Systems and Control Methods for Cyberphysical Security
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NEXT EXAMS:
19/06/2025 Aula T1, Via Regina Elena, h 9:00-12:00;
08/07/2025 Aula T1, Via Regina Elena, h 9:00-12:00;
22/09/2025 Aula T1, Via Regina Elena, h 9:00-12:00;
Goal of the course.
In a nutshell, at the end of the course the student will be able to understand how well-crafted cyberattacks can lead to the physical disruption of a target system, while remaining undetected to the operator of the system for a sufficiently long time. The student will learn how to model the attack and its physical effect on the system, and in which cases the attack can remain undetected. Several important attack types and defence strategies will be examined, also with the help of simulations. The knowledge gained proves useful in practice also for vulnerability assessment and for improving the design of the systems, to make them more resilient to attacks.
Logistic and course description
Logistic and course description
Lectures:
Monday, 14:00-17:00, Aula Magna RM111, Via Regina Elena, Edificio C., Google maps link: https://maps.app.goo.gl/whUjURt8CZAX8qTM8
Thursday 17:00-19:00, Aula T1, Via Regina Elena, Edificio E, Google maps link: https://maps.app.goo.gl/oE9YJqrcSgGVrNuTA
Each lesson will be recorded and the recording made available in the section Lecture Summary below. This is to facilitate students who cannot always attend in presence due to overlaps.
Office hours: Thursday at 10:00-12:00 in room A213, DIAG department, or online (Google Meet link). Please send me an email in advance. We can agree on a different day/hour if needed.
Contact: liberati@diag.uniroma1.it. Write me for any question.
Google Class: A Google class is used for communications and for sharing study materials. Please subscribe at the following link using your Sapienza student email. Please unsubscribe from the group if you do not plan to take the exam.
Description: The goal of the course it to provide an in-depth introduction to cyber-physical systems modelling, analysis, and protection against cyber-physical attacks. The course starts with an overview of practical examples of cyber-physical systems, and the study of known recent cyber-physical attacks, to familiarize with the important concepts. The key concepts and standards in risk management are presented, as risk management is the correct framework to systematically organize and manage all the activities related with cyber-physical security of a system. The practical concepts introduced are then abstracted and formalized by relying methodologies from system theory. This allows to model a cyber-physical system, the attack, and the perturbation that the attack causes in the system. Conditions are then developed to check whether it is possible or not to attack a system in an undetectable way. The most common and important types of attacks are modelled and analysed (bias injection attacks, replay attacks, false data injection attacks, switching attacks, zero dynamics attacks, covert attacks, etc.). Finally, methods are presented to build attack detectors, and to optimally protect a system againts attacks. During the entire course, most of the concepts introduced will be demonstrated through simulations (of attacks and detectors/defence schemes) in Matlab and Julia. In this latest edition of the course we will also cover new topics such as encrypted control and control allocation.
Prerequisites: Fundamentals of mathematical analysis (derivatives, integrals, differential equations), geometry (linear systems, matrices, determinant, rank), physics (elementary physical systems: circuits, mechanical systems, etc.). These propaedeutic concepts will be recalled where useful during the course, so to make the course accessible for everyone.
Study materials: For each lesson of the course, the specific study references (book sections, papers, etc.) will be indicated in the lesson summary (see section "Lecture summaries"). Link to the lecture slides, the blackboard notes and the zoom recordings of the lessons will be available. You can also take advantage of the slides, notes and zoom recordings of the previous version of the course, see website at this link.
Program
Program
(Subject to minor variations before the course starts)
- Introduction to cyber-physical systems. What is a cyber-physical system. Examples from the critical infrastructures domain. Overview of known past and recent cyber-physical attaks to power systems and other critical infrastructures. Goal of the attackers and goal of the defender. Introduction to the protection of cyber-physical systems. Introduction to risk management and to a quantitative risk-based approach for securing cyber-physcal systems. Overview of main risk management standards and regulations;
- Modelling of cyber-physical systems: Modelling of an attack (the attack space, model knowledge, disclosure resources, disruption resources). First general detectability and identifiability conditions. Introduction to the design of attack detectors. The consistency property of detectors;
- Modelling and analysis of the main cyber-physical attack types, from static to more complex dynamical ones: false data injection attacks (FDIAs) against state estimation, denial of service attacks, replay attacks, switching attacks, covert attacks, zero dynamics attacks, etc.;
- Detection and mitigation techniques: Detectability of cyber-physical attacks in presence of side initial state information. Detectors and observers. Watermarking. Secure control allocation. Encrypted control. Resilient control.
- Experiments: during the course, many of the theoretical concepts will be implemented through simulations in Matlab and Julia, presenting design and simulations of attacks and detection/defence strategies.
Exams and Grading
Exams and Grading
The student has two alternative options (you have to book the exam in Infostud in any case):
Written exam plus optional oral exam. The date of the written exam is the one listed below and specified in infostud. After the correction of the written exam, the student can decide to have the oral exam to try to improve the grade. The date of the oral exam will be fixed later, few days after the written exam. The written test lasts 2 to 3 hours, and includes one or two exercises, and one or two open-ended questions. No materials (notes, books, etc.) may be consulted. Students may ask for an additional oral exam after the written exam. Past exams are available at the bottom of the website. The exam dates for the written exam are listed below.
Project assignement plus mandatory oral exam. Towards the end of the course, the interested students (groups of 1 or 2 students max per project) can ask for a project, which will be typically on the study of one or two papers in the cyber-physical security field, and in the replication of their simulations. The students might also propose to me a topic of their interest for the project - I will evaluate if it is suitable for the development of a project. The project must be discussed in a period that goes from the written exam date to max 10 days after (because I have to close the exams in infostud). The students must send me the completed project at least 2 days before the day of discussion of the project. We will agree on a discussion date via email, once you have finished the project.
IN ANY CASE (1 or 2 above) THE STUDENT MUST BOOK THE EXAM ON INFOSTUD.
Written exam dates are at this link. The student must book the exam on infostud.
20/01/2025. Hour 09:00-12:00, Aula S1 - Edficio E. Maps: maps.app.goo.gl/Rr8Wo8DpfFAnPa9i8 . Only for the students who attended 2024 course.
13/02/2025. Hour 09:00-12:00, Aula 34 Dipartimento Scienze Statistiche - Città Universitaria. Maps: maps.app.goo.gl/LQjN1muPjDR6YdRG8. Only for the students who attended 2024 course.
Appello straordinario. Attention: the exam hour/room has changed. Wednesday 2/4/25, 15:00-17:00, room A222 (second floor, stairs on the left after entering), DIAG Department (Via Ariosto 25).
19/06/2025 Aula T1 Regina Elena h 9-12;
08/07/2025 Aula T1 Regina Elena h 9-12;
22/09/2025 Aula T1 Regina Elena h 9-12;
Lecture Summaries and Study Materials
Lecture Summaries and Study Materials
This section will be populated during the course. After each lesson, the specific study references (book sections, papers, etc.) will be indicated in the lesson summary. Link to the lecture slides, the blackboard notes and the zoom recordings of the lessons will be available. You can also take advantage of the slides, notes and zoom recordings of the previous version of the course, see website at this link.To have an idea of the detailed, you can have a look at the past year website - link (as explained above, this year we will not have the initial lessons with the recap of system theory concept. These concept will be introduced only when needed during the explanation of the attack and defence schemes. This will make the course much more accessible for students from cybersecurity.
Lesson 1 - 27/02/2025 Introduction to the Course
Introduction to the logistics of the course. Tour of the website of the course - check it carefully. We discussed the logistic, the exam modalities, the teaching materials, etc. Then we presented an overview of all the technical content of the course, which then we will study in details in each lesson.
No lecture slides for this lesson, no book chapter to read.
Lesson 2 - 03/03/2025 Introduction to Cyber-physical Systems
Introduction to cyber-physical systems (CPS). We discussed an important example of a CPS: the power grid. It will be the subject of some cyber-physical attacks discussed in the course.
No blackboard notes in this lesson.
Link to book chapter: Chapter 1 - Introduction. If you want, you can use this form to send comments on errors or unclear parts of the book.
See the study materials listed at the end of the chapter 1.
Lesson 3 - 06/03/2025 Risk Management Framework
In this lesson we will discuss about risk management. Most of the techniquest we see in this course can help in performing quantitative risk management.
Then we discussed about modelling of a physical system, starting from a first simple example (check the recordings and the blackboard notes).
Blackboard notes (example of mathematical modelling of a system).
Lecture slides (updated on 16/03/2025 with new reference to study materials at slide 22).
Link to book chapter: Chapter 2 - Risk Management. If you want, you can use this form to send comments on errors or unclear parts of the book.
See the study materials listed at the end of the slide and at the end of the book chapter.
Lesson 4 - 10/03/2025 Modelling of Cyber-physical Systems - State space model of the physical process
In this lesson, we finished the example, started in the previous lesson, on the modelling of a physical system (we modelled a simple mass-spring-damper system). From this quite simple example, we derived the notion of the state space model of a linear system. We presented a procedure to follow to find the state space model of a generic physical system.
Blackboard notes 1 (derivation of the state space model of the mass-spring-damper system).
Blackboard notes 2 (start of the modelling of a cyber-physical system).
Link to book chapter: Chapter 3 - Part I - Modelling of CPS and Attacks. If you want, you can use this form to send comments on errors or unclear parts of the book.
See the additional study materials listed at the end of the slide and at the end of the book chapter.
Lesson 5 - 13/03/2025 Modelling of Cyber-physical Systems - The overall architecture
In this lesson, we presented a general model of a networked cyber-physical system, interconnecting a process with the controller and the detector. We discussed also modelling of an attack performing data deception and a physical attack on the process.
Link to book chapter: Chapter 3 - Part I - Modelling of CPS and Attacks. If you want, you can use this form to send comments on errors or unclear parts of the book.
See the additional study materials listed at the end of the slide and at the end of the book chapter.
Lesson 6 - 17/03/2025 First Modelling of Cyber-physical Attacks
In this lesson, we present a first modelling of the main cyber-physical attacks, based on the cyber-physical system modelling framework presented in the previous two lessons.
Recording of the first part, plus Zoom recording of the second part of the lesson. There were network issues during the lesson. The first part is recorded in meet. The second part in Zoom. During the second part, at some point the video recording failed (you can see the blackboard notes togheter with the audio for that part. The content in any case is covered by the book chapter).
Link to book chapter: Chapter 3 - Part I - Modelling of CPS and Attacks. If you want, you can use this form to send comments on errors or unclear parts of the book.
See the additional study materials listed at the end of the slide and at the end of the book chapter.
Lesson 7 - 20/03/2025 Solution of the state space equations (calculation of the output of a physical system)
In this lesson, we discussed about the solution of the state space model describing a physical system. This will allow us to evaluate the impact, the effect of an attack on a physical system
No lecture slides for this lesson
Appendix A of the book, on feedback control and the state space. If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 8 - 24/03/2025 Solution of the state space equations - The natural modes of the system
We derived the spectral formula for the matrix exponential and for the state solution. The state solution can be decomposed as the sum of n independent evolutions, which are called the natural modes of the system. We saw the different modes that can appear in a system: the exponential aperiodic ones, the pseudoperiodic ones, the polynomial ones.
No lecture slides for this lesson
Appendix A of the book, on feedback control and the state space. If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 9 - 27/03/2025 Solution of the state space equations - Example. The steady state.
We summarized key concepts related to the state space models. We did a simple example on the computation of the spectral form of the exponential matrix and the free evolution of the state. We defined the transient and the steady state response of a system.
No lecture slides for this lesson.
Appendix A of the book, on feedback control and the state space. If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 10 - 31/03/2025 Second CPS Modelling Approach + Monitors and Attack Detection/Identification.
We presented a second approach (by Pasqualetti et al.) to model a cyber-physical system. This approach focuses on the model describing the plant and the controller, together. We then, based on this model, present the monitor, which is the system in charge of detecting and isolating the attacks. We define key concepts related with attack detection and identification and the fundamental properties of consistency of the detectors. In the next lesson, we will present criteria for understanding when an attack is detectable or not.
Full Chapter 3: On Modelling of CPS and Attacks. If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 11 - 03/04/2025 Fundamental Theorem on Attack Detection.
We presented the fundamental theorem on attack detection, which explains the condition for an attack to be undetectable (when the output of the cyberphysical system under attack is compatible with a normal operation).
Full Chapter 3: On Modelling of CPS and Attacks. If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 12 - 10/04/2025 Fundamental Theorem on Attack Detection - Final Considerations.
We discussed final remarks on the fundamental limitations of detectability of attacks. We presented a theorem on unidentifiable attacks. We discussed one type of attack detectors, the observer-based and resildual-based detector.
Full Chapter 3: On Modelling of CPS and Attacks. If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 13 - 14/04/2025 False data Injection Attack Against State Estimation in Power Systems.
We started the discussion of the first example of attack seen in the course, the false data injection attack (FDIA) against state estimation in power systems. This attack targets the algorithms of the power system control centers which performs the estimation of the state of the power network. We studies how the state estimation works (weighted least square state estimation algorithm), and how the bad data correction procedure works (which removes bad data from the sensors - e.g., due to faults of the sensors). In the next lesson we are going to study the working principle of the attack, showing how an attacker can modify the measurements, alter the state estimation, without being detected by the bad data detector.
Zoom recording 1. The recording was interrupted tue to internet disconnection. See the book for the missing recoreded explanation. I will also briefly recap key concepts in the next lesson.
Chapter on FDIA against state estimation in power systems (first part of chapter). If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 14 - 28/04/2025 False data Injection Attack Against State Estimation in Power Systems. Attack formulation
We discussed the attack formulation, presenting the attack equation, and studing the effect of the attack on the bad data detector residual, and on the state estimation. We discussed targeted FDIA.
Chapter on FDIA against state estimation in power systems (almost finalized version). If you want, you can use this form to send comments on errors or unclear parts of the book.
Lesson 15 - 30/04/2025 False data Injection Attack Against State Estimation in Power Systems. Security indices and protection strategies.
We discussed the definition of three security indices useful to measure the vulnerability of the whole grid and the single meters against the attack. We formulated a simple problem for optimal protection of the grid from the attack.
Chapter on FDIA against state estimation in power systems (almost finalized version). If you want, you can use this form to send comments on errors or unclear parts of the book.
Slides (ignore the part on the simulations, we are going to cover it in more detail on Monday)
Lesson 16 - 05/05/2025 False data Injection Attack Against State Estimation in Power Systems - Simulations and Exercises
We run some simulations in Matlab to perform experiments on state estimation in normal, faulted and under attack conditions (see first folder below). We then use Julia language to compute the security index alpha_i (second folder).
FOLDER WITH CODE FOR SIMULATING FDIA IN MATLAB. Install Matlab with the free academic licence for students. See Sapienza Università di Roma - Accesso a MATLAB per tutti - MATLAB & Simulink.
FOLDER WITH JULIA CODE TO COMPUTE THE SECURITY INDEX ALPHA. Install Julia programming language The Julia Programming Language. Then change directory to the folder and run file main.jl (run file by typing instruction include("main.jl") ).
Lesson 17 - 08/05/2025 Switching Attacks
We discussed switching attacks in power systems. The aim of the attack is to cause the disconnection of one target generator by switching on and off one load in the network.
Lesson 18 - 12/05/2025 Switching Attacks and Load Altering Attacks
We finished the discussion of switching attacks, with the attack formulation and the simulations. We then started the discussion of the load altering attacks, introducing the attack idea and the initial part of the formulation, up to the swing equations.
Lesson 19 - 15/05/2025 Load Altering Attacks
We continued with load altering attacks, arriving to the model of the system (swing equations + power flow equations), in feedback with the prime mover governor and the attack control equations.
Lesson 20 - 16/05/2025 Load Altering Attacks
We continued with load altering attacks, up to the first formulation of the optimal protection problem.
Lesson 21 - 16/05/2025 Load Altering Attacks - Stability Constraints
We studied the Lyapunov stability theory, useful to derive a stability constraint to be embedded into the optimal protection problem for dynamic load altering attacks. Part of the zoom recording failed due to poor Internet connection.
Lesson 22 - 22/05/2025 Load Altering Attacks - Conclusions. Started FDIA-based Attacks
We completed the derivation, based on the Lyapunov stability theory, of a stability constraint to be embedded into the optimal protection problem for dynamic load altering attacks. We started the discussion of FDIA-based complex, multilevel attacks.
8 - FDIA based attacks.pdf Slides on FDIA based attacks (complex, multilevel attacks).
Lesson 23 - 23/05/2025 Finished FDIA-based Attacks. Overview of Covert Attacks
We finished presenting the complex, multi-level attacks based on FDIA attack against state estimation.
Then, we provided an introduction to covert attacks, presenting the overall concept and the attack scheme. It is required that the students understand the overall concept of the attack, while it is not mandatory to study the detailed mathematical derivation and analysis of the attack. It is expected at the exam that the student is able at least to sketch the block diagram of the attack presented at lesson and explain it in detail, describing the attack goal and mechanism, as done in the lesson.
8 - FDIA based attacks.pdf Slides on FDIA based attacks (complex, multilevel attacks).
Lesson 24 - 26/05/2025 Zero Dynamics Attacks
We started discussing zero dynamics attacks. They ar eaimed at finding a modification of the inputs that causes a modification of some internal state variables of the system (so to cause some sort of damage), while having no impact on the measured output of the system (the ones observed by the detector), so to make the attack not detectable.
Zoom recording 1. Part of the recording failed, after the break. You can read the chapter (soon available), or see the recording from past year (see here, lessons 20 and 21), which is full.
Slides: 9 - Zero dynamics attacks.pdf. You can skip slides 14, 15, 16.
Lesson 25 - 28/05/2025 Zero Dynamics Attacks - conclusion
We finished the discussion of zero dynamics attacks, analysing the unmatched initial conditions case, and briefly mentioning the detection strategies.
Slides: 9 - Zero dynamics attacks.pdf . You can skip slides 14, 15, 16.
Lesson 26 - 29/05/2025 Detection in Presence of Side Initial State Information
We discussed some detectability results which consider the presence of some knowledge of the operator about the initial state of the system (this knowledge is called side initial state information). We derived one result that can be used to check wether for a given system it is possible or not to launch undetectable attacks based on the falsification of inputs and measurements.
Slides: 13 - Attack detection with side state information.pdf
No book chapter on this. Study the slides. You can skip slides 7 (output nulling subspace), 12 (revisitation of zero dynamics attacks) and 16.
Lesson 27 - 30/05/2025 Conclusions
We recap the topics covered during the course and checked the past exams.
Some Readings
Some Readings
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