Parallel Implementation of Hybrid MPC

  • D. AxehillEmail author
  • A. Hansson
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 69)


In this chapter parallel implementations of hybrid MPC will be discussed. Different methods for achieving parallelism at different levels of the algorithms will be surveyed. It will be seen that there are many possible ways of obtaining parallelism for hybrid MPC, and it is by no means clear which possibilities that should be utilized to achieve the best possible performance. To answer this question is a challenge for future research.


Quadratic Programming Model Predictive Control Quadratic Programming Problem Mixed Integer Quadratic Programming Good Integer Solution 
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.
    S. Arvindam, V. Kumar, V.N. Rao, Floorplan optimization on multiprocessors, in Proceedings of the 1989 International Conference on Computer Design, pp. 109–114, Hyatt Regency Hotel, Cambridge, USA, October 1989Google Scholar
  2. 2.
    D. Axehill, Integer quadratic programming for control and communication, PhD thesis, Linköping University, 2008Google Scholar
  3. 3.
    D. Axehill, A. Hansson, A mixed integer dual quadratic programming algorithm tailored for MPC, in Proceedings of the 45th IEEE Conference on Decision and Control, pp. 5693–5698, Manchester Grand Hyatt, San Diego, USA, December 2006Google Scholar
  4. 4.
    D. Axehill, A. Hansson, A dual gradient projection quadratic programming algorithm tailored for model predictive control, in Proceedings of the 47th IEEE Conference on Decision and Control, pp. 3057–3064, Fiesta Americana Grand Coral Beach, Cancun, Mexico, December 2008Google Scholar
  5. 5.
    D. Axehill, A. Hansson, L. Vandenberghe, Relaxations applicable to mixed integer predictive control—comparisons and efficient computations, in Proceedings of the 46th IEEE Conference on Decision and Control, pp. 4103–4109, Hilton New Orleans Riverside, New Orleans, USA, December 2007Google Scholar
  6. 6.
    D. Axehill, M. Morari, Improved complexity analysis of branch and bound for hybrid MPC, in Proceedings of the 49th IEEE Conference on Decision and Control, pp. 4216–4222, Hilton Atlanta, Atlanta, USA, December 2010Google Scholar
  7. 7.
    D. Axehill, J. Sjöberg, Adaptive cruise control for heavy vehicles—hybrid control and MPC, Master’s thesis, Linköpings universitet, February 2003Google Scholar
  8. 8.
    D. Axehill, L. Vandenberghe, A. Hansson, Convex relaxations for mixed integer predictive control. Automatica 46(9), 1540–1545 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    D. Axehill, A. Hansson, Towards parallel implementation of hybrid MPC, in Distributed Decision Making and Control, chapter 14, ed. by R. Johansson, A. Rantzer (Springer, Berlin, 2011), pp. 313–338Google Scholar
  10. 10.
    M. Baotic, Optimal control of piecewise affine systems—a multi-parametric approach. PhD thesis, ETH, March 2005Google Scholar
  11. 11.
    T. Barth, B. Freisleben, M. Grauer, F. Thilo, Distributed solution of optimal hybrid control problems on networks of workstations, in Proceedings Second IEEE International Conference on Cluster Computing, p. 162, Chemnitz, Germany, November 2000Google Scholar
  12. 12.
    R.A. Bartlett, L.T. Biegler, J. Backstrom, V. Gopal, Quadratic programming algorithms for large-scale model predictive control. J. Process Control 12, 775–795 (2002)CrossRefGoogle Scholar
  13. 13.
    A. Bemporad, Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form. IEEE Trans. Automat. Control 49(5), 832–838 (2004)Google Scholar
  14. 14.
    A. Bemporad, N. Giorgetti, Logic-based solution methods for optimal control of hybrid systems. IEEE Trans. Automat. Control 51(6):963–976 (2006)Google Scholar
  15. 15.
    A. Bemporad, D. Mignone, A Matlab function for solving mixed integer quadratic programs version 1.02 user guide. Technical report, Institut für Automatik, ETH, 2000Google Scholar
  16. 16.
    A. Bemporad, M. Morari, Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    J.F. Benders, Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238–252 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    D.P. Bertsekas, J.N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Upper Saddle River, 1989)zbMATHGoogle Scholar
  19. 19.
    L.S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, R.C. Whaley, ScaLAPACK Users’ Guide (Society for Industrial and Applied Mathematics, Philadelphia, 1997)CrossRefzbMATHGoogle Scholar
  20. 20.
    G.B. Dantzig, P. Wolfe, Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)CrossRefzbMATHGoogle Scholar
  21. 21.
    M. Diehl, H.J. Ferreau, N. Haverbeke, Nonlinear model predictive control, in Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation (Springer, Berlin, 2009), pp. 391–417Google Scholar
  22. 22.
    H. Everett, Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Oper. Res. 11(3), 399–417 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    G. Ferrari-Trecate, D. Mignone, D. Castagnoli, M. Morari, Mixed logical dynamical model of a hydroelectric power plant, in Proceedings of the 4th International Conference Automation of Mixed Processes: Hybrid Dynamic Systems, Dortmund, Germany, 2000Google Scholar
  24. 24.
    H.J. Ferreau, H.G. Bock, M. Diehl, An online active set strategy to overcome the limitations of explicit MPC. Int. J. Robust Nonlinear Control 18(8), 816–830 (2008)MathSciNetCrossRefGoogle Scholar
  25. 25.
    R. Fletcher, S. Leyffer, Numerical experience with lower bounds for MIQP branch-and-bound. SIAM J. Optim. 8(2), 604–616 (May 1998)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    A.Y. Grama, V. Kumar, A survey of parallel search algorithms for discrete optimization problems. ORSA J. Comput. 7(4), 365–385 (1995)CrossRefzbMATHGoogle Scholar
  27. 27.
    A. Hansson, A primal-dual interior-point method for robust optimal control of linear discrete-time systems. IEEE Trans. Automat. Control 45(9):1639–1655 (2000)Google Scholar
  28. 28.
    I. Harjunkoski, V. Jain, I. Grossmann, Hybrid mixedinteger/constraint logic programming strategies for solving scheduling and combinatorical optimization problems. Comput. Chem. Eng. 24, 337–343 (2000)CrossRefGoogle Scholar
  29. 29.
    W.P.M.H. Heemels, B. De Schutter, A. Bemporad, Equivalence of hybrid dynamical models. Automatica 37, 1085–1091 (2001)CrossRefzbMATHGoogle Scholar
  30. 30.
    H. Jonson, A Newton method for solving non-linear optimal control problems with general constraints, PhD thesis, Linköpings Tekniska Högskola, 1983Google Scholar
  31. 31.
    M. Åkerblad, A. Hansson, Efficient solution of second order cone program for model predictive control. Int. J. Control 77(1), 55–77 (2004)CrossRefGoogle Scholar
  32. 32.
    L.S. Lasdon, Optimization Theory for Large Systems (MacMillan, New York, 1970)zbMATHGoogle Scholar
  33. 33.
    L.S. Lasdon, Optimization Theory for Large Systems (Dover, New York, 2002)zbMATHGoogle Scholar
  34. 34.
    J. Löfberg, Yalmip: a toolbox for modeling and optimization in MATLAB, in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004Google Scholar
  35. 35.
    B. Lie, M.D. Díez, T.A. Hauge, A comparison of implementation strategies for MPC. Model. Identif. Control 26(1), 39–50 (2005)MathSciNetCrossRefGoogle Scholar
  36. 36.
    E. Mestan, E.M. Turkay, Y. Arkun, Optimization of operations in supply chain systems using hybrid systems approach and model predictive control. Ind. Eng. Chem. Res. 45, 6493–6503 (2006)CrossRefGoogle Scholar
  37. 37.
    P.J. Modi, W.-M. Shen, M. Tambe, Adopt: asynchronous distributed constraint optimization with quality guarantees. Artif. Intell. 161, 149–180 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    J. Nocedal, S.J. Wright, Numerical Optimization, 2nd edn (Springer, Berlin, 2006)Google Scholar
  39. 39.
    G. Ottosson, Integration of constraint programming and integer programming for combinatorial optimization, PhD thesis, Computer Science Department, Information Technology, Uppsala, Sweden, 2000Google Scholar
  40. 40.
    P.M. Pardalos, L. Pitsolulis, T. Mavridou, M.G.C. Resende, Parallel search for combinatorial optimization: Genetic algorithms, simulated annealing, tabu search and GRASP, in Parallel Algorithms for Irregularly Structured Problems, vol. 980, Lecture Notes in Computer Science, ed. by P. Sanders (Springer, Berlin, 1995), pp. 317–331Google Scholar
  41. 41.
    C.V. Rao, S.J. Wright, J.B. Rawlings, Application of interior-point methods to model predictive control. J. Optim. Theory Appl. 99(3), 723–757 (1998)Google Scholar
  42. 42.
    S. Richter, C.N. Jones, M. Morari, Real-time input-constrained MPC using fast gradient methods, in Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp. 7387–7393, Shanghai, China, 2009Google Scholar
  43. 43.
    A.N. Tarau, B. de Schutter, J. Hellendoorn, Centralized, decentralized, and distributed model predictive control for route choice in automated baggage handling systems. J. Control Eng. Appl. Inf. 11(3), 24–31 (2009)Google Scholar
  44. 44.
    F.D. Torrisi, A. Bemporad, HYSDEL—a tool for generating computational hybrid models for analysis and synthesis problems. IEEE Trans. Automat. Control 12(2):235–249 (2004)Google Scholar
  45. 45.
    E.P.K. Tsang, Foundations of Constraint Satisfaction (Academic Press, London, 1993)Google Scholar
  46. 46.
    L. Vandenberghe, S. Boyd, M. Nouralishahi, Robust linear programming and optimal control. Technical report, Department of Electrical Engineering, University of California Los Angeles, 2002, 2002)Google Scholar
  47. 47.
    O.V. Volkovich, V.A. Roshchin, I.V. Sergienko, Models and methods of solution of quadratic integer programming problems. Cybernetics 23, 289–305 (1987)CrossRefzbMATHGoogle Scholar
  48. 48.
    Y. Wang, S. Boyd, Fast model predictive control using online optimization. IEEE Trans. Control Syst. Technol. 18(2):267–278 (2010)Google Scholar
  49. 49.
    L.A. Wolsey, Integer Programming (John Wiley, New York, 1998)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Division of Automatic ControlLinköping UniversityLinköpingSweden

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