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It is shown that there exist a finite number of indicator functions, whichallow us to track an arbitrary given trajectory of the Schl\"ogl model, bymeans of an explicit saturated feedback control input whose magnitude isbounded by a constant independent of the given targeted trajectory. Simulationsare presented showing the stabilizing performance of the explicit feedbackconstrained control. Further, such performance is compared to that of areceding horizon constrained control minimizing the classical energy costfunctional.

Saturated feedback stabilizability to trajectories for the Schl\"{o}gl parabolic equation