HECTOR
O. FATTORINI
Professor of Mathematics
Research Interests: Control theory,
differential equations in linear spaces.
e-mail: hof@math.ucla.edu
Phone: 310-825-4948
Fax: 310-206-6673
Mailing address: UCLA Mathematics Department
Box 951555,
Los Angeles, CA 90095-1555
Office: 6137 Math Sciences Building, UCLA
Education:
Licenciado en Matematica, Universidad de Buenos
Aires, 1960.
Ph. D., New York University, Courant Institute of
Mathematical
Sciences, 1965.
Research statement:
About half a century ago, the Soviet mathematician L. S.
Pontryagin formulated
completely for the first time the fundamental problem of the
calculus of variations
and solved it with PontryaginÕs Maximum Principle. This result unified
calculus of
variations and control theory of ordinary differential equations.
I have been working
for many years on infinite dimensional generalizations of the
maximum principle. The aim
is the control theory of partial differential equations, a subject
of much theoretical and
practical interest.
Books:
1.
H. O. Fattorini, The Cauchy Problem, Encyclopedia of Mathematics and its
Applications
vol 18, Addison-Wesley 1983.
2.
H. O. Fattorini Second Order Linear Differential Equations in Banach Spaces,
Notas
de Matem‡tica vol. 99, Elsevier - North Holland 1985.
3. H. O. Fattorini, Infinite Dimensional
Optimization and Control Theory,
Encyclopedia of Mathematics and its Applications
vol. 62, Cambridge University
Press, 1999.
4.
H. O. Fattorini, Infinite Dimensional Optimization and Control Theory (reprint
edition
of 3), Beijing World Publishing Company, Beijing, 2001.
5.
H. O. Fattorini, Infinite Dimensional Linear Control Systems; the Time Optimal
and
Norm Optimal Problems, North-Holland Mathematical Studies vol 201,
Elsevier,
Amsterdam 2005.
1. H.
O. Fattorini, Some remarks on the
time optimal control problem in infinite
dimension,
Calculus of Variations and Optimal Control (Proc. International
Conference
on Calculus of Variations and Related Topics, Haifa, 1998, Chapman
&
Hall/CRC Research Notes in Mathematics Series, Vol. 411, CRC Press, Boca
Raton
(1999) 77-96.
2.
H. O. Fattorini, The maximum principle in infinite dimension, Discrete &
Continuous
Dynamical Systems 6 (2000) 557-574.
3.
H. O. Fattorini, The maximum principle for control systems described by linear
parabolic
equations, Jour. Math. Anal. Appl. 259 (2001) 630-651.
4.
H. O. Fattorini, A survey of the time optimal problem and the norm optimal
problem
in infinite dimension, Cubo Mat. Educational 3 (2001) 147-169.
5.
H. O. Fattorini, Existence of singular extremals and singular functionals in
reachable
spaces, Jour. Evolution Equations 1 (2001) 325-347.
6.
H. O. Fattorini, Time optimality and the maximum principle in infinite
dimension, Optimization 50 (2001) 361-385.
7.
H. O. Fattorini, Time and norm optimal controls for linear parabolic equations:
necessary
and sufficient conditions, Control
and Estimation of Distributed
Parameter
Systems, Proc. International Conference, Maria Trost, 2001, Int.
Series
of Numerical Math. vol. 143,
BirkhŠuser,Basel (2002) 151-168.
8.
H. O. Fattorini, Optimal control of diffusions, Applied Math & Optimization 46
(2002)
207-230.
9.
H. O. Fattorini, Vanishing of the costate in Pontryagin's maximum principle
and
singular time optimal controls,
Jour. Evolution Equations 4 (2004) 99-123.
10.
H. O. Fattorini, Sufficiency of the maximum principle for time optimality,
Cubo:
A Mathematical Journal 7 (2005) 27-37.
11.
H. O. Fattorini, Smoothness of the costate and the target in the time and
norm
optimal problems, Optimization 55 (2006) 19-36.
To appear:
12.
H. O. Fattorini, Linear Control Systems in Sequence Spaces, to appear in
Gunter
Lumer Memorial Volume (BirkhŠuser, Basel) preprint
13.
H. O. Fattorini, Regular and strongly regular time and norm optimal
controls,
to appear in Cubo: A Mathematical Journal preprint