OVERVIEW

Optimization is the discipline that concerns the investigation of the algorithms for searching the points of minimum or maximum of cost functions and functionals.

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide students with basic and advanced skills on the properties and control of dynamic systems, with a focus on the control of traffic systems. Knowledge will be provided on the treatment of linear and non-linear systems, as well as on the concept of equilibrium point and stability. On the control side, optimisation-based controllers will be developed to minimise KPIs typical of the traffic networks domain, focusing on both complete and incomplete information problems.

AIMS AND LEARNING OUTCOMES

The course aims at achieving the ability to model dynamical systems and solve control problems that may require the optimization of performance indices. Attendance and active participation in lessons and individual study will allow the student to
- know in depth the structural properties of linear and nonlinear dynamical systems;
- apply the results of the theory developed on dynamical systems to simple case studies related to traffic networks;
- determine the taxonomy and the solution of simple optimization problems;
- Ensure the correct terminology for the analysis of dynamic systems and the formulation of an optimization problem.

TEACHING METHODS

Theoretical lectures and exercises for a number of about 50 hours on the overall. 

SYLLABUS/CONTENT

• Introduction to Dynamical Systems 

  • Continuous-time systems
  • Discrete-time systems
  • Linear systems
  • Linearization
  • Example using Matlab Simulink

• Equilibrium and Stability of Dynamic Systems 

  • Concept of equilibrium point
  • Stability of continuous-time and discrete-time linear systems
  • Stability of continuous-time and discrete-time nonlinear systems (direct and indirect Lyapunov method)
  • Example using Matlab Simulink

• Optimization 

  • What is an optimization problem
  • Classification of optimization problems (LP, QP, MILP, NLP) (overview of algorithms)
  • Formalization of optimization problems
  • Examples using Matlab

• Predictive Control 

  • What is MPC with Matlab examples

RECOMMENDED READING/BIBLIOGRAPHY

D. Xue, Y. Chen, D.P. Atherton, Linear Feedback Control: Analysis and Design with MATLAB (Advances in Design and Control), SIAM, 2007.

D. Bertsekas, Introduction to Linear Optimization, Athena Scientific, 1997.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/en/corsi/10377/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written examination (with possible oral check) on appointment to agree by email. Students with learning disorders ("Disturbi Specifici di Apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities."

ASSESSMENT METHODS

The capability to formulate and solve problems of control and optimization under linear assumptions will be verified. The verification concerns questions on

- continuous-time linear systems;

- discrete-time linear systems;

- linear programming.

FURTHER INFORMATION

For questions, contact the lecturer to agree on the time of meeting.