  We consider the problem of shaping the transient step response of nonlinear
systems to satisfy a class of integral constraints. Such constraints are
inherent in hybrid energy systems consisting of energy sources and storage
elements. While typical transient specifications aim to minimize overshoot,
this problem is unique in that it requires the presence of an appreciable
overshoot to satisfy the foregoing constraints. The problem was previously
studied in the context of stable linear systems. A combined integral and
feedforward control, that requires minimal knowledge of the plant model, was
shown to make the system amenable to meeting such constraints. This paper
extends that work to nonlinear systems and proves the effectiveness of the same
compensation structure under added conditions. Broadly, it is shown that the
integral constraint is satisfied when this compensation structure is applied to
nonlinear systems with stable open-loop step response and a positive DC gain.
However, stability of the resulting closed-loop system mandates bounds on the
controller gain.
