Model Predictive Control: Foundations, Recent Results And Applications
Prof.
Gianni Bianchini
University of Siena - Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche
Course Type
Type B
Calendar
May 5 h 9-11 Aula 103 May 6 h 9-13 Aula 103 May 8 h 9-13 Aula 103 May 12 h 9-11 Aula 103 May 13 h 9-13 Aula 14 May 15 h 9-13 Aula 103
Room
Program
Brief abstract
Model Predictive Control (MPC) is an optimization-based control design technique for multivariable systems in the presence of constraints. Such technique exploits dynamical state-space prediction models of the process to be regulated. At each control instant, the control action is computed as the solution of an optimization problem in which constraint specifications on system variables (inputs, outputs, and states) are enforced, while performance requirements are specified through suitable design of the objective function.
MPC theory has been developed over the last 20 years and is nowadays a mature and widespread technology in industry. It is still, however, a subject of heavy investigation, e.g., in contexts where uncertainty, peculiar performance requirements, or distributed implementation need to be considered.
The purpose of this course is to provide the student with the basics of classical Model Predictive Control theory and an insight on more recent advances such as robust and time-optimal formulations. Implementation of MPC schemes using Python and CVXPy will be discussed, along with a case study from aerospace control literature.
Syllabus:
- Introduction: linear systems, Lyapunov stability, and convex optimization basics.
- Optimal control problems. The Linear Quadratic Regulator. Constrained optimal control.
- The receding horizon paradigm and Model Predictive Control.
- Recursive feasibility and stability of constrained MPC.
- Design of quadratic MPC problems for linear systems.
- Robust and time-optimal MPC (hints).
- Simulation of MPC schemes using Python and CVXPy.
- Case study: orbital control of spacecraft.
