Advertisement

On the Selection of Tuning Parameters in Predictive Controllers Based on NSGA-II

  • R. C. Gutiérrez-Urquídez
  • G. Valencia-Palomo
  • O. M. Rodríguez-Elías
  • F. R. López-Estrada
  • J. A. Orrante-Sakanassi
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 785)

Abstract

In the design of linear (model) predictive controllers (MPC), tuning plays a very important role. However, there is a problem not yet fully resolved: how to determine the best strategy for the selection of the optimal tuning parameters in order to obtain good performance with a large feasibility region, but maintaining a low computational load of the control algorithm? Because these objectives determine the proper functioning of the controller and are committed to each other, adjusting the controller parameters becomes a difficult task. The main contribution of this paper is to revise a method that uses the Nondominated Sorting Genetic Algorithm II (NSGA-II) for the parameter selection of a predictive control algorithm that has been parameterized with Laguerre functions (LOMPC) in order to explore the efficiency and provide statistical significance of the algorithm. Numerical simulations show that NSGA-II is a useful tool to obtain consistently good solutions for the selection of MPC tuning parameters.

Keywords

Predictive control NSGA-II Tuning Multi-objective optimization 

References

  1. 1.
    Aicha, F.B., Bouani, F., Ksouri, M.: A multivariable multiobjective predictive controller. Int. J. Appl. Math. Comput. Sci. 23(1), 35–45 (2013)MathSciNetMATHGoogle Scholar
  2. 2.
    Bacic, M., Cannon, M., Lee, Y.I., Kouvaritakis, B.: General interpolation in MPC and its advantages. IEEE Trans. Autom. Control 48(6), 1092–1096 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bemporad, A., Filippi, C.: Suboptimal explicit MPC via approximate multiparametric quadratic programming. In: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida (2001)Google Scholar
  4. 4.
    Bemporad, A., Munoz de la Peña, D.: Multiobjective model predictive control. Automatica 45, 2823–2830 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bunin, G., Fraire-Tirado, F., Francois, G., Bonvin, D.: Run-to-run MPC tuning via gradient descent. In: 22nd European Symposium on Computer Aided Process Engineering, London (2012)Google Scholar
  6. 6.
    Camacho, E.F., Bordons, C.: Control predictivo: pasado, presente y futuro. Revista Iberoamericana de Automática e Informática Industrial 1(3), 5–28 (2004)Google Scholar
  7. 7.
    Coello-Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation). Springer-Verlag New York, Inc., New York (2006)MATHGoogle Scholar
  8. 8.
    Cutler, C.R., Ramarker, B.C.: Dynamic matrix control - a computed algoritm. In: Proceedings of the 86th National Meeting of the American Institute of Chemical Engineers (AIChe) (1979)Google Scholar
  9. 9.
    Deb, K.: A fast and elitist multiobjetive genetic algorithm NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  10. 10.
    Deb, K.: Optimization using evolutionary algorithms: an introduction. Technical report KanGAL 2011003, Department of Mechanical Engineering, Kanpur, India, February 2011Google Scholar
  11. 11.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)MathSciNetMATHGoogle Scholar
  12. 12.
    Deb, K., Anand, A., Joshi, D.: A computationally efficient evolutionary algorithm for real-parameter optimization. Evol. Comput. 10(4), 371–395 (2002)CrossRefGoogle Scholar
  13. 13.
    Deb, K., Beyer, H.G.: Self-adaptive genetic algorithms with simulated binary crossover. Technical report CI-61 \(\backslash \) 99, Self-Adaptive Genetic Algorithms with Simulated Binary Crossover. Department of Computer Science University of Dortmund, Dortmund, Germany, March 1999Google Scholar
  14. 14.
    Dellnitz, M., Ober-Blöbaum, S., Post, M., Schütze, O., Thiere, B.: A multi-objective approach to the design of low thrust space trajectories using optimal control. Celest. Mech. Dyn. Astron. 105(13), 33–59 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Dellnitz, M., Schütze, O., Hestermeyer, T.: Covering Pareto sets by multilevel subdivision techniques. J. Optim. Theory Appl. 124(1), 113–136 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fernández, J., Schütze, O., Hernández, C.: Parallel simple cell mapping for multi-objective optimization. Eng. Optim. 48(11), 1845–1868 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Fleming, P.J., Purshouse, R.C.: Evolutionary algorithms in control systems engineering: a survey. Control Eng. Pract. 10(11), 1223–1241 (2002)CrossRefGoogle Scholar
  18. 18.
    Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. Series on Computational Intelligence, vol. 3. Wiley-IEEE Press, Hoboken (2006)MATHGoogle Scholar
  19. 19.
    Gambier, A.: MPC and PID control based on multi-objective optimization. In: American Control Conference, 2008, pp. 4727–4732. IEEE (2008)Google Scholar
  20. 20.
    Garriga, J., Soroush, M.: Model predictive control tuning methods: a review. Ind. Eng. Chem. Res. 49, 3505–3515 (2010)CrossRefGoogle Scholar
  21. 21.
    Gutiérrez-Urquídez, R., Valencia-Palomo, G., Rodrıguez-Elıas, O.M., Trujillo, L.: Systematic selection of tuning parameters for efficient predictive controllers using a multiobjective evolutionary algorithm. Appl. Soft Comput. 31, 326–338 (2015)CrossRefGoogle Scholar
  22. 22.
    Johansson, K.H.: The quadruple-tank process: a multivariable laboratory process with an adjustable zero. IEEE Trans. Control Syst. Technol. 8(3), 456–465 (2000)CrossRefGoogle Scholar
  23. 23.
    Khan, B., Rossiter, J.A.: Robust MPC algorithms using alternative parameterisations. In: UKACC International Conference on Control 2012, Cardiff, UK, pp. 3–5 (2012)Google Scholar
  24. 24.
    Khan, B., Rossiter, J.A.: Alternative parameterisation within predictive control: a systematic selection. Int. J. Control 86(8), 1397–1409 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Khan, B., Rossiter, J.A., Valencia-Palomo, G.: Exploiting Kautz functions to improve feasibility in MPC. In: Procceedings of the 18th IFAC World Congress (2011)CrossRefGoogle Scholar
  26. 26.
    Lee, J.H.: Model predictive control review of the three decades of development. Int. J. Control Autom. Syst. 9(3), 415–424 (2011)CrossRefGoogle Scholar
  27. 27.
    Li, M., Zhou, P., Wang, H., Chai, T.: Nonlinear multiobjective MPC-based optimal operation of a high consistency refining system in papermaking. IEEE Trans. Syst. Man Cybern. Syst. (2017)Google Scholar
  28. 28.
    Maciejowski, J.M.: Predictive Control with Constraints. Prentice Hall, Harlow (2006)MATHGoogle Scholar
  29. 29.
    Mahmoudi, H., Lesani, M., Arab-Khabouri, D.: Online fuzzy tuning of weighting factor in model predictive control of PMSM. In: 13th Iranian Conference on Fuzzy Systems (IFSC), Qazvin, Iran (2013)Google Scholar
  30. 30.
    Mayne, D.Q., Rawllings, J.B., Rao, C.V., Skokaert, P.O.M.: Constrained model predictive control: stability and optimality. Automatica 36(6), 789–814 (2000)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Merabti, H., Belarbi, K.: Multi-objective predictive control: a solution using metaheuristics. Int. J. Comput. Sci. Inf. Technol. 6(6), 147 (2014)Google Scholar
  32. 32.
    Muske, K.R., Badgwell, T.A.: Disturbance modeling for offset-free linear model predictive control. J. Process Control 12(5), 617–632 (2002)CrossRefGoogle Scholar
  33. 33.
    Pareto, V.: Manual of Political Economy. Macmillan, London (1971)Google Scholar
  34. 34.
    Rossiter, J.A.: Model Predictive Control: A Practical Approach. CRC Press, Boca Raton (2005)Google Scholar
  35. 35.
    Rossiter, J.A.: A global approach to feasibility in linear MPC. In: Proceedings of the UKACC ICC (2006)Google Scholar
  36. 36.
    Rossiter, J.A., Wang, L., Valencia-Palomo, G.: Efficient algorithms for trading off feasibility and performance in predictive control. Int. J. Control 83(4), 789–797 (2010)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Ruchika, N.R.: Model predictive control: history and development. Int. J. Eng. Trends Technol. (IJETT) 4(6), 2600–2602 (2013)Google Scholar
  38. 38.
    Sardahi, Y., Sun, J.Q., Hernández, C., Schütze, O.: Many-objective optimal and robust design of PID controls with a state observer. J. Dyn. Syst. Meas. Control 139(2), 024502-2–024502-4 (2017)Google Scholar
  39. 39.
    Schütze, O., Vasile, M., Junge, O., Dellnitz, M., Izzo, D.: Designing optimal low thrust gravity assist trajectories using space pruning and a multi-objective approach. Eng. Optim. 41(2), 155–181 (2009)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Scokaert, P.O.M., Rawlingsm, J.B.: Constrained linear quadratic regulation. IEEE Trans. Autom. Control 43(8), 1163–1169 (1998)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Scokaert, P.O.M., Rawlings, J.B.: Feasibility issues in linear model predictive control. Am. Inst. Chem. Eng. (AIChE) J. 45(8), 1649–1659 (1999)CrossRefGoogle Scholar
  42. 42.
    Sun, J.Q., Xiong, F.R.: Cell mapping methods-beyond global analysis of nonlinear dynamic systems. Adv. Mech. 47(05), 201705 (2017)Google Scholar
  43. 43.
    Suzuki, R., Kawai, F., Ito, H., Nakazawa, C., Fukuyama, Y., Aiyoshi, E.: Automatic tuning of model predictive control using particle swarm optimization. In: IEEE Swarm Intelligence Symposium, HI, Honolulu, p. 2007 (2007)Google Scholar
  44. 44.
    Valencia-Palomo, G., Rossiter, J.A.: PLC implementation of a predictive controller using laguerre functions and multi-parametric solutions. In: Proceedings of the United Kingdom Automatic Control Conference, Coventry, UK (2010)Google Scholar
  45. 45.
    Valencia-Palomo, G., Rossiter, J.A., Jones, C.N., Gondhalekar, R., Khan, B.: Alternative parameterisations for predictive control: how and why. In: American Control Conference, San Francisco, CA, USA (2011)Google Scholar
  46. 46.
    Zitzler, E.: A tutorial on evolutionary multiobjective optimization. Technical report, Swiss Federal Institute of Technology, Computer Engineering and Networks Laboratory, Zurich (2002)Google Scholar
  47. 47.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Proceedings of the 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII), Birmingham, UK (2004)Google Scholar
  48. 48.
    Zitzler, E., Laumanns, M., Thiele, L.: Spea2: Improving the strength Pareto evolutionary algorithm. Technical report 103, SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Federal Institute of Technology (ETH), Department of Electrical Engineering Swiss, Zurich (2001)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • R. C. Gutiérrez-Urquídez
    • 1
  • G. Valencia-Palomo
    • 1
  • O. M. Rodríguez-Elías
    • 1
  • F. R. López-Estrada
    • 2
  • J. A. Orrante-Sakanassi
    • 3
  1. 1.Tecnológico Nacional de MéxicoInstituto Tecnológico de HermosilloHermosilloMexico
  2. 2.Tecnológico Nacional de MéxicoInstituto Tecnológico de Tuxtla GutiérrezTuxtla GutiérrezMexico
  3. 3.CONACYT-Tecnológico Nacional de MéxicoInstituto Tecnológico de HermosilloHermosilloMexico

Personalised recommendations