Lyapunov-Based Model Predictive Control

  • Panagiotis D. Christofides
  • Jinfeng Liu
  • David Muñoz de la Peña
Part of the Advances in Industrial Control book series (AIC)


In Chap. 2, some basic results on Lyapunov-based control, model predictive control and Lyapunov-based model predictive control of nonlinear systems are first reviewed and then two Lyapunov-based model predictive control (LMPC) designs for systems subject to data losses and time-varying measurement delays are presented. In order to provide guaranteed closed-loop stability results, the constraints that define the LMPC optimization problems as well as the implementation procedures are carefully designed to account for data losses (or asynchronous measurements) and time-varying measurement delays. The presented LMPC designs possess an explicit characterization of the closed-loop system stability region. Using a nonlinear chemical reactor example, it is demonstrated that the presented LMPC approaches are robust to data losses and measurement delays.


Stability Region Data Loss Continuously Stir Tank Reactor Prediction Horizon Measurement Delay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Allgöwer, F., & Chen, H. (1998). Nonlinear model predictive control schemes with guaranteed stability. In R. Berber & C. Kravaris (Eds.), NATO ASI on nonlinear model based process control (pp. 465–494). Dordrecht: Kluwer Academic. Google Scholar
  2. 2.
    Antoniades, C., & Christofides, P. D. (1999). Feedback control of nonlinear differential difference equation systems. Chemical Engineering Science, 54, 5677–5709. CrossRefGoogle Scholar
  3. 4.
    Bemporad, A., & Morari, M. (1999). Control of systems integrating logic, dynamics and constraints. Automatica, 35, 407–427. CrossRefMATHMathSciNetGoogle Scholar
  4. 6.
    Bitmead, R. R., Gevers, M., & Wertz, V. (1990). Adaptive optimal control—the thinking man’s GPC. Englewood Cliffs: Prentice-Hall. MATHGoogle Scholar
  5. 11.
    Christofides, P. D., & El-Farra, N. H. (2005). Control of nonlinear and hybrid process systems: Designs for uncertainty, constraints and time-delays. Berlin: Springer. Google Scholar
  6. 14.
    Clarke, F., Ledyaev, Y., & Sontag, E. (1997). Asymptotic controllability implies feedback stabilization. IEEE Transactions on Automatic Control, 42, 1394–1407. CrossRefMATHMathSciNetGoogle Scholar
  7. 18.
    El-Farra, N. H., & Christofides, P. D. (2001). Integrating robustness, optimality and constraints in control of nonlinear processes. Chemical Engineering Science, 56, 1841–1868. CrossRefGoogle Scholar
  8. 19.
    El-Farra, N. H., & Christofides, P. D. (2003). Bounded robust control of constrained multivariable nonlinear processes. Chemical Engineering Science, 58, 3025–3047. CrossRefGoogle Scholar
  9. 21.
    Fogler, H. S. (1999). Elements of chemical reaction engineering. Englewood Cliffs: Prentice Hall. Google Scholar
  10. 25.
    García, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: theory and practice—a survey. Automatica, 25, 335–348. CrossRefMATHGoogle Scholar
  11. 36.
    Jeong, S. C., & Park, P. (2005). Constrained MPC algorithm for uncertain time-varying systems with state-delay. IEEE Transactions on Automatic Control, 50, 257–263. CrossRefMathSciNetGoogle Scholar
  12. 40.
    Khalil, H. K. (1996). Nonlinear systems (2nd ed.). New York: Prentice Hall. Google Scholar
  13. 41.
    Kokotovic, P., & Arcak, M. (2001). Constructive nonlinear control: a historical perspective. Automatica, 37, 637–662. MATHMathSciNetGoogle Scholar
  14. 42.
    Kothare, S. L. D., & Morari, M. (2000). Contractive model predictive control for constrained nonlinear systems. IEEE Transactions on Automatic Control, 45, 1053–1071. CrossRefMATHGoogle Scholar
  15. 47.
    Lin, Y., & Sontag, E. D. (1991). A universal formula for stabilization with bounded controls. Systems & Control Letters, 16, 393–397. CrossRefMATHMathSciNetGoogle Scholar
  16. 48.
    Lin, Y., Sontag, E. D., & Wang, Y. (1996). A smooth converse Lyapunov theorem for robust stability. SIAM Journal on Control and Optimization, 34, 124–160. CrossRefMATHMathSciNetGoogle Scholar
  17. 49.
    Liu, G.-P., Xia, Y., Chen, J., Rees, D., & Hu, W. (2007). Networked predictive control of systems with random networked delays in both forward and feedback channels. IEEE Transactions on Industrial Electronics, 54, 1282–1297. CrossRefGoogle Scholar
  18. 50.
    Liu, J., Muñoz de la Peña, D., Christofides, P. D., & Davis, J. F. (2008a). Lyapunov-based model predictive control of particulate processes subject to asynchronous measurements. Particle & Particle Systems Characterization, 25, 360–375. CrossRefGoogle Scholar
  19. 53.
    Liu, J., Muñoz de la Peña, D., Christofides, P. D., & Davis, J. F. (2009). Lyapunov-based model predictive control of nonlinear systems subject to time-varying measurement delays. International Journal of Adaptive Control and Signal Processing, 23, 788–807. CrossRefMATHGoogle Scholar
  20. 59.
    Maeder, U., Cagienard, R., & Morari, M. (2007). Explicit model predictive control. In S. Tarbouriech, G. Garcia, & A. H. Glattfelder (Eds.), Lecture notes in control and information sciences: Vol. 346. Advanced strategies in control systems with input and output constraints (pp. 237–271). Berlin: Springer. CrossRefGoogle Scholar
  21. 64.
    Massera, J. L. (1956). Contributions to stability theory. Annals of Mathematics, 64, 182–206. CrossRefMathSciNetGoogle Scholar
  22. 65.
    Mayne, D. Q., Rawlings, J. B., Rao, C. V., & Scokaert, P. O. M. (2000). Constrained model predictive control: stability and optimality. Automatica, 36, 789–814. CrossRefMATHMathSciNetGoogle Scholar
  23. 67.
    Mhaskar, P., El-Farra, N. H., & Christofides, P. D. (2005). Predictive control of switched nonlinear systems with scheduled mode transitions. IEEE Transactions on Automatic Control, 50, 1670–1680. CrossRefMathSciNetGoogle Scholar
  24. 68.
    Mhaskar, P., El-Farra, N. H., & Christofides, P. D. (2006). Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control. Systems & Control Letters, 55, 650–659. CrossRefMATHMathSciNetGoogle Scholar
  25. 69.
    Mhaskar, P., Gani, A., McFall, C., Christofides, P. D., & Davis, J. F. (2007). Fault-tolerant control of nonlinear process systems subject to sensor faults. AIChE Journal, 53, 654–668. CrossRefGoogle Scholar
  26. 70.
    Montestruque, L. A., & Antsaklis, P. J. (2003). On the model-based control of networked systems. Automatica, 39, 1837–1843. CrossRefMATHMathSciNetGoogle Scholar
  27. 71.
    Montestruque, L. A., & Antsaklis, P. J. (2004). Stability of model-based networked control systems with time-varying transmission times. IEEE Transactions on Automatic Control, 49, 1562–1572. CrossRefMathSciNetGoogle Scholar
  28. 72.
    Muñoz de la Peña, D., & Christofides, P. D. (2008). Lyapunov-based model predictive control of nonlinear systems subject to data losses. IEEE Transactions on Automatic Control, 53, 2076–2089. CrossRefGoogle Scholar
  29. 74.
    Naghshtabrizi, P., & Hespanha, J. (2005). Designing an observer-based controller for a network control system. In Proceedings of the 44th IEEE conference on decision and control and the European control conference 2005 (pp. 848–853). Seville, Spain. CrossRefGoogle Scholar
  30. 75.
    Naghshtabrizi, P., & Hespanha, J. (2006). Anticipative and non-anticipative controller design for network control systems. In Lecture notes in control and information sciences: Vol. 331. Networked embedded sensing and control (pp. 203–218). CrossRefGoogle Scholar
  31. 78.
    Nešić, D., & Teel, A. R. (2004b). Input-to-state stability of networked control systems. Automatica, 40, 2121–2128. MATHGoogle Scholar
  32. 79.
    Nešić, D., Teel, A., & Kokotovic, P. (1999). Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete time approximations. Systems & Control Letters, 38, 259–270. CrossRefMATHMathSciNetGoogle Scholar
  33. 86.
    Primbs, J. A., Nevistic, V., & Doyle, J. C. (2000). A receding horizon generalization of pointwise min-norm controllers. IEEE Transactions on Automatic Control, 45, 898–909. CrossRefMATHMathSciNetGoogle Scholar
  34. 89.
    Qin, S. J., & Badgwell, T. A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, 11, 733–764. CrossRefGoogle Scholar
  35. 91.
    Rawlings, J. B. (2000). Tutorial overview of model predictive control. IEEE Control Systems Magazine, 20, 38–52. CrossRefGoogle Scholar
  36. 97.
    Sontag, E. (1989). A ‘universal’ construction of Artstein’s theorem on nonlinear stabilization. Systems & Control Letters, 13, 117–123. CrossRefMATHMathSciNetGoogle Scholar
  37. 110.
    Walsh, G., Beldiman, O., & Bushnell, L. (2001). Asymptotic behavior of nonlinear networked control systems. IEEE Transactions on Automatic Control, 46, 1093–1097. CrossRefMATHMathSciNetGoogle Scholar
  38. 111.
    Walsh, G., Ye, H., & Bushnell, L. (2002). Stability analysis of networked control systems. IEEE Transactions on Control Systems Technology, 10, 438–446. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Panagiotis D. Christofides
    • 1
  • Jinfeng Liu
    • 1
  • David Muñoz de la Peña
    • 2
  1. 1.Department of Chemical and Biomolecular EngineeringUniversity of California, Los AngelesLos AngelesUSA
  2. 2.Departamento de Ingeniería de Sistemas y AutomáticaUniversidad de SevillaSevillaSpain

Personalised recommendations