Implementation of Mixed-integer Programming on Embedded System
One of the most widespread modern control strategies is the discrete-time Model Predictive Control (MPC) method which requires the solution of the quadratic programming problem. For systems with binary input variables the quadratic problem is replaced by more challenging Mixed-Integer Quadratic Prog...
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| Vydáno v: | Procedia engineering Ročník 100; s. 1649 - 1656 |
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| Jazyk: | angličtina |
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Elsevier Ltd
2015
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| ISSN: | 1877-7058, 1877-7058 |
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| Abstract | One of the most widespread modern control strategies is the discrete-time Model Predictive Control (MPC) method which requires the solution of the quadratic programming problem. For systems with binary input variables the quadratic problem is replaced by more challenging Mixed-Integer Quadratic Programming (MIQP) problem. The objective of this work is the implementation of MIQP problem solver in a low power embedded computing platform with limited computational power and limited memory. The MIQP problem is solved using branch-and-bound method and the solution of the relaxed original quadratic problems with equality and inequality constraints solved in the nodes of a binary tree is found with interior-point algorithm. A simulation study of the reserve constrained economic dispatch problem for power generators with prohibited zones is presented. Simulation results show the applicability of the proposed solver for small size MIQP problems. |
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| AbstractList | One of the most widespread modern control strategies is the discrete-time Model Predictive Control (MPC) method which requires the solution of the quadratic programming problem. For systems with binary input variables the quadratic problem is replaced by more challenging Mixed-Integer Quadratic Programming (MIQP) problem. The objective of this work is the implementation of MIQP problem solver in a low power embedded computing platform with limited computational power and limited memory. The MIQP problem is solved using branch-and-bound method and the solution of the relaxed original quadratic problems with equality and inequality constraints solved in the nodes of a binary tree is found with interior-point algorithm. A simulation study of the reserve constrained economic dispatch problem for power generators with prohibited zones is presented. Simulation results show the applicability of the proposed solver for small size MIQP problems. |
| Author | Novak, Jakub Chalupa, Petr |
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| CitedBy_id | crossref_primary_10_1016_j_apenergy_2016_12_068 crossref_primary_10_1002_2050_7038_12681 crossref_primary_10_1051_matecconf_20167602013 |
| Cites_doi | 10.1109/TCST.2013.2296211 10.1007/s12532-008-0001-1 10.1109/ACC.2012.6315076 10.1109/TCST.2009.2017934 10.1007/BF01074820 10.1137/1.9780898719604 10.1109/59.221233 10.2507/23rd.daaam.proceedings.006 10.1016/S0005-1098(98)00178-2 |
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| Keywords | Embedded System Mixed-Integer Quadratic Programming Optimization Branch-and-Bound Economic Dispatch |
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| References | J. Currie, A. Prince-Pike, D.I. Wilson, Auto-code generation for fast embedded model predictive controllers, Proceedings of the International Conference on Mechatronics and Machine Vision in Practice (2012) 122-128. M.Z. Djurovic, A. Milancic, M. Krsulja, A simplified model of quadratic cost function for thermal generators. Proceedings of the 23rd DAAAM Symposium (2012) 25-25. R.T. Meyer, M. Žefran, R.A. DeCarlo, A comparison of the embedding method with multiparametric programming, mixed-integer programming, gradient-descent, and hybrid minimum principle-based methods, IEEE Transactions on Control Systems Technology 22(2014), 1784-1800. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, LAPACK Users’ Guide. Warrendale, PA: SIAM, 1999. A. Bemporad, M. Morari, Control of systems integrating logic, dynamics and constraints, Automatica 35(1999) 407-427. P. Zometa, M. Kogel, T. Faulwasser, R. Findeisen, Implementation aspects of model predictive control for embedded systems, Proceeding of the American Control Conference (2012) 1205-1210. J.R. Bunch, L. Kaufman. Some stable methods for calculating inertia and solving symmetric linear systems. Math. Comp. 31 (1977) 163-179. Y. Wang, S. Boyd, Fast model predictive control using online optimization, IEEE Transactions on Control Systems Technology 18(2010), 267-278. L. A. Wolsey, Integer programming, John Wiley & Sons, Inc., 1998. O. V. Volkovich, V.A. Roshchin, and I. V. Sergienko. Models and methods of solution of quadratic integer programming problems. Cybernetics 23(1987) 289-305. T. Achterberg, SCIP: Solving constraint integer programs, Mathematical Programming Computation 1(2009) 1-41. J. Clausen, Branch and Bound Algorithms - Principles and Examples, 1999: http://janders.eecg.toronto.edu/1387/readings/b_and_b.pdf. J. Nocedal, S. Wright, Numerical Optimization, Springer, 2006. A. Bemporad, Hybrid Toolbox - User's Guide, 2004. http://cse.lab.imtlucca.it/∼bemporad/hybrid/toolbox. F. N. Lee, A.M. Breipohl, Reserve constrained economic dispatch with prohibited operating zones. IEEE Transactions on Power Systems 8(1993) 246-254. B. Huyck, H.J. Ferreau, M. Diehl, J. De Brabanter, J.F. M. Van Impe, B. De Moor, F. Logist, Towards Online Model Predictive Control on a Programmable Logic Controller: Practical Considerations, Mathematical Problems in Engineering, Volume 2012 (2012). M. Vašak, N. Peric, Model predictive control – a recent advance in control theory, Proceedings of the International Conference “Business System Management – UPS 2004” (2004) 263-267. 10.1016/j.proeng.2015.01.539_bib0050 10.1016/j.proeng.2015.01.539_bib0040 10.1016/j.proeng.2015.01.539_bib0030 10.1016/j.proeng.2015.01.539_bib0085 10.1016/j.proeng.2015.01.539_bib0020 10.1016/j.proeng.2015.01.539_bib0075 10.1016/j.proeng.2015.01.539_bib0080 10.1016/j.proeng.2015.01.539_bib0070 10.1016/j.proeng.2015.01.539_bib0060 10.1016/j.proeng.2015.01.539_bib0025 10.1016/j.proeng.2015.01.539_bib0015 10.1016/j.proeng.2015.01.539_bib0005 10.1016/j.proeng.2015.01.539_bib0010 10.1016/j.proeng.2015.01.539_bib0065 10.1016/j.proeng.2015.01.539_bib0055 10.1016/j.proeng.2015.01.539_bib0045 10.1016/j.proeng.2015.01.539_bib0035 |
| References_xml | – reference: A. Bemporad, Hybrid Toolbox - User's Guide, 2004. http://cse.lab.imtlucca.it/∼bemporad/hybrid/toolbox. – reference: B. Huyck, H.J. Ferreau, M. Diehl, J. De Brabanter, J.F. M. Van Impe, B. De Moor, F. Logist, Towards Online Model Predictive Control on a Programmable Logic Controller: Practical Considerations, Mathematical Problems in Engineering, Volume 2012 (2012). – reference: T. Achterberg, SCIP: Solving constraint integer programs, Mathematical Programming Computation 1(2009) 1-41. – reference: O. V. Volkovich, V.A. Roshchin, and I. V. Sergienko. Models and methods of solution of quadratic integer programming problems. Cybernetics 23(1987) 289-305. – reference: P. Zometa, M. Kogel, T. Faulwasser, R. Findeisen, Implementation aspects of model predictive control for embedded systems, Proceeding of the American Control Conference (2012) 1205-1210. – reference: F. N. Lee, A.M. Breipohl, Reserve constrained economic dispatch with prohibited operating zones. IEEE Transactions on Power Systems 8(1993) 246-254. – reference: L. A. Wolsey, Integer programming, John Wiley & Sons, Inc., 1998. – reference: J. Currie, A. Prince-Pike, D.I. Wilson, Auto-code generation for fast embedded model predictive controllers, Proceedings of the International Conference on Mechatronics and Machine Vision in Practice (2012) 122-128. – reference: J.R. Bunch, L. Kaufman. Some stable methods for calculating inertia and solving symmetric linear systems. Math. Comp. 31 (1977) 163-179. – reference: J. Clausen, Branch and Bound Algorithms - Principles and Examples, 1999: http://janders.eecg.toronto.edu/1387/readings/b_and_b.pdf. – reference: E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, LAPACK Users’ Guide. Warrendale, PA: SIAM, 1999. – reference: J. Nocedal, S. Wright, Numerical Optimization, Springer, 2006. – reference: M. Vašak, N. Peric, Model predictive control – a recent advance in control theory, Proceedings of the International Conference “Business System Management – UPS 2004” (2004) 263-267. – reference: A. Bemporad, M. Morari, Control of systems integrating logic, dynamics and constraints, Automatica 35(1999) 407-427. – reference: Y. Wang, S. Boyd, Fast model predictive control using online optimization, IEEE Transactions on Control Systems Technology 18(2010), 267-278. – reference: M.Z. Djurovic, A. Milancic, M. Krsulja, A simplified model of quadratic cost function for thermal generators. Proceedings of the 23rd DAAAM Symposium (2012) 25-25. – reference: R.T. Meyer, M. Žefran, R.A. DeCarlo, A comparison of the embedding method with multiparametric programming, mixed-integer programming, gradient-descent, and hybrid minimum principle-based methods, IEEE Transactions on Control Systems Technology 22(2014), 1784-1800. – ident: 10.1016/j.proeng.2015.01.539_bib0060 – ident: 10.1016/j.proeng.2015.01.539_bib0040 doi: 10.1109/TCST.2013.2296211 – ident: 10.1016/j.proeng.2015.01.539_bib0025 doi: 10.1007/s12532-008-0001-1 – ident: 10.1016/j.proeng.2015.01.539_bib0010 – ident: 10.1016/j.proeng.2015.01.539_bib0005 – ident: 10.1016/j.proeng.2015.01.539_bib0065 – ident: 10.1016/j.proeng.2015.01.539_bib0050 doi: 10.1109/ACC.2012.6315076 – ident: 10.1016/j.proeng.2015.01.539_bib0035 doi: 10.1109/TCST.2009.2017934 – ident: 10.1016/j.proeng.2015.01.539_bib0020 doi: 10.1007/BF01074820 – ident: 10.1016/j.proeng.2015.01.539_bib0070 doi: 10.1137/1.9780898719604 – ident: 10.1016/j.proeng.2015.01.539_bib0045 – ident: 10.1016/j.proeng.2015.01.539_bib0085 doi: 10.1109/59.221233 – ident: 10.1016/j.proeng.2015.01.539_bib0030 – ident: 10.1016/j.proeng.2015.01.539_bib0080 doi: 10.2507/23rd.daaam.proceedings.006 – ident: 10.1016/j.proeng.2015.01.539_bib0055 – ident: 10.1016/j.proeng.2015.01.539_bib0015 doi: 10.1016/S0005-1098(98)00178-2 – ident: 10.1016/j.proeng.2015.01.539_bib0075 |
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| Title | Implementation of Mixed-integer Programming on Embedded System |
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