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Design of Robust Model-Based Controllers via Parametric Programming

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Book cover Encyclopedia of Optimization

Article Outline

Introduction/Background

Definitions

Formulation

  Open-Loop Robust Parametric Model Predictive Controller

  Closed-Loop Robust Parametric Model-Based Control

Methods/Applications

  Parametric Solution of the Inner Maximization Problem of the Open-Loop Robust pMPC Problem

  Solution of the Closed-Loop RpMPC Problem

Cases

  Robust Counterpart (RC) Problem

  Interval Robust Counterpart Problem

Conclusions

References

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References

  1. Acevedo J, Pistikopoulos EN (1999) An algorithm for multiparametric mixed-integer linear programming problems. Oper Res Lett 24:139–148

    Article  MATH  MathSciNet  Google Scholar 

  2. Bemporad A, Borelli F, Morari M (2003) Min–max control of constrained uncertain discrete-time linear systems. IEEE Trans Autom Contr 48(9):1600–1606

    Article  Google Scholar 

  3. Bemporad A, Morari M (1999) Robust model predictive control: a survey Robustness in indentification and control. Springer, Berlin, pp 207–226

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424

    Article  MATH  MathSciNet  Google Scholar 

  6. Bertsekas DP, Rhodes IB (1971) On the minimax reachability of target sets and target tubes. Automatica 7:233–247

    Article  MATH  MathSciNet  Google Scholar 

  7. Camacho E, Bordons C (1999) Model Predictive Control. Springer, Berlin

    Google Scholar 

  8. Chisci L, Rossiter JA, Zappa G (2001) Systems with persistent disturbances: predictive control with restricted constraints. Automatica 37:1019–1028

    Article  MATH  MathSciNet  Google Scholar 

  9. Dua V, Bozinis NA, Pistikopoulos EN (2002) A multiparametric programming approach for mixed integer and quadratic engineering problems. Comput Chem Eng 26:715–733

    Article  Google Scholar 

  10. Fiacco A (1983) Introduction to sensitivity and stability analysis in nonlinear programming. Academic, New York

    MATH  Google Scholar 

  11. Kothare MV, Balakrishnan V, Morari M (1996) Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10):1361–1379

    Article  MATH  MathSciNet  Google Scholar 

  12. Langson W, Chryssochoos I, Raković SV, Mayne DQ (2004) Robust model predictive control using tubes. Automatica 40:125–133

    Article  MATH  Google Scholar 

  13. Lee J, Cooley B (1997) Recent advances in model predictive control and other related areas. In: Carnahan B, Kantor J, Garcia C (eds) Proceedings of chemical process control – V: Assesment and new directions for research, vol 93 of AIChE Symposium Series No. 316, AIChE and CACHE, pp 201–216

    Google Scholar 

  14. Mayne D, Rawlings J, Rao C, Scokaert PO (2000) Constrained model predictive control: stability and optimality. Automatica 36:789–814

    Article  MATH  MathSciNet  Google Scholar 

  15. Morari M, Lee J (1999) Model predictive control: past, present and future. Comput Chem Eng 23:667–682

    Article  Google Scholar 

  16. Pistikopoulos EN, Dua V, Bozinis NA, Bemporad A, Morari M (2002) On-line optimization via off-line parametric optimization tools. Automatica 26:175–185

    Google Scholar 

  17. Pistikopoulos EN, Georgiadis M, Dua V (eds) (2007) Multi-parametric Model-Based Control. In: Process Systems Engineering, vol 2. Wiley-VCH, Weinheim

    Google Scholar 

  18. Pistikopoulos EN, Georgiadis M, Dua V (eds) (2007) Multi-parametric Programming. In: Process Systems Engineering, vol 1. Wiley-VCH, Weinheim

    Google Scholar 

  19. Pistikopoulos EN, Grossmann I (1988) Optimal retrofit design for improving process flexibility in linear systems. Comput Chem Eng 12(7):719–731

    Article  Google Scholar 

  20. Sakizlis V, Kakalis NMP, Dua V, Perkins JD, Pistikopoulos EN (2004) Design of robust model-based controllers via parametric programming. Automatica 40:189–201

    Article  MATH  MathSciNet  Google Scholar 

  21. Scokaert P, Mayne D (1998) Min–max feedback model predictive control for constrained linear systems. IEEE Trans Autom Contr 43(8):1136–1142

    Article  MATH  MathSciNet  Google Scholar 

  22. Wang YJ, Rawlings JB (2004) A new robust model predictive control method I: theory and computation. J Process Control 14:231–247

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Centre for Process Systems Engineering, Imperial College London, London, UK

    K.I. Kouramas & Efstratios N. Pistikopoulos

  2. Bechtel Co. Ltd., London, UK

    V. Sakizlis

Authors
  1. K.I. Kouramas
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  2. V. Sakizlis
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  3. Efstratios N. Pistikopoulos
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Kouramas, K., Sakizlis, V., Pistikopoulos, E.N. (2008). Design of Robust Model-Based Controllers via Parametric Programming . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_122

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