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Convergence of approximate solutions of variational problems

Zaslavski A. J.

Control and Cybernetics

2009

Vol. 38, no 4B

1607-1629

We study the structure of approximate solutions of autonomous variational problems on large finite intervals. In our previous research, which was summarized in Zaslavski (2006b), we showed that approximate solutions are determined mainly by the integrand, and are essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time interval. In the present paper we establish convergence of approximate solutions in regions close to the endpoints of the time intervals.

Turnpike properties of approximate solutions of autonomous variational problems

Zaslavski A. J.

Control and Cybernetics

2008

Vol. 37, no 2

491-512

In this work we study the structure of approximate solutions of autonomous variational problems with vector-valued functions. We are interested in turnpike properties of these solutions, which are independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike properties are stable under small perturbations of integrands.