  In this work, we address the output--feedback control problem for nonlinear
systems under bounded disturbances using a moving horizon approach. The
controller is posed as an optimization-based problem that simultaneously
estimates the state trajectory and computes future control inputs. It minimizes
a criterion that involves finite forward and backward horizon with respect the
unknown initial state, measurement noises and control input variables and it is
maximized with respect the unknown future disturbances. Although simultaneous
state estimation and control approaches are already available in the
literature, the novelty of this work relies on linking the lengths of the
forward and backward windows with the closed-loop stability, assuming
detectability and decoding sufficient conditions to assure system
stabilizability. Simulation examples are carried out to compare the performance
of simultaneous and independent estimation and control approaches as well as to
show the effects of simultaneously solving the control and estimation problems.
