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Global Stability and Simultaneous Compensation of State and Output Delays for Nonlinear Systems via Output-Feedback Sliding Mode Control

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Abstract

This paper proposes a sliding mode control scheme for a class of nonlinear systems with multiple time delays, in the state variables and in the output signal. The unmeasured state of the system is estimated by an asymptotic observer for the zero dynamics and by cascaded high-gain observers for a chain of integrators with a nonlinear input disturbance which compose the complete state. Global asymptotic stability of the closed-loop system is obtained using only output feedback. The use of observers prevents undesirable chattering phenomena. Simulation results show effective performance in different scenarios, including application to missile guidance in the presence of seeker delays.

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References

  • Ahmed-Ali, T., Cherrier, E., & Lamnabhi-Lagarrigue, F. (2012). Cascade high gain predictors for a class of nonlinear systems. IEEE Transactions on Automatic Control, 57(1), 224–229.

    Article  MathSciNet  Google Scholar 

  • Babu, K. R., Sarma, I. G., & Swamy, K. N. (1994). Switched bias proportional navigation for homing guidance against highly maneuvering targets. Journal of Guidance, Control and Dynamics, 17(6), 1357–1363.

    Article  Google Scholar 

  • Basin, M., Fridman, L., Rodríguez-González, J., & Acosta, P. (2003). Optimal and robust sliding mode control for linear systems with multiple time delays in control input. Asian Journal of Control, 5(4), 557–567.

    Article  Google Scholar 

  • Bobtsov, A. A., Pyrkin, A. A., & Kolyubin, S. A. (2014). Simple output feedback adaptive control based on passification principle. International Journal of Adaptive Control and Signal Processing, 28(7–8), 620–632.

    Article  MathSciNet  MATH  Google Scholar 

  • Cloutier, J. R., Evers, J. H., & Feeley, J. J. (1989). Assessment of air-to-air missile guidance and control technology. IEEE Control Systems Magazine, 9(6), 27–34.

    Article  Google Scholar 

  • Coutinho, C. L., Oliveira, T. R., & Cunha, J. P. V. S. (2013). Output-feedback sliding-mode control of multivariable systems with uncertain time-varying state delays and unmatched non-linearities. IET Control Theory & Applications, 7(12), 1616–1623.

    Article  MathSciNet  Google Scholar 

  • Coutinho, C. L., Oliveira, T. R., & Cunha, J. P. V. S. (2014). Output-feedback sliding-mode control via cascade observers for global stabilisation of a class of nonlinear systems with output time delay. International Journal of Control, 87(11), 2327–2337.

    MathSciNet  MATH  Google Scholar 

  • Cunha, J. P. V. S., Costa, R. R., & Hsu, L. (2008). Design of first-order approximation filters for sliding-mode control of uncertain systems. IEEE Transactions on Industrial Electronics, 55(11), 4037–4046.

    Article  Google Scholar 

  • Cunha, J. P. V. S., Costa, R. R., Lizarralde, F., & Hsu, L. (2009). Peaking free variable structure control of uncertain linear systems based on a high-gain observer. Automatica, 45(5), 1156–1164.

    Article  MathSciNet  MATH  Google Scholar 

  • Dhananjay, N., Lum, K. Y., & Xu, J. X. (2013). Proportional navigation with delayed line-of-sight rate. IEEE Transactions on Control Systems Technology, 21(1), 247–253.

    Article  Google Scholar 

  • Feng, Y., Yu, X., & Zheng, X. (2006). Second-order terminal sliding mode control of input-delay systems. Asian Journal of Control, 8(1), 12–20.

    Article  MathSciNet  Google Scholar 

  • Figueredo, L. F. C., Ishihara, J. Y., Borges, G. A., & Bauchspiess, A. (2013). Delay-dependent robust stability analysis for time-delay T-S fuzzy systems with nonlinear local models. Journal of Control, Automation and Electrical Systems, 24(1), 11–21. doi:10.1007/s40313-013-0007-4.

    Article  Google Scholar 

  • Filippov, A. F. (1964). Differential equations with discontinuous right-hand side. American Mathematical Society Translations, 42(2), 199–231.

    Article  MATH  Google Scholar 

  • Fridman, E. (2001). New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters, 43(4), 309–319.

    Article  MathSciNet  MATH  Google Scholar 

  • Germani, A., Manes, C., & Pepe, P. (2002). A new approach to state observation of nonlinear systems with delayed output. IEEE Transactions on Automatic Control, 47(1), 96–101.

    Article  MathSciNet  Google Scholar 

  • Gomes da Silva Jr, J. M., Bender, F. A., Tarbouriech, S., & Biannic, J. M. (2009). Dynamic anti-windup synthesis for state delayed systems: an LMI approach. In Proceedings of the 48th IEEE Conference Decision and Control held jointly with the 28th Chinese Control Conference, Shanghai, China (pp. 6904–6909).

  • Gouaisbaut, F., Blanco, Y., & Richard, J. P. (2004). Robust sliding mode control of non-linear systems with delay: A design via polytopic formulation. International Journal of Control, 77(2), 206–215.

    Article  MathSciNet  MATH  Google Scholar 

  • Gu, K., Kharitonov, V. L., & Chen, J. (2003). Stability of Time-Delay Systems. Cambridge: Birkhäuser.

    Book  MATH  Google Scholar 

  • Han, X., Fridman, E., & Spurgeon, S. K. (2010). Sliding-mode control of uncertain systems in the presence of unmatched disturbances with applications. International Journal of Control, 83(12), 2413–2426.

    Article  MathSciNet  MATH  Google Scholar 

  • Holloway, J. C., & Krstic, M. (2015). A predictor observer for seeker delay in the missile homing loop. In 12th IFAC workshop on time delay systems, Ann Arbor, MI, USA (vol. 48, pp. 416–421).

  • Khalil, H. K. (2002). Nonlinear systems (3rd ed.). New York: Prentice Hall.

    MATH  Google Scholar 

  • Krstic, M. (2009). Delay compensation for nonlinear, adaptive, and PDE systems. Cambridge: Birkhäuser.

    Book  MATH  Google Scholar 

  • Li, X., & DeCarlo, R. A. (2003). Robust sliding mode control of uncertain time delay systems. International Journal of Control, 76(13), 1296–1305.

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, G., Zinober, A., & Shtessel, Y. B. (2009). Second-order SM approach to SISO time-delay system output tracking. IEEE Transactions on Industrial Electronics, 56(9), 3638–3645.

    Article  Google Scholar 

  • Michiels, W., & Niculescu, S. I. (2007). Stability and stabilization of time-delay systems: An eigenvalue-based approach. Philadelphia: SIAM.

  • Nam, P. T. (2009). Exponential stability criterion for time-delay systems with nonlinear uncertainties. Applied Mathematics and Computation, 214(2), 374–380.

    Article  MathSciNet  MATH  Google Scholar 

  • Niu, Y., Lam, J., Wang, X., & Ho, D. W. C. (2004). Observer-based sliding mode control for nonlinear state-delayed systems. International Journal of Systems Science, 35(2), 139–150.

    Article  MathSciNet  MATH  Google Scholar 

  • Oliveira, T. R., & Cunha, J. P. V. S. (2014). Global output feedback sliding mode control of nonlinear systems with multiple time delays. In Proceedings of the 19th IFAC world congress, Cape Town (Vol. 19, pp. 4619–4624).

  • Orlov, Y., Perruquetti, W., & Richard, J. P. (2003). Sliding mode control synthesis of uncertain time-delay systems. Asian Journal of Control, 5(4), 568–577.

    Article  Google Scholar 

  • Ramakrishnan, K., & Ray, G. (2015). Improved results on delay-dependent stability of LFC systems with multiple time-delays. Journal of Control, Automation and Electrical Systems, 26(3), 235–240. doi:10.1007/s40313-015-0171-9.

    Article  Google Scholar 

  • Richard, J. P. (2003). Time-delay systems: An overview of some recent advances and open problems. Automatica, 39(10), 1667–1694.

    Article  MathSciNet  MATH  Google Scholar 

  • Shi, P., Zhang, Y., Chadli, M., & Agarwal, R. K. (2016). Mixed H-infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Transactions on Neural Networks and Learning Systems, 27(4), 903–909.

    Article  MathSciNet  Google Scholar 

  • Shtessel, Y. B., Shkolnikov, I. A., & Levant, A. (2007). Smooth second-order sliding modes: Missile guidance application. Automatica, 43(8), 1470–1476.

    Article  MathSciNet  MATH  Google Scholar 

  • Si-Ammour, A., Djennoune, S., & Bettayeb, M. (2009). A sliding mode control for linear fractional systems with input and state delays. Communications in Nonlinear Science and Numerical Simulation, 14(5), 2310–2318.

    Article  MathSciNet  MATH  Google Scholar 

  • Song, J., Song, S., Guo, Y., & Zhou, H. (2015). Nonlinear disturbance observer-based fast terminal sliding mode guidance law with impact angle constraints. International Journal of Innovative Computing, Information and Control, 11(3), 787–802.

    Google Scholar 

  • Sontag, E. D., & Wang, Y. (1997). Output-to-state stability and detectability of nonlinear systems. Systems & Control Letters, 29(5), 279–290.

    Article  MathSciNet  MATH  Google Scholar 

  • Su, X., Shi, P., Wu, L., & Basin, M. V. (2014). Reliable filtering with strict dissipativity for T-S fuzzy time-delay systems. IEEE Transactions on Cybernetics, 44(12), 2470–2483.

    Article  Google Scholar 

  • Su, X., Shi, P., Wu, L., & Song, Y. D. (2013). A novel control design on discrete-time Takagi–Sugeno fuzzy systems with time-varying delays. IEEE Transactions on Fuzzy Systems, 21(4), 655–671.

    Article  Google Scholar 

  • Utkin, V., Guldner, J., & Shi, J. (1999). Sliding mode control in electromechanical systems. London: Taylor & Francis Ltd.

    Google Scholar 

  • Wu, L., Su, X., & Shi, P. (2012). Sliding mode control with bounded \({\cal L}_2\) gain performance of Markovian jump singular time-delay systems. Automatica, 48(8), 1929–1933.

    Article  MathSciNet  MATH  Google Scholar 

  • Yan, X. G., Spurgeon, S. K., & Edwards, C. (2010). Sliding mode control for time-varying delayed systems based on a reduced-order observer. Automatica, 46(8), 1354–1362.

    Article  MathSciNet  MATH  Google Scholar 

  • Yan, X. G., Spurgeon, S. K., & Edwards, C. (2014a). Memoryless static output feedback sliding mode control for nonlinear systems with delayed disturbances. IEEE Transactions on Automatic Control, 59(7), 1906–1912.

    Article  MathSciNet  Google Scholar 

  • Yan, X. G., Spurgeon, S. K., & Orlov, Y. (2014b). Output feedback control synthesis for non-linear time-delay systems using a sliding-mode observer. IMA Journal of Mathematical Control and Information, 31(4), 501–518.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work was supported in part by Brazilian funding agencies CNPq, FAPERJ and CAPES.

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Authors and Affiliations

  1. Department of Electronics and Telecommunication Engineering, State University of Rio de Janeiro, Rio de Janeiro, Brazil

    Tiago Roux Oliveira, José Paulo V. S. Cunha & Andrei Battistel

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  1. Tiago Roux Oliveira
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  2. José Paulo V. S. Cunha
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  3. Andrei Battistel
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Correspondence to Andrei Battistel.

Additional information

A preliminary version of the manuscript was presented at 19th IFAC World Congress, see reference (Oliveira and Cunha 2014)

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Oliveira, T.R., Cunha, J.P.V.S. & Battistel, A. Global Stability and Simultaneous Compensation of State and Output Delays for Nonlinear Systems via Output-Feedback Sliding Mode Control. J Control Autom Electr Syst 27, 608–620 (2016). https://doi.org/10.1007/s40313-016-0274-y

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  • DOI: https://doi.org/10.1007/s40313-016-0274-y

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