A Tracking Controller Design for Discrete Nonlinear Singularly Perturbed Systems Based on Fuzzy Singularly Perturbed Model

Abstract:

For a class of discrete nonlinear singularly perturbed systems, a tracking controller based on fuzzy singularly perturbed model (FSPM) and linear matrix inequality (LMI) approach is developed. Firstly, a series of dynamic TS fuzzy singularly perturbed subsystems are built to approximate a discrete nonlinear singularly perturbed system and a discrete reference model with the same fuzzy premise is chosen to design expected trajectory, then a kind of controller is developed to make the slow states of the closed-loop system follow those of the reference model. The linear feedback gain of the controller can be solved by the LMI approach. Discrete Lyapunov constitute techniques prove the stability of the closed-loop systems. The effectiveness of the approach is illustrated by the simulation experimentation.

• Periodical: Advanced Materials Research (Volumes 834-836)
• Pages: 1210-1213
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.834-836.1210
• Online since: October 2013
• Authors: Cheng Gong Sun, Li Li*
• Keywords: Discrete Nonlinear Singularly Perturbed System, LMI, T-S Fuzzy Logic System

References

[1] Z. Gajic, M.T. Lim, Optimal Control Of Singularly Perturbed Linear Systems And Applications-High Accuracy Techniques, Marcel Dekker, Inc. New York. (2001).

[2] J. H. Chow and P. V. Kokotovic, A decomposition of near-optimum regulators for systems with slow and fast modes, IEEE Trans. on Automatic Control, vol. 21, no. 5(1976), pp.701-705.

DOI: 10.1109/tac.1976.1101342

[3] X. Y Zhang, H. Z Jin, H. P Zhang, G. B Li, and M. Ji, Robust sliding mode control for a class of uncertain nonlinear singularly perturbed systems, Proc. of the 41st SICE Annual Conference, vol. 4(2002), pp.2616-2621.

DOI: 10.1109/sice.2002.1195834

[4] H.P. Liu, F.C. Sun et al. Survey of singularly perturbed systems: theory and application, Control Theory and Applications, vol. 20, no. 1(2003), pp.1-7.

[5] Kanti B. Datta, Aparajita RaiChaudhuri. H2/H∞ Control of Singularly Perturbed Systems: The State Feedback Case, European Journal of Control, Vol. 16, no. 1(2010), pp.54-69.

DOI: 10.3166/ejc.16.54-69

[6] J. J.E. Slotine and J.A. Coetsee, Adaptive sliding controller synthesis for non-linear systems, Int. J. Control, vol. 43, no. 6(1986), pp.1631-1651.

DOI: 10.1080/00207178608933564

[7] Li Li, Fuchun Sun, The Direct Adaptive Control Based on the Singularly Perturbed Model with the Unknown Consequence Parameters, International Journal of Control, Automation, and Systems, vol. 8, no. 2 (2010), pp.238-243.

DOI: 10.1007/s12555-010-0208-6

[8] J. Dong, G.H. Yang, Robust control for standard discrete-time singularly perturbed systems, IET Control Theory and Applications vol. 1, no. 4 (2007), pp.1141-1148.

DOI: 10.1049/iet-cta:20060234