  Suboptimal methods in optimal control arise due to a limited computational
budget, unknown system dynamics, or a short prediction window among other
reasons. Although these methods are ubiquitous, their transient performance
remains relatively unstudied. We consider the control of discrete-time,
nonlinear time-varying dynamical systems and establish sufficient conditions to
analyze the finite-time closed-loop performance of such methods in terms of the
additional cost incurred due to suboptimality. Finite-time guarantees allow the
control design to distribute a limited computational budget over a time horizon
and estimate the on-the-go loss in performance due to sub-optimality. We study
exponential incremental input-to-state stabilizing policies, and show that for
nonlinear systems, under some mild conditions, this property is directly
implied by exponential stability without further assumptions on global
smoothness. The analysis is showcased on a suboptimal model predictive control
use case.
