  The stabilizability to trajectories of the Schl\"ogl model is investigated in
the norm of the natural state space for strong solutions, which is strictly
contained in the standard pivot space of square integrable functions. As
actuators a finite number of indicator functions are used and the control input
is subject to a bound constraint. A stabilizing saturated explicit feedback
control is proposed, where the set of actuators and the input bound are
independent of the targeted trajectory. Further, the existence of open-loop
optimal stabilizing constrained controls and related first-order optimality
conditions are investigated. These conditions are then used to compute
stabilizing receding horizon based controls. Results of numerical simulations
are presented comparing their stabilizing performance with that of saturated
explicit feedback controls.
