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Higher Analysis

Academic Year 2021/2022 - 1° Year - Curriculum APPLICATIVO
Teaching Staff: Alfonso VILLANI and Biagio RICCERI
Credit Value: 6
Scientific field: MAT/05 - Mathematical analysis
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester:

Learning Objectives

The aim of the course is to make the students familiar with basic concepts, main theorems and most used techniques in Control theory for linear ordinary differential systems.

Course Structure

The course main topics will be explained by the teacher during formal lectures. These will be focusing on each topic's general principles and new concepts that have not been studied before. Each's topic's additional resources and subchapters will be presented by turning over groups of students. The goal is to have students develop study autonomy and teaching abilities, skills that are essential for students who want to pursue a career in research or teaching.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Detailed Course Content

Bounded variation and absolutely continuous functions. Linear differential systems of the first order with coefficients in L ^ 1_loc. Related control processes. Evolution matrix. Accessible set. Complete controllability. Controllability variable in time. Differential inclusions and their applications to Control theory.

Textbook Information

1. . H. Royden, Real Analysis, 2nd ed., Macmillan

2. R. Conti, Problemi di controllo e di controllo ottimale, 3a ed., UTET

3. J.-P. Aubin - A. Cellina, Differential Inclusions, Springer-Verlag, 1984.