Stability of a turnpike phenomenon for approximate solutions of nonautonomous discrete-time optimal control systems

We study turnpike properties of approximate solutions of nonautonomous discrete-time optimal control systems which are determined by sequences of lower semicontinuous objective functions. To have these properties means that the approximate solutions of the problems are determined mainly by the objective functions, and are essentially independent of the choice of intervals and endpoint conditions, except in regions close to the endpoints. We show that these turnpike properties are stable under small perturbations of the objective functions.