Conf. on Decision and Control. Tampa, FL. pp. 1384–1391.

    Google Scholar 

  6. Bemporad, A., A. Casavola and E. Mosca (1997). Nonlinear control of constrained linear systems via predictive reference management. IEEE Trans. Automatic Control AC-42(3), 340–349.

    Article  MathSciNet  Google Scholar 

  7. Bemporad, A. and A. Garulli (1997). Predictive control via set-membership state estimation for constrained linear systems with disturbances. In: Proc. European Control Conf.. Bruxelles, Belgium.

    Google Scholar 

  8. Bemporad, A. and E. Mosca (1998). Fulfilling hard constraints in uncertain linear systems by reference managing. Automatica 34(4), 451–461.

    Article  MATH  MathSciNet  Google Scholar 

  9. Bemporad, A. and M. Morari (1999). Control of systems integrating logic, dynamics, and constraints. Automatica 35(3), 407–427. ftp://control.ethz.ch/pub/reports/postscript/AUT98-04.ps.

    Article  MATH  MathSciNet  Google Scholar 

  10. Bemporad, A., L. Chisci and E. Mosca (1994). On the stabilizing property of the zero terminal state receding horizon regulation. Automatica 30(12), 2013–2015.

    Article  MATH  MathSciNet  Google Scholar 

  11. Benvenuti, L. and L. Farina (1998). Constrained control for uncertain discrete-time linear systems. Int. J. Robust Nonlinear Control 8, 555–565.

    Article  MATH  MathSciNet  Google Scholar 

  12. Berber, R., Ed. (1995). Methods of Model Based Process Control. Vol. 293 of NATO ASI Series E: Applied Sciences. Kluwer Academic Publications. Dortrecht, Netherlands.

    Google Scholar 

  13. Bertsekas, D.P. and I.B. Rhodes (1971). Recursive state estimation for a set-membership description of uncertainty. IEEE Trans. Automatic Control 16, 117–128.

    Article  MathSciNet  Google Scholar 

  14. Bitmead, R. R., M. Gevers and V. Wertz (1990). Adaptive Optimal Control. The Thinking Man's GPC. International Series in Systems and Control Engineering. Prentice Hall.

    Google Scholar 

  15. Blanchini, F. (1990). Control synthesis for discrete time systems with control and state bounds in the presence of disturbances. J. of Optimization Theory and Applications 65(1), 29–40.

    Article  MATH  MathSciNet  Google Scholar 

  16. Blanchini, F. (1999). Set invariance in control — a survey. Automatica. In press.

    Google Scholar 

  17. Camacho, E.F. and C. Bordons (1995). Model Predictive Control in the Process Industry. Advances in Industrial Control. Springer Verlag.

    Google Scholar 

  18. Campo, P.J. and M. Morari (1987). Robust model predictive control. In: Proc. American Contr. Conf.. Vol. 2. pp. 1021–1026.

    Google Scholar 

  19. Campo, P.J. and M. Morari (1989). Model predictive optimal averaging level control. AIChE Journal 35(4), 579–591.

    Article  Google Scholar 

  20. Chen, H., C. W. Scherer and F. Allgöwer (1997). A game theoretic approach to nonlinear robust receding horizon control of constrained systems. In: Proc. American Contr. Conf.. Vol. 5. pp. 3073–3077.

    Google Scholar 

  21. Chisci, L., A. Garulli and G. Zappa (1996). Recursive state bounding by parallelotopes. Automatica 32(7), 1049–1056.

    Article  MathSciNet  Google Scholar 

  22. Clarke, D. W., C. Mohtadi and P. S. Tuffs (1987a). Generalized predictive control-I. The basic algorithm. Automatica 23, 137–148.

    Article  MATH  Google Scholar 

  23. Clarke, D. W., C. Mohtadi and P. S. Tuffs (1987b). Generalized predictive control-II. Extensions and interpretations. Automatica 23, 149–160.

    Article  MATH  Google Scholar 

  24. Clarke, D.W., (Ed.) (1994). Advances in Model-Based Predictive Control. Oxford University Press.

    Google Scholar 

  25. Cutler, C. R. and B. L. Ramaker (1979). Dynamic matrix control-A computer control algorithm. In: AIChE 86th National Meeting. Houston, TX.

    Google Scholar 

  26. Cutler, C. R. and B. L. Ramaker (1980). Dynamic matrix control-A computer control algorithm. In: Joint Automatic Control Conf.. San Francisco, California.

    Google Scholar 

  27. De Nicolao, G., L. Magni and R. Scattolini (1996). Robust predictive control of systems with uncertain impulse response. Automatica 32(10), 1475–1479.

    Article  MATH  MathSciNet  Google Scholar 

  28. Garcia, C.E., D.M. Prett and M. Morari (1989). Model predictive control: Theory and practice — a survey. Automatica.

    Google Scholar 

  29. Genceli, H. and M. Nikolaou (1993). Robust stability analysis of constrained l 1-norm model predictive control. AIChE J. 39(12), 1954–1965.

    Article  MathSciNet  Google Scholar 

  30. Gilbert, E.G. and I. Kolmanovsky (1995). Discrete-time reference governors for systems with state and control constraints and disturbance inputs. In: Proc. 34th IEEE Conf. on Decision and Control. pp. 1189–1194.

    Google Scholar 

  31. Gilbert, E.G. and K. Tin Tan (1991). Linear systems with state and control constraints: the theory and applications of maximal output admissible sets. IEEE Trans. Automatic Control 36, 1003–1020.

    Article  Google Scholar 

  32. Gilbert, E.G., I. Kolmanovsky and K. Tin Tan (1995). Discrete-time reference governors and the nonlinear control of systems with state and control constraints. Int. J. Robust Nonlinear Control 5(5), 487–504.

    Article  MATH  Google Scholar 

  33. Hansson, A. and S. Boyd (1998). Robust optimal control of linear discrete time systems using primal-dual interior-point methods. In: Proc. American Contr. Conf.. Vol. 1. pp. 183–187.

    Google Scholar 

  34. Keerthi, S.S. and E.G. Gilbert (1988). Optimal infinite-horizon feedback control laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations. J. Opt. Theory and Applications 57, 265–293.

    Article  MATH  Google Scholar 

  35. Kothare, M.V., V. Balakrishnan and M. Morari (1996). Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10), 1361–1379.

    Article  MATH  MathSciNet  Google Scholar 

  36. Kwon, W. H. (1994). Advances in predictive control: Theory and application. In: 1st Asian Control Conf.. Tokyo. (updated in October, 1995).

    Google Scholar 

  37. Kwon, W.H., A.M. Bruckstein and T. Kailath (1983). Stabilizing statefeedback design via the moving horizon method. Int. J. Control 37(3), 631–643.

    Article  MATH  MathSciNet  Google Scholar 

  38. Kwon, W.H. and A.E. Pearson (1977). A modified quadratic cost problem and feedback stabilization of a linear system. IEEE Trans. Automatic Control 22(5), 838–842.

    Article  MATH  MathSciNet  Google Scholar 

  39. Kwon, W.H. and A.E. Pearson (1978). On feedback stabilization of finevarying discrete linear systems. IEEE Trans. Automatic Control 23, 479–481.

    Article  MATH  MathSciNet  Google Scholar 

  40. Kwon, W.H. and D. G. Byun (1989). Receding horizon tracking contral as a predictive control and its stability properties. Int. J. Control 50(5), 1807–1824.

    Article  MATH  MathSciNet  Google Scholar 

  41. Lee, J. H. and Z. Yu (1997). Worst-case formulations of model preditive control for systems with bounded parameters. Automatica 33(5), 763–781.

    Article  MATH  MathSciNet  Google Scholar 

  42. Lee, J.H. and B. Cooley (1997). Recent advances in model predictive control. In: Chemical Process Control — V. Vol. 93, no. 316. pp. 201–216b. AIChe Symposium Series — American Institute of Chemical Engineers.

    Google Scholar 

  43. Lee, K. H., W. H. Kwon and J. H. Lee (1996). Robust receding-horizon control for linear systems with model uncertainties. In: Proc. 35th IEEE Conf. on Decision and Control. pp. 4002–4007.

    Google Scholar 

  44. Lobo, M., L. Vandenberghe and S. Boyd (1997). Software for second-order cone programming. user's guide. http://www-isl.stanford.edu/ boyd/SOCP.html.

    Google Scholar 

  45. Mäkilä, P. M., J. R. Partington and T. K. Gustafsson (1995). Worst-case control-relevant identification. Automatica 31, 1799–1819.

    Article  MATH  Google Scholar 

  46. Martín Sánchez, J.M. and J. Rodellar (1996). Adaptive Predictive Control. International Series in Systems and Control Engineering. Prentice Hall.

    Google Scholar 

  47. Mayne, D. Q. and W. R. Schroeder (1997). Robust time-optimal control of constrained linear systems. Automatica 33(12), 2103–2118.

    Article  MATH  MathSciNet  Google Scholar 

  48. Mayen, D.Q. (1997). Nonlinear model predictive control: an assessment. In: Chemical Process Control — V. Vol. 93, no. 316. pp. 217–231. AIChe Symposium Series — American Institute of Chemical Engineers.

    Google Scholar 

  49. Megretski, A. and A. Rantzer (1997). System analysis via integral quadratic constraints. IEEE Trans. Automatic Control 42(6), 819–830.

    Article  MATH  MathSciNet  Google Scholar 

  50. Milanese, M. and A. Vicino (1993). Information-based complexity and nonparametric worst-case system identification. Journal of Complexity 9, 427–446.

    Article  MATH  MathSciNet  Google Scholar 

  51. Morari, M. (1994). Model predictive control: Multivariable control technique of choice in the 1990s?. In: Advances in Model-Based Predictive Control. pp. 22–37. Oxford University Press Inc.. New York.

    Google Scholar 

  52. Noh, S. B., Y. H. Kim, Y. I. Lee and W. H. Kwon (1996). Roubst generalised predictive control with terminal output weightings. J. Process Control 6(2/3), 137–144.

    Article  Google Scholar 

  53. Polak, E. and T.H. Yang (1993a). Moving horizon control of linear systems with input saturation and plant uncertainty-part 1. robustness. Int. J. Control 58(3), 613–638.

    Article  MATH  MathSciNet  Google Scholar 

  54. Polak, E. and T.H. Yang (1993b). Moving horizon control of linear systems with input saturation and plant uncertainty-part 2. disturbance rejection and tracking. Int. J. Control 58(3), 639–663.

    Article  MATH  MathSciNet  Google Scholar 

  55. Primbs, J.A. (1999). The analysis of optimization based controllers. In: Proc. American Contr. Conf.. San Diego, CA.

    Google Scholar 

  56. Primbs, J.A. and V. Nevistíc (1998). A framework for robustness analysis of constrained finite receding horizon control. In: Proc. American Contr. Conf.. pp. 2718–2722.

    Google Scholar 

  57. Qin, S.J. and T.A. Badgewell (1997). An overview of industrial model predictive control technology. In: Chemical Process Control — V. Vol. 93, no. 316. pp. 232–256. AIChe Symposium Series — American Institute of Chemical Engineers.

    Google Scholar 

  58. Rawlings, J.B. and K.R. Muske (1993). The stability of constrained recedinghorizon control. IEEE Trans. Automatic Control 38, 1512–1516.

    Article  MATH  MathSciNet  Google Scholar 

  59. Richalet, J., A. Rault, J.L. Testud and J. Papon (1978). Model predictive heuristic control: applications to industrial processes. Automatica 14(5), 413–428.

    Article  Google Scholar 

  60. Santis, E. De (1994). On positively invariant sets for discrete-time linear systems with disturbance: an application of maximal disturbance sets. IEEE Trans. Automatic Control 39(1), 245–249.

    Article  MATH  Google Scholar 

  61. Santos, L. O. and L. T. Biegler (1998). A tool to analyze robust stability for model predictive controllers. J. Process Control.

    Google Scholar 

  62. Schweppe, F.C. (1968). Recursive state estimation: unknown but bounded errors and system inputs. IEEE Trans. Automatic Control 13, 22–28.

    Article  Google Scholar 

  63. Scokaert, P.O.M. and D.Q. Mayne (1998). Min-max feedback model predictive control for constrained linear systems. IEEE Trans. Automatic Control 43(8), 1136–1142.

    Article  MATH  MathSciNet  Google Scholar 

  64. Scokaert, P.O.M. and J.B. Rawlings (1996). Infinite horizon linear quadratic control with constraints. In: Proc. IFAC. Vol. 7a-04 1. San Francisco, USA. pp. 109–114.

    Google Scholar 

  65. Soeterboek, R. (1992). Predictive Control — A Unified Approach. International Series in Systems and Control Engineering. Prentice Hall.

    Google Scholar 

  66. Vicino, A. and G. Zappa (1996). Sequential approximation of feasible parameter sets for identification with set membership uncertainty. IEEE Trans. Automatic Control 41, 774–785.

    Article  MATH  MathSciNet  Google Scholar 

  67. Yang, T.H. and E. Polak (1993). Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty. Int. J. Control 58, 875–903.

    Article  MATH  MathSciNet  Google Scholar 

  68. Zafiriou, E. (1990). Robust model predictive control of processes with hard constraints. Computers & Chemical Engineering 14(4/5), 359–371.

    Article  Google Scholar 

  69. Zheng, A. and M. Morari (1993). Robust stability of constrained model predictive control. In: Proc. American Contr. Conf., Vol. 1. San Francisco, CA. pp. 379–383.

    Google Scholar 

  70. Zheng, A. and M. Morari (1994). Robust control of linear time-varying systems with constraints. In: Proc. American Contr. Conf., Vol. 3. pp. 2416–2420.

    Google Scholar 

  71. Zheng, A. and M. Morari (1995). Stability of model predictive control with mixed constraints. IEEE Trans. Automatic Control 40, 1818–1823.

    Article  MATH  MathSciNet  Google Scholar 

  72. Zheng, A. and M. Morari (1998). Robust control of lineary systems with constraints. Unpublished report.

    Google Scholar 

  73. Zheng, Z. Q. (1995). Robust Control of Systems Subject to Constraints. Ph.D. dissertation. California Institute of Technology. Pasadena, CA, U.S.A.

    Google Scholar 

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A. Garulli (Assistant Professor)A. Tesi (Assistant Professor)

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Bemporad, A., Morari, M. (1999). Robust model predictive control: A survey. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109870

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  • DOI: https://doi.org/10.1007/BFb0109870

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  • Print ISBN: 978-1-85233-179-5

  • Online ISBN: 978-1-84628-538-7

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