Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Asymptotic tracking and dynamic regulation of SISO non-linear system based on discrete multi-dimensional Taylor network

For non-linear control, it is important to secure a generally structured controller that promises wide application and desirable performance. This study deals with the problem of asymptotic tracking and dynamic regulation of single-input single output (SISO) non-linear systems via output feedbacks by the discrete multi-dimensional Taylor network (MTN) controller, a novel controller with fixed structure and sampled-data control mechanism. For verification of its validity, differential geometry and polynomial approximation are adopted. Using the emulation technique and regional pole assignment, the asymptotic tracking and dynamic regulation without online optimisation of the system by discrete MTN controller is tested. With the dynamic change of error signals, the dynamic regulation by given index is realised. As a convex optimisation problem, the controller parameters can be acquired by parametric learning. Based on the delta operator model, the procedure of the controller design is given in detail. Simulation results confirm the feasibility and effectiveness of the proposed approach.

References

    1. 1)
      • 20. Shu, H.-L., Shu, H.: ‘Simulation study of PID neural network temperature control system in plastic injecting-moulding machine’. Proc. 2007 Int. Conf. Mach. Learn. Cyb., 2007, pp. 492497.
    2. 2)
      • 38. Guo, X.-G., Yang, G.-H.: ‘H∞ output tracking control for delta operator systems with insensitivity to controller coefficient variations’, Int. J. Syst. Sci., 2013, 44, (4), pp. 652662.
    3. 3)
      • 9. Yang, H.J., Li, Z.W., Shi, P., et al: ‘Control of periodic sampling systems subject to actuator saturation’, Int. J. Robust Nonlinear Control, 2015, 25, (18), pp. 36613678.
    4. 4)
      • 29. Bartolini, G., Punta, E.: ‘Reduced-order observer in the sliding-mode control of nonlinear nonaffine systems’, IEEE Trans. Autom.Control, 2010, 55, (10), pp. 23682373.
    5. 5)
      • 27. Park, J.-H., Huh, S.-H., Kim, S.-H., et al: ‘Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks’, IEEE Trans. Neural Netw. Learn. Syst., 2005, 16, (2), pp. 414422.
    6. 6)
      • 35. Yuz, J.I., Goodwin, G.C.: ‘On sampled-data models for nonlinear systems’, IEEE Trans. Autom. Control, 2005, 50, (10), pp. 14771489.
    7. 7)
      • 31. Ishitobi, M., Yamaguchi, K., Nagayama, T.: ‘Model following control of nonlinear sampled-data systems by Lyapunov-based redesign’. Proc. Int.Conf. Networking, Sensing and Control, 2009, pp. 368372.
    8. 8)
      • 32. Khalil, H.K.: ‘Nonlinear systems’ (Prentice Hall, New Jersey, 1996, 3rd edn.).
    9. 9)
      • 36. Li, H.G., Wu, B., Li, G.Y., et al: ‘Global theory of Delta operator control and its robustness control’ (National Defense Industry Press, Beijing, 2005) (in Chinese).
    10. 10)
      • 19. Koo, G.B., Park, J.B., Joo, Y.H.: ‘Intelligent digital redesign for non-linear systems: observer-based sampled-data fuzzy control approach’, IET Control Theory Appl., 2016, 10, (1), pp. 19.
    11. 11)
      • 34. Yuz, J.I., Goodwin, G.C.: ‘Sampled-data models for linear and nonlinear systems’ (Springer, London, 2014).
    12. 12)
      • 39. Li, K.: ‘PID tuning for optimal closed-loop performance with specified gain and phase margins’, IEEE Trans. Control Syst. Technol., 2013, 21, (3), pp. 10241030.
    13. 13)
      • 12. Fei, J., Ding, H.: ‘Adaptive sliding mode control of dynamic system using RBF neural network’, Nonlinear Dyn., 2012, 70, (2), pp. 15631573.
    14. 14)
      • 7. Wu, B., Ding, Z.: ‘Asymptotic stabilisation of a class of nonlinear systems via sampled-data output feedback control’, Int. J. Control, 2009, 82, (9), pp. 17381746.
    15. 15)
      • 23. Yang, C., Ma, H., Fu, M.: ‘Adaptive predictive control of periodic NARMA systems using nearest-neighbor compensation’, IET Control Theory Appl., 2013, 7, (7), pp. 936951.
    16. 16)
      • 3. Ling, Q., Yan, Z., Ji, H., et al: ‘Sufficient conditions to stabilize time-varying nonlinear sampled-data systems via approximation’, Int. J. Robust Nonlinear Control, 2017, 27, (1), pp. 108120.
    17. 17)
      • 10. Isidori, A.: ‘Nonlinear Control Systems’ (Springer, London, 1995, 3rd edn.).
    18. 18)
      • 25. Zhou, B., Yan, H.: ‘Financial time series forecasting based on wavelet and multi-dimensional Taylor network dynamics model’, Systems Engineering-Theory & Practice, 2013, 33, (10), pp. 26542662, (in Chinese).
    19. 19)
      • 30. Chen, W.-H., Ballance, D.J., Gawthrop, P.J.: ‘Optimal control of nonlinear systems: a predictive control approach’, Automatica, 2003, 39, (4), pp. 633641.
    20. 20)
      • 14. Yang, C., Ge, S.S., Xiang, C., et al: ‘Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach’, IEEE Trans. Neural Netw. Learn. Syst., 2008, 19, (11), pp. 18731886.
    21. 21)
      • 8. Lam, H.: ‘Output-feedback sampled-data polynomial controller for nonlinear systems’, Automatica, 2011, 47, (11), pp. 24572461.
    22. 22)
      • 33. He, S., Li, Z., Zhang, S.: ‘Inhomogeneous polynomial optimization over a convex set: An approximation approach’, Math. Comput., 2015, 84, (292), pp. 715741.
    23. 23)
      • 4. Kim, D.W., Park, J.B., Joo, Y.H.: ‘Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign’, IET Control Theory Appl., 2009, 3, (8), pp. 10701080.
    24. 24)
      • 22. Yang, C., Li, Y., Ge, S.S., et al: ‘Adaptive control of a class of discrete-time MIMO nonlinear systems with uncertain couplings’, Proc. Ame. Control Conf., 2010, pp. 24282433.
    25. 25)
      • 13. Wang, H., Liu, X., Liu, K.: ‘Adaptive neural data-based compensation control of non-linear systems with dynamic uncertainties and input saturation’, IET Control Theory Appl., 2015, 9, (7), pp. 10581065.
    26. 26)
      • 21. Hong, T.P., Lee, C.Y.: ‘Induction of fuzzy rules and membership functions from training examples’, Fuzzy Sets Syst., 1996, 84, (1), pp. 3347.
    27. 27)
      • 18. Liu, Y.J., Gao, Y., Tong, S., et al: ‘Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone’, IEEE Trans. Fuzzy Syst., 2016, 24, (1), pp. 1628.
    28. 28)
      • 16. Gao, Y., Liu, Y.J.: ‘Adaptive fuzzy optimal control using direct heuristic dynamic programming for chaotic discrete-time system’, J. Vibr. Control, 2016, 22, (2), pp. 595603.
    29. 29)
      • 2. Boyd, S., Hast, M., Åström, K.J.: ‘MIMO PID tuning via iterated LMI restriction’, Int. J. Robust Nonlinear Control, 2015, 26, (8), pp. 17181731.
    30. 30)
      • 15. Liu, Y.-J., Wang, Z.-F.: ‘Adaptive fuzzy controller design of nonlinear systems with unknown gain sign’, Nonlinear Dyn., 2009, 58, (4), pp. 687695.
    31. 31)
      • 28. Liu, Y.J., Tong, S.: ‘Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints’, Automatica, 2016, 64, pp. 7075.
    32. 32)
      • 26. Eidson, B.L., Hung, J.Y., Nelms, R.M.: ‘An experimental evaluation of the PID controller represented by the delta operator’. Proc. 2012 IEEE Southeastcon, 2012, pp. 16.
    33. 33)
      • 37. Hu, H., Jiang, B., Yang, H.: ‘Robust fault-tolerant control for uncertain delta operator switched systems’, IET Control Theory Appl., 2014, 8, (2), pp. 120130.
    34. 34)
      • 6. NešIć, D., Grüne, L.: ‘Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation’, Automatica, 2005, 41, (7), pp. 11431156.
    35. 35)
      • 1. Omran, H., Hetel, L., Petreczky, M., et al: ‘Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control’, Automatica, 2016, 70, pp. 266274.
    36. 36)
      • 24. Lin, Y., Yan, H., Zhou, B.: ‘Nonlinear time series prediction method based on multi-dimensional Taylor network and its applications’, Control Decis., 2014, 29, (5), pp. 795801, (in Chinese).
    37. 37)
      • 17. Smith, A.M., Yang, C., Ma, H., et al: ‘Novel hybrid adaptive controller for manipulation in complex perturbation environments’, PLOS One, 2015, 10, (6), pp. 119.
    38. 38)
      • 11. Li, D.P.: ‘Basic of nonlinear control system theory’ (Tsinghua University Press, Beijing, 2014, 2nd edn.) (in Chinese).
    39. 39)
      • 5. Nešić, D., Teel, A.R., Kokotović, P.V.: ‘Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations’, Syst. Control Lett., 1999, 38, (4-5), pp. 259270.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0100
Loading

Related content

content/journals/10.1049/iet-cta.2017.0100
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address