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The stabilizability to trajectories of the Schl\"ogl model is investigated inthe norm of the natural state space for strong solutions, which is strictlycontained in the standard pivot space of square integrable functions. Asactuators a finite number of indicator functions are used and the control inputis subject to a bound constraint. A stabilizing saturated explicit feedbackcontrol is proposed, where the set of actuators and the input bound areindependent of the targeted trajectory. Further, the existence of open-loopoptimal stabilizing constrained controls and related first-order optimalityconditions are investigated. These conditions are then used to computestabilizing receding horizon based controls. Results of numerical simulationsare presented comparing their stabilizing performance with that of saturatedexplicit feedback controls.

Global stabilizability to trajectories for the Schl\"ogl equation in a Sobolev norm