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Boundaries of the receding horizon control for interconnected systems

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Abstract

In recent years, the finite-horizon quadratic minimization problem has become popular in process control, where the horizon is constantly rolled back. In this paper, this type of control, which is also called the receding horizon control, is considered for interconnected systems. First, the receding horizon control equations are formulated; then, some stability conditions depending on the interconnection norms and the horizon lengths are presented. For ∈-coupled systems, stability results similar to centralized systems are obtained. For interconnected systems which are not ∈-coupled, the existence of a horizon length and a corresponding stabilizing receding horizon control are derived. Finally, the performance of a locally computed receding horizon control for time-invariant and time-varying systems with different updating intervals is examined in an example.

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References

  1. Bitmead, R. R., Gevers, M., andWertz, V.,Adaptive Optimal Control: The Thinking Man's GPC, Prentice-Hall, Englewood Cliffs, New Jersey, 1990.

    Google Scholar 

  2. Kleinman, D. L.,An Easy Way to Stabilize a Linear Constant System, IEEE Transactions on Automatic Control, Vol. 15, p. 692, 1970.

    Article  Google Scholar 

  3. Thomas, Y. A.,Linear Quadratic Optimal Estimation and Control with Receding Horizon, Electronics Letters, Vol. 11, pp. 19–21, 1975.

    Google Scholar 

  4. Kleinman, D. L.,Stabilizing a Discrete, Constant, Linear System with Applications to Iterative Methods for Solving the Riccati Equation, IEEE Transactions on Automatic Control, Vol. 19, pp. 252–254, 1974.

    Article  Google Scholar 

  5. Kwon, W. H., andPearson, A. E.,A Modified Quadratic Cost Problem and Fedback Stabilization of a Linear System, IEEE Transactions on Automatic Control, Vol. 22, pp. 838–842, 1977.

    Article  Google Scholar 

  6. Kwon, W. H., andPearson, A. E.,On Feedback Stabilization of Time-Varying Discrete Linear Systems, IEEE Transactions on Automatic Control, Vol. 23, pp. 479–481, 1978.

    Article  Google Scholar 

  7. Thomas, Y., Sarlat, D., andShaw, L.,Receding-Horizon Approach to the Synthesis of Nonlinear Multivariable Regulators, Electronics Letters, Vol. 13 pp. 329–331, 1977.

    Google Scholar 

  8. Shaw, L.,Nonlinear Control of Linear Multivariable Systems via State-Dependent Feedback Gains, IEEE Transactions on Automatic Control, Vol. 24, pp. 108–112, 1979.

    Article  Google Scholar 

  9. Chen, C. C., andShaw, L.,On Receding Horizon Feedback Control, Automatica, Vol. 18, pp. 349–352, 1982.

    Article  Google Scholar 

  10. Parlar, M.,Efficiency of Rolling Schedules for a Class of Stochastic Control Problems, Automatica, Vol. 18, pp. 493–495 1982.

    Article  Google Scholar 

  11. Longchamp, R.,Singular Perturbation Analysis of a Receding Horizon Controller, Automatica, Vol. 19, pp. 303–308, 1983.

    Article  Google Scholar 

  12. Ortega, R., andGalindo, G. S.,A Globally Convergent Multistep Receding Horizon Adaptive Controller, Proceedings of the 1987 American Control Conference, Minneapolis, Minnesota, pp. 566–570, 1987.

  13. Yaz, E., andSelbuz, H.,Deadbeat Property of the Receding Horizon Control Scheme, Proceedings of the 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida, pp. 41–42, 1985.

  14. Selbuz, H., andEldem, V.,A Further Stabilization Property of Receding Horizon Controllers, Proceedings of the 25th IEEE Conference on Decision and Control, Athens, Greece, pp. 705–706, 1986.

  15. Yaz, E.,A Suboptimal Terminal Controller for Linear Discrete-Time Systems, International Journal of Control, Vol. 40, pp. 271–279, 1984.

    Google Scholar 

  16. Kwon, W. H., Byun, D. G., andKwon, O. K.,Receding Horizon Tracking Control as a Predictive Control and Its Stability Properties, Proceedings of the 1988 American Control Conference, Atlanta, Georgia, pp. 2070–2075, 1988.

  17. Mayne, D. Q., andMichalska, H.,Receding Horizon Control of Nonlinear Systems, Proceedings of the 27th IEEE Conference on Decision and Control, Austin, Texas, pp. 464–465, 1988.

  18. Mayne, D. Q., andMichalska, H.,Receding Horizon Control of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. 35, pp. 814–824, 1990.

    Article  Google Scholar 

  19. Baker, K. R.,An Experimental Study of the Effectiveness of Rolling Schedules in Production Planning, Decision Sciences, Vol. 8, pp. 19–27, 1977.

    Google Scholar 

  20. Baker, K. R., andPeterson, D. W.,An Analytic Framework for Evaluating Rolling Schedules, Management Science, Vol. 25, pp. 341–351, 1979.

    Google Scholar 

  21. Ng, L. C., andLatourette, R. A.,Fast Moving Average Recursive Least Mean Square Fit, Proceedings of the 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida, pp. 1635–1636, 1985.

  22. Maybeck, P. S., andHentz, K. P.,Investigation of Moving-Bank Multiple Model Adaptive Algorithms, Proceedings of the 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida, pp. 1874–1881, 1985.

  23. Bofah, P., andChoudhury, A. K.,Modelling and Design of Nonlinear Feedback Control Law for a Large Space Hoop-Column Antenna, Proceedings of the 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida, pp. 637–641, 1985.

  24. Clarke, D. W., Mohtadi, C., andTuffs, P. S.,Generalized Predictive Control, Part 1: The Basic Algorithm, Automatica, Vol. 23, pp. 137–148, 1987.

    Article  Google Scholar 

  25. Clarke, D. W., Mohtadi, C., andTuffs, P. S.,Generalized Predictive Control, Part 2: Extensions and Interpretations, Automatica, Vol. 23, pp. 149–160, 1987.

    Article  Google Scholar 

  26. De Keyser, R. M. C., Van De Velde, P. G. A., andDumortier, F. A. G.,A Comparative Study of Self-Adaptive Long-Range Predictive Control Methods, Automatica, Vol. 24, pp. 149–163, 1988.

    Article  Google Scholar 

  27. Prett, D. M., andGarcía, C. E.,Fundamental Process Control, Butterworth-Heinemann, Boston, Massachusetts, 1988.

    Google Scholar 

  28. Scattolini, R., andBittanti, S.,On the Choice of the Horizon in Long-Range Predictive Control: Some Simple Criteria, Automatica, Vol. 26, pp. 915–917, 1990.

    Article  Google Scholar 

  29. Kirk, D. E.,Optimal Control. Theory: An Introduction, Prentice-Hall, Englewood Cliffs, New Jersey, 1970.

    Google Scholar 

  30. Acar, L., andÖzgüner, Ü.,A Locally Computed Suboptimal Control Strategy for a Class of Interconnected Systems, Journal of Optimization Theory and Applications, Vol. 62, pp. 189–210, 1989.

    Article  MathSciNet  Google Scholar 

  31. Acar, L.,Local Control Strategies for a Class of Interconnected and Knowledge-Rich Hierarchical Systems, PhD Thesis, Department of Electrical Engineering, Ohio State University, Columbus, Ohio, 1988.

    Google Scholar 

  32. Acar, L., andÖzgüner, Ü.,Distributed Computations of Optimal Control Strategies for a Class of Interconnected Systems, Proceedings of the 25th Annual Allerton Conference on Communications, Control, and Computing, Monticello, Illinois, pp. 1162–1171, 1987.

  33. Kwakernaak, H., andSivan, R.,Linear Optimal Control Systems, John Wiley and Sons, New York, New York, 1972.

    Google Scholar 

  34. Yanchevsky, A. E., andHirkonen, V. J.,Optimization of Feedback Systems with Constrained Information Flow, International Journal on Systems Sciences, Vol. 12, pp. 1459–1468, 1981.

    Google Scholar 

  35. Acar, L., andÖzgüner, Ü.,A Completely Decentralized Suboptimal Control Strategy for Moderately Coupled Interconnected Systems, Proceedings of the 1988 American Control Conference, Atlanta, Georgia, pp. 1521–1525, 1988.

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Authors and Affiliations

  1. Department of Electrical Engineering, and Research Investigator, Intelligent Systems Center, University of Missouri-Rolla, Rolla, Missouri

    L. Acar (Associate Professor)

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  1. L. Acar
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Communicated by M. Simaan

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Acar, L. Boundaries of the receding horizon control for interconnected systems. J Optim Theory Appl 84, 251–271 (1995). https://doi.org/10.1007/BF02192114

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