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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 358))

Abstract

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm that uses hard variable constraints to allow for control objective prioritization. Traditional prioritized objective approaches can require the solution of a complex mixed-integer program. The formulation presented in this work relies on the feasibility and solution of a relatively small logical sequence of purely continuous nonlinear programs (NLP). The proposed solution method for accomodation of discrete control objectives is equivalent to solution of the overall mixed-integer nonlinear programming problem. The performance of the algorithm is demonstrated on a simulated multivariable network of air pressure tanks.

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References

  1. C.S. Adjiman, I. P. Androulakis, and C. A. Floudas. Global Optimization of Mixed-Integer Nonlinear Problems. AIChE J., 46(9):1769–1797, 2000.

    Article  Google Scholar 

  2. C. S. Adjiman, S. Dalliwig, C. A. Floudas, and A. Neumaier. A Global Opti-mization Method, αBB, for General Twice-Differentiable Constrained NLPs-I Theoretical Advances. Comput. Chem. Eng., 22(9):1137–1158, 1998.

    Article  Google Scholar 

  3. A. Bemporad and M. Morari. Control of Systems Integrating Logic, Dynamics, and Constraints. Automatica, 35:407–427, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  4. E. P. Gatzke and F. J. Doyle III. Multi-Objective Control of a Granulation System. Journal of Powder Technology, 121(2):149–158, 2001.

    Article  Google Scholar 

  5. E. P. Gatzke, J. E. Tolsma, and P. I. Barton. Construction of Convex Function Relaxations Using Automated Code Generation Techniques. Optimization and Engineering, 3(3):305–326, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  6. ILOG. ILOG GPLEX 9.1: User’s Manual. Mountain View, CA, April 2005.

    Google Scholar 

  7. E. C. Kerrigan, A. Bemporad, D. Mignone, M. Morari, and J. M. Maciejowski. Multi-objective Prioritisation and Reconfiguration for the Control of Constrained Hybrid Systems. In Proceedings of the American Controls Conference, Chicago, Illinois, 2000.

    Google Scholar 

  8. C. E. Long and E. P. Gatzke. Globally Optimal Nonlinear Model Predictive Con-trol. In DYCOPS 7, the 7th International Symposium on Dynamics and Control of Process Systems, Boston, MA, 2004.

    Google Scholar 

  9. C. E. Long and E. P. Gatzke. Model Predictive Control Algorithm for Prioritized Objective Inferential Control of Unmeasured States Using Propositional Logic. Ind. Eng. Chem. Res., 44(10):3575–3584, 2005.

    Article  Google Scholar 

  10. C. E. Long, P. K. Polisetty, and E. P. Gatzke. Nonlinear Model Predictive Control Using Deterministic Global Optimization. J. Proc. Cont., accepted, 2005.

    Google Scholar 

  11. G. P. McCormick. Computability of Global Solutions to Factorable Nonconvex Programs: Part I-Convex Underestimating Problems. Mathematical Program-ming, 10:147–175, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. E. Moore. Methods and Applications of Interval Analysis. SIAM, Philadelphia, 1979.

    MATH  Google Scholar 

  13. R. S. Parker, E. P. Gatzke, and F. J. Doyle III. Advanced Model Predictive Control (MPC) for Type I Diabetic Patient Blood Glucose Control. In Proc. American Control Conf., Chicago, IL, 2000.

    Google Scholar 

  14. A. N. Reyes, C. S. Dutra, and C. B. Alba. Comparison of Different Predictive Controllers with Multi-objective Optimization: Application to An Olive Oil Mill. In Proceedings of the 2002 IEEE International Conference on Control Applications and International Symposium on Computer Aided Control Systems Designs, pages 1242–1247, Glasgow, UK, 2002.

    Google Scholar 

  15. H. S. Ryoo and N. V. Sahinidis. Global Optimization of Nonconvex NLPS and MINLPs with Application to Process Design. Comput. Chem. Eng., 19(5):551–566, 1995.

    Article  Google Scholar 

  16. E. M. B. Smith. On the Optimal Design of Continuous Processes. PhD thesis, Imperial College, London, 1996.

    Google Scholar 

  17. M. L. Tyler and M. Morari. Propositional Logic in Control and Monitoring Prob-lems. Automatica, 35:565–582, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Vada, O. Slupphaug, and T. A. Johansen. Optimal Prioritized Infeasibility Handling in Model Predictive Control: Parameteric Preemptive Multiobjective Linear Programming Approach. Journal of Optimization Theory and Applica-tions, 109(2):385–413, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Vada, O. Slupphaug, T. A. Johansen., and B. A. Foss. Linear MPC with Optimal Prioritized Infeasibility Handling: Application, Computational Issues, and Stability. Automatica, 37:1835–1843, 2001.

    Article  MATH  Google Scholar 

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Long, C.E., Gatzke, E.P. (2007). Hard Constraints for Prioritized Objective Nonlinear MPC. In: Findeisen, R., Allgöwer, F., Biegler, L.T. (eds) Assessment and Future Directions of Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72699-9_17

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  • DOI: https://doi.org/10.1007/978-3-540-72699-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72698-2

  • Online ISBN: 978-3-540-72699-9

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