Nonlinear Dynamics

, Volume 83, Issue 3, pp 1601–1619 | Cite as

An extended Neuro-Fuzzy-based robust adaptive sliding mode controller for linearizable systems and its application on a new chaotic system

  • Baraka Olivier Mushage
  • Jean Chamberlain Chedjou
  • Kyandoghere Kyamakya
Original Paper


In this paper, a new approach based on neuro-fuzzy systems is proposed to efficiently address some well-known and challenging problems related to the design and implementation of efficient (i.e. accurate, robust and stable) controllers for nonlinear and chaotic systems subject to external disturbances and uncertain dynamics. To tackle the uncertainty problem, a neuro-fuzzy system is used to approximate the uncertain dynamics. Considering the risk that the control gain function can be close or equal to zero, this issue is addressed in order to guaranty singularity avoidance in the control law. The proposed approach guarantees that the estimation errors and external disturbances cannot affect the stability of the control system. This approach ensures that the control action remains realistic in its characteristics such as amplitude and frequency. Another contribution of this paper is to demonstrate the application of the proposed approach to the control of a new system exhibiting a strange bifurcation scenario characterized by a transition from transient chaos to torus states. As proof of concepts in order to validate the approach, a benchmarking is performed, leading to a comparison of the proposed approach with two neural networks-based controllers recently presented in the literature. Specifically, all the three aforementioned controllers are applied to a nonlinear system used in the literature and it is clearly demonstrated how the proposed controller outperforms its counterparts. The performance criteria (of controllers) are expressed in terms of metrics like the control signal, and the controllers’ performances in both transient and steady states.


Neuro-fuzzy system Adaptive SMC Robust control Linearizable system Chaotic system  


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Baraka Olivier Mushage
    • 1
  • Jean Chamberlain Chedjou
    • 1
  • Kyandoghere Kyamakya
    • 1
  1. 1.Institute of Smart Systems TechnologiesUniversity of KlagenfurtKlagenfurtAustria

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