  Limited bandwidth and limited saturation in actuators are practical concerns
in control systems. Mathematically, these limitations manifest as constraints
being imposed on the control actions, their rates of change, and more
generally, the global behavior of their paths. While the problem of actuator
saturation has been studied extensively, little attention has been devoted to
the problem of actuators having limited bandwidth. While attempts have been
made in the direction of incorporating frequency constraints on state-action
trajectories before, rate constraints on the control at the design stage have
not been studied extensively in the discrete-time regime. This article
contributes toward filling this lacuna. In particular, we establish a new
discrete-time Pontryagin maximum principle with rate constraints being imposed
on the control trajectories, and derive first-order necessary conditions for
optimality. A brief discussion on the existence of optimal control is included,
and numerical examples are provided to illustrate the results.
