The course covers safety and security aspects in cyber-physical systems. In particular, cyber-physical systems that can be modelled as dynamic systems are studied, with applications in critical infrastructure and autonomous systems where cyber-attacks and failures can have physical consequences. We introduce discrete-time dynamical systems using linear algebra. A large part of the course is devoted to presentation by basic principles and methods for modelling, analysis and detection of errors and cyberattacks in dynamic system. In particular, the following is studied

− Documented attacks against cyber-physical systems, system architectures, safety and accessibility, risk management and attack-space in cyber-physical systems.

− Model-based quantification of physical consequences of faults and cyber-attacks, false data injection and DoS attacks, discrete-time linear state models, observers (UIO), strong observability and detectability.

− Model and data-based error detection, fault identification and redundancy, parity space methods, observer based methods, setting of threshold.

− Statistical anomaly detection, hypothesis testing, Neyman-Pearson's lemma, generalised likelihood ratio (GLR), Bayes' theorem, principal component analysis (PCA), detection of abrupt process changes, cumulative sum test (CUSUM), machine-learning based methods.

After passing the course, the student should be able to:

− formulate basic theory and definitions of important concepts in safety and security in cyber-physical systems in general and discrete time systems in particular

− apply model and data-based methods for safety and security in cyber-physical systems particularly for discrete time systems.

• Lectures: Review and introduction of basic theory and definitions of important concepts in safety and security in cyber-physical systems in general and time-critical systems in particular.
• Exercises: Practice application of model and data-based methods for safety and security in cyber-physical systems, particularly for time-critical systems, together with teacher assistant (TA).
• Assignments:
  • INL1: Demonstrate ability to apply model and data-based methods for safety and security in cyber-physical systems, particularly for time-critical systems. Individually solve problems and hand them in for assessment.
  • INL2: Demonstrate ability to formulate basic theory and definitions of important concepts in safety and security in cyber-physical systems in general, and time-critical systems in particular. Individually write essay and present in class.
• Written exam (TEN1): Demonstrate ability to apply model and data-based methods for safety and security in cyber-physical systems, particularly for time-critical systems, and formulate basic theory and definitions of important concepts. Individual solution of exam problems.

Course Modules: The course is organized into three modules:

• M1: Cyber-physical systems (CPSs) safety and security
• M2: Dynamical systems and anomaly detection/identification
• M3: Statistical tools

Lectures:

• [AC] Alvaro Cardenas, "Cyber-Physical Systems Security Knowledge Area," CyBOK, 2021.  [Link]
• [ED] Elena Dubrova, "Fault-Tolerant Design," Springer, 2013. [Link]
• [SS] Shreyas Sundaram, "Fault-Tolerant and Secure Control Systems," Lecture Notes, 2012. [Link]
• [HS] Henrik Sandberg, "EL2850 Lecture Notes," KTH, 2025. [Made available in Canvas]

Exercises: See Canvas and Schedule

Assignments: INL1 are due by the end of each module. The essay for INL2 is due by L9.

Written exam: Ordinary exam Oct 17 at 8:00-13:00. Re-exam Dec 18 at 8:00-13:00.

Parts of the following texts are covered in the course (see Reading in the Lectures table):

• [AC] Alvaro Cardenas, "Cyber-Physical Systems Security Knowledge Area," CyBOK, 2021.  [Link]
• [ED] Elena Dubrova, "Fault-Tolerant Design," Springer, 2013. [Link]
• [SS] Shreyas Sundaram, "Fault-Tolerant and Secure Control Systems," Lecture Notes, 2012. [Link]
• [HS] Henrik Sandberg, "EL2850 Lecture Notes," KTH, 2023. [Made available in Canvas] 

With submitted solutions to the Homework Assignments, Python or MATLAB code should be attached. The following Python packages are recommended:

• NumPy [link] 
• SciPy [link]
• Python Control Systems Library [link] [installation]

The Anaconda distribution [link] is recommended to download these packages freely (use the conda-forge channel for all packages to avoid problems with dependencies).

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

• INL1 - Assignment, 2.5 credits, grading scale: P, F
• INL2 - Assignment, 2.5 credits, grading scale: P, F
• TEN1 - Written exam, 2.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

If the course is discontinued, students may request to be examined during the following two academic years.

The course is divided into three modules. Each module is examined by an assignment (INL1-1,1-2,1-3), and one exam problem each. To pass the course, INL1, INL2 and TEN1 all need to be passed. The final grade is based on TEN1.

INL1 - Assignment, 2.5 credits

INL1 consists of Homework 1-1, 1-2, and 1-3. These are problems that should be solved by hand or in Python/MATLAB where requested, and should be submitted by the due date in Canvas.

To get a pass grade (P) on INL1, you need  to pass all of Homework 1-1, 1-2, and 1-3.

INL2 - Assignment, 2.5 credits

INL2 consists of writing a short essay and a presentation in class.

To get a pass grade (P) on INL2, both the essay and the presentation need to be approved.

TEN1 - Written exam, 2.5 credits

The exam will have five problems: one per module and two additional more advanced problem that may combine material from all modules. The written exam is solved individually.

The final exam will decide the final grade (which also requires pass grade on INL1 and INL2). There are five problems with max 10 points per problem.

Grade Fx: 21 points or more, and 5 points or more on two out of problems 1-3.

Grade E: 23 points or more, and 5 points or more on each of problems 1-3.

Grade D: 28 points or more, and 5 points or more on each of problems 1-3.

Grade C: 33 points or more, and 5 points or more on each of problems 1-3.

Grade B: 38 points or more, and 5 points or more on each of problems 1-3.

Grade A: 43 points or more, and 5 points or more on each of problems 1-3.

Formulate basic theory and definitions of important concepts in safety and security in cyber-physical systems in general and time-critical systems in particular. Apply model and data-based methods for safety and security in cyber-physical systems particularly for time-critical systems.

E: to solve basic problems

D: to solve advanced problems within some part of the course

C: to solve advanced problems within several parts of the course

B: to solve advanced problems with all parts of the course or to solve problems combining several parts of the course

A: to solve advanced problems within all parts of the course and to solve problems combining several parts of the course.

Students with Fx on the written exam should contact the examiner for an opportunity for supplementary examination to grade to E. 

Students with F on some assignements will be given the chance to resubmit again after the written exam if, and only if, the written exam is passed. The same chance is given after the re-exam.

Assignments are submitted and corrected in Canvas.

The result on the written exam is reported directly via LADOK.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Code of honor

In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex. 

The official course syllabus is valid from autumn semester 2025 according to the decision of Director of First and Second Cycle Education: HS-2025-0552

Date of decision: 2025-04-02