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Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model

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Abstract

In this paper, an output feedback model predictive tracking control method is proposed for constrained nonlinear systems, which are described by a slope bounded model. In order to solve the problem, we consider the finite horizon cost function for an off-set free tracking control of the system. For reference tracking, the steady state is calculated by solving by quadratic programming and a nonlinear estimator is designed to predict the state from output measurements. The optimized control input sequences are obtained by minimizing the upper bound of the cost function with a terminal weighting matrix. The cost monotonicity guarantees that tracking and estimation errors go to zero. The proposed control law can easily be obtained by solving a convex optimization problem satisfying several linear matrix inequalities. In order to show the effectiveness of the proposed method, a novel slope bounded nonlinear model-based predictive control method is applied to the set-point tracking problem of solid oxide fuel cell systems. Simulations are also given to demonstrate the tracking performance of the proposed method.

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References

  1. Angeli, D., Casavola, A., Mosca, E.: Constrained predictive control of nonlinear plant via polytopic linear system embedding. Int. J. Robust Nonlinear Control 10, 1091–1103 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Wan, Z., Kothare, M.V.: Efficient scheduled stabilizing output feedback model predictive control for constrained nonlinear systems. IEEE Trans. Autom. Control 49, 1172–1177 (2004)

    Article  MathSciNet  Google Scholar 

  3. Angeli, D., Casavola, A., Franze, G., Mosca, E.: An ellopsoidal off-line MPC scheme for uncertain polytopic discrete-time systems. Automatica 44, 3113–3119 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Casavola, A., Famularo, D., Franze, G.: Robust constrained predictive control of uncertain norm-bounded linear systems. Automatica 40, 1865–1876 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Ding, B., Xi, Y., Cychowski, M.T., O’Mahony, T.: A synthesis approach for output feedback robust constrained model predictive control. Automatica 44, 258–264 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Magni, L., De Nicolao, G., Scattolini, R.: Output feedback and tracking of nonlinear systems with model predictive control. Automatica 37, 1601–1607 (2001)

    Article  MATH  Google Scholar 

  8. Zhang, T., Feng, G., Lu, J.H.: Fuzzy constrained min–max model predictive control using piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 15, 686–698 (2007)

    Article  Google Scholar 

  9. Lu, T., Arkun, Y.: Quasi-min–max MPC algorithms for LPV systems. Automatica 36, 527–540 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Findeisen, R., Imsland, L., Allgower, F., Foss, B.A.: Output feedback stabilization of constrained systems with nonlinear predictive control. Int. J. Robust Nonlinear Control 13, 211–227 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhang, T., Feng, G.: Rapid load following of an SOFC power system via stable fuzzy predictive tracking controller. IEEE Trans. Fuzzy Syst. 17, 357–371 (2009)

    Article  Google Scholar 

  12. Thuan, M.V., Phat, V.N., Trinh, H.: Dynamic output feedback guaranteed cost control of linear systems with interval time-varying delays in states and outputs. Appl. Math. Comput. 218, 10697–10707 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  13. Fernando, T.L., Phat, V.N., Trinh, H.M.: Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays. Applied Mathematical Modelling (2012, in press). doi:10.1016/j.apm.2012.04.035

    Google Scholar 

  14. Findeisen, R., Imsland, L., Allgower, F., Foss, B.A.: Output feedback nonlinear predictive control—a separation principle approach. In: Proceedings of 15th IFAC World Congress (2002)

    Google Scholar 

  15. Rahideh, A., Shaheed, M.H.: Constrained output feedback model predictive control for nonlinear systems. Control Eng. Pract. 20, 431–443 (2012)

    Article  Google Scholar 

  16. Bohm, C., Findeisen, R., Allgower, F.: Robust control of constrained sector bounded Lur’e systems with applications to nonlinear model predictive control. Dyn. Contin. Discrete Impuls. Syst. 17, 935–958 (2010)

    MathSciNet  Google Scholar 

  17. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

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Acknowledgements

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0011460).

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Authors and Affiliations

  1. Department of Electronic Engineering, Daegu University, Gyungsan, 712-714, Republic of Korea

    S. M. Lee

  2. School of Electrical Engineering, Chungbuk National University, Cheongju, 361-763, Republic of Korea

    O. M. Kwon

  3. Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749, Republic of Korea

    Ju H. Park

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  1. S. M. Lee
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  2. O. M. Kwon
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  3. Ju H. Park
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Correspondence to Ju H. Park.

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Communicated by F.E. Udwadia.

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Lee, S.M., Kwon, O.M. & Park, J.H. Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model. J Optim Theory Appl 160, 239–254 (2014). https://doi.org/10.1007/s10957-012-0201-8

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  • DOI: https://doi.org/10.1007/s10957-012-0201-8

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