  The paper presents a data-driven predictive control framework based on an
implicit input-output mapping derived directly from the signal matrix of
collected data. This signal matrix model is derived by maximum likelihood
estimation with noise-corrupted data. By linearizing online, the implicit model
can be used as a linear constraint to characterize possible trajectories of the
system in receding horizon control. The signal matrix can also be updated
online with new measurements. This algorithm can be applied to large datasets
and slowly time-varying systems, possibly with high noise levels. An additional
regularization term on the prediction error can be introduced to enhance the
predictability and thus the control performance. Numerical results demonstrate
that the proposed signal matrix model predictive control algorithm is effective
in multiple applications and performs better than existing data-driven
predictive control algorithm.
