Model predictive control for ARMAX processes with additive outlier noise

The Autoregressive Moving Average (ARMAX) model with exogenous input is a widely used discrete time series model, but its special structure allows outliers of its process to affect multiple output data items, thereby significantly affecting the output. In this paper, a regularized model predictive control (MPC) is proposed for an ARMAX process affected by outlier noise. The outlier noise is modeled as an auxiliary variable in the ARMAX model, and the MPC cost function is reconstructed to reduce the influence of outlier noise on multiple data items. The stability of the proposed method and the convergence of output/input and state are guaranteed. The degree to which regularization affects the system can be adjusted by an optional parameter. This paper provides some helpful insights on how to choose this optional parameter in the cost function. The effectiveness of the proposed method is demonstrated by the results of 200 repeated simulations.