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On Polytopic Approximations of Systems with Time-Varying Input Delays

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Nonlinear Model Predictive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 384))

Abstract

Networked control systems (NCS) have recently received an increasing attention from the control systems community. One of the major problems in NCS is how to model the highly nonlinear terms caused by uncertain delays such as time-varying input delays. A straightforward solution is to employ polytopic approximations. In this paper we develop a novel method for creating discrete-time models for systems with time-varying input delays based on polytopic approximations. The proposed method is compared to several other existing approaches in terms of quality, complexity and scalability. Furthermore, its suitability for model predictive control is demonstrated.

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References

  1. Branicky, M.S., Phillips, S.M., Zhang, W.: Stability of Networked Control Systems: Eplicit Analysis of Delay. In: Proceedings of the American Control Conference, vol. 4, pp. 2352–2357 (2000)

    Google Scholar 

  2. Cayley, A.: A memoir on the theory of matrices. Philosophical Transactions London 158, 17–37 (1857)

    Google Scholar 

  3. Cloosterman, M.B.G.: Control of Systems over Communication Networks: Modelling, Analysis and Design. Ph.D. dissertation, Eindhoven University of Technology, The Netherlands (2008)

    Google Scholar 

  4. Gantmacher, F.R.: Theory of Matrices, vols. 1, 2. Chelsea Publishing Company, New York (1959)

    MATH  Google Scholar 

  5. Hetel, L., Daafouz, J., Iung, C.: Stabilization of arbitrary switched linear systems with unknown time-varying delays. IEEE Transactions on Automatic Control 51(10), 1668–1674 (2006)

    Article  MathSciNet  Google Scholar 

  6. Hespanha, J., Naghshtabrizi, P., Xu, Y.: A survey of Recent Results in Networked Control Systems. Proceedings of the IEEE 95, 138–161 (2007)

    Article  Google Scholar 

  7. Kothare, M.V., Balakrishnan, V., Morari, M.: Robust Constrained Model Predictive Control using Linear Matrix Inequalities. Automatica 32(10), 1361–1379 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Murray, R.M., Åström, K.J., Boyd, S.P., Brockett, R.W., Stein, G.: Future Directions in Control in an Information-Rich World. IEEE Control Systems Magazine 23(2), 20–33 (2003)

    Article  Google Scholar 

  9. Olaru, S., Niculescu, S.I.: Predictive control for linear systems with delayed input subject to constraints. IFAC World Congress, Seoul, Korea (2008)

    Google Scholar 

  10. Tipsuwan, Y., Chow, M.-Y.: Control methodologies in networked control systems. Control Engineering Practice 11, 1099–1111 (2003)

    Article  Google Scholar 

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Gielen, R., Olaru, S., Lazar, M. (2009). On Polytopic Approximations of Systems with Time-Varying Input Delays. In: Magni, L., Raimondo, D.M., Allgöwer, F. (eds) Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01094-1_18

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  • DOI: https://doi.org/10.1007/978-3-642-01094-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01093-4

  • Online ISBN: 978-3-642-01094-1

  • eBook Packages: EngineeringEngineering (R0)

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