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Predictor Feedback: Time-Varying, Adaptive, and Nonlinear

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Book cover Time Delay Systems: Methods, Applications and New Trends

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 423))

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Abstract

We present a tutorial introduction to methods for stabilization of systems with long input delays—the so-called “predictor feedback” techniques. The methods are based on techniques originally developed for boundary control of partial differential equations using the “backstepping” approach. We start with a consideration of linear systems, first with a known delay and then subject to a small uncertainty in the delay. Then we study linear systems with constant delays that are completely unknown, which requires an adaptive control approach. For linear systems, we also present a method for compensating arbitrarily large but known time-varying delays. Next, we consider nonlinear control problems in the presence of arbitrarily long input delays. Finally, we close with a design for general nonlinear systems with delays that have a general dependency on the system state.

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References

  1. Sipahi, R., Niculescu, S.-I., Abdallah, C.T., Michiels, W., Gu, K.: Stability and stabilization of systems with time delay. Control Systems Magazine 31, 38–65 (2011)

    MathSciNet  Google Scholar 

  2. Smith, O.J.M.: A controller to overcome dead time. ISA 6, 28–33 (1959)

    Google Scholar 

  3. Manitius, A.Z., Olbrot, A.W.: Finite spectrum assignment for systems with delays. IEEE Trans. on Automatic Control 24, 541–553 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kwon, W.H., Pearson, A.E.: Feedback stabilization of linear systems with delayed control. IEEE Trans. on Automatic Control 25, 266–269 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. Artstein, Z.: Linear systems with delayed controls: a reduction. IEEE Trans. on Automatic Control 27, 869–879 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhong, Q.-C.: Robust Control of Time-delay Systems. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  7. Michiels, W., Niculescu, S.-I.: Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach. SIAM (2007)

    Google Scholar 

  8. Mondie, S., Michiels, W.: Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Trans. on Automatic Control 48, 2207–2212 (2003)

    Article  MathSciNet  Google Scholar 

  9. Zhong, Q.-C.: On distributed delay in linear control laws—Part I: Discrete-delay implementation. IEEE Transactions on Automatic Control 49, 2074–2080 (2006)

    Article  Google Scholar 

  10. Zhong, Q.-C., Mirkin, L.: Control of integral processes with dead time—Part 2: Quantitative analysis. IEE Proc. Control Theory & Appl. 149, 291–296 (2002)

    Article  Google Scholar 

  11. Krstic, M., Smyshlyaev, A.: Boundary Control of PDEs: A Course on Backstepping Designs. SIAM (2008)

    Google Scholar 

  12. Vazquez, R., Krstic, M.: Control of Turbulent and Magnetohydrodynamic Channel Flows. Birkhäuser (2007)

    Google Scholar 

  13. Krstic, M.: Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Birkhäuser (2009)

    Google Scholar 

  14. Krstic, M.: On compensating long actuator delays in nonlinear control. IEEE Transactions on Automatic Control 53, 1684–1688 (2008)

    Article  MathSciNet  Google Scholar 

  15. Krstic, M.: Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica 44, 2930–2935 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Krstic, M.: Compensating actuator and sensor dynamics governed by diffusion PDEs. Systems and Control Letters 58, 372–377 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Krstic, M.: Compensating a string PDE in the actuation or sensing path of an unstable ODE. IEEE Transactions on Automatic Control 54, 1362–1368 (2009)

    Article  MathSciNet  Google Scholar 

  18. Krstic, M.: Input delay compensation for forward complete and feedforward nonlinear systems. IEEE Transactions on Automatic Control 55, 287–303 (2010)

    Article  MathSciNet  Google Scholar 

  19. Krstic, M.: Lyapunov stability of linear predictor feedback for time-varying input delay. IEEE Transactions on Automatic Control 55, 554–559 (2010)

    Article  MathSciNet  Google Scholar 

  20. Krstic, M.: Control of an unstable reaction-diffusion PDE with long input delay. Systems and Control Letters 58, 773–782 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Krstic, M.: Compensation of infinite-dimensional actuator and sensor dynamics: Nonlinear and delay-adaptive systems. IEEE Control Systems Magazine 30, 22–41 (2010)

    Article  MathSciNet  Google Scholar 

  22. Bresch-Pietri, D., Krstic, M.: Adaptive trajectory tracking despite unknown input delay and plant parameters. Automatica 45, 2075–2081 (2009)

    Article  Google Scholar 

  23. Bresch-Pietri, D., Krstic, M.: Delay-adaptive predictor feedback for systems with unknown long actuator delay. IEEE Transactions on Automatic Control 55, 2106–2112 (2010)

    Article  MathSciNet  Google Scholar 

  24. Bekiaris-Liberis, N., Krstic, M.: Delay-adaptive feedback for linear feedforward systems. Systems and Control Letters 59, 277–283 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. Bekiaris-Liberis, N., Krstic, M.: Compensating the distributed effect of a wave PDE in the actuation or sensing path of MIMO LTI Systems. Systems & Control Letters 59, 713–719 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Bekiaris-Liberis, N., Krstic, M.: Stabilization of linear strict-feedback systems with delayed integrators. Automatica 46, 1902–1910 (2010)

    Article  MATH  Google Scholar 

  27. Bekiaris-Liberis, N., Krstic, M.: Lyapunov stability of linear predictor feedback for distributed input delay. IEEE Transactions on Automatic Control 56, 655–660 (2011)

    Article  MathSciNet  Google Scholar 

  28. Bekiaris-Liberis, N., Krstic, M.: Compensating distributed effect of diffusion and counter-convection in multi-input and multi-output LTI systems. IEEE Transactions on Automatic Control 56, 637–642 (2011)

    Article  MathSciNet  Google Scholar 

  29. Teel, A.R.: Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE Transactions on Automatic Control 43, 960–964 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  30. Datko, R.: Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM Journal on Control and Optimization 26, 697–713 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ortega, R., Lozano, R.: Globally stable adaptive controller for systems with delay. Internat. J. Control 47, 17–23 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  32. Niculescu, S.-I., Annaswamy, A.M.: An Adaptive Smith-Controller for Time-delay Systems with Relative Degree n* ≥ 2. Systems and Control Letters 49, 347–358 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. Jankovic, M.: Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Trans. on Automatic Control 46, 1048–1060 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  34. Germani, A., Manes, C., Pepe, P.: Input-output linearization with delay cancellation for nonlinear delay systems: the problem of the internal stability. International Journal of Robust and Nonlinear Control 13, 909–937 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. Karafyllis, I.: Finite-time global stabilization by means of time-varying distributed delay feedback. SIAM Journal of Control and Optimization 45, 320–342 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Mazenc, F., Bliman, P.-A.: Backstepping design for time-delay nonlinear systems. IEEE Transactions on Automatic Control 51, 149–154 (2006)

    Article  MathSciNet  Google Scholar 

  37. Mazenc, F., Mondie, S., Francisco, R.: Global asymptotic stabilization of feedforward systems with delay at the input. IEEE Trans. Automatic Control 49, 844–850 (2004)

    Article  MathSciNet  Google Scholar 

  38. Smyshlyaev, A., Krstic, M.: Closed form boundary state feedbacks for a class of 1D partial integro-differential equations. IEEE Trans. on Automatic Control 49(12), 2185–2202 (2004)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, 92093-0411, USA

    Miroslav Krstic

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  1. Miroslav Krstic
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Correspondence to Miroslav Krstic .

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Editors and Affiliations

  1. Dept. Mechanical Engineering, Northeastern University, Huntingdon Ave. 360, Boston, 02115, Massachusetts, USA

    Rifat Sipahi

  2. Technicka Street 4, Prague, 166 07, Czech Republic

    Tomáš Vyhlídal

  3. , CNRSSupélec, L2S (UMR CNRS 8506), rue Joliot Curie 3, Gif-sur-Yvette, 91192, France

    Silviu-Iulian Niculescu

  4. , Department of Electrical and Information, University of L’Aquila, Via G. Gronchi 18, L’Aquila, 67100, Italy

    Pierdomenico Pepe

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Krstic, M. (2012). Predictor Feedback: Time-Varying, Adaptive, and Nonlinear. In: Sipahi, R., Vyhlídal, T., Niculescu, SI., Pepe, P. (eds) Time Delay Systems: Methods, Applications and New Trends. Lecture Notes in Control and Information Sciences, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25221-1_22

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25220-4

  • Online ISBN: 978-3-642-25221-1

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