Appl Math Optim 37:127–149 (1998)
1998 Springer-Verlag New York Inc.
Optimal Solutions of Linear Periodic Control Systems
with Convex Integrands
A. J. Zaslavski and A. Leizarowitz
Department of Mathematics, Technion—Israel Institute of Technology,
Haifa 32000, Israel
Communicated by D. Kinderlehrer
Abstract. In this work we study the existence and asymptotic behavior of over-
taking optimal trajectories for linear control systems with convex integrands. We
extend the results obtained by Artstein and Leizarowitz for tracking periodic prob-
lems with quadratic integrands  and establish the existence and uniqueness of
optimal trajectories on an inﬁnite horizon. The asymptotic dynamics of ﬁnite time
optimizers is examined.
Key Words. Inﬁnite horizon, Overtaking optimality criterion, Turnpike property.
AMS Classiﬁcation. Primary 49J15, Secondary 93C15.
The study of optimal control problems deﬁned on inﬁnite intervals has recently been a
rapidly growing area of research (see – and ). These problems arise in various
areas of research, e.g., in engineering (see  and ), in models of economic growth
(see  and ), and in continuum mechanics (see  and ).
In this paper we analyze the existence and asymptotic behavior of optimal tra-
jectories for a linear control system with a convex cost function. The system under
This research was supported in part by a grant from the Ministry of Science and the “MA-AGARA”—
special project for absorption of new immigrants in the Department of Mathematics, Technion. It was also
supported in part by the fund for the promotion of research at the Technion.