Abstract
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.
With kind permission from Springer Science+Business Media: Distributed Decision Making and Control, Towards Parallel Implementation of Hybrid MPC—A Survey and Directions for Future Research, 417/2012, 2012, 313–338, D. Axehill and A. Hansson, figure 14.2, \(\copyright \) Springer-Verlag London Limited 2012.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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 1989
D. Axehill, Integer quadratic programming for control and communication, PhD thesis, Linköping University, 2008
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 2006
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 2008
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 2007
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 2010
D. Axehill, J. Sjöberg, Adaptive cruise control for heavy vehicles—hybrid control and MPC, Master’s thesis, Linköpings universitet, February 2003
D. Axehill, L. Vandenberghe, A. Hansson, Convex relaxations for mixed integer predictive control. Automatica 46(9), 1540–1545 (2010)
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. 313–338
M. Baotic, Optimal control of piecewise affine systems—a multi-parametric approach. PhD thesis, ETH, March 2005
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 2000
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)
A. Bemporad, Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form. IEEE Trans. Automat. Control 49(5), 832–838 (2004)
A. Bemporad, N. Giorgetti, Logic-based solution methods for optimal control of hybrid systems. IEEE Trans. Automat. Control 51(6):963–976 (2006)
A. Bemporad, D. Mignone, A Matlab function for solving mixed integer quadratic programs version 1.02 user guide. Technical report, Institut für Automatik, ETH, 2000
A. Bemporad, M. Morari, Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)
J.F. Benders, Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238–252 (1962)
D.P. Bertsekas, J.N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Upper Saddle River, 1989)
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)
G.B. Dantzig, P. Wolfe, Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)
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. 391–417
H. Everett, Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Oper. Res. 11(3), 399–417 (1963)
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, 2000
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)
R. Fletcher, S. Leyffer, Numerical experience with lower bounds for MIQP branch-and-bound. SIAM J. Optim. 8(2), 604–616 (May 1998)
A.Y. Grama, V. Kumar, A survey of parallel search algorithms for discrete optimization problems. ORSA J. Comput. 7(4), 365–385 (1995)
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)
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)
W.P.M.H. Heemels, B. De Schutter, A. Bemporad, Equivalence of hybrid dynamical models. Automatica 37, 1085–1091 (2001)
H. Jonson, A Newton method for solving non-linear optimal control problems with general constraints, PhD thesis, Linköpings Tekniska Högskola, 1983
M. Åkerblad, A. Hansson, Efficient solution of second order cone program for model predictive control. Int. J. Control 77(1), 55–77 (2004)
L.S. Lasdon, Optimization Theory for Large Systems (MacMillan, New York, 1970)
L.S. Lasdon, Optimization Theory for Large Systems (Dover, New York, 2002)
J. Löfberg, Yalmip: a toolbox for modeling and optimization in MATLAB, in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004
B. Lie, M.D. Díez, T.A. Hauge, A comparison of implementation strategies for MPC. Model. Identif. Control 26(1), 39–50 (2005)
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)
P.J. Modi, W.-M. Shen, M. Tambe, Adopt: asynchronous distributed constraint optimization with quality guarantees. Artif. Intell. 161, 149–180 (2005)
J. Nocedal, S.J. Wright, Numerical Optimization, 2nd edn (Springer, Berlin, 2006)
G. Ottosson, Integration of constraint programming and integer programming for combinatorial optimization, PhD thesis, Computer Science Department, Information Technology, Uppsala, Sweden, 2000
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. 317–331
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)
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, 2009
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)
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)
E.P.K. Tsang, Foundations of Constraint Satisfaction (Academic Press, London, 1993)
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)
O.V. Volkovich, V.A. Roshchin, I.V. Sergienko, Models and methods of solution of quadratic integer programming problems. Cybernetics 23, 289–305 (1987)
Y. Wang, S. Boyd, Fast model predictive control using online optimization. IEEE Trans. Control Syst. Technol. 18(2):267–278 (2010)
L.A. Wolsey, Integer Programming (John Wiley, New York, 1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Axehill, D., Hansson, A. (2014). Parallel Implementation of Hybrid MPC. In: Maestre, J., Negenborn, R. (eds) Distributed Model Predictive Control Made Easy. Intelligent Systems, Control and Automation: Science and Engineering, vol 69. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7006-5_23
Download citation
DOI: https://doi.org/10.1007/978-94-007-7006-5_23
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-7005-8
Online ISBN: 978-94-007-7006-5
eBook Packages: EngineeringEngineering (R0)