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

TL;DR

This paper demonstrates that finite indicator functions enable explicit saturated feedback control to track trajectories of the Schlögl parabolic equation, with bounded control magnitude, and compares its effectiveness to receding horizon control.

Contribution

It introduces a finite set of indicator functions for explicit saturated feedback stabilization of the Schlögl model trajectories, providing a novel control approach with bounded inputs.

Findings

Explicit feedback control effectively stabilizes trajectories.

Control magnitude remains bounded independently of the target trajectory.

Simulation results confirm the stabilizing performance and comparison with receding horizon control.

Abstract

It is shown that there exist a finite number of indicator functions, which allow us to track an arbitrary given trajectory of the Schl\"ogl model, by means of an explicit saturated feedback control input whose magnitude is bounded by a constant independent of the given targeted trajectory. Simulations are presented showing the stabilizing performance of the explicit feedback constrained control. Further, such performance is compared to that of a receding horizon constrained control minimizing the classical energy cost functional.