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Optimization in Model Predictive Control

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Part of the book series: NATO ASI Series ((NSSE,volume 293))

Abstract

This paper explores the interaction between model predictive control and optimization. The success of model predictive control in controlling constrained linear systems is due, in large part, to the fact that the online optimization problem is convex, usually a quadratic programme, for which reliable software is available. If the system is nonlinear, a more complex optimization, whose success is not guaranteed, is required. It is therefore important to modify, if possible, the online optimization problem to facilitate its solution, while maintaining the desirable properties of model predictive control. The paper shows how this may be done using, inter alia, a variable horizon. Secondly it examines how the structure of the optimal control problem impacts on the choice of optimization algorithm.

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References

  1. Garcia, C. E., Prett, D. M. and Morari, M. (1989) Model Predictive Control, Theory and Practice — a Survey, Automatica, 25, 335–348, 1989.

    Article  MATH  Google Scholar 

  2. Rawlings, J.B., Meadows, E.S. and Muske, K.R. (1994) Nonlinear Model Predictive Control: a Tutorial and Survey, Proc. Adchem’ 94, Kyoto.

    Google Scholar 

  3. Meadows, E.S., Henson, M.A., Eaton, J.W. and Rawlings, J.B. (1995) Receding Horizon Control and Discontinuous State Feedback Stabilization, International Journal of Control, to appear.

    Google Scholar 

  4. Keerthi, S.S. and Gilbert, E.G. (1988) Optimal, Infinite Horizon Feedback Laws for a General Class of Constrained Discrete Time Systems, Journal of Optimization Theory and Applications, 57, 265–293.

    Article  MathSciNet  MATH  Google Scholar 

  5. Mayne, D.Q. and Michalska, H. (1990) Receding Horizon Control of Nonlinear Systems, IEEE Transactions on Automatic Control, AC-35, 814–824.

    Article  MathSciNet  Google Scholar 

  6. Rawlings, J.B. and Muske, K.R. (1993) The Stability of Constrained Receding Horizon Control, IEEE Transactions on Automatic Control, AC-38, 1512–1516.

    Article  MathSciNet  Google Scholar 

  7. Kershenbaum, L., Mayne, D.Q., Pytlak, R. and Vinter, R.B. (1993) Receding Horizon Control, Proc. Symposium on Advances in Model Based Predictive Control, Oxford, 233–246.

    Google Scholar 

  8. Polak, E. (1993) On the Use of Consistent Approximations in the Solution of Semi-Infinite Optimization and Optimal Control Problems, Mathematical Programming, 62, 385–414.

    Article  MathSciNet  MATH  Google Scholar 

  9. Polak, E. and Mayne, D.Q. (1981) Design of Feedback Controllers, IEEE Transactions on Automatic Control, AC-26, 730–733.

    Article  MathSciNet  Google Scholar 

  10. Yang, T. H., and Polak, E. (1993) Moving Horizon Control of Nonlinear Systems with Input Saturation, Disturbances and Plant Uncertainty, International Journal of Control, 58, 875–903.

    Article  MathSciNet  MATH  Google Scholar 

  11. Michalska, H. and Mayne, D.Q. (1993) Robust Receding Control of Nonlinear Systems, IEEE Transactions on Automatic Control, AC-36, pp. 1623–1632.

    Article  MathSciNet  Google Scholar 

  12. Michalska, H. and Mayne, D.Q. (1995) Moving Horizon Observers and Observer-Based Control, IEEE Transactions on Automatic Control, to appear.

    Google Scholar 

  13. Clarke, D.W., Mosca, E. and Scattaloni, R. (1991) Robustness of an Adaptive Predictive Controller, Proc.30th IEEE Conference on Decision and Control, Brighton, 979–984.

    Google Scholar 

  14. Mayne, D.Q. and Michalska, H. (1994) Adaptive Control of Linear Constrained Systems with Inaccessible States, Proc. American Control Conference, Boston.

    Google Scholar 

  15. Mayne, D.Q. and Michalska, H. (1995) Adaptive Receding Horizon Control for Constrained Nonlinear Systems, Proc. 32nd IEEE Conference on Decision and Control, San Antonio 1286–1291.

    Google Scholar 

  16. Polak, E., Sargent, R.W.H., and Sebastian, D.J. (1974) On the Convergence of Sequential Minimization Algorithms, Journal of Optimization Theory and Applications, 14, 439–442.

    Article  MathSciNet  MATH  Google Scholar 

  17. Vassiliadis, V.S., Sargent, R.W.H. and Pantelides, C. C. (1993) Solution of a Class of Multistage Dynamic Optimization Problems, Technical Report, Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine.

    Google Scholar 

  18. Vlassenbroeck, J. and van Dooren, R. (1988) A Chebyshev Method for solving Nonlinear Optimal Control Problems, IEEE Transactions on Automatic Control, AC-33, 333–340.

    Article  Google Scholar 

  19. Vasantharajan, S. and Biegler, L.T. (1990) Simultaneous Strategies for the Optimization of Differential-Algebraic Systems with Enforcement of Error Criteria, Computing in Chemical Engineering, 14, 1083–1100.

    Article  Google Scholar 

  20. Bertsekas, D. (1982) Projection Newton Methods for Optimization Problems with Simple Constraints, SIAM Journal of Optimization and Control, 20, 221–246.

    Article  MathSciNet  MATH  Google Scholar 

  21. Dunn, J.C. (1988) Gradient Projection Methods for Systems Optimization Problems, Control and Dynamic Systems 29, 135–195.

    Google Scholar 

  22. Polak, E. and Mayne, D.Q. (1987) An exact penalty function algorithm for control problems with state and control constraints, IEEE Transactions on Automatic Control, AC-32, 380–387.

    MathSciNet  Google Scholar 

  23. Pytlak, R. (1994) A Range-Space Method for Piecewise Linear Quadratic Programming: an Application to Optimal Control Algorithms, Technical Report C94-02, Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine.

    Google Scholar 

  24. Pytlak, R. and Vinter, R.B. (1993) PH2SOL Solver: an O(N) Implementation of an Optimization Algorithm for a General Optimal Control Problem, Technical Report, Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine.

    Google Scholar 

  25. Pytlak, R. and Vinter, R.B. (1993) A Feasible Directions Type Algorithm for Optimal Control Problems with Hard State and Control Constraints, Technical Report, Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine.

    Google Scholar 

  26. Jacobson, D.H. and Mayne, D.Q. (1970) Differential Dynamic Programming, 24, Vol. 24, Modern Analytic and Computational Methods in Science and Mathematics, editor R. Bellman, Elsevier, New York.

    Google Scholar 

  27. Dunn, J.C. and Bertsekas, D. (1989) Efficient Implementation of Newton’s Method for Unconstrained Optimal Control Problems, Journal of Optimization Theory and Applications, 63, 23–38.

    Article  MathSciNet  MATH  Google Scholar 

  28. Pantoja, J.F.A. de O. and Mayne, D.Q. (1991) Sequential Quadratic Programming Algorithm for Discrete Optimal Control Problems with Control Inequality Constraints, International Journal of Control, 53, 823–836.

    Article  MathSciNet  MATH  Google Scholar 

  29. Polak, E., Yang, T. H. Mayne, D. Q. (1993) A Method of Centers based on Barrier Functions for Solving Optimal Control Problems with Continuous State and Control Constraints, SIAM J. of Control and Optimization, 31, 159–179.

    Article  MathSciNet  MATH  Google Scholar 

  30. Wright, S J. (1992) Interior Point Methods for Optimal Control of Discrete-Time Systems, Journal of Optimization Theory and Applications, 77, 161–188.

    Article  Google Scholar 

  31. Moré, J.J. and Wright, S.J. (1993) Optimization Software Guide, SIAM.

    Google Scholar 

  32. Zhou, J. L., and Tits, A. (1989) A Fortran Code for Solving Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying all Inequality and Equality Constraints, Technical Report, Systems Research Center, University of Maryland.

    Google Scholar 

  33. Polak, E. (1987) On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design, SIAM Review, 29, 21–89.

    Article  MathSciNet  Google Scholar 

  34. Hettich, R. and Kortanek, K.D. (1993) Semi-Infinite Programming: Theory, Methods and Applications, SIAM Review, 35, 380–429.

    Article  MathSciNet  MATH  Google Scholar 

  35. Gilbert, E. C. and Tan, K.C. (1991) Linear Systems with State and Control Constraints: the Theory and Application of Maximal Output Admissible Sets, IEEE Transactions on Automatic Control, AC-36, 1008–1020.

    Article  MathSciNet  Google Scholar 

  36. Tan, K.C. (1991) Maximal Output Admissible Sets and the Nonlinear Control of Linear Discrete-Time Systems with State and Control Constraints, Ph.D. Dissertation, University of Michigan.

    Google Scholar 

  37. Mayne, D.Q. and Schroeder, W.R. (1994) Nonlinear Control of Constrained Dynamic Systems, International Journal of Control, to appear.

    Google Scholar 

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© 1995 Springer Science+Business Media Dordrecht

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Mayne, D.Q. (1995). Optimization in Model Predictive Control. In: Berber, R. (eds) Methods of Model Based Process Control. NATO ASI Series, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0135-6_15

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  • DOI: https://doi.org/10.1007/978-94-011-0135-6_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4061-7

  • Online ISBN: 978-94-011-0135-6

  • eBook Packages: Springer Book Archive

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