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Decentralized Model Predictive Control for Networks of Linear Systems with Coupling Delay

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Abstract

This paper presents a new dissipativity-based decentralized model predictive control strategy for networks of linear systems suffering from a bounded coupling delay. The notion of delay-robust dissipativity is introduced and applied to the development of interconnection stability conditions. The dissipation inequality of system trajectories is converted into a prognostic stability constraint for the optimization problem of model predictive control to guarantee the system stability. A recursive feasibility condition is derived for the constrained optimization problem, which is formulated in a semi-definite program. A numerical example of an interconnected three-unit process system is provided for illustrations.

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References

  1. Barrabasi, A.L., Albert, R.: Emerging of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  2. Li, C., Chen, G.: Synchronization in general complex dynamical networks with coupling delays. Physica A 343, 263–278 (2004)

    Article  MathSciNet  Google Scholar 

  3. Dunbar, W.B., Murray, R.M.: Distributed receding horizon control with application to multi-vehicle formation stabilization. Automatica 42(4), 1549–1558 (2006)

    Article  MathSciNet  Google Scholar 

  4. De Oliveira, L.B., Camponogara, E.: Multi-agent model predictive control of signaling split in urban traffic networks. Transp. Res., Part C, Emerg. Technol. 18(1), 120–139 (2010)

    Article  Google Scholar 

  5. Negenborn, R.R., et al.: A novel coordination strategy for multi-agent control using overlapping subnetworks with application to power systems. In: Mohammadpour, J., Grigoriadis, K.M. (eds.) Efficient Model and Control of Large-Scale Systems, pp. 251–278. Springer, Norwell (2010)

    Chapter  Google Scholar 

  6. Rawlings, J.B., Stewart, B.T.: Coordinating multiple optimization-based controllers: new opportunities and challenges. J. Process Control 18, 839–845 (2008)

    Article  Google Scholar 

  7. Scorletti, G., Duc, G.: An LMI approach to decentralized H ∞ control. Int. J. Control 74(3), 211–224 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. D’Andrea, R., Dullerud, G.E.: Distributed control of spatially interconnected systems. IEEE Trans. Autom. Control 48, 1478–1495 (2003)

    Article  MathSciNet  Google Scholar 

  9. Niculescu, S.I.: Delay Effects on Stability—A Robust Control Approach. Springer, Berlin (2001)

    MATH  Google Scholar 

  10. Mahmoud, M.S., Al-Rayyah, A.Y.: Decentralized reliable control of interconnected time-delays systems against sensor failures. J. Optim. Theory Appl. 147(2), 318–336 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mahmoud, M.S., Chen, G.: Decentralized reliable control of interconnected systems with time varying delays. J. Optim. Theory Appl. 143, 497–518 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Siljak, D.D.: Decentralized Control of Complex Systems. Academic Press, San Diego (1991)

    Google Scholar 

  13. Lunze, J.: Feedback Control of Large Scale Systems. Prentice Hall, New York (1992)

    MATH  Google Scholar 

  14. Tran, T., Tuan, H.D., Ha, Q.P., Nguyen, H.T.: Decentralised model predictive control of time-varying splitting parallel systems. In: Mohammadpour, J., Scherer, C. (eds.) Control of Linear Parameter Varying Systems with Applications, pp. 217–251. Springer, Berlin (2012)

    Chapter  Google Scholar 

  15. Keviczky, T., Borrelli, F., Balas, G.J.: Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica 42(12), 2105–2115 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Dashkovskiy, S., Rüffer, B.S., Wirth, F.: Decentralized model predictive control of nonlinear systems: an input-to-state stability approach. Math. Control Signals Syst. 19(2), 93–122 (2007)

    Article  MATH  Google Scholar 

  17. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constraint predictive control: stability and optimality. Automatica 36, 789–814 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Magni, L., Raimondo, D.M., Allgöwer, F.: Nonlinear Model Predictive Control: Towards New Challenging Applications. LNCIS, vol. 384. Springer, Berlin (2009)

    Book  Google Scholar 

  19. Wang, S.-H., Davison, E.J.: On the stabilization of decentralized control systems. IEEE Trans. Autom. Control 18(5), 473–478 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  20. Willems, J.C.: Dissipative dynamical systems, parts I and II. Arch. Ration. Mech. Anal. 45, 321–393 (1972)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

We greatly thank the anonymous reviewers for their comments that have helped improve the paper presentation.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Curtin University, Lvl 4, Building 314, Bentley Campus, Perth, WA, 6845, Australia

    Tri Tran

  2. School of Electrical, Mechanical and Mechatronic Systems, University of Technology, Sydney, 15 Broadway, Ultimo, NSW, 2007, Australia

    Q. P. Ha

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  1. Tri Tran
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  2. Q. P. Ha
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Correspondence to Tri Tran.

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Communicated by Kok Lay Teo.

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Tran, T., Ha, Q.P. Decentralized Model Predictive Control for Networks of Linear Systems with Coupling Delay. J Optim Theory Appl 161, 933–950 (2014). https://doi.org/10.1007/s10957-013-0379-4

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  • DOI: https://doi.org/10.1007/s10957-013-0379-4

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