The course is aimed at providing the main ideas, algorithms, and properties of Model Predictive Control (MPC) and Moving Horizon Estimation (MHE).

The basic formulation of MPC will be introduced for linear systems. Then, the most popular industrial methods will be described, and some application examples will be discussed. Prototype MPC algorithms with guaranteed stability properties will be derived, based on implicit or explicit solutions of the underlying optimization problem to be solved on-line. In the second part of the course some extensions and future research challenges of MPC will be discussed to cope with the problems related to (i) robustness with respect to unmodeled dynamics and/or disturbances, (ii) MPC algorithms for systems subject to stochastic noise,  (iii) inclusion of logic constraints, (iv) distributed implementations. Relations of MPC with the problem of constrained state estimation will be highlighted and a prototype Moving Horizon Estimation algorithm will be presented.

The goal is to allow the students to design and implement MPC algorithms in different application scenarios.

1. Motivations

2. Resumé of optimal control and filtering for discrete-time linear systems

3. Introduction to MPC

4. Industrial formulations of MPC

5. Implicit Linear Quadratic optimal control and Receding Horizon implementation

6. Explicit MPC

7. MPC wit stability guarantees

8. Economic MPC

9. Robust MPC

10. Stochastic MPC

11. Hybrid MPC

12. Distributed MPC

13. Moving Horizon Estimation

14. Applications of MPC and sofware environments for the design of MPC controllers

The final exam will consist in the discussion of the application of MPC algorithms to specific control problems.