  This brief addresses the design of a Nonlinear Model Predictive Control
(NMPC) strategy for exponentially incremental Input-to-State Stable (ISS)
systems. In particular, a novel formulation is devised, which does not
necessitate the onerous computation of terminal ingredients, but rather relies
on the explicit definition of a minimum prediction horizon ensuring closed-loop
stability. The designed methodology is particularly suited for the control of
systems learned by Recurrent Neural Networks (RNNs), which are known for their
enhanced modeling capabilities and for which the incremental ISS properties can
be studied thanks to simple algebraic conditions. The approach is applied to
Gated Recurrent Unit (GRU) networks, providing also a method for the design of
a tailored state observer with convergence guarantees. The resulting control
architecture is tested on a benchmark system, demonstrating its good control
performances and efficient applicability.
