Dipartimento di Ingegneria Elettrica ed Elettronica
Università di Cagliari, Italy

Schedule during the first week: on Thursday, 5 March class will be held in room I_ID.

[Syllabus]

Texbook: A. Giua. Notes for the course Analysis and Control of Cyber-Physical Systems, 30 April 2025. The material in Chapter 12 is not currently part of the syllabus.

Schedule 2026 :

Tuesdays	15:00-18:00 h	Room: B_TA
Thursdays	15:00-18:00 h	Room: I_1F

Office hours: By appointment, in person or via Teams. Preferably Wed 11:00-13:00.

Channel Teams: ACCPS 2026

Tutor: Virginia M. Alterio (email/teams: virginiam.alterio@unica.it)

Presentation

The course provides an introduction to cyber-physical systems (CPSs), i.e., dynamical systems composed by logical components (driven by event occurrences) interacting with physical components (described by time-driven models). From a control systems perspective CPSs are hybrid systems, combining discrete event and continuous dynamics. The course is structured into two parts. The first part presents discrete event systems and supervisory control. The second part is devoted to the modeling and analysis of hybrid systems and introduces some approaches for formal modeling and verification.

Syllabus

1. Classification of dynamical systems (2h lecture)
   Time-driven systems. Discrete-event systems. Hybrid systems.
2. Automata models for discrete event systems (12h lecture + 4h homework)
   Formal languages: alphabets and words, languages and operators. Deterministic finite automata: languages and properties. Nondeterministic finite automata and their languages. Equivalence between deterministic and nondeterministic automata. Fault diagnosis using automata: diagnoser, diagnosability. Modeling with automata and concurrent composition.
3. Supervisory control of discrete event systems (6h lecture + 2h homework)
   Plant, specification, supervisor and closed-loop system. Controllability and supremal controllable sublanguage. Supervisory design for language specifications. Supervisory design for state specifications.
4. Hybrid systems and hybrid automata (12h lecture+ 2h homework + 2h lab)
   State variable models of time-driven systems. Examples of hybrid systems. Autonomous hybrid automata and generalizations. Hybrid automata with inputs. Evolution of a hybrid automaton. Pathological cases of continuous and hybrid evolutions.
5. Reachability analysis of hybrid systems (6h lecture + 2h homework)
   State transition systems (STSs). STS associated with a hybrid automaton. Reachability of a STS. Equivalences between states of a STS. Bisimulation between states of an STS and quotient system.
6. Stability and stabilization of linear switched systems (8h lecture + 2h homework/ lab)
   Elements of stability for linear and time invariants systems. Direct method of Lyapunov. Quadratic forms and singular values. Stability analysis of switched systems by common Lyapunov function. Quadratic Stabilization Stabilization by slow switching.

Mid-term 2026: Thursday, 16 April 2026

Final exam 2026: To be arranged

Homeworks 2026:

Mid-term and final test (previous years):

• 2025: [Mid-term] [Final]
• 2024: [Mid-term] [Final]
• 2023: [Mid-term] [Final]
• 2022: [Mid-term] [Final]
• 2021: [Mid-term] [Final]

Homeworks (previous years):

• 2025: [Hw1] [Hw2] [Hw3] [Hw4] [Hw5] [Hw6]
• 2024: [Hw1] [Hw2] [Hw3] [Hw4] [Hw5] [Hw6]
• 2023: [Hw1] [Hw2] [Hw3] [Hw4] [Hw5] [Hw6]
• 2022: [Hw1] [Hw2] [Hw3] [Hw4] [Hw5] [Hw6]
• 2021: [Hw1] [Hw2] [Hw3] [Hw4] [Hw5]
• 2020: [Hw1] [Hw2] [Hw3] [Hw4]* [Hw5] [Hw6] (*) Homework 4 is on fluid models for infective disease propagation which is not currently part of the syllabus.

Other material

• For the first part of the course (discrete event systems) you can find useful material (in Italian) on the webpage of the course [Automi e reti di Petri].
• For the second part of the course (hybrid systems) here is a series of additional [exercises on HS].

References

• A. Giua. Notes for the course Analysis and Control of Cyber-Physical Systems, 30 April 2025.
• D. Deplano, A. Giua. Fluid models for infective disease propagation, 14 May 2020.
• A. Giua. Mathematical models for the diffusion of innovation in social networks, 2 May 2020.
• A. Giua. Nota sull'integrazione numerica di equazioni differenziali, 7 May 2020. (In Italian)

Evaluation

• All tests during regular exam sessions are oral.
• Students attending classes are offered the additional opportunity to pass the exam taking two written tests: a mid-term and a final one. The final test can be replaced by a project.Mid-term and final test consists in a series of problems to be solved in class and may include some theoretical questions. Students cannot consult any material during the test, except for a single A4 sheet where they can summarize notes, diagrams or other reference material.
• Scores for the written tests (or project) are as follows:
  

  - Mid-term written test (Part I: discrete event systems)	25 points
  - Final written test (Part II: hybrid systems) or project	25 points
  - Homework	15 points

The final grade G will depend on the total points (TP): G = 30 if TP ≥ 60, else G = floor(TP/2).