Mathematics

1) Knowledge and understanding At the end of the course, the students will know and understand: a) the idea of control system and of differential inclusion, and their basic properties; b) thr idea of optimal control and necessary and/or sufficient conditions for its existence; c) the relationship between optimal solutions of a control problem and the Hamilton-Jacobi-Bellman equation; d) the idea of viscosity solution for the Hamilton-Jacobi equation. 2) Applying knowledge and understanding At the end of the course, the students will be able to: a) write the mathematical formulation of an optimal control problem; b) determine, using the Pontryagin Maximum Principle, the optimal solutions of an optimal control problem; c) analyze, from a theoretical point of view, the solutions of an optimal control problem through the study of the associated Hamilton-Jacobi-Bellman equation. 3) Making judgements During the lessons, several problems will be proposed to the students. Thanks to the autonomous resolution of the problems, and the subsequent discussion in the classroom, the students will acquire both the ability to evaluate their knowledge and the ability to tackle a wide range of optimal control problems. 4) Communication skills The written form of the exercises, assigned either during lessons or during the written test, and the oral exam will allow the students to evaluate their skill in correctly communicating the knowledges acquired during the course. 5) Learning skills At the end of the course the students will be able to analyze optimal control problems; such skill is acquired by means of several model problems assigned during the course.