Master 1 & 2
In our everyday life, we rely on a multitude of systems controlling critical aspects of our life, such as transportation (e.g., airplanes, trains, and cars), medical devices (e.g., pacemakers, and insulin pumps), and infrastructure (e.g., smart electrical grid). Such *Cyber-Physical Systems (CPS)* are formed by digital components interacting with the physical environment.
The modeling, design, and implementation of reliable, secure, and optimal CPS are fundamental but challenging tasks due to the interplay of the software with the physical environment. Moreover, the complexity of designing a CPS will increase significantly in the future, for example requiring more autonomy (i.e., less human intervention).
The CPS program focuses on courses in Computer Science and Applied Mathematics providing the theory and tools to rigorously model, design, and implement the software of the CPS we use in core domains like aerospace, automotive, robotics, and medical devices.
Language of instruction: English
ECTS: 120 (60 ECTS obtained in the 1st year and 60 ECTS in the 2nd year)
Duration: 2 years
Courses Location: Palaiseau
The main objective of the program is to form the next generation of researchers that will lead the innovation in the field of Cyber-Physical Systems.
The program is multidisciplinary and provides both basic and advanced knowledge in fundamental areas in the design of CPS. The basic topics span Computer Science, Embedded Systems, and Control Theory, to cover the principles of modeling CPS. The advanced topics cover the tools used to rigorously design and analyze CPS and further other relevant areas, like Artificial Intelligence and Robotics.
The program further aims at developing the skills required to pursue a research career. The program achieves such goals through advanced, more research-oriented, courses and a research internship in one of the IP-Paris laboratories.
The program is structured over 2 years, M1 and M2, and the courses are classified as “Core CPS”, “Elective CPS”, and “Optional”.
During the first year (M1) the students acquire the basic competencies and concepts to work in the area of CPS, while in the second year (M2) the students should specialize their knowledge and interest to a specific research area (e.g., formal methods, real-time systems, robotics).
The students will acquire 60 ECTS credits during the first year (M1). The 60 ECTS credits are divided into 15.5 ECTS credits of compulsory “Core CPS” courses, 15 ECTS credits of a compulsory research project, and 29.5 ECTS credits of “Optional” courses or “Elective CPS” courses.
The research project is a semester-long project that amounts to 15 ECTS credits and will take place in one of the IPP laboratories: Laboratoire d’Informatique de l’École Polytechnique (LIX), Laboratoire de Traitement et Communication de l’Information (LTCI), and Computer Science and Systems Engineering Laboratory (U2IS). The goal of this project is to investigate a research problem in one of the research topics of interest for the CPS track.
The “Core CPS” courses are the following (compulsory, for a total of 15.5 ECTS):
- A Programmer’s Introduction to Computer Architectures and Operating Systems
- Concurrent Programming
- Numerical methods for dynamical systems
- Principes fondamentaux de l’Automatique: dynamique et contrôle des systèmes
- Safe Intelligent Systems
- Tolérance aux fautes
The “Optional” courses recommended for the first program’s year are:
- Algorithmique parallèle et distribuée
- Fondements des algorithmes répartis
- From the Internet to the IoT: Fundamentals of Modern Computer Networking
- Introduction to Cryptology
- Machine Learning
- Modélisation d’architectures logicielles
- Network Security
- Optimisation discrète
- Wireless Networks: from Cellular to Connected Objects
The “Elective CPS” courses are listed next and are recommended for the second year. However, a student can attend one of such courses during its first year, provided all the student’s curriculum already satisfies the requirements for the “Elective CPS” course and after approval of his study plan.
The free choices of “Optional” and “Elective CPS” will amount to a total of 29.5 ECTS credits in the first year.
During the second year (M2) the students will acquire a total of 60 ECTS credits to choose among a list of “Elective CPS” courses, “Optional” courses, and a compulsory research project.
The research project is organized similarly to the first year: it amounts to 15 ECTS credits, it lasts for an entire semester, and is held in one of the laboratories (LIX, LTCI, and U2IS). The main requirement for the research project is that each student should perform the M2 research project in a different institution from the one that hosted the student’s M1 research project.
The “Elective CPS” courses are:
- Data-based Modeling
- Real-time Systems Scheduling
- Modeling Physics with Differential Algebraic Equations
- Modélisation et analyse des risques de sécurité dans les systèmes complexes
- Navigation pour les systèmes autonomes
- Procédures de décisions SAT/SMT
- Real-Time Systems Design
- Research Seminar in CPS (from invited professors)
- Réseaux de capteurs
- Réseaux pour l’internet des objets
- Systèmes réactifs et synchrones
- Systèmes répartis et autonomiques
- Validation inductive de programmes et de systemes hybrides
The “Optional” CPS courses recommended for the second year are:
- Advanced Cryptology
- Advanced Topics in Artificial Intelligence
- Algorithmic Basis for BlockChain
- Architectures logicielles pour la robotique
- Automatique: commande avancée des systèmes
- Computational Logic
- Distributed Computing
- Large scale mathematical optimization
- Perception pour les systèmes autonomes
The choices of “Elective CPS” and “Optional” courses should amount to a total of 45 ECTS credits.
The detailed program is available here.
- Computer Science Laboratory (LIX)
- Information Processing and Communications Laboratory (LTCI)
- Computer Science and System Engineering Laboratory (U2IS)
- ENSTA Paris
- École Polytechnique
- Télécom Paris
- Télécom SudParis
- Dassault Aviation
- DCNS Researc
- The French Directorate General of Armaments (DGA)
Chairs and partnerships
- « Complex Systems Engineering » Chair
Year 1: Candidates for the Master program should hold at least a Bachelor’s degree in Computer Science, Electrical Engineering, or Applied Mathematics, and have an outstanding academic record.
Year 2: Admission can be granted directly into the 2nd year (M2), provided that necessary prerequisites have been met, and are documented. Any student (from France or abroad) who has completed at least an M1 (first year of a Masters program) in computer science, electronic engineering, applied mathematics, and other related disciplines.
Deadlines for the Master application sessions are as follows:
– First session: February 28, 2020
– Second session: April 30, 2020
– Third Session (optional): June 30, 2020 (only if there are availabilities remaining after the 2 first sessions)
Applications not finalized for a session will automatically be carried over to the next session.
You shall receive an answer 2 months after the application deadline of the session.
You can check your application status by logging in your candidate space.
International Master: EU students : 4250 euros / Non-EU students: 6250 euros