access icon free Predictor control for multi-input non-linear systems with time- and state-dependent input delays

Predictor control for a class of multi-input non-linear systems with time- and state-dependent input delays is considered. First, a delay-free control law is given for the original system in the absence of delays based on the control Lyapunov function. Second, sufficient conditions are obtained and a predictor control for the original system is presented. Stability analysis is done by a Lyapunov functional. Due to the delay dependent on time and state, a region of attraction is estimated. Further, the stabilisation formula is optimal with respect to a meaningful cost functional. The proposed design is illustrated by a mobile robot with input delay.

Inspec keywords: delay systems; Lyapunov methods; nonlinear control systems; predictive control; stability

Other keywords: predictor control; control Lyapunov function; sufficient conditions; delay-free control law; state-dependent input delays; mobile robot; time-dependent input delays; stability analysis; multiinput nonlinear systems

Subjects: Nonlinear control systems; Optimal control; Distributed parameter control systems; Stability in control theory

References

    1. 1)
      • 1. Krstic, M.: ‘Delay compensation for nonlinear, adaptive, and PDE systems’ (Birkhauser, 2009).
    2. 2)
      • 21. Sontag, E.D.: ‘A Lyapunov-like characterization of asymptotic controllability’, SIAM J. Control Optim., 1983, 21, pp. 462471.
    3. 3)
      • 19. Diagne, M., Bekiaris-Liberis, N., Krstic, M.: ‘Time- and state-dependent input delay-compensated bang-bang control of a screw extruder for 3D printing’. ASME Dynamic Systems and Control Conf., 2015.
    4. 4)
      • 2. Cai, X., Han, Z., Zhang, W.: ‘Globally uniformly asymptotical stabilization of time-delay nonlinear systems’, Int. J. Syst. Sci., 2011, 41, pp. 11751183.
    5. 5)
      • 10. Cai, X., Lin, Y., Zhang, J.: ‘Universal stabilisation design for general non-linear systems under wave partial differential equation actuator dynamics with time-varying moving boundary’, IET Control Theory Appl., 2016, 10, pp. 253264.
    6. 6)
      • 22. Sontag, E.D.: ‘A ‘universal’ construction of Artstein's theorem on nonlinear stabilization’, Syst. Control Lett., 1989, 13, pp. 117123.
    7. 7)
      • 15. Sipahi, R., Atay, F.M., Niculescu, S.I.: ‘Stability of traffic flow behavior with distributed delays modeling the memory effect of the drivers’, SIAM J. Appl. Math., 2007, 68, pp. 738759.
    8. 8)
      • 16. Mahaffy, J., Blair, J., Mackey, M.: ‘Hematopoietic model with moving boundary condition and state dependent delay: applications in erythopoiesis’, J. Theor. Biol., 1998, 190, pp. 135146.
    9. 9)
      • 5. Mazenc, F., Malisoff, M.: ‘Reduction model method for local stabilization of time-varying nonlinear systems with input delays, structured nonlinearities, and uncertainties’. Proc. of American Control Conf. (ACC), 2014, pp. 41694174.
    10. 10)
      • 25. Pomet, J.B.: ‘Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift’, Syst. Control Lett., 1992, 18, pp. 147158.
    11. 11)
      • 3. Bresch-Pietri, D., Petit, N., Krstic, M.: ‘Prediction-based control for nonlinear state- and input-delay systems with the aim of delay-robustness analysis’. Proc. of 54th IEEE Conf. on Decision and Control (CDC), 2015, pp. 64036409.
    12. 12)
      • 4. Kamalapurkar, R., Fischer, N., Obuz, S.: ‘Time-varying input and state delay compensation for uncertain nonlinear systems’, IEEE Trans. Autom. Control, 2016, 61, pp. 834839.
    13. 13)
      • 24. Krstic, M., Li, Z.H.: ‘Inverse optimal design of input-to-state stabilizing nonlinear controllers’, IEEE Trans. Autom. Control, 1998, 43, pp. 336350.
    14. 14)
      • 7. Bekiaris-Liberis, N., Krstic, M.: ‘Compensation of time-varying input and state delays for nonlinear systems’, J. Dyn. Syst. Meas. Control, 2012, 34, pp. 011009-1011009-14.
    15. 15)
      • 11. Krstic, M.: ‘Compensating a string PDE in the actuation or sensing path of an unstable ODE’, IEEE Trans. Autom. Control, 2009, 54, pp. 13621368.
    16. 16)
      • 12. Cai, X., Krstic, M.: ‘Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary’, Int. J. Robust. Nonlinear Control, 2015, 25, pp. 222253.
    17. 17)
      • 8. Bekiaris-Liberis, N., Krstic, M.: ‘Compensation of state-dependent input delay for nonlinear systems’, IEEE Trans. Autom. Control, 2013, 58, pp. 275289.
    18. 18)
      • 20. Artstein, Z.: ‘Stabilization with relaxed controls’, Nonlinear Anal. Theory Methods Appl., 1983, 7, pp. 11631173.
    19. 19)
      • 17. Sterman, J.D.: ‘Business dynamics: systems thinking and modeling for a complex world’ (McGraw-Hill, 2000).
    20. 20)
      • 9. Bekiaris-Liberis, N., Krstic, M.: ‘Robustness of nonlinear predictor feedback laws to time- and state-dependent delay perturbations’, Automatica, 2013, 49, pp. 15761590.
    21. 21)
      • 14. Niemeyer, G., Slotine, J.: ‘Toward bilateral internet teleoperation. in beyond webcams: an introduction to online robots’ (Cambridge, MIT Press, 2001).
    22. 22)
      • 18. Diagne, M., Krstic, M.: ‘State-dependent input delay-compensated bang-bang control: application to 3D printing based on screw-extruder’. Proc. of American Control Conf., 2015, pp. 56535658.
    23. 23)
      • 6. Krstic, M.: ‘Input delay compensation for forward complete and feed forward nonlinear systems’, IEEE Trans. Autom. Control, 2010, 55, pp. 287303.
    24. 24)
      • 23. Cai, X., Lin, Y., Liu, L.: ‘Universal stabilisation design for a class of non-linear systems with time-varying input delays’, IET Control Theory Appl., 2015, 9, pp. 14811490.
    25. 25)
      • 13. Cai, X., Krstic, M.: ‘Nonlinear stabilization through wave PDE dynamics with a moving uncontrolled boundary’, Automatica, 2016, 68, pp. 2738.
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