Data-Driven Predictive Control under Insufficient Data: An Online Updating-Based Approach

This paper proposes a robust online-updating data-driven predictive control method that relaxes the persistency of excitation condition. For unknown linear time-invariant systems with additive output measurement noises, an online updating strategy is proposed to enrich the data by incorporating the optimal input-output sequences generated during the predictive control process into the Hankel matrix. Subsequently, a robust data-driven predictive control scheme is constructed using the enriched data, where a terminal equality constraint and a constraint on the slack variables are incorporated. It is shown that the terminal output tracking problems can be addressed by utilizing the insufficient data even in the presence of measurement noises. Moreover, the prediction error between the predicted output and the actual output is rigorously analyzed and proved to be bounded. The effectiveness of the proposed method is demonstrated through the simulations.