Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Tipo incarico Dottorato
Docente Prandini Maria
Cfu 5.00 Tipo insegnamento Monodisciplinare

Corso di Dottorato Da (compreso) A (escluso) Insegnamento

Programma dettagliato e risultati di apprendimento attesi

Mission and goals

This course will introduce the students to a mathematical framework for the analysis and design of distributed decision making schemes in multi-agent systems seeking convergence to the optimal cooperative solution. The case when uncertainty is affecting the multi-agent system is also addressed.

Subject and program

Energy systems, transportation systems, and social networks are examples of large-scale systems involving multiple agents aiming at taking decisions in the most profitable way, while interacting with each other. Motivated by such applications, this course will present a mathematical framework for modeling, algorithm design and analysis for cooperative decision making problems arising in multi-agent systems. We will start from basic concepts in optimization, and then will apply them to distributed multi-agent dynamics seeking convergence to cooperative equilibria.

The course is structured in 4 parts:

1 - Motivation and illustrative applications

Introduction to decision making problems arising in energy efficient control of district buildings; smart grid control and optimization; coordination and control for electric vehicle fleets.
These applications will set a common ground to highlight the main complexity issues arising in multi-agent systems, namely, scalability due to the large scale nature of these problems, heterogeneity of the agents, privacy, and uncertainty.

2 - Mathematical tools

Convex analysis, optimization and duality theory; fixed point algorithms.
These tools constitute the theoretical backbone for the analysis and design of cooperative algorithms that arise in multi-agent decision making problems.

3 - Distributed optimization algorithms

Primal-based algorithms: Topics covered are gradient and scaled projected gradient methods, Jacobi algorithm, and Gauss Seidel algorithm.
The background notions on convex optimization and fixed point algorithms provided in Part 2 will be used. 

Duality-based algorithms: Topics covered are distributed dual decomposition and distributed alternating direction method of multipliers (ADMM).
The background notions on duality theory and dual algorithms provided in Part 2 will be used.

4 - Distributed optimization in uncertain networks

The algorithmic solutions described in Part 3 will be extended to the case when the multi-agent optimization problem is affected by uncertainty, which is known locally to each agent through a private set of data.  The application of the scenario approach to a distributed setting will be described, thus leading to a data-driven solution.

Expected learning outcomes

Students attending the course will acquire the mathematical background for the analysis and design of decision making algorithms in multi-agent cooperative systems and will familiarize with multi-agent applications and problems of contemporary interest.

Note Sulla Modalità di valutazione

Students will be evaluated based on a small project or on the study of an advanced topic related to the course.


Intervallo di svolgimento dell'attività didattica
Data inizio
Data termine

Calendario testuale dell'attività didattica

Schedule of the course

Monday, February 10 

11:15 - 13:15 Motivation and illustrative applications
14:15 - 17:15 Mathematical tools

Tuesday, February 11 

09:15 - 12:15 Mathematical tools
14:15 - 16:15 Primal-based algorithms

Wednesday, February 12 

09:15 - 12:15 Primal-based algorithms
14:15 - 16:15 Primal-based algorithms

Thursday, February  13 

09:15 - 12:15 Duality-based algorithms
14:15 - 16:15 Duality-based algorithms

Friday, February  14 

09:15 - 12:15 Distributed optimization in uncertain networks
14:15 - 16:15 Distributed optimization in uncertain networks

Risorsa bibliografica facoltativaD. Bertsekas, J.N. Tsitsiklis, Parallel and distributed computation: Numerical methods, Editore: Athena Scientific
Risorsa bibliografica facoltativaK. Margellos, A. Falsone, S. Garatti, M. Prandini., Distributed Constrained Optimization and Consensus in Uncertain Networks via Proximal Minimization/ IEEE Transactions on Automatic Control, Anno edizione: 2018, Fascicolo: 63
Risorsa bibliografica facoltativaA. Falsone, K. Margellos, S. Garatti, M. Prandini., Dual decomposition for multi-agent distributed optimization with coupling constraints/ Automatica, Anno edizione: 2017, Fascicolo: 84
Risorsa bibliografica facoltativaA. Falsone, K. Margellos, S. Garatti, M. Prandini., Multi-agent scenario approach with application to distributed optimization. Submitted, Anno edizione: 2019

Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
laboratorio informatico
laboratorio sperimentale
laboratorio di progetto

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese

Note Docente
Lectures will take place at Sala Seminari Nicola Schiavoni Building n. 20 of the Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, via Ponzio 34/5, 20133 Milano. See http://www.deib.polimi.it/eng/how-to-reach-us for directions on how to reach the Dipartimento di Elettronica, Informazione e Bioingegneria. Lecturers: Kostas Margellos, University of Oxford, UK; Alessandro Falsone, Politecnico di Milano; Simone Garatti, Politecnico di Milano; Maria Prandini, Politecnico di Milano
schedaincarico v. 1.6.2 / 1.6.2
Area Servizi ICT