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Structure of approximate solutions for a class of optimal control systems

Zaslavski A. J.

Journal of Mathematics and Applications

2011

Vol. 34

135--149

We study a turnpike property of approximate solutions of a discrete-time control system with a compact metric space of states which arises in economic dynamics. To have this property means that the approximate solutions of the optimal control problems are determined mainly by an objective function, and are essentially independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike property is stable under perturbations of an objective function.

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.