- Docente: Angelo Favini
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course, the students know the main notions of
control theory for ordinary differential equations , i.e.,
controllability, observability, bang-bang controllers, the notion
of cost function and optimal control, the Pontryagin maximum
principle.They know also the basic notion of strongly continuous
semigroup of linear operators together with the one of evolution
equations, basic for future applications to partial differential
equations and related control problems, of very large interest in
various applied sciences.
Course contents
Controllability of a dynamical linear system.Observability.
Stability and stabilizability.Examples from Physics, Chemistry,
Economy.Optimal control.Pontryagin maximum Principle, bang-bang
controllers. Quadratic optimal control for linear equations.Riccati
equation.Optimal control on infinite horizon.The algebraic Riccati
equation.Singular dynamical systems and related quadratic optimal
control.
Semigroups of linear operators. Examples of semigroups. control of
evolution equations.
Readings/Bibliography
A.Favini, Notes;
A.Bensoussan,G.Da Prato, M.Delfour, S.Mitter, Representation and control of infinite dimensional systems II, ed.Birkauser, 1992;
J.Zabczyck, Mathematical control theory, ed.Birkhauser, 1992;
E.Sontag, Mathematical control theory, Springer-Verlag, 1998.
Teaching methods
The course is structured in lessons in a room, where there are
described the basic elements of control theory for ordinary
differential equations. The first aspect concern differential
equation in finite-dimensional space. In a second time semi groups
of linear operators in Banach spaces are introduced and this allows
to present infinite dimensional control theory. At the end of the
course students can follow the most recent development on control
of dynamical systems.
Assessment methods
Assessment methods consists in an oral examination that wants to
establish the achievement of the knowledge required by the program
of the course. The prove has the further aim to verify the degree
of knowledge of the main concepts of the matter.
Office hours
See the website of Angelo Favini