Optimal cost convergence with respect to the time horizon

The asymptotic behaviour of the optimal cost for problems with increasing time horizon is studied. The dynamics and costs are general nonlinear, possibly with state and control constraints. Apart from basic consistency assumptions, a uniform detectability hypothesis provides the setup for the analysis, which is based on direct evaluations of bounds for costs and trajectories. This investigation is motivated by approximations to infinite horizon problems that would require large amount of computational effort, and by the stability study of receding horizon control problems.