Adaptive sliding-mode observer for second order discrete-time MIMO nonlinear systems based on recurrent neural-networks

Ivan Salgado, Hafiz Ahmed, Oscar Camacho, Issac Chairez

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)
    88 Downloads (Pure)


    This manuscript introduces a novel methodology to solve the state estimation of discrete-time multi-input multi-output (MIMO) nonlinear systems with uncertain dynamics. The mathematical model of the nonlinear systems considered in this paper satisfies the usual Lagrangian structure that characterizes many mechanical, electrical or electromechanical systems. A recurrent neural network (RNN) estimates the uncertain dynamics of the MIMO system with an updating law based on a particular variant of the discrete-time version of the super-twisting algorithm (DSTA). A Lyapunov stability analysis defines the convergence zone for the state estimation error throughout the solution of a matrix inequality. The convergence zone for the estimation is smaller when the DSTA and the RNN work together in an observer. Numerical examples demonstrate how the adaptive observer reduces the zone of convergence and the oscillations in the steady state compared with a discrete version of the STA with additional linear correcting terms. An experimental implementation shows how the observer estimates the unknown states of a Van Der Pol Oscillator. A comparison against some variations of the DSTA justifies the advantages of the mixed DSTA-RNN observer.
    Original languageEnglish
    Pages (from-to)2851-2866
    Number of pages16
    JournalInternational Journal of Machine Learning and Cybernetics
    Issue number10
    Early online date7 Jan 2019
    Publication statusPublished - 1 Oct 2019

    Bibliographical note

    The final publication is available at Springer via


    • Discrete-time super twisting algorithm
    • Lyapunov theory
    • Recurrent neural networks
    • Second order systems
    • Sliding modes
    • State estimation

    ASJC Scopus subject areas

    • Software
    • Computer Vision and Pattern Recognition
    • Artificial Intelligence


    Dive into the research topics of 'Adaptive sliding-mode observer for second order discrete-time MIMO nonlinear systems based on recurrent neural-networks'. Together they form a unique fingerprint.

    Cite this