Instructors: Stefano Battilotti, Daniela Iacoviello
Course web pages:
Part I. https://sites.google.com/a/uniroma1.it/danielaiacoviello/didattica/filtering-and-optimal-control-2020-2021
Part II. www.diag.uniroma1.it/~batti/ifsd.html
Credits: 12
Infostud code: 10596148

Objectives

The course illustrates the basic methodologies in estimation, filtering, prediction and optimal control. The student will be able to use the main estimation, filtering, and prediction techniques and to formulate, analyze, and search for solutions of optimization problems of different nature by an appropriate use of optimality conditions, with particular emphasis on optimal control problems.

Program

Part I. Extrema of functions and functionals, with and without constraints. Calculus of variations. Variational approach to optimal control with and without constraints. Pontryagin maximum principle. Dynamic programming and the Hamilton-Jacobi-Bellman equation. Linear-quadratic optimal control problems. Optimal regulation in minimum time.

Part II. Probability theory. Estimates: Definitions and properties. Cramer-Rao lower bound. Optimal estimates: Least squares, maximum likelihood, and Bayesian estimates. Kalman filtering and prediction. Model identification.

Type of exam: Part I: Oral test, Project; Part II: Oral test, Project

Reference texts

• D. Liberzon, "Calculus of Variations and Optimal Control Theory: A Concise Introduction", Princeton University Press, 2011 (also dowloadable from liberzon.csl.illinois.edu/publications.html)
• C. Bruni, G. Di Pillo, "Metodi variazionali per il controllo ottimo", Aracne, 2007
• A. Locatelli, "Optimal Control: An Introduction", Birkhäuser, 2001
• C. Bruni, C. Ferrone, "Metodi di stima per il filtraggio e l'identificazione dei sistemi", Aracne, 2008
• Notes on Part II of the course (by S. Battilotti)