This course aims to teach the students the basic concepts and methods related to random dynamic systems. They apply to dynamic systems originated from Engineering as well as from Economics. General principles as well as more specific techniques will be presented.
The state representation approach will be used. The way decisions are taken will be explained, in relation with the available information. The concept of feedback control will be discussed.
The course will develop estimation techniques, for identification as well as for forecasting. In particular the Kalman filter will be fully presented.
Particular attention will be devoted to the Dynamic Programming approach to define optimal control. We will also present Pontryagin’s Maximum principle. Examples will be developed. Special attention will be given to solving linear quadratic problems, by direct methods. Attention will be devoted to studying the stability of dynamic systems. Riccati equations will be fully solved in this context.