Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter

Rudolf Emil Kalman (R.E.K.) passed away on July, 2nd, 2016. Among contemporary economists Kalman is mainly remembered for his filter, an algorithm that allows recursive estimation of unobserved time varying variables in a system. However, he has also a key part on the whole of recursive macroeconomic theory as is notably expressed by Lars Ljungqvist's and Thomas Sargent's book [Ljunqvist and Sargent, 2012]. Our paper is a contribution to show the links between Kalman's works on filtering, linear quadratic optimal control, and system theory. We also provide a model on cooperative advertising to show that Kalman's works on dynamics and control can be useful in macroeconomics as in microeconomics, a domain where his contributions seem to be unfortunately less used.