Structure Of Approximate Solutions Research Articles

Structure of approximate solutions of Bolza variational problems on large intervals

In this paper we study the structure of approximate solutions of autonomous Bolza variational problems on large finite intervals. We show that approximate solutions are determined mainly by the integrand, and are essentially independent of the choice of time interval and data.

Convergence of Extremals of Variational Problems on Large Intervals

Abstract We study the structure of approximate solutions of autonomous variational problems on large finite intervals. In our previous research 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 study the convergence of approximate solutions to solutions of the corresponding infinite horizon problems, in regions close to the endpoints of the time intervals.

Structure of Solutions of Variational Problems with Extended-Valued Integrands in the Regions Close to the Endpoints

We study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous extended-valued integrand. In our recent research 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 study the structure of approximate solutions in regions close to the endpoints of the time intervals.

Structure of extremals of variational problems in the regions close to the endpoints

We study the structure of approximate solutions of autonomous variational problems on large finite intervals. In our research which was summarized in Zaslavski, Turnpike properties in the calculus of variations and optimal control, Springer, New York, 2006 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 study the structure of approximate solutions in regions close to the endpoints of the time intervals.

Structure of approximate solutions of dynamic continuous time zero-sum games

In this paper we study a turnpike property of approximate solutions for a class of dynamic continuous-time two-player zero-sum games. These properties describe the structure of approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

Turnpike Results for a Class of Discrete-Time Optimal Control Problems Arising in Economic Dynamics

In this paper we establish turnpike results for a class of discrete-time optimal control problems. These control problems arise in economic dynamics and describe a nonstationary model proposed by Robinson, Solow and Srinivasan. We study the structure of approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

Solutions for a class of optimal control problems with time delay, part 1

The optimal control of a system whose state is governed by a nonlinear autonomous Volterra integrodifferential equation with unbounded time interval is considered. Specifically, it is assumed that the delay occurs only in the state variable. We are concerned with the existence of an overtaking optimal trajectory over an infinite horizon. The existence result that we obtain extends the result of Carlson (Ref. 1) to a situation where the trajectories are not necessary bounded. Also, we study the structure of approximate solutions for the problem on a finite interval.