055059 - DISTRIBUTED ALGORITHMS FOR OPTIMIZATION AND CONTROL OVER NETWORKS

Docente

Prandini Maria

Cfu

5.00

Tipo insegnamento

Monodisciplinare

Corso di Dottorato

Da (compreso)

A (escluso)

Insegnamento

MI (1380) - INGEGNERIA DELL'INFORMAZIONE / INFORMATION TECHNOLOGY

A

ZZZZ

055059 - DISTRIBUTED ALGORITHMS FOR OPTIMIZATION AND CONTROL OVER NETWORKS

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.

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

Bibliografia

D. Bertsekas, J.N. Tsitsiklis, Parallel and distributed computation: Numerical methods, Editore: Athena Scientific
K. 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
A. Falsone, K. Margellos, S. Garatti, M. Prandini., Dual decomposition for multi-agent distributed optimization with coupling constraints/ Automatica, Anno edizione: 2017, Fascicolo: 84
A. 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

lezione

25.0

esercitazione

0.0

laboratorio informatico

0.0

laboratorio sperimentale

0.0

progetto

0.0

laboratorio di progetto

0.0

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