Course description
Model Predictive Control (MPC) is a well-established technique for controlling multivariable systems subject to constraints on manipulated variables and outputs in an optimized way. Following a long history of success in the process industries, in recent years MPC is rapidly expanding in several other domains, such as in the automotive and aerospace industries, smart energy grids, and financial engineering.
The course is intended for students and engineers who want to learn the theory and practice of Model Predictive Control (MPC) of constrained linear, linear time-varying, nonlinear, stochastic, and hybrid dynamical systems, and numerical optimization methods for the implementation of MPC. The course will make use of the MPC Toolbox for MATLAB developed by the teacher and co-workers (distributed by The MathWorks, Inc.) for basic linear MPC, and of the Hybrid Toolbox for explicit and hybrid MPC.
Syllabus
General concepts of Model Predictive Control (MPC). MPC based on quadratic programming. General stability properties. MPC based on linear programming. Linear parameter-varying, time-varying, and nonlinear MPC. Models of hybrid systems: discrete hybrid automata, mixed logical dynamical systems, piecewise affine systems. MPC for hybrid systems based on on-line mixed-integer optimization. Multiparametric programming and explicit linear MPC, explicit solutions of hybrid MPC. Stochastic MPC: basic concepts, approaches based on scenario enumeration. Learning-based MPC. Selected applications of MPC in various domains, with practical demonstration of the MATLAB toolboxes.
Prerequisites
Linear algebra and matrix computation, linear control systems, numerical optimization.
Timetable
| Wednesday | April 3, 2024 | 09.00-11.00 |
|---|---|---|
| Friday | April 5, 2024 | 09.00-11.00 |
| Monday | April 8, 2024 | 09.00-11.00 | Wednesday | April 10, 2024 | 09.00-11.00 |
| Friday | April 12, 2024 | 09.00-11.00 |
| Monday | April 15, 2024 | 09.00-11.00 |
| Wednesday | April 17, 2024 | 09.00-11.00 |
| Thursday | April 18, 2024 | 09.00-11.00 |
| Friday | April 19, 2024 | 09.00-11.00 |
| Monday | April 22, 2024 | 09.00-11.00 |
Location
IMT School for Advanced Studies Lucca, Piazza San Francesco 19, Lucca, Italy. Remote attendance is also possible.
Lecture slides
| Linear MPC | (last update: March 27, 2024) |
|---|---|
| LPV/LTV and Nonlinear MPC | (last update: March 27, 2024) |
| Embedded QP Solvers and explicit MPC | (last update: March 27, 2024) |
| Hybrid dynamical models for MPC | (last update: March 27, 2024) |
| Hybrid MPC | (last update: March 27, 2024) |
| Examples of hybrid MPC | (last update: March 27, 2024) |
| Stochastic MPC | (last update: March 27, 2024) |
| Learning-based MPC | (last update: March 27, 2024) |
| Conclusions | (last update: March 27, 2024) |
| Introductory material on linear control systems | (last update: August 26, 2021) |
Toolboxes
Model Predictive Control Toolbox for MATLAB
Hybrid Toolbox for MATLAB
Main references
[1] A. Bemporad, M. Morari, V. Dua, and E.N. Pistikopoulos, The explicit linear quadratic regulator for constrained systems, Automatica, vol. 38, no. 1, pp. 3–20, 2002 [2] A. Bemporad, A multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squares, IEEE Trans. Automatic Control, vol. 60, no. 11, pp. 2892–2903, 2015. [3] A. Bemporad and M. Morari, Control of systems integrating logic, dynamics, and constraints, Automatica, vol. 35, no. 3, pp. 407–427, 1999 [4] F.D. Torrisi and A. Bemporad, HYSDEL — A tool for generating computational hybrid models, IEEE Trans. Contr. Systems Technology, vol. 12, no. 2, pp. 235–249, Mar. 2004 [5] D. Bernardini and A. Bemporad, Stabilizing model predictive control of stochastic constrained linear systems, IEEE Trans. Automatic Control, vol. 57, no. 6, pp. 1468–1480, 2012