- ECTS Credits: 7.5
- Semester: 1
- Year: 2
- Campus: Karlstad University
- Language: English
- ECTS Credits: 4
- Year: 2
- Campus: Brno University of Technology
- Language: English
- Unit Coordinator: Roberto Civino
- Programme: Pre Master's Foundation
- ECTS Credits: 3
- Taught hours: 18
- Campus: University of L'Aquila
- Language: English
- Delivery: Online
- Content:
Linear spaces, linear dependence, bases of a linear space, dimension of a linear space, linear subspaces.
Matrices, basic operations with matrices, change of coordinates, determinants, rank. A brief account on linear systems and Gauss elimination.
Diagonalisation of squared matrices, eigenvalues, eigenvectors. Inner products, bilinear forms and quadratic forms.
- Code: DT0821
- Unit Coordinator: Cristina Pignotti, Michele Palladino
- Programme: InterMaths
- ECTS Credits: 3
- Semester: 1
- Year: 1
- Campus: University of L'Aquila
- Language: English
- Delivery: In-class
- Aims:
To get the mathematical basics of control theory and optimal control theory.
To know classical problems of control theory governed by ordinary differential equations and to deal with them by using the concepts learned.
To know and construct significant applications of optimal control theory in life sciences, physics, and economics.
To know some examples of control problems for models governed by partial differential equations. - Content:
Controllability of linear systems and bang-bang principle. Controllability of nonlinear systems. Stabilizability of linear and nonlinear systems.
Basic optimal control problems. Necessary conditions. Adjoint equation. Pontryagin’s Maximum Principle. Existence and uniqueness results for minimizers. Hamiltonian and autonomous problems. Optimality conditions. State conditions at the final time. Payoff terms. States with fixed endpoints.
Dynamic Programming and Hamilton-Jacobi Equations.
Optimal control problems in biology, physics, and economics. Control problems for multiagent systems.An introduction to controllability and stabilization of partial differential equations: the wave equation and the heat equation.
- Pre-requisites:
Basic calculus and analysis (differential and integral calculus with functions of many variables). Ordinary differential equations.
- Reading list:
-L.C. Evans, An introduction to mathematical control theory, Berkley, Lecture notes.
-A. Bressan, B. Piccoli, Introduction to Mathematical Theory of Control, AIMS Book Series, 2007
-A. Isidori, Nonlinear Control Systems: An Introduction, Springer
-S. Lenhart and J.T. Workman, Optimal Control Applied to Biological Models, Chapman & Hall/CRC.
-S. Anita, V. Arnautu and V. Capasso, An Introduction to Optimal Control Problems in Life Sciences and Economics, Birkhauser.
