OVERVIEW

The course "Elements of Systems Engineering" provides the methodologies required to model, analyze, and control complex, large-scale systems (Systems of Systems), with a vertical focus on sustainability, resource efficiency, and resilience.

By integrating concepts from Systems Theory and Operations Research, the program adopts discrete-time as a unifying methodological framework and MATLAB/Simulink as the core operating environment. The first part covers the Leontief Input-Output model (both static and dynamic) to quantitatively assess environmental impacts (carbon footprint) and the structural robustness of supply chains against exogenous shocks. The second part analyzes decentralized and distributed control architectures (graph-based consensus algorithms) for interconnected networks such as smart grids. The course concludes with the practical design of Model Predictive Control (MPC) algorithms for constrained dynamic optimization.

AIMS AND CONTENT

LEARNING OUTCOMES

This teaching unit offers an introduction to the fundamental principles and methodologies of systems engineering. Students will explore the processes involved in designing, implementing, and managing complex engineering systems across a variety of applications, including the study of system lifecycle phases, requirements engineering, system architecture design, verification and validation, and risk management. Emphasis is placed on practical skills and problem-solving techniques that are essential in real-world projects.

AIMS AND LEARNING OUTCOMES

The course aims to guide students through the transition from the mathematical analysis of single, isolated dynamic systems to the design, optimization, and management of complex, interconnected Systems of Systems (SoS). Synergizing prior knowledge of constrained optimization (Operations Research) and modeling (Systems Theory), the course focuses on discrete-time as the unifying language for simulation and digital control.

The educational path is driven by modern engineering challenges in environmental sustainability and structural resilience. Students will learn both macroscopic structural analysis techniques (via ecological and dynamic extensions of the Leontief Input-Output model) and advanced control and network coordination methodologies (decentralized, distributed control, and Model Predictive Control). The entire course is supported by the intensive use of MATLAB/Simulink to translate theoretical models into algorithmic solutions ready for industrial implementation.

Expected Learning Outcomes (Risultati di Apprendimento Attesi)

Upon successful completion of the course, in accordance with the Dublin Descriptors, students will have acquired the following competencies:

1. Knowledge and Understanding

• Understand the taxonomy and fundamental properties of Systems of Systems (SoS) and complex networks.

• Master the fundamentals of discrete-time dynamics, discretization methods, and stability within the unit circle.

• Understand the theory behind the Leontief economic-ecological model in both its static and dynamic formulations.

• Know the structural differences, advantages, and limitations of centralized, decentralized, and distributed control architectures.

• Understand the receding horizon principle underlying Model Predictive Control (MPC) and techniques for handling hard constraints.

2. Applying Knowledge and Understanding

• Ability to model and evolve the discrete-time dynamics of an interconnected system described by graphs.

• Ability to apply the Leontief model in MATLAB to quantify environmental footprints ($CO_2$, resources) and simulate the effects of shocks or failures on supply chain resilience.

• Ability to analyze couplings between subsystems using the Relative Gain Array (RGA) matrix for decentralized control synthesis.

• Ability to formulate and implement an MPC controller in MATLAB/Simulink for energy or process optimization, translating it into a Quadratic Programming (QP) problem.

3. Making Judgements

• Independently evaluate the trade-offs between computational performance, communication requirements, and control performance when selecting an architecture (decentralized vs. distributed).

• Critically interpret dynamic simulation results to validate the effectiveness and sustainability of a resource management strategy.

4. Communication Skills

• Clearly and formally describe design choices, constraints, and sustainability metrics adopted within a complex system.

• Effectively present and defend the outcomes of a team-based technical project (Project Work), utilizing appropriate engineering terminology.

5. Learning Skills

• Develop the ability to independently investigate advanced simulation software technical documentation (MATLAB/Simulink Toolboxes).

• Acquire a flexible methodological approach that allows the application of optimization and predictive control techniques to new application domains (e.g., smart buildings, logistics, green energy transition).

PREREQUISITES

To attend the course successfully, students must possess the following competencies:

• Systems Theory: State-space representation of Linear Time-Invariant (LTI) systems, calculation of free and forced evolution, stability concepts, and linearization of non-linear systems around an equilibrium point.

• Function Optimization (Operations Research): Formulation and resolution of constrained optimization problems, Linear Programming (LP), and Quadratic Programming (QP). Applied linear algebra (matrix operations, eigenvalues, and quadratic forms).

TEACHING METHODS

• Lectures (approx. 28 hours): Presentation of methodological frameworks, mathematical models, and optimization/control algorithms.

• Guided Exercises and Lab Sessions (approx. 20 hours): Hands-on sessions where students implement the studied models (dynamic Leontief, consensus algorithms, MPC controllers) using MATLAB and Simulink.

• Parallel Project Work: Independent development (individually or in small groups) of a year-long project assisted by the professor during lab hours, aimed at applying course techniques to a real-world case study focused on sustainability or energy efficiency.

SYLLABUS/CONTENT

Module 1: Discrete-Time Systems and Interconnected Networks (10 hours)

• Fundamentals of discrete-time dynamics: Difference equations, discrete state-space representation, free and forced evolution, stability within the unit circle.

• Discretization: Sampling methods (Euler, Tustin) and sampling time selection.

• Graph modeling of Systems of Systems (SoS): Adjacency and Laplacian matrices to describe the topology of infrastructure networks (water, logistics, energy).

Module 2: The Leontief Model for Sustainability and Resilience (12 hours)

• Static Input-Output model: Technical coefficient matrix, Leontief inverse, and productivity conditions.

• Ecological extensions: Calculation of embedded $CO_2$ emissions and environmental footprints of a supply chain.

• Dynamic Leontief model: Introduction of capital coefficients and discrete-time inventory accumulation dynamics.

• Robustness analysis: Simulating exogenous shocks and node failures on the resilience of economic/industrial systems.

Module 3: Decentralized and Distributed Control Architectures (10 hours)

• Dynamic interactions: Coupling in Multi-Input Multi-Output (MIMO) systems and discrete-time Relative Gain Array (RGA) analysis.

• Decentralized Control: Independent block structures and local regulator tuning.

• Distributed Control: Discrete-time consensus algorithms and cooperation over communication graphs.

• Applications: Resource management in Renewable Energy Communities (RECs) and green logistics networks.

Module 4: Model Predictive Control (MPC) and MATLAB/Simulink Lab (16 hours)

• Receding Horizon principle: Mathematical formulation of discrete-time predictions.

• Real-time constrained optimization: Cost functions oriented toward energy efficiency and management of hard constraints on inputs and states.

• Mathematical translation: Transforming the MPC problem into a Quadratic Programming (QP) problem.

• Practical Laboratory (MATLAB/Simulink):

  • Lab 1: Predictive control of a Smart Building for energy savings under comfort constraints.

  • Lab 2: Decentralized/distributed control for load management of an electric vehicle fleet.

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes and handouts provided by the instructor.

TEACHERS AND EXAM BOARD

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of two integrated components to be completed in a single session:

1. Project Work Development and Submission: A practical project carried out individually or in small groups (max 3 students) using MATLAB/Simulink, focusing on the application of the course methodologies (e.g., dynamic Leontief model or MPC control) to a real-world case study.

2. Individual Oral Discussion: An oral examination comprising the presentation of the project and individual questions aimed at verifying the understanding of both the theoretical course contents and the developed code.

ASSESSMENT METHODS

The final grade will be determined based on the following criteria:

• Project Quality (50%): Scientific correctness of the model, effectiveness of the MATLAB/Simulink implementation, critical analysis of the results, and rigor in report/code preparation.

• Individual Oral Discussion (50%): The student's ability to justify design choices, demonstration of theoretical knowledge from the syllabus (discrete-time systems, control architectures, optimization), and command of technical engineering terminology.