A Data-Driven Predictive Controller Design Based on Reduced Hankel Matrix

A data-driven predictive control methodology based on reduced Hankel matrix is proposed in this paper. Undersome assumptions, the properties of a system can be simply and visually behaved by the construction of input-output Hankel matrix. The row size of the Hankel matrix depends on the request of system excitation, which also determines the prediction and control horizons. In order to show the required order and thus help to choose the number size of the manipulated parameters, the Hankel matrix is reduced based on orthogonal projection. Thus, the prediction is accomplished using the latent space projection of a vector of inputs onto the outputs plan, serving exactly the similar role as order reduction of state estimators. Based on the prediction, MPC formulations and optimization are presented. For the unconstrained case, the control law is analytically determined direct from the data Hankel matrices, avoiding model identification or any intermediate step to meet the given performance specifications. Additionally, integrator action is added to the controller to obtain offset-free tracking.