Robust Self-tuning Control Based on Discrete-time Sliding Mode for Auto-regressive Mathematical Model in the Presence of Unmodelled Dynamics

In this paper, we propose a new robust self-tuning control, called the generalized minimum variance al-equivalent selftuning control (GMVSTC-al) for the linear timevarying (LTV) systems, which can be described by the discrete-time auto-regressive exogenous (ARX) mathematical model in the presence of unmodelled dynamics. The estimation of the parameters contained in this mathematical model is made on the basis of the proposed modified recursive least squares (m-RLS) parametric estimation algorithm with dead zone and forgetting factor. The stability analysis of the proposed parametric estimation algorithm m-RLS is treated on the basis of a Lyapunov function. A numerical simulation example is used to prove the performances and the effectiveness of the explicit scheme of the proposed robust self-tuning control GMVSTC-al.