Reduced order models and controllers for distributed parameter systems using the Kullback-Leibler information divergence

We consider reduced order digital controllers for distributed parameter systems (DPS). we use the reduced order model (ROM) as the truth model, and a finite past predictor to compute the Kullback-Leibler information divergence (KLID). The finite past predictor makes our method computationally attractive for DPS. We include a random observation noise, thus small differences in process statistics have negligible effect. We do not obtain an analytical solution, an iterative search is used instead to find the model parameters. We present two control designs: 1) a ROM is found and an LQG controller is designed based on the ROM; and 2) the optimal LQG controller for a high order approximation of the DPS is found, then a reduced order controller is found to minimize the KLID between outputs of the closed loop systems under each controller.