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Towards Parallel Implementation of Hybrid MPC—A Survey and Directions for Future Research

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Distributed Decision Making and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 417))

Abstract

In this chapter parallel implementations of hybridMPC 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 should be utilized to achieve the best possible performance. This question is a challenge for future research.

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References

  1. Åkerblad, M., Hansson, A.: Efficient solution of second order cone program for model predictive control. International Journal of Control 77(1), 55–77 (2004)

    Article  MathSciNet  Google Scholar 

  2. Antsaklis, P.: A brief introduction to the theory and applications of hybrid systems. Proc. IEEE, Special Issue on Hybrid Systems: Theory and Applications 88(7), 879–886 (2000)

    Google Scholar 

  3. Arvindam, S., Kumar, V., Rao, V.N.: Floorplan optimization on multiprocessors. In: Proc. 1989 Int. Conf. Computer Design (1989)

    Google Scholar 

  4. Axehill, D.: Integer quadratic programming for control and communication. Ph.D. thesis, Linköping University (2008), http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10642

  5. Axehill, D., Besselmann, T., Raimondo, D.M., Morari, M.: Suboptimal explicit hybrid MPC via branch and bound. In: Proc. 18th IFAC World Congress (IFAC 2011), Milan, Italy (2011)

    Google Scholar 

  6. Axehill, D., Hansson, A.: A mixed integer dual quadratic programming algorithm tailored for MPC. In: Proc. 45th IEEE Conf. Decision and Control (CDC 2006), San Diego, CA, pp. 5693–5698 (2006)

    Google Scholar 

  7. Axehill, D., Hansson, A.: A dual gradient projection quadratic programming algorithm tailored for model predictive control. In: Proc. 47th IEEE Conf. Decision and Control (CDC 2008), Cancun, Mexico, pp. 3057–3064 (2008)

    Google Scholar 

  8. Axehill, D., Hansson, A., Vandenberghe, L.: Relaxations applicable to mixed integer predictive control- Comparisons and efficient computations. In: Proc. 46th IEEE Conf. Decision and Control (CDC 2007), New Orleans, LA, pp. 4103–4109 (2007)

    Google Scholar 

  9. Axehill, D., Morari, M.: Improved complexity analysis of branch and bound for hybrid MPC. In: Proc. 49th IEEE Conf. Decision and Control (CDC 2010), Atlanta, GA, pp. 4216–4222 (2010)

    Google Scholar 

  10. Axehill, D., Sjöberg, J.: Adaptive cruise control for heavy vehicles—Hybrid control and MPC. Master’s thesis, Linköping University (2003)

    Google Scholar 

  11. Axehill, D., Vandenberghe, L., Hansson, A.: Convex relaxations for mixed integer predictive control. Automatica 46(9), 1540–1545 (2010)

    Article  MATH  Google Scholar 

  12. Baotic, M.: Optimal control of piecewise affine systems—A multi-parametric approach. Ph.D. thesis, ETH (2005), http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=2235

  13. Barth, T., Freisleben, B., Grauer, M., Thilo, F.: Distributed solution of optimal hybrid control problems on networks of workstations. In: Proc. Second IEEE Int. Conf. Cluster Computing (2000)

    Google Scholar 

  14. Bartlett, R.A., Biegler, L.T., Backstrom, J., Gopal, V.: Quadratic programming algorithms for large-scale model predictive control. Journal of Process Control 12, 775–795 (2002)

    Article  Google Scholar 

  15. Bemporad, A.: Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form. IEEE Trans. Audio and Electroacoustics 49(5), 832–838 (2004)

    MathSciNet  Google Scholar 

  16. Bemporad, A., Borrelli, F., Morari, M.: Model predictive control based on linear programming—The explicit solution. IEEE Trans. Automatic Control 47(12), 1974–1985 (2002)

    Article  MathSciNet  Google Scholar 

  17. Bemporad, A., Ferrari-Trecate, G., Morari, M.: Observability and controllability of piecewise affine and hybrid systems. IEEE Trans. Automatic Control 45(10), 1864–1876 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Bemporad, A., Giorgetti, N.: Logic-based solution methods for optimal control of hybrid systems. IEEE Trans. Automatic Control 51(6), 963–976 (2006)

    Article  MathSciNet  Google Scholar 

  19. Bemporad, A., Mignone, D.: A Matlab function for solving mixed integer quadratic programs version 1.02 user guide. Tech. rep., Institut fur Automatik, ETH (2000)

    Google Scholar 

  20. Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38, 3–20 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  21. Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1), 238–252 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bertsekas, D.P.: Nonlinear Programming. Athena Scientific (1995)

    Google Scholar 

  24. Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall (1989)

    Google Scholar 

  25. Blackford, L.S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK Users’ Guide. Society for Industrial and Applied Mathematics (1997)

    Google Scholar 

  26. Bockmayr, A., Kasper, T.: Branch and infer: a unifying framework for integer and finite domain constraint programming. INFORMS J. Comput. 10(3), 287–300 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  27. Borrelli, F., Baotić, M., Bemporad, A., Morari, M.: Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica 41, 1709–1721 (2005)

    Article  MATH  Google Scholar 

  28. Boyd, S., Xiao, L., Mutapcic, A., Mattingley, J.: Notes on decomposition methods— Notes for EE364B, Stanford University, Winter 2006-2007. Tech. rep., Information Systems Laboratory, Department of Electrical Engineering, Stanford (2008), http://see.stanford.edu/materials/lsocoee364b/08-decomposition_notes.pdf

  29. Camponogara, E., Jia, D., Krogh, B.H., Talukdar, S.: Distributed model predictive control. IEEE Control Systems Magazine 22(1), 44–52 (2002)

    Article  Google Scholar 

  30. Cassandras, C., Pepyne, D., Wardi, Y.: Optimal control of a class of hybrid systems. IEEE Trans. Automatic Control 46(3), 398–415 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  31. Cutler, C.R., Ramaker, B.L.: Dynamic matrix control—A computer control algorithm. In: Proc. AIChE National Meeting, Houston, TX (1979)

    Google Scholar 

  32. Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Operations Research 8(1), 101–111 (1960)

    Article  MATH  Google Scholar 

  33. De Schutter, B., van den Boom, T.J.J.: MPC for continuous piecewise-affine systems. Systems & Control Letters 52, 179–192 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  34. Diehl, M., Ferreau, H.J., Haverbeke, N.: Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation. In: Nonlinear Model Predictive Control, pp. 391–417. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  35. Du, X., Xi, Y., Li, S.: Distributed model predictive control for large-scale systems. In: Proc. American Control Conference (ACC 2001), vol. 4, pp. 3142–3143 (2001)

    Google Scholar 

  36. Dua, V., Bozinis, N.A., Pistikopoulos, E.N.: A multiparametric programming approach for mixed-integer quadratic engineering problems. Computers and Chemical Engineering 26, 715–733 (2002)

    Article  Google Scholar 

  37. Dua, V., Pistikopoulos, E.N.: An algorithm for the solution of multiparametric mixed integer linear programming problems. Annals of Operations Research 99, 123–139 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  38. Dunbar, W.B.: Distributed receding horizon control of dynamically coupled nonlinear systems. IEEE Trans. Automatic Control 52(7), 1249–1263 (2007)

    Article  MathSciNet  Google Scholar 

  39. Dunbar, W.B., Murray, R.M.: Distributed receding horizon control for multi-vehicle formation stabilization. Automatica 42(4), 549–558 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  40. Everett, H.: Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Operations Research 11(3), 399–417 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  41. Fawal, H.E., Georges, D., Bornard, G.: Optimal control of complex irrigation systems via decomposition-coordination and the use of augmented Lagrangian. In: Proc. 1998 IEEE Int. Conf. Systems, Man, and Cybernetics, vol. 4, pp. 3874–3879 (1998)

    Google Scholar 

  42. Ferrari-Trecate, G., Mignone, D., Castagnoli, D., Morari, M.: Mixed logical dynamical model of a hydroelectric power plant. In: Proc. 4th Int. Conf. Automation of Mixed Processes: Hybrid Dynamic Systems (2000)

    Google Scholar 

  43. Ferreau, H.J., Bock, H.G., Diehl, M.: An online active set strategy to overcome the limitations of explicit MPC. International Journal of Robust and Nonlinear Control 18(8), 816–830 (2008)

    Article  MathSciNet  Google Scholar 

  44. Fletcher, R., Leyffer, S.: Numerical experience with lower bounds for MIQP branch-and- bound. SIAM Journal on Optimization 8(2), 604–616 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  45. Floudas, C.A.: Nonlinear and Mixed-Integer Optimization. Oxford University Press (1995)

    Google Scholar 

  46. Garcia, C.E., Prett, D.M., Morari, M.: Model predictive control: Theory and practice—A survey. Automatica 3, 335–348 (1989)

    Article  Google Scholar 

  47. Georges, D.: Decentralized adaptive control for a water distribution system. In: Proc. Third IEEE Conf. Control Applications, vol. 2, pp. 1411–1416 (1994)

    Google Scholar 

  48. Gómez, M., Rodellar, J., Vea, F., Mantecón, J., Cardona, J.a.: Decentralized predictive control of multi-reach canals. In: Proc. 1998 IEEE Int. Conf. Systems, Man, and Cybernetics, vol. 4, pp. 3885–3890 (1998)

    Google Scholar 

  49. Grama, A.Y., Kumar, V.: A survey of parallel search algorithms for discrete optimization problems. ORSA Journal of Computing 7(4), 365–385 (1995)

    MATH  Google Scholar 

  50. Hansson, A.: A primal-dual interior-point method for robust optimal control of linear discrete-time systems. IEEE Trans. Automatic Control 45(9), 1639–1655 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  51. Harjunkoski, I., Jain, V., Grossmann, I.: Hybrid mixedinteger/constraint logic programming strategies for solving scheduling and combinatorical optimization problems. Comp. Chem. Eng. 24, 337–343 (2000)

    Article  Google Scholar 

  52. Heemels, W.P.M.H., De Schutter, B., Bemporad, A.: Equivalence of hybrid dynamical models. Automatica 37, 1085–1091 (2001)

    Article  MATH  Google Scholar 

  53. Heemels, W.P.M.H., De Schutter, B., Bemporad, A.: On the equivalence of classes of hybrid dynamical models. In: Proc. 40th IEEE Conf. Decision and Control (CDC 2001), Orlando, FL, pp. 364–369 (2001)

    Google Scholar 

  54. Jia, D., Krogh, B.H.: Distributed model predictive control. In: Proc. American Control Conference (ACC 2001), vol. 4, pp. 2767–2772 (2001)

    Google Scholar 

  55. Jonson, H.: A Newton method for solving non-linear optimal control problems with general constraints. Ph.D. thesis, Linköpings Tekniska Högskola (1983)

    Google Scholar 

  56. Katebi, M.R., Johnson, M.A.: Predictive control design for large-scale systems. Automatica 33(3), 421–425 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  57. Lasdon, L.S.: Optimization Theory for Large Systems. MacMillan Publishing Co. Inc., (1970)

    Google Scholar 

  58. Lasdon, L.S.: Optimization Theory for Large Systems. Dover Publications (2002)

    Google Scholar 

  59. Lie, B., Díez, M.D., Hauge, T.A.: A comparison of implementation strategies for MPC. Modeling, identification and control 26(1), 39–50 (2005)

    Article  MathSciNet  Google Scholar 

  60. Lincoln, B., Rantzer, A.: Optimizing linear system switching. In: Proc. 40th IEEE Conf. Decision and Control, Barcelona, pp. 2063–2068 (2001)

    Google Scholar 

  61. Löfberg, J.: Yalmip: A toolbox for modeling and optimization in MATLAB. In: Proc. CACSD Conference. Taipei, Taiwan (2004), http://control.ee.ethz.ch/joloef/yalmip.php

  62. Maciejowski, J.M.: Predictive Control with Constraints. Pearson Education Ltd (2002)

    Google Scholar 

  63. Mailler, R., Lesser, V.: Solving distributed constraint optimization problems using cooperative mediation. In: Proc. AAMAS, New York, USA, pp. 438–445 (2004)

    Google Scholar 

  64. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: Stability and optimality. Automatica 36, 789–814 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  65. Mestan, E., Turkay, E.M., Arkun, Y.: Optimization of operations in supply chain systems using hybrid systems approach and model predictive control. Ind. Eng. Chem. Res. 45, 6493–6503 (2006)

    Article  Google Scholar 

  66. Modi, P.J., Shen, W.M., Tambe, M.: Adopt: asynchronous distributed constraint optimization with quality guarantees. Artificial Intelligence 161, 149–180 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  67. Negenborn, R.R.: Multi-agent model predictive control with applications to power networks. Ph.D. thesis, Technische Universiteit Delft, Delft, Netherlands (2007)

    Google Scholar 

  68. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  69. Ottosson, G.: Integration of constraint programming and integer programming for combinatorial optimization. Ph.D. thesis, Computer Science Department, Information Technology, Uppsala, Sweden (2000)

    Google Scholar 

  70. Pardalos, P.M., Pitsolulis, L., Mavridou, T., Resende, M.G.C.: Parallel search for combinatorial optimization: Genetic algorithms, simulated annealing, tabu search and GRASP. In: Ferreira, A., Rolim, J.D.P. (eds.) IRREGULAR 1995. LNCS, vol. 980, pp. 317–331. Springer, Heidelberg (1995)

    Google Scholar 

  71. Qin, S.J., Badgwell, T.A.: A survey ofindustrial model predictive control technology. Control Engineering Practice 11, 722–764 (2003)

    Article  Google Scholar 

  72. Rao, C.V., Wright, S.J., Rawlings, J.B.: Application of interior-point methods to model pre¬dictive control. Journal of Optimization Theory and Applications 99(3), 723–757 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  73. Richter, S., Jones, C.N., Morari, M.: Real-time input-constrained MPC using fast gradient methods. In: Proc. 48h IEEE Conf. Decision and Control (CDC 2009) held jointly with 2009 28th Chinese Control Conference, Shanghai, China, pp. 7387–7393 (2009)

    Google Scholar 

  74. Rodosek, R., Wallace, M., Hajian, M.: A new approach to integrating mixed integer programming and constraint logic programming. Ann. Oper. Res. 86, 63–87 (1997)

    Article  MathSciNet  Google Scholar 

  75. Scattolini, R.: Architectures for distributed and hierarchical model predictive control. J. Process Control 19, 723–731 (2009)

    Article  Google Scholar 

  76. Sontag, E.D.: Nonlinear regulation: The piecewise linear approach. IEEE Trans. Automatic Control 26(2), 346–358 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  77. Tarau, A.N., de Schutter, B., Hellendoorn, J.: Centralized, decentralized, and distributed model predictive control for route choice in automated baggage handling systems. Journal of Control Engineering and Applied Informatics 11(3), 24–31 (2009)

    Google Scholar 

  78. Tøndel, P., Johansen, T.A., Bemporad, A.: An algorithm for multi-parametric quadratic programming and explicit MPC solutions. Automatica 39, 489–497 (2003)

    Article  Google Scholar 

  79. Torrisi, F.D., Bemporad, A.: HYSDEL—A tool for generating computational hybrid models for analysis and synthesis problems. IEEE Trans. Control Systems Technology 12(2), 235–249 (2004)

    Article  MathSciNet  Google Scholar 

  80. Tsang, E.P.K.: Foundations of Constraint Satisfaction. Academic Press, London (1993)

    Google Scholar 

  81. Vandenberghe, L., Boyd, S., Nouralishahi, M.: Robust linear programming and optimal control. Tech. rep., Dept. Electrical Engineering, Univ. California Los Angeles (2002)

    Google Scholar 

  82. Venkat, A.N., Hiskens, I.A., Rawlings, J.B., Wright, S.J.: Distributed MPC strategies with application to power system automatic generation control. IEEE Trans. Control Systems Technology 16(6), 1192–1206 (2008)

    Article  Google Scholar 

  83. Volkovich, O.V., Roshchin, V.A., Sergienko, I.V.: Models and methods of solution of quadratic integer programming problems. Cybernetics 23, 289–305 (1987)

    Article  MATH  Google Scholar 

  84. Wang, Y., Boyd, S.: Fast model predictive control using online optimization. IEEE Trans. Control Systems Technology 18(2), 267–278 (2010)

    Article  Google Scholar 

  85. Wolsey, L.A.: Integer Programming. John Wiley & Sons, Inc., New York (1998)

    MATH  Google Scholar 

  86. Xu, X., Antsaklis, P.: An approach to switched systems optimal control based on parameterization of the switching instants. In: Proc. IFAC World Congress, Barcelona, Spain (2002)

    Google Scholar 

  87. Zhu, G.Y., Henson, M.A.: Model predictive control of interconnected linear and nonlinear processes. Industrial and Engineering Chemistry Research 41(4), 801–816 (2002)

    Article  Google Scholar 

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Axehill, D., Hansson, A. (2012). Towards Parallel Implementation of Hybrid MPC—A Survey and Directions for Future Research. In: Johansson, R., Rantzer, A. (eds) Distributed Decision Making and Control. Lecture Notes in Control and Information Sciences, vol 417. Springer, London. https://doi.org/10.1007/978-1-4471-2265-4_14

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