On the equivalence of closed-loop subspace predictive control with LQG

Subspace predictive control (SPC) is recently seen in the literature for joint system identification and control design. The existing SPCs parameterize H₂ optimal control laws by the identified Markov parameters from data. It has been proved that the SPCs based on open-loop subspace identification are equivalent to the classical LQG design, when the data horizon goes to infinity. It is the purpose of this paper to establish this equivalence for the closed-loop SPC algorithm we have recently developed. When the data horizon is finite, we also present in this paper a state-feedback LQG control law based on the identified Markov parameters, where the states are estimated in an optimal sense from the past I/O samples of a plant.