Pseudoinverse and Distributed Robust Data-Enabled Predictive Control for Linear Time-Invariant Systems with Disturbances

The integration of the pseudoinverse and distributionally robust data-enabled predictive control (DeePC) for managing disturbances in linear time-invariant systems is investigated in this paper. This combination offers a distributionally robust optimization and data based predictive control strategy that can effectively handle uncertainties and disturbances. To be specific, firstly, we implies the Willem’s fundamental lemma to describe the system that only uses the input and output data generated during the operation of the system to design the controller without clearly knowing the internal mechanism and other helpful information of the system. Then, the Wasserstein metric is utilized to construct a ball with the probability distributions of disturbance. The center of this ball is established at the empirical probability distribution based on the training samples. It has been demonstrated that considering the probability distributions of disturbance within this Wasserstein ball and using the DeePC algorithm yield a tractable reformulation of optimal results. Finally, the effectiveness of the proposed method is proven through a simulation example.