Advanced Topics of Control Systems

In this course we will venture to go through some of the most advanced control schemes whose development has been motivated by problems in process control and economics. The course's main objective will be to bring students in touch with the state of the art in MPC theory and explore various research opportunities that emerge. We will see how the mature concept of model predictive control (MPC) can be combined with process economics to yield a unifying framework -- known as economic model predictive control (EMPC) -- for simultaneous control and process optimization. The EMPC-controlled closed-loop trajectories need not be stable/convergent, but they provide certain performance/cost guarantees for the process. We establish stability conditions for the closed-loop system and study various EMPC formulations and their properties. Special emphasis will be put on the study of MPC methodologies for uncertain systems. We will discuss various stochastic MPC methodologies and study their closed-loop properties. We will provide a comprehensive theory of Markovian systems for which we will define new notions of stability such as mean square stability, almost sure stability and uniform stability.

Prerequisites: Linear algebra & calculus; Linear discrete-time dynamical systems; Model predictive control theory.

(course topics and grading plan available at