The course aims to provide solid mathematical principles for understanding interconnected dynamical systems, also known as multi-agent distributed systems, with particular attention to the Perron-Frobenius theory.
The learning objectives of the course include an understanding of dynamic phenomena related to multi-agent systems, including consensus, as well as the ability to design and analyze distributed algorithms for such systems.
During the course knowledge will be acquired in the analysis of multi-agent dynamical systems using matrix and graph theory. In particular, mathematical methods will be proposed to analyze matrices with non-negative components, representing the interconnection between heterogeneous actors, in order to identify the structural properties of the underlying network.
During the course students will deepen the analysis of interconnected dynamical systems through matrix and graph theory, working on examples to better understand the concepts presented.
The learning objectives of the course include an understanding of dynamic phenomena related to multi-agent systems, including consensus, as well as the ability to design and analyze distributed algorithms for such systems.
During the course knowledge will be acquired in the analysis of multi-agent dynamical systems using matrix and graph theory. In particular, mathematical methods will be proposed to analyze matrices with non-negative components, representing the interconnection between heterogeneous actors, in order to identify the structural properties of the underlying network.
During the course students will deepen the analysis of interconnected dynamical systems through matrix and graph theory, working on examples to better understand the concepts presented.
scheda docente
materiale didattico
Review of matrix theory with emphasis on Perron-Frobenius theory
Graph theory and algebraic graph theory
Stability analysis for connected systems
Examples of coordination of multi-robot systems
Introduction to Model Predictive Control and mathematical fundamentals
Formulation of the MPC Problem
Stability of MPC
MPC for Multi-agent Systems
- Camacho, E. F., & Bordons, C., Model Predictive control, Springer, ISBN: 978-1-85233-694-3, 2013.
- Lecture notes
Programma
Introduction to multi-agent systemsReview of matrix theory with emphasis on Perron-Frobenius theory
Graph theory and algebraic graph theory
Stability analysis for connected systems
Examples of coordination of multi-robot systems
Introduction to Model Predictive Control and mathematical fundamentals
Formulation of the MPC Problem
Stability of MPC
MPC for Multi-agent Systems
Testi Adottati
- F. Bullo, Lectures on Network Systems, CreateSpace Independent Publishing Platform, ISBN 978-1986425643, 2022- Camacho, E. F., & Bordons, C., Model Predictive control, Springer, ISBN: 978-1-85233-694-3, 2013.
- Lecture notes
Bibliografia Di Riferimento
- Veysel Gazi and Kevin Passino. 2011. Swarm Stability and Optimization. Springer Publishing Company, Incorporated. ISBN 978-3642422706 - F. Bullo, J. Cortes, and S. Martinez, Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms, Princeton University Press, Princeton, NJ, USA, 2009. - M. Mesbahi and M. Egerstedt, Graph Theoretic Methods for Multiagent Networks, Princeton University Press, Princeton, NJ, 2010. - Maciejowski, J., Predictive Control with Constraints, Pearson Education POD, 2002. - Rossiter, J. A., Model-Based Predictive Control: A Practical Approach, CRC Press, 2003. - Maestre, J. M., & Negenborn, R. R. (Eds.). (2014). Distributed model predictive control made easy (Vol. 69). Dordrecht, Netherlands: Springer.Modalità Frequenza
Attendance is strongly recommended given the practical nature of the course.Modalità Valutazione
The exam consists of an oral test to discuss the theoretical aspects of the course and a project to explore the practical aspects of the course.
scheda docente
materiale didattico
- Review of matrix theory with emphasis on Perron-Frobenius theory
- Graph theory and algebraic graph theory
- Stability analysis for connected systems
- Examples of coordination of multi-robot systems
- Introduction to Model Predictive Control and mathematical fundamentals
- Formulation of the MPC Problem
- Stability of MPC
- MPC for Multi-agent Systems
- Camacho, E. F., & Bordons, C., Model Predictive control, Springer, ISBN: 978-1-85233-694-3, 2013.
- Lecture notes
Programma
- Introduction to multi-agent systems- Review of matrix theory with emphasis on Perron-Frobenius theory
- Graph theory and algebraic graph theory
- Stability analysis for connected systems
- Examples of coordination of multi-robot systems
- Introduction to Model Predictive Control and mathematical fundamentals
- Formulation of the MPC Problem
- Stability of MPC
- MPC for Multi-agent Systems
Testi Adottati
- F. Bullo, Lectures on Network Systems, CreateSpace Independent Publishing Platform, ISBN 978-1986425643, 2022- Camacho, E. F., & Bordons, C., Model Predictive control, Springer, ISBN: 978-1-85233-694-3, 2013.
- Lecture notes
Bibliografia Di Riferimento
- Veysel Gazi and Kevin Passino. 2011. Swarm Stability and Optimization. Springer Publishing Company, Incorporated. ISBN 978-3642422706 - F. Bullo, J. Cortes, and S. Martinez, Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms, Princeton University Press, Princeton, NJ, USA, 2009. - M. Mesbahi and M. Egerstedt, Graph Theoretic Methods for Multiagent Networks, Princeton University Press, Princeton, NJ, 2010. - Maciejowski, J., Predictive Control with Constraints, Pearson Education POD, 2002. - Rossiter, J. A., Model-Based Predictive Control: A Practical Approach, CRC Press, 2003. - Maestre, J. M., & Negenborn, R. R. (Eds.). (2014). Distributed model predictive control made easy (Vol. 69). Dordrecht, Netherlands: Springer.Modalità Frequenza
Attendance is strongly recommended given the practical nature of the course.Modalità Valutazione
The exam consists of an oral test to discuss the theoretical aspects of the course and a project to explore the practical aspects of the course.