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This paper deals with the self-tuning control problem of linear systems described by autoregressive exogenous (ARX) mathematical models in the presence of unmodelled dynamics. An explicit scheme of control is described, which we use a recursive algorithm on the basis of the robustness σ-modification approach to estimate the parameters of the system, to solve the problem of regulation tracking of the system. This approach was designed with the assumptions that the norm of the vector of the parameters is well-known. A new quadratic criterion is proposed to develop a modified recursive least squares (M-RLS) algorithm with σ-modification. The stability condition of the proposed estimation scheme is proved using the concepts of the small gain theorem. The effectiveness and reliability of the proposed M-RLS algorithm are shown by an illustrative simulation example. The effectiveness of the described explicit self-tuning control scheme is demonstrated by simulation results of the cruise control system for a vehicle.

Self-Tuning Control Scheme Based on the Robustness σ-Modification Approach