Skip to main content
SpringerLink
Log in

Introduction to Model Based Optimization of Chemical Processes on Moving Horizons

  • Chapter
Online Optimization of Large Scale Systems

Abstract

Dynamic optimization problems are typically quite challenging for large-scale applications. Even more challenging are on-line applications with demanding real-time constraints. This contribution provides a concise introduction into problem formulation and standard numerical techniques commonly found in the context of moving horizon optimization using nonlinear differential algebraic process models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. O. Abel, A. Helbig, W. Marquardt: DYNOPT User Manual, Release 2.4, Lehrstuhl für Prozesstechnik, RWTH Aachen (1999)

    Google Scholar 

  2. B. D. O. Anderson, J. B. Moore: Optimal Control: Linear Quadratic Methods. PrenticeHall (1989)

    Google Scholar 

  3. F. Allgöwer, T. A. Badgwell, J. S. Qin, J. B. Rawlings, S. J. Wright: Nonlinear Predictive Control and Moving Horizon Estimation — An introductory overview. In: P.M. Frank (ed.): Advances in Control. Highlights of ECC’99, Springer (1999) 391–449

    Chapter  Google Scholar 

  4. R. Aris: Mathematical Modeling Techniques. Dover Publications (1994)

    Google Scholar 

  5. J. A. Arwell, B. B. King: Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations. Report 99–01-01, Interdisciplinary Center for Applied Mathematics, Virginia Tech (1999)

    Google Scholar 

  6. U. Ascher, J. Christiansen, R. D. Russell: A collocation solver for mixed order systems of boundary value problems. Math. Comp. 33, (1979) 659–679

    Article  MathSciNet  MATH  Google Scholar 

  7. U. Ascher, R. Mattheij, R. D. Russell: Numerical Solution of Boundary Value Problems for Differential Equations. SIAM (1988)

    MATH  Google Scholar 

  8. E. Baake, M. Baake, H. G. Bock, K. Briggs: Fitting Ordinary Differential Equations to Chaotic Data. Phys. Rev. A, 45 (1992)

    Google Scholar 

  9. V. Bär: Ein Kollokationsverfahren zur numerischen Lösung allgemeiner Mehrpunktrandwertaufgaben mit Schalt- und Sprungbedingungen mit Anwendungen in der Optimalen Steuerung und der Parameteridentifizierung. Diplomarbeit, Bonn (1983)

    Google Scholar 

  10. M. Bardi, I. C. Dolcetta: Optimal Control and Viscosity Solutions of Hamilton-JacobiBellman Equations. Birkhäuser (1996)

    Google Scholar 

  11. A. Barclay, P. E. Gill, J. B. Rosen: SQP methods and their application to numerical optimal control. In: W. H. Schmidt, K. Heier, L. Bittner, R. Bulirsch (eds.): Variational Calculus. Optimal Control and Application (1998)

    Google Scholar 

  12. I. Bauer: Numerische Verfahren zur Lösung von Anfangswertaufgaben und zur Generierung von ersten und zweiten Ableitungen mit Anwendungen bei Optimierungsaufgaben in Chemie und Verfahrenstechnik. PhD thesis, University of Heidelberg (2000).

    MATH  Google Scholar 

  13. I. Bauer, H. G. Bock, S. Körkel, J. P. and Schlöder: Numerical Methods for Optimum Experimental Design in DAE Systems. J. Comp. Appl. Math. Vol. 120 (2000) 1–25

    Article  MATH  Google Scholar 

  14. R. E. Bellman: Dynamic Programming. Princeton University Press (1957)

    MATH  Google Scholar 

  15. D. P. Bertsekas, J. N. Tsitsiklis: Neuro-Dynamic Programming. Athena Scientific (1996)

    MATH  Google Scholar 

  16. J. T. Betts: Survey of numerical methods for trajectory optimization. AIAA J. Guidance, Control, and Dynamics 21, 2 (1998) 193–207.

    Article  MATH  Google Scholar 

  17. J. T. Betts, P. D. Frank: A sparse nonlinear optimization algorithm. J. Optimization Theory and Applications 82, 3 (1994) 519–541.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. T. Betts, W. P. Huffmann: Mesh refinement in direct transcription methods for optimal control. Optim. Control Appl. Meth. 19, (1998) 1–21

    Article  Google Scholar 

  19. L. T. Biegler: Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation. Comput. chem. Engng, 8 3/4 (1984) 243–248.

    Article  Google Scholar 

  20. T. Binder, L. Blank, W. Dahmen, W. Marquardt: Towards Multiscale Dynamic and Data Reconciliation. In: R. Berber, C. Kravaris (eds.): Nonlinear Model Based Process Control Kluwer Academic Publishers, (1998), 623–665

    Chapter  Google Scholar 

  21. T. Binder, L. Blank, Dahmen W., Marquardt W.: Multiscale Concepts for Moving Horizon Optimization. In: M. Groetschel, S.O. Krumke, J. Rambau (eds.): Online Optimization of Large Scale Systems: State of the Art, Springer (2001)

    Google Scholar 

  22. R. R. Bitmead, M. Gevers, V. Wertz: Adaptive optimal Control — The Thinking Man’s GPC. Prentice Hall (1990)

    MATH  Google Scholar 

  23. H. G. Bock: Numerische Berechnung zustandsbeschränkter optimaler Steuerungen. Carl-Cranz-Gesellschaft, Tech. Rep 1.06/78 Heidelberg (1978)

    Google Scholar 

  24. H. G. Bock: Numerical Solution of Nonlinear Multipoint Boundary Value Problems with Applications to Optimal Control. ZAMM 58, T407 (1978)

    Article  MathSciNet  Google Scholar 

  25. H. G. Bock: Numerical treatment of inverse problems in chemical reaction kinetics. In: K. H. Ebert, P. Deuflhard, and W. Jäger, (eds.): Modelling of Chemical Reaction Systems. volume 18 of Springer Series in Chemical Physics, Springer (1981)

    Google Scholar 

  26. H. G. Bock: Recent advances in parameter identification techniques for O.D.E. In: P. Deuflhard und E. Hairer (eds.): Numerical Treatment of Inverse Problems in Differential and Integral Equations. Birkhäuser (1983)

    Google Scholar 

  27. H. G. Bock, K. J. Plitt: A multiple shooting algorithm for direct solution of optimal control problems. In Proc. 9th IFAC World Congress Budapest, July 2–6, Pergamon Press (1984), 242–247

    Google Scholar 

  28. H. G. Bock: Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen. Bonner Mathematische Schriften 183, University of Bonn (1987)

    MATH  Google Scholar 

  29. H. G. Bock, E. Eich, J. P. Schlöder: Numerical solution of constrained least squares boundary value problems in differential-algebraic equations. In: K. Strehmel (ed.): Numerical Treatment of Differential Equations. Teubner (1988)

    Google Scholar 

  30. H. G. Bock, J. P. Schlöder, V. Schulz: Numerik großer Differentiell-Algebraischer Gleichungen — Simulation und Optimierung. In: H. Schuler (ed.): Prozeßsimulation. VCH Verlagsgesellschaft mbH (1995) 35–80

    Google Scholar 

  31. R. Bulirsch, E. Nerz, H. J. Pesch, O. von Stryk: Combining direct and indirect methods in optimal control: range maximization of a hang glider. In: R. Bulirsch, A. Miele, J. Stoer, K.-H. Well (eds.): Optimal Control — Calculus of Variations, Optimal Control Theory and Numerical Methods, International Series of Numerical Mathematics 111, Birkhäuser (1993) 273–288.

    Google Scholar 

  32. K. E. Brenan, S. L. Campbell, L. R. Petzold: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM (1996)

    MATH  Google Scholar 

  33. A. E. Bryson, Y. C. Ho: Applied Optimal Control. Ginn and Company, (1969), Rev. printing, Hemisphere (1975)

    Google Scholar 

  34. O. Buchauer, P. Hiltmann, M. Kiehl: Sensitivity analysis of initial-value problems with application to shooting techniques. Numerische Mathematik 67 (1994) 151–159

    Article  MathSciNet  MATH  Google Scholar 

  35. R. Bulirsch: Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung. Report of the Carl-CranzGesellschaft e.V., DLR, Oberpfaffenhofen (1971)

    Google Scholar 

  36. R. Bulirsch, D. Kraft (eds.): Computational Optimal Control. International Series in Numerical Mathematics 115 Birkhäuser-Verlag (1994)

    Google Scholar 

  37. J. A. Burns, B. B. King: A reduced basis approach to the design of low order feedback controllers for nonlinear continuous systems. To appear in: Journal of Vibration and Control

    Google Scholar 

  38. C. Büskens, M. Gerdts: Real-time optimization of DAE-systems. In: M. Groetschel, S.O. Krumke, J. Rambau (eds.): Online Optimization of Large Scale Systems: State of the Art. Springer (2001)

    Google Scholar 

  39. R. Callies: Habilitationsschrift. Technische Universität München, submitted

    Google Scholar 

  40. M. Caracotsios, W. E. Stewart: Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations. Computers & Chemical Engineering 9, 4 (1985) 359–365

    Article  Google Scholar 

  41. A. L. Cauchy: Méthode générale pour la résolution systémes d’équations simultanées. Compt. rend. acad. sci. 25 (1847) 536–538

    Google Scholar 

  42. A. Cervantes, L. T. Biegler: Large-scale DAE optimization using a simultaneous NLP formulation. AIChE Journal 44, 5 (1998) 1038–1050.

    Article  Google Scholar 

  43. F. L. Chernousko, A. A. Luybushin: Method of successive approximations for optimal control problems (survey paper). Opt. Contr. Appl. and Meth. 3, (1982) 101–114

    Article  MATH  Google Scholar 

  44. P. Deuflhard: A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numer. Math. 22 (1974) 289–315

    Article  MathSciNet  MATH  Google Scholar 

  45. E. D. Dickmanns, K. H. Well: Approximate solution of optimal control problems using third order Hermite polynomial functions. Lec. Notes in Comp. Sc., Vol. 27, Springer (1975) 158–166

    Article  Google Scholar 

  46. M. Diehl, H. G. Bock, D. B. Leineweber, J. P. Schlöder: Efficient direct multiple shooting in nonlinear model predictive control. In: F. Keil, W. Mackens, H. Voß, and J. Werther (eds.): Scientific Computing in Chemical Engineering II, volume 2, Springer(1999), 218–227

    Google Scholar 

  47. M. Diehl, I. Disli-Uslu, S. Schwarzkopf, F. Allgöwer, H. G. Bock, T. Bürner, R. Findeisen, E. D. Gilles, A. Kienle, J. P. Schlöder, E. Stein: Real-Time Optimization of Large Scale Process Models: Nonlinear Model Predictive Control of a High Purity Distillation Column. In: M. Groetschel, S.O. Krumke, J. Rambau (eds.): Online Optimization of Large Scale Systems: State of the Art. Springer (2001)

    Google Scholar 

  48. G. Engl, A. Kröner, T. Kronseder, O. von Stryk: Numerical simulation and optimal control of air separation plants. In: H.-J. Bungartz, F. Durst, Chr. Zenger (eds.): High Performance Scientific and Engineering Computing. Lecture Notes in Computational Science and Engineering 8, Springer (1999) 221–231

    Chapter  Google Scholar 

  49. M. Falcone, R. Ferretti: Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations. Numerische-Mathematik 67, 3 (1994) 315–344

    Article  MathSciNet  MATH  Google Scholar 

  50. C. A. Fletcher: Computational Galerkin Methods. Springer (1984)

    Book  MATH  Google Scholar 

  51. L. Fox: Some numerical experiments with eigenvalue problems in ordinary differential equations. In: Langer R.E. (ed): Boundary Value Problems in Differential Equations. (1960)

    Google Scholar 

  52. S. Galán, W. F. Feehery, P. I. Barton: Parametric sensitivity functions for hybrid discrete/continuous systems. Applied Numerical Mathematics 31, 1 (1999) 17–47

    Article  MathSciNet  MATH  Google Scholar 

  53. J. V. Gallitzendörfer, H. G. Bock: Parallel algorithms for optimization boundary value problems in DAE. In: H. Langendörfer (ed.): Praxisorientierte Parallelverarbeitung. Hanser (1994)

    Google Scholar 

  54. P. E. Gill, W. Murray, M. A. Saunders: SNOPT: An SQP algorithm for large-scale constrained optimization. Report NA 97–2, Department of Mathematics, University of California, San Diego (1997)

    Google Scholar 

  55. P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright: Some theoretical properties of an augmented Lagrangian merit function. In: P. M. Pardalos (ed.): Advances in Optimization and Parallel Computing. Elsevier Science Publishers (1992) 101–128

    Google Scholar 

  56. P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright: User’s Guide for NPSOL (Version 5.0): a Fortran package for nonlinear programming. Numerical Analysis Report 98–2, Department of Mathematics, University of California, San Diego (1998)

    Google Scholar 

  57. N. I. M. Gould, P. L. Toint: SQP Methods for Large-Scale Nonlinear Programming. Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization, Cambidge, England, July 12th to 16th 1999, also available as: Rutherford Appleton Laboratory Technical Report RAL-TR-1999–055

    Google Scholar 

  58. A. Griewank: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Frontiers in Applied Mathematics 19 SIAM (2000)

    MATH  Google Scholar 

  59. S. P. Han: Superlinearly convergent variable-metric algorithms for general nonlinear programming problems. Math. Progr. 11 (1976) 263–282

    Article  Google Scholar 

  60. R. F. Hartl, S. P. Sethi, R. G. Vickson: A survey of the Maximum Principles for optimal control problems with state constraints. SIAM Review 37, 2 (1995) 181–218

    Article  MathSciNet  MATH  Google Scholar 

  61. A. Helbig, O. Abel, W. Marquardt: Structural concepts for optimization based control of transient processes, In: F. Allgöwer, A. Zheng (eds.): Nonlinear Predictive Control. Birkhäuser (2000) 295–312

    Chapter  Google Scholar 

  62. A. Heim: Parameteridentifizierung in differential-algebraischen Gleichungssystemen. Diploma thesis, Department of Mathematics, Technische Universität München (1992)

    Google Scholar 

  63. A. Heim, O. von Stryk: Documentation of PAREST — A multiple shooting code for optimization problems in differential-algebraic equations. Report TUM-M9616, Mathematisches Institut, Technische Universität München (1996)

    Google Scholar 

  64. M. A. Henson: Nonlinear model predictive control: Current status and future directions. Comp. Chem. Eng. 23 (1998) 187–202

    Article  Google Scholar 

  65. M. R. Hestenes: Calculus of Variations and Optimal Control Theory. Wiley (1966)

    MATH  Google Scholar 

  66. P. Hiltmann: Numerische Lösung von Mehrpunkt-Randwertproblemen und Aufgaben der optimalen Steuerung mit Steuerfunktionen über endlichdimensionalen Räumen. Dissertation, Fakultät für Mathematik und Informatik, Technische Universität München (1990)

    Google Scholar 

  67. H. Hinsberger: Ein direktes Mehrzielverfahren zur Lösung von Optimalsteuerungsproblemen mit großen, differential-algebraischen Gleichungssystemen und Anwendungen aus der Verfahrenstechnik. Dissertation, Mathematisch-Naturwissenschaftliche Fakultät, Technische Universität Clausthal (1997)

    Google Scholar 

  68. R. Isaacs: Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. J. Wiley & Sons (1965)

    MATH  Google Scholar 

  69. D. H. Jacobson, D. H. Martin, M. Pachter, T. Geveci: Extensions of Linear-Quadratic Control Theory. Lecture Notes in Control and Inform. Sciences 27, Springer (1980)

    Book  Google Scholar 

  70. J. Kallrath, H. G. Bock, J. P. Schlöder: Least Squares Parameter Estimation in Chaotic Differential Equations. Celestial Mechanics and Dynamical Astronomy, 56 (1993)

    Google Scholar 

  71. R. E. Kalman: A new approach to linear filtering and prediction problems. Trans. ASME, J. Basic Engineering (1960) 35–45

    Google Scholar 

  72. T. Kailath: Linear systems. Prentice Hall (1980)

    MATH  Google Scholar 

  73. S. S. Keerthi, E. G. Gilbert: Optimal infinite-horizon feedback laws for a general class of constraint discrete-time systems: Stability and moving horizon approximations. J. Opt. Theory and Appl. 57(2) (1988) 265–293

    Article  MathSciNet  MATH  Google Scholar 

  74. H. J. Kelley: Gradient theory of optimal flight paths. Journal of the American Rocket Society 30 (1960) 947–953

    MATH  Google Scholar 

  75. H. J. B. Keller: Numerical Methods for Two-Point Boundary Value problems. Waltham: Blaisdell (1968)

    MATH  Google Scholar 

  76. M. Kiehl: Vektorisierung der Mehrzielmethode zur Lösung von Mehrpunkt-Randwertproblemen und Aufgaben der optimalen Steuerung. PhD Thesis, Mathematisches Institut, Technische Universität München (1989)

    Google Scholar 

  77. M. Kiehl: Sensitivity analysis of ODEs and DAEs — theory and implementation guide. Optimization Methods and Software 10, 6 (1999) 803–821

    Article  MathSciNet  MATH  Google Scholar 

  78. B. B. King, E. W. Sachs: Semidefinite programming techniques for reduced order systems with guaranteed stability margins. Submitted to: Computational Optimization and Applications

    Google Scholar 

  79. D. Kraft: On converting optimal control problems into nonlinear programming problems. In: K. Schittkowski (ed.): Computational Mathematical Programming. NATO ASI Series, Vol. F15, Springer (1985) 261–280.

    Chapter  Google Scholar 

  80. D. Kraft: Algorithm 733: TOMP — Fortran modules for optimal control calculations. ACM Transactions on Mathematical Software 20, 3 (1994) 262–281.

    Article  MATH  Google Scholar 

  81. P. Krämer-Eis: Ein Mehrzielverfahren zur numerischen Berechnung optimaler FeedbackSteuerungen bei beschränkten nichtlinearen Steuerungsproblemen. Bonner Mathematische Schriften 166, University of Bonn (1985)

    Google Scholar 

  82. P. Krämer-Eis, H. G. Bock: Numerical Treatment of State and Control Constraints in the Computation of Feedback Laws for Nonlinear Control Problems. In: P. Deuflhard et al. (eds.): Large Scale Scientific Computing. Birkhäuser (1987), 287–306

    Chapter  Google Scholar 

  83. A. Kröner, W. Marquardt, E. D. Gilles: Computing consistent initial conditions for differential algebraic process models. Comp. Chem. Eng., 16 (1992) 131–138

    Article  Google Scholar 

  84. A. Kröner, T. Kronseder, G. Engl, O. von Stryk: Dynamic optimization for air separation plants. Proceesdings of the European Symposium on Computer Aided Process Engineering (ESCAPE-11), Kolding, Denmark, May 27–30, 2001 (2001)

    Google Scholar 

  85. T. Kronseder, O. von Stryk, R. Bulirsch: Towards Nonlinear Model Based Predictive Optimal Control of Large-Scale Process Models with Application to Air Separation Plants. In: M. Groetschel, S.O. Krumke, J. Rambau, (eds.): Online Optimization of Large Scale Systems: State of the Art. Springer (2001)

    Google Scholar 

  86. B. Kugelmann, H. J. Pesch: New general guidance method in constrained optimal control, Part 1: Numerical method. J. Optimization Theory and Applications 67, 3 (1990) 421–435.

    Article  MathSciNet  MATH  Google Scholar 

  87. B. Kugelmann, H. J. Pesch: New general guidance method in constrained optimal control, Part 2: Application to space shuttle guidance. J. Optimization Theory and Applications 67, 3 (1990) 437–446.

    Article  MathSciNet  MATH  Google Scholar 

  88. K. Kunisch, S. Volkwein: Control of Burger’s equation by a reduced order approach using proper orthogonal decomposition. Karl-Franzens-Universität Graz, Spezialforschungsbereich F003, Bericht Nr. 138 (Sep. 1998)

    Google Scholar 

  89. D. B. Leineweber: Efficient reduced SQP methods for the optimization of chemical processes described by large sparse DAE models. volume 613 of Fortschr.-Ber. VDI Reihe 3, Verfahrenstechnik. VDI Verlag (1999)

    Google Scholar 

  90. D. B. Leineweber, H. G. Bock, J. P. Schlöder: Fast direct methods for real-time optimization of chemical processes. , Berlin, Wissenschaft- und Technik-Verlag (1997)

    Google Scholar 

  91. J. R. Leis, M. A. Kramer: Sensitivity analysis of systems of differential and algebraic equations. Comput. Chem. Eng. 9 (1985) 93–96

    Article  Google Scholar 

  92. P. L. Lions: Generalized Solutions of Hamilton-Jacobi Equations. Pittman (1982)

    MATH  Google Scholar 

  93. T. Maly, L. R. Petzold: Numerical methods and software for sensitivity analysis of differential-algebraic equations. Applied Numerical Mathematics 20 (1996) 57–79

    Article  MathSciNet  MATH  Google Scholar 

  94. B. R. Maner, F. J. Doyle, B. A. Ogunnaike, R. K. Pearson: Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models. Automatica 32, (1996) 1285–1301

    Article  MathSciNet  MATH  Google Scholar 

  95. W. Marquardt: Nonlinear model reduction for optimization based control of transient chemical processes. Proceedings of Chemical Process Control-6, Tuscon USA (2001)

    Google Scholar 

  96. D. Q. Mayne: Optimization in model based control. In: J. B. Rawlings (ed.): The 4-th IFAC symposium on dynamics and control of chemical reactors, distillation columns, and batch processes. DYCORD 95 (1995) 229–242

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  98. E. S. Meadows, J. B. Rawlings: Topics in model predictive control. In: R. Berber (ed.): Methods of Model-Based Control. NATO-ASI Series, Kluwer Press (1995) 331–347

    Chapter  Google Scholar 

  99. R. Mehlhorn, G. Sachs: A new tool for efficient optimization by automatic differentiation and program transparency. Optimization Methods and Software 4 (1994) 225–242

    Article  Google Scholar 

  100. V. L. Mehrmann: The Autonomous Linear Quadratic Control Problem. Lecture Notes in Control and Information Sciences 163 Springer (1991)

    Book  MATH  Google Scholar 

  101. H. Michalska, D. Mayne: Moving horizon observers-based control. IEEE Transactions on Automatic Control 40(6) (1995) 995–1006

    Article  MathSciNet  MATH  Google Scholar 

  102. A. Miele: Gradient algorithms for the optimization of dynamic systems. In: C.T. Leondes (ed.): Control and Dynamic Systems 16 (1980) 1–52

    Google Scholar 

  103. M. Morari, J. H. Lee: Model predictive control: past, present and future. Computers and Chemical Engineering 23 (1999) 667–682

    Article  Google Scholar 

  104. K. R. Muske, J. B. Rawlings: Nonlinear receding horizon state estimation. In: R. Berber (ed.): Methods of Model-Based Control. NATO-ASI Series. Kluwer Press (1995) 489–504

    Google Scholar 

  105. B. Naumer: Über approximative Methoden der Dynamischen Programmierung in der Optimalen Steuerung. Utz (1999)

    Google Scholar 

  106. J. Nocedal, S. J. Wright: Numerical optimization. Springer (1999)

    Book  MATH  Google Scholar 

  107. S. J. Norquay, A. Palazoglu, J. A. Romagnoli: Application of Wiener model predictive control (WMPC) to an industrial C2-splitter. J. Process Control 9 (1999) 461–473

    Article  Google Scholar 

  108. H. J. Oberle: Numerische Berechnung optimaler Steuerungen von Heizung und Kühlung für ein realistisches Sonnenhausmodell. Habilitationsschrift, Technische Universität München, Germany (1982)

    Google Scholar 

  109. B. A. Ogunnaike, W. H. Ray: Process Dynamics, Modelling and Control. Oxford University Press (1994)

    Google Scholar 

  110. N. M. C. de Oliveira, L. T. Biegler An extension of Newton-type algorithms for nonlinear process control. Automatica 31 (2) (1995) 281–286

    Article  MathSciNet  MATH  Google Scholar 

  111. R. K. Pearson, M. Pottmann: Gray-box identification of block-oriented nonlinear models. J. Process Control 10 (2000) 301–314

    Article  Google Scholar 

  112. H. J. Pesch: Numerische Berechnung optimaler Flugbahnkorrekturen in Echtzeitrechnung. Ph.D. thesis, TU München (1978)

    Google Scholar 

  113. H. J. Pesch, R. Bulirsch: The Maximum Principle, BellMan’s equation, and Caratheodory’s work. J. Optimization Theory and Applications 80, 2 (1994) 199–225

    Article  MathSciNet  MATH  Google Scholar 

  114. L. Petzold, J. B. Rosen, P. E. Gill, L. O. Jay, K. Park: Numerical optimal control of parabolic PDEs using DASOPT. In: Biegler, Coleman, Conn, Santosa (eds.): Large Scale Optimization with Applications, Part II. Springer (1997), 271–299

    Chapter  Google Scholar 

  115. K. J. Plitt: Ein superlinear konvergentes Mehrzielverfahren zur direkten Berechnung beschränkter optimaler Steuerungen, Diplomarbeit, Bonn (1981)

    Google Scholar 

  116. L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze, E. F. Miscenko: The Mathematical Theory of Optimal Processes. Wiley (1962)

    MATH  Google Scholar 

  117. M. J. D. Powell: A fast algorithm for nonlinearly constrained optimization calculations. in G.A. Watson (Hrsg.), Numerical Analysis, Dundee 1977, Lecture Notes in Mathematics 630, Springer (1978).

    Google Scholar 

  118. Process Systems Enterprise Ltd: gPROMS Advanced User Guide (Release 1.8), London (2000)

    Google Scholar 

  119. R. Pytlak: Numerical Methods for Optimal Control Problems with State Constraints. Springer (1999)

    MATH  Google Scholar 

  120. C. V. Rao, J. B. Rawlings: Nonlinear Horizon State Estimation, In: F. Allgöwer, A. Zheng (eds.): Nonlinear Predictive Control. Birkhäuser (2000) 45–70

    Chapter  Google Scholar 

  121. N. L. Ricker: Model predictive control: State of the art. In: Y. Arkun and W. H. Ray (eds.): Chemical Process Control — CPC IV, CACHE. Elsevier (1991) 271–296

    Google Scholar 

  122. D. Robertson, K. H. Lee, J. B. Rawlings: A moving horizon-based approach for leastsquares estimation. AIChE Journal 42(8) (1996) 2209–2223

    Article  Google Scholar 

  123. E. N. Rozenvasser: General sensitivity equations of discontinuous systems. Automat. Remote Control (1967) 400–404

    Google Scholar 

  124. V. Schulz: Reduced SQP methods for large-scale optimal control problems in DAE with application to path planning problems for satellite mounted robots. Dissertation, Naturwiss.-Math. Gesamtfakultät, Universität Heidelberg (1996).

    Google Scholar 

  125. V. H. Schulz: Solving discretized optimization problems by partially reduced SQP methods. Comput. Visual. Sci. 1 (1998) 83–96

    Article  MATH  Google Scholar 

  126. V. H. Schulz, H. G. Bock, and M. C. Steinbach: Exploiting invariants in the numerical solution of multipoint boundary value problems for DAEs. SIAM J. Sci. Comput. 19 (1998) 440–467

    Article  MathSciNet  MATH  Google Scholar 

  127. G. R. Sriniwas, Y. Arkun: A global solution to the nonlinear model predictive control algorithms using polynomial ARX models. Comp. Chem. Engng 21, (1997) 431–439

    Article  Google Scholar 

  128. M. C. Steinbach: Fast recursive SQP methods for large-scale optimal control problems. PhD thesis. University of Heidelberg (1995)

    MATH  Google Scholar 

  129. J. Stoer, R. Bulirsch: Introduction to Numerical Analysis. 2nd ed., Springer (1993)

    MATH  Google Scholar 

  130. H. T. Su, T. J. McAvoy: Artificial neural networks for nonlinear process identification and control. In: M. A. Henson, D. E. Seborg (eds.): Nonlinear Process Control. PrenticeHall (1997) 371–428

    Google Scholar 

  131. P. Terwiesch, M. Agarwal: On-line corrections of pre-optimized input profiles for batch reactors. Comp. Chem. Eng. 18 (1994) S433-S437

    Article  Google Scholar 

  132. H. Tolle: Optimization Methods. Springer (1975)

    Book  MATH  Google Scholar 

  133. J. Unger, A. Kröner, W. Marquardt: Structural analysis of DAE-systems — Theory and applications. Comput. Chem. Eng. 19, 8 (1995) 867–882

    Article  Google Scholar 

  134. V. S. Vassiliadis, R. W. H. Sargent, C. C. Pantelides: Solution of a class of multistage dynamic optimization problems. 1. problems without path constraints. Ind. Eng. Chem. Res. 33 (1994) 2111–2122

    Article  Google Scholar 

  135. V. S. Vassiliadis, R. W. H. Sargent, C. C. Pantelides: Solution of a class of multistage dynamic optimization problems. 2. problems with path constraints. Ind. Eng. Chem. Res. 33 (1994) 2123–2133

    Article  Google Scholar 

  136. R. von Schwerin, M. J. Winckler, V. H. Schulz: Parameter estimation in discontinuous descriptor models. In: Bestle and Schiehlen (eds.): IUTAM Symposium on Optimization of Mechanical Systems. Kluwer Academic Publishers (1996) 269–276

    Chapter  Google Scholar 

  137. O. von Stryk: Numerical solution of optimal control problems by direct collocation. In: R. Bulirsch, A. Miele, J. Stoer, K. H. Well (eds.): Optimal Control — Calculus of Variations, Optimal Control Theory and Numerical Methods. International Series of Numerical Mathematics 111 Birkhäuser (1993) 129–143

    Google Scholar 

  138. O. von Stryk: Numerische Lösung optimaler Steuerungsprobleme: Diskretisierung, Parameteroptimierung und Berechnung der adjungierten Variablen. Fortschritt-Berichte VDI, Reihe 8, Nr. 441, VDI-Verlag (1995).

    MATH  Google Scholar 

  139. O. von Stryk: Numerical Hybrid Optimal Control and Related Topics. Habilitation, Department of Mathematics, Technische Universität München (2000), submitted

    Google Scholar 

  140. O. von Stryk, R. Bulirsch: Direct and indirect methods for trajectory optimization. Annals of Operations Research 37 (1992) 357–373

    Article  MathSciNet  MATH  Google Scholar 

  141. O. von Stryk, M. Schlemmer: Optimal control of the industrial robot Manutec r3. In: R. Bulirsch, D. Kraft (eds.): Computational Optimal Control. International Series of Numerical Mathematics 115, Basel (1994) 367–382

    Chapter  Google Scholar 

  142. W. Waldraff, R. King, E. D. Gilles: Optimal feeding strategies by adaptive mesh selection for fed-batch bioprocesses. Bioprocess Engineering 17 (1997) 221–227

    Article  Google Scholar 

  143. P. J. Werbos: Approximate dynamic programming for real-time control and neural modeling. In: D. A. White and D. A. Sofge (eds.): Handbook of Intelligent Control. Van Nostrand Reinhold (1992) 493–559

    Google Scholar 

  144. M. Wellers, H. Rake: Nonlinear model predictive control based on stable Wiener and Hammerstein models. In: F. Allgöwer, A. Zheng (eds.): Nonlinear Predictive Control. Birkhäuser (2000) 357–368

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Prozesstechnik, Rheinisch-Westfälische Technische Hochschu1e Aachen, Germany

    Thomas Binder & Wolfgang Marquardt

  2. Institut für Geometrie und praktische Mathematik, Rheinisch-Westfälische Technische Hochschule Aachen, Germany

    Luise Blank & Wolfgang Dahmen

  3. Interdisziplinäres Zentrum für wissenschaftliches Rechnen, Universität Heidelberg, Germany

    H. Georg Bock, Moritz Diehl & Johannes P. Schlöder

  4. Lehrstuhl für Höhere Mathematik und Numerische Mathematik, Technische Universität München, Germany

    Roland Bulirsch & Thomas Kronseder

  5. Fachgebiet Simulation und Systemoptimierung, Technische Universität Darmstadt, Germany

    Oskar von Stryk

Authors
  1. Thomas Binder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luise Blank
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Georg Bock
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Roland Bulirsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wolfgang Dahmen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Moritz Diehl
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Thomas Kronseder
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Wolfgang Marquardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Johannes P. Schlöder
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Oskar von Stryk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustraße 7, 14195, Berlin-Dahlem, Germany

    Martin Grötschel , Sven O. Krumke  & Jörg Rambau ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Binder, T. et al. (2001). Introduction to Model Based Optimization of Chemical Processes on Moving Horizons. In: Grötschel, M., Krumke, S.O., Rambau, J. (eds) Online Optimization of Large Scale Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04331-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-04331-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07633-6

  • Online ISBN: 978-3-662-04331-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation