메뉴 건너뛰기




Volumn 22, Issue 3, 2012, Pages 540-550

Efficient direct multiple shooting for nonlinear model predictive control on long horizons

Author keywords

Benchmarks; Direct and simultaneous methods for optimal control; Nonlinear model predictive control; Sensitivity generation

Indexed keywords

ADJOINTS; BENCH-MARK PROBLEMS; BENCHMARKS; COMPUTATIONAL EFFORT; DERIVATIVE INFORMATION; DIRECT MULTIPLE SHOOTING; DYNAMIC PROCESS; EXPLICIT ONE-STEP METHOD; FINITE ELEMENT; MULTIPLE SHOOTING; NONLINEAR MODEL PREDICTIVE CONTROL; NUMERICAL DIFFERENTIATION; OPTIMAL CONTROLS; PREDICTION HORIZON; RELATIVE PERFORMANCE; SENSITIVITY GENERATION; SEQUENTIAL QUADRATIC PROGRAMMING METHOD; SIMULTANEOUS METHODS;

EID: 84857781474     PISSN: 09591524     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jprocont.2012.01.008     Document Type: Article
Times cited : (62)

References (52)
  • 1
    • 0037441411 scopus 로고    scopus 로고
    • An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization (Parts i and II)
    • Leineweber D., Bauer I., Schäfer A., Bock H., and Schlöder J. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization (Parts I and II) Computers & Chemical Engineering 27 2003 157 174
    • (2003) Computers & Chemical Engineering , vol.27 , pp. 157-174
    • Leineweber, D.1    Bauer, I.2    Schäfer, A.3    Bock, H.4    Schlöder, J.5
  • 2
    • 77956424886 scopus 로고    scopus 로고
    • A combined approach to nonlinear model predictive control of fast systems
    • Tamimi J., and Li P. A combined approach to nonlinear model predictive control of fast systems Journal of Process Control 20 2010 1092 1102
    • (2010) Journal of Process Control , vol.20 , pp. 1092-1102
    • Tamimi, J.1    Li, P.2
  • 5
    • 0002564462 scopus 로고
    • A Multiple Shooting algorithm for direct solution of optimal control problems
    • Pergamon Press Budapest Available at http://www.iwr.uni-heidelberg.de/ groups/agbock/FILES/Bock1984.pdf
    • Bock H., and Plitt K. A Multiple Shooting algorithm for direct solution of optimal control problems in: Proceedings of the 9th IFAC World Congress 1984 Pergamon Press Budapest 242 247 Available at http://www.iwr.uni-heidelberg.de/ groups/agbock/FILES/Bock1984.pdf
    • (1984) Proceedings of the 9th IFAC World Congress , pp. 242-247
    • Bock, H.1    Plitt, K.2
  • 6
    • 79957481281 scopus 로고    scopus 로고
    • Acado toolkit - An open-source framework for automatic control and dynamic optimization
    • Houska B., Ferreau H., and Diehl M. Acado toolkit - an open-source framework for automatic control and dynamic optimization Optimal Control Applications and Methods 32 2011 298 312
    • (2011) Optimal Control Applications and Methods , vol.32 , pp. 298-312
    • Houska, B.1    Ferreau, H.2    Diehl, M.3
  • 7
    • 77956874345 scopus 로고    scopus 로고
    • Modeling and optimization with Optimica and JModelica.org - Languages and tools for solving large-scale dynamic optimization problems
    • kesson J., rzén K., Gräfvert M., Bergdahl T., and Tummescheit H. Modeling and optimization with Optimica and JModelica.org - Languages and tools for solving large-scale dynamic optimization problems Computers & Chemical Engineering 34 2008 1737 1749
    • (2008) Computers & Chemical Engineering , vol.34 , pp. 1737-1749
    • Kesson, J.1    Rzén, K.2    Gräfvert, M.3    Bergdahl, T.4    Tummescheit, H.5
  • 10
    • 0033876326 scopus 로고    scopus 로고
    • Constrained model predictive control: Stability and optimality
    • DOI 10.1016/S0005-1098(99)00214-9
    • Mayne D.Q., Rawlings J.B., Rao C.V., and Scokaert P.O.M. Constrained model predictive control: stability and optimality Automatica 26 2000 789 814 (Pubitemid 30587683)
    • (2000) Automatica , vol.36 , Issue.6 , pp. 789-814
    • Mayne, D.Q.1    Rawlings, J.B.2    Rao, C.V.3    Scokaert, P.O.M.4
  • 12
    • 0037291591 scopus 로고    scopus 로고
    • Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximations
    • Rao C.V., Rawlings J.B., and Mayne D.Q. Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations IEEE Transactions on Automatic Control 48 2003 246 258
    • (2003) IEEE Transactions on Automatic Control , vol.48 , pp. 246-258
    • Rao, C.V.1    Rawlings, J.B.2    Mayne, D.Q.3
  • 13
    • 85014262532 scopus 로고    scopus 로고
    • Schnelle Algorithmen für die Zustands- und Parameterschätzung auf bewegten Horizonten
    • Diehl M., Kuehl P., Bock H., and Schlöder J. Schnelle Algorithmen für die Zustands- und Parameterschätzung auf bewegten Horizonten Automatisierungstechnik 54 2006 602 613
    • (2006) Automatisierungstechnik , vol.54 , pp. 602-613
    • Diehl, M.1    Kuehl, P.2    Bock, H.3    Schlöder, J.4
  • 16
    • 61349131958 scopus 로고    scopus 로고
    • A minima tracking variant of semi-infinite programming for the treatment of path constraints within direct solution of optimal control problems
    • Potschka A., Bock H., and Schlöder J. A minima tracking variant of semi-infinite programming for the treatment of path constraints within direct solution of optimal control problems Optimization Methods and Software 24 2009 237 252
    • (2009) Optimization Methods and Software , vol.24 , pp. 237-252
    • Potschka, A.1    Bock, H.2    Schlöder, J.3
  • 17
    • 0003982971 scopus 로고    scopus 로고
    • 2nd edition Springer Verlag Berlin Heidelberg New York ISBN 0-387-30303-0 (hardcover)
    • Nocedal J., and Wright S. Numerical Optimization 2nd edition 2006 Springer Verlag Berlin Heidelberg New York ISBN 0-387-30303-0 (hardcover)
    • (2006) Numerical Optimization
    • Nocedal, J.1    Wright, S.2
  • 19
    • 44349122057 scopus 로고    scopus 로고
    • Constrained Optimal Feedback Control for DAE
    • Biegler L. Ghattas O. Heinkenschloss M. Keyes D. van Bloemen Waanders B. SIAM
    • Bock H., Diehl M., Kostina E., and Schlöder J. Constrained Optimal Feedback Control for DAE Biegler L. Ghattas O. Heinkenschloss M. Keyes D. van Bloemen Waanders B. Real-Time PDE-Constrained Optimization 2007 SIAM 3 24
    • (2007) Real-Time PDE-Constrained Optimization , pp. 3-24
    • Bock, H.1    Diehl, M.2    Kostina, E.3    Schlöder, J.4
  • 20
    • 0012650693 scopus 로고
    • Über die numerische Auflösung von Differentialgleichungen
    • Runge C.D.T. Über die numerische Auflösung von Differentialgleichungen Mathematische Annalen 46 1895 167 178
    • (1895) Mathematische Annalen , vol.46 , pp. 167-178
    • Runge, C.D.T.1
  • 21
    • 0006451452 scopus 로고
    • Beitrag zur näherungsweisen Integration totaler Differentialgleichungen
    • Kutta M. Beitrag zur näherungsweisen Integration totaler Differentialgleichungen Zeitschrift für Mathematik und Physik 46 1901 435 453
    • (1901) Zeitschrift für Mathematik und Physik , vol.46 , pp. 435-453
    • Kutta, M.1
  • 22
    • 34250490894 scopus 로고
    • Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
    • Fehlberg E. Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle Computing 4 1969 93 106
    • (1969) Computing , vol.4 , pp. 93-106
    • Fehlberg, E.1
  • 23
    • 0000727595 scopus 로고    scopus 로고
    • Numerical methods for initial value problems and derivative generation for DAE models with application to optimum experimental design of chemical processes
    • Keil F. Mackens W. Voß H. Werther J. Springer
    • Bauer I., Bock H., Körkel S., and Schlöder J. Numerical methods for initial value problems and derivative generation for DAE models with application to optimum experimental design of chemical processes Keil F. Mackens W. Voß H. Werther J. Scientific Computing in Chemical Engineering II 1999 Springer 282 289
    • (1999) Scientific Computing in Chemical Engineering II , pp. 282-289
    • Bauer, I.1    Bock, H.2    Körkel, S.3    Schlöder, J.4
  • 24
    • 33747889036 scopus 로고    scopus 로고
    • Sensitivity analysis of differential-algebraic equations and partial differential equations
    • DOI 10.1016/j.compchemeng.2006.05.015, PII S0098135406001487, Papers from Chemical Process Control VII CPC VII
    • Petzold L., Li S., Cao Y., and Serban R. Sensitivity analysis of differential-algebraic equations and partial differential equations Computers & Chemical Engineering 30 2006 1553 1559 (Pubitemid 44292270)
    • (2006) Computers and Chemical Engineering , vol.30 , Issue.10-12 , pp. 1553-1559
    • Petzold, L.1    Li, S.2    Cao, Y.3    Serban, R.4
  • 25
    • 0021940614 scopus 로고
    • Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations
    • DOI 10.1016/0098-1354(85)85014-6
    • Caracotsios M., and Stewart W. Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations Computers & Chemical Engineering 9 1985 359 365 (Pubitemid 15565965)
    • (1985) Computers and Chemical Engineering , vol.9 , Issue.4 , pp. 359-365
    • Caracotsios Makis1    Stewart Warren, E.2
  • 26
    • 0002753571 scopus 로고
    • A description of DASSL: A differential/algebraic system solver
    • Stepleman R.S. North-Holland Amsterdam
    • Petzold L. A description of DASSL: a differential/algebraic system solver Stepleman R.S. Scientific Computing 1983 North-Holland Amsterdam 65 68
    • (1983) Scientific Computing , pp. 65-68
    • Petzold, L.1
  • 29
    • 0004073948 scopus 로고
    • Technical Report 291/94, Department of Computer Science, University of Toronto, Canada, Toronto, M5S 1A4, Canada
    • W. Enright, D. Higham, B. Owren, W. Sharp, A Survey of the Explicit Runge-Kutta Method, Technical Report 291/94, Department of Computer Science, University of Toronto, Canada, Toronto, M5S 1A4, Canada, 1995.
    • (1995) A Survey of the Explicit Runge-Kutta Method
    • Enright, W.1    Higham, D.2    Owren, B.3    Sharp, W.4
  • 31
    • 0036604963 scopus 로고    scopus 로고
    • Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations
    • DOI 10.1016/S0959-1524(01)00023-3, PII S0959152401000233
    • Diehl M., Bock H., Schlöder J., Findeisen R., Nagy Z., and Allgöwer F. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations J. Proc. Contr. 12 2002 577 585 (Pubitemid 34302551)
    • (2002) Journal of Process Control , vol.12 , Issue.4 , pp. 577-585
    • Diehl, M.1    Bock, H.G.2    Schloder, J.P.3    Findeisen, R.4    Nagy, Z.5    Allgower, F.6
  • 33
    • 0011323861 scopus 로고    scopus 로고
    • An algorithm for the solution of the parametric quadratic programming problem
    • Fischer H. Riedmüller B. Schäffler S. Physica-Verlag Heidelberg
    • Best M. An algorithm for the solution of the parametric quadratic programming problem Fischer H. Riedmüller B. Schäffler S. Applied Mathematics and Parallel Computing - Festschrift for Klaus Ritter 1996 Physica-Verlag Heidelberg 57 76
    • (1996) Applied Mathematics and Parallel Computing - Festschrift for Klaus Ritter , pp. 57-76
    • Best, M.1
  • 34
    • 44349127211 scopus 로고    scopus 로고
    • An online active set strategy to overcome the limitations of explicit MPC
    • DOI 10.1002/rnc.1251
    • Ferreau H., Bock H., and Diehl M. An online active set strategy to overcome the limitations of explicit MPC International Journal of Robust and Nonlinear Control 18 2008 816 830 (Pubitemid 351743519)
    • (2008) International Journal of Robust and Nonlinear Control , vol.18 , Issue.8 , pp. 816-830
    • Ferreau, H.J.1    Bock, H.G.2    Diehl, M.3
  • 37
    • 2942690049 scopus 로고    scopus 로고
    • MA57 - A code for the solution of sparse symmetric definite and indefinite systems
    • Duff I. MA57 - a code for the solution of sparse symmetric definite and indefinite systems ACM Transactions on Mathematical Software 30 2004 118 144
    • (2004) ACM Transactions on Mathematical Software , vol.30 , pp. 118-144
    • Duff, I.1
  • 38
    • 2942653250 scopus 로고    scopus 로고
    • Algorithm 832: UMFPACK - An unsymmetric-pattern multifrontal method with a column pre-ordering strategy
    • Davis T. Algorithm 832: UMFPACK - an unsymmetric-pattern multifrontal method with a column pre-ordering strategy ACM Transactions on Mathematical Software 30 2004 196 199
    • (2004) ACM Transactions on Mathematical Software , vol.30 , pp. 196-199
    • Davis, T.1
  • 40
    • 0742319773 scopus 로고
    • A structured interior point SQP method for nonlinear optimal control problems
    • Bulirsch R. Kraft D. Birkhäuser Basel Boston Berlin ISBN 0-8176-5015-6
    • Steinbach M. A structured interior point SQP method for nonlinear optimal control problems Bulirsch R. Kraft D. Computational Optimal Control, volume 115 of International Series of Numerical Mathematics 1994 Birkhäuser Basel Boston Berlin 213 222 ISBN 0-8176-5015-6
    • (1994) Computational Optimal Control, Volume 115 of International Series of Numerical Mathematics , pp. 213-222
    • Steinbach, M.1
  • 43
    • 33644505545 scopus 로고    scopus 로고
    • QPSchur: A dual, active set, Schur complement method for large-scale and structured convex quadratic programming algorithm
    • Bartlett R., and Biegler L. QPSchur: A dual, active set, Schur complement method for large-scale and structured convex quadratic programming algorithm Optimization and Engineering 7 2006 5 32
    • (2006) Optimization and Engineering , vol.7 , pp. 5-32
    • Bartlett, R.1    Biegler, L.2
  • 44
    • 84857792231 scopus 로고    scopus 로고
    • A factorization with update procedures for a KKT matrix arising in direct optimal control
    • Kirches C., Bock H., Schlöder J., and Sager S. A factorization with update procedures for a KKT matrix arising in direct optimal control Mathematical Programming Computation 3 4 2011 319 348
    • (2011) Mathematical Programming Computation , vol.3 , Issue.4 , pp. 319-348
    • Kirches, C.1    Bock, H.2    Schlöder, J.3    Sager, S.4
  • 46
    • 79951897071 scopus 로고    scopus 로고
    • Block structured quadratic programming for the direct multiple shooting method for optimal control
    • Kirches C., Bock H., Schlöder J., and Sager S. Block structured quadratic programming for the direct multiple shooting method for optimal control Optimization Methods and Software 26 2011 239 257
    • (2011) Optimization Methods and Software , vol.26 , pp. 239-257
    • Kirches, C.1    Bock, H.2    Schlöder, J.3    Sager, S.4
  • 49
    • 0037328973 scopus 로고    scopus 로고
    • Disturbance models for offset-free model-predictive control
    • DOI 10.1002/aic.690490213
    • Pannocchia G., and Rawlings J. Disturbance models for offset-free model-predictive control AIChE Journal 49 2003 426 437 (Pubitemid 36228207)
    • (2003) AIChE Journal , vol.49 , Issue.2 , pp. 426-437
    • Pannocchia, G.1    Rawlings, J.B.2
  • 51
    • 79961020382 scopus 로고    scopus 로고
    • An adjoint-based numerical method for fast nonlinear model predictive control
    • M. Chung, P. Misra (Eds.) Seoul, Korea, July 6-11, 2008, IFAC-PapersOnLine
    • L. Wirsching, J. Albersmeyer, P. Kühl, M. Diehl, H. Bock, An adjoint-based numerical method for fast nonlinear model predictive control, in: M. Chung, P. Misra (Eds.), Proceedings of the 17th IFAC World Congress, Seoul, Korea, July 6-11, 2008, volume 17, IFAC-PapersOnLine, 2008, pp. 1934-1939.
    • (2008) Proceedings of the 17th IFAC World Congress , vol.17 , pp. 1934-1939
    • L. Wirsching1
  • 52
    • 84857790975 scopus 로고    scopus 로고
    • Efficient numerics for nonlinear model predictive control
    • Diehl M. Glineur F. Jarlebring E. Michiels W. Springer ISBN 978-3-6421-2597-3
    • Kirches C., Wirsching L., Sager S., and Bock H. Efficient numerics for nonlinear model predictive control Diehl M. Glineur F. Jarlebring E. Michiels W. Recent Advances in Optimization and its Applications in Engineering 2010 Springer 339 359 ISBN 978-3-6421-2597-3
    • (2010) Recent Advances in Optimization and Its Applications in Engineering , pp. 339-359
    • Kirches, C.1    Wirsching, L.2    Sager, S.3    Bock, H.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.