Robust self-tuning controller under outliers

In this paper, we propose a robust self-tuning controller (STC) under outliers. A parameter update law of a conventional STC consists of a recursive least squares estimation, and the estimation is given by a solution of a minimization problem of estimated errors. In the proposed method, we estimate parameters and outliers explicitly by addition of a l₁ regression term to the minimization problem like a robust Kalman filter via l₁ regression, and the estimated outliers are removed from measurement outputs in the controller. We also analyze control performances of the proposed method under outliers, and it is shown theoretically that performances in the proposed method with outliers are nearly equal to ones in the conventional STC without outliers. A numerical simulation, in which a controlled plant is a non-minimum phase system, demonstrates effectiveness of the proposed method.