1 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems and quadratic costs. We will start with the basic minimal variance problem and then move on to more complex and applicable strategies such as GMV, GPC and LQG control. These methods can be regarded as extension to the basic minimal variance strategy and have all a close relation to prediction. Consequently a section on that topic can be found in appendix.