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Composite Learning Fuzzy Control of Uncertain Nonlinear Systems

Abstract

Function approximation accuracy and computational cost are two major concerns in approximation-based adaptive fuzzy control. In this paper, a model reference composite learning fuzzy control strategy is proposed for a class of affine nonlinear systems with functional uncertainties. In the proposed approach, a modified modeling error that utilizes data recorded online is defined as a prediction error, a linear filter is applied to estimate time derivatives of plant states, and both the tracking error and the prediction error are exploited to update parametric estimates. It is proven that the closed-loop system achieves semiglobal practical exponential stability by an interval-excitation condition which is much weaker than a persistent-excitation condition. Compared with a concurrent learning approach that has the same aim as this study, the computational cost of the proposed approach is significantly reduced for the guarantee of accurate function approximation. An illustrative example of aircraft wing rock control has been provided to verify effectiveness of the proposed control strategy.

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Notes

  1. The special definition is based on a consideration that \(\Theta (t_e) W^*\) is not computable by (11) due to the unmeasurable \(\dot{e}_n\).

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Acknowledgments

This work was supported in part by the Future System Directorate, Ministry of Defence, Singapore under Grant No. MINDEF-NUS-DIRP/2012/02, and in part by the Ministry of Education, Singapore (Tier 1 AcRF, RG29/15).

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Correspondence to Haoyong Yu.

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Pan, Y., Er, M.J., Liu, Y. et al. Composite Learning Fuzzy Control of Uncertain Nonlinear Systems. Int. J. Fuzzy Syst. 18, 990–998 (2016). https://doi.org/10.1007/s40815-016-0243-4

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  • DOI: https://doi.org/10.1007/s40815-016-0243-4

Keywords

  • Adaptive control
  • Fuzzy approximation
  • Composite learning
  • Interval excitation
  • Parameter convergence
  • Online modeling