This paper introduces a novel Gaussian process approach for systems with unknown disturbances with quasi-periodic patterns to enhance the performance of a robust economic model predictive controller. A self-tuning kernel is proposed to substitute the periodic kernel used in the hybrid Gaussian process models in order to predict forthcoming disturbances more accurately while demanding a shorter training horizon. The proposed method is applied to a domestic solar thermal system, in which the hot water demand has a recurrent pattern, yet there is a slight variation daily. The simulation results demonstrate that the proposed controller has a reliable and precise prediction of future demand, and therefore it is able to manage the solar thermal system properly under various hot water load scenarios. Specifically, the proposed controller yields more than 5% improvement over a proportional–integral–derivative controller in terms of energy saving associated with the electricity usage for an auxiliary heat source.
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