Nonlinear Control
Download in PDF- Lecturer: Pascal Morin (pascal.morin@sorbonne-universite.fr)
- Course code: MU5RBR30-NL
- Student workload: 12 h of lectures, 8 h of tutorials, 8 h of labs
- Credits: 3 ECTS
- Specialization tracks: ROBOT (elective) SI MeDH
- Semester offered: S1 S2 S3 S4
- Language of instruction: French English
- Targeted audience: Eng. Sc. department Other : ENSAM
- Localization : PMC Campus Other :
Course Overview
The objective of this course unit is to present the main control techniques used to stabilize nonlinear control systems. The course is divided into three parts. The first covers techniques based on exact linearization, the second covers Lyapunov-based approaches, and the third covers model predictive control. Strong emphasis is placed on numerical tools (Matlab, Simulink, etc.) for implementing and assimilating the techniques.
Mots-clés : Nonlinear control systems, output-feedback linearization, state-feedback linearization, Lyapunov functions, predictive control.
Prerequisites
Students should have previously acquired the following prerequisites to follow this course:
- Linear control in state-space form (equilibrium points, tangent linearized systems, controllability, observability, controller design by pole placement, linear-observer design, LQR control).
- Matlab/Simulink, Python
Intended Learning Outcomes
By the end of this course, students will be able to:
- Analyze and control a system using its tangent linearization
- Master Matlab/Simulink tools for designing linear state-feedback controllers
- Control a system using exact output-feedback linearization
- Control a system using exact state-feedback linearization
- Analyze the stability of a linear system using a Lyapunov function
- Design a state-feedback controller from a candidate Lyapunov function
- Master the implementation of nonlinear controllers using Matlab/Simulink
- Understand predictive-control algorithms
- Implement predictive control using Python toolboxes
Indicative Teaching Sequence and Methods
| Week | C/TD/TP* | Content | Preparation | Learn.\ outc. |
|---|---|---|---|---|
| S1 | C1 | Review of linear state-space control | AAV1 | |
| S2 | TD1 | Covers C1 | AAV1 | |
| S3 | TP1 | Matlab-Simulink practical: control using tangent linearization | Practical-session preparation | AAV1-AAV2 |
| S4 | C2 | Exact-linearization control methods (Part I) | AAV3 | |
| S5 | C3 | Exact-linearization control methods (Part II) | AAV4 | |
| S6 | TD2 | Covers C2-C3 | AAV3-AAV4 | |
| S7 | C4 | Lyapunov-based techniques (Part I) | AAV5 | |
| S8 | C5 | Lyapunov-based techniques (Part II) | AAV6 | |
| S9 | TD3 | Covers C2-C5 | AAV3-AAV6 | |
| S10 | TD4 | Covers C4-C5 | AAV5-AAV6 | |
| S11 | TP2 | Matlab-Simulink practical: control using Lyapunov techniques | Review C4-C5 and TD4 | AAV1-AAV7 |
| S12 | C6 | Predictive control | AAV8 | |
| S13 | TP3 (4h) | Numerical practical on C6 | Review C6 and prepare for the practical session | AAV8-AAV9 |
- C/TD/TP respectively corresponds to lectures, tutorials and lab sessions.
Indicative Assessment of Intended Learning Outcomes (1st session)
| Week | Individ./group | In-person/remote | Type of exam | Evaluated outcomes | Scale % |
|---|---|---|---|---|---|
| S11 | Individual | In-person | Other | AAV1-AAV7 | 30% |
| S15 | Individual | Remote | Other | AAV8-AAV9 | 20% |
| S14 | Individual | In-person | Written exam | AAV1-AAV9 | 50% |
2nde session
| Session | Individ./group | In-person/remote | Type of exam | Evaluated outcomes | Scale % |
|---|---|---|---|---|---|
Date of generation of this unit description: 06/10/2026
