• Corpus ID: 240419814

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

@inproceedings{Azmi2021SaturatedFS,
  title={Saturated feedback stabilizability to trajectories for the Schl\"\{o\}gl parabolic equation},
  author={Behzad Azmi and Karl Kunisch and S{\'e}rgio S. Rodrigues},
  year={2021}
}
It is shown that there exist a finite number of indicator functions, which allow us to track an arbitrary given trajectory of the Schlögl 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… 

References

SHOWING 1-10 OF 49 REFERENCES

Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control

  • M. Slemrod
  • Mathematics
    Math. Control. Signals Syst.
  • 1989
A feedback control is derived, which forces the infinite-dimensional control systemdu/dt=Au+Bf, u(0)=uo≠H to have the asymptotic behavioru(t)→0 ast→∞ inH.

On Finite-Gain Stabilizability of Linear Systems Subject to Input Saturation

This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by

Local Stabilization of an Unstable Parabolic Equation via Saturated Controls

A saturated feedback control is derived, which locally stabilizes a linear reaction-diffusion equation and provides estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities.

Oblique projection based stabilizing feedback for nonautonomous coupled parabolic-ode systems

Global feedback stabilizability results are derived for nonautonomous coupled systems arising from the linearization around a given time-dependent trajectory of FitzHugh-CNagumo type systems. The

Feedback Boundary Stabilization to Trajectories for 3D Navier–Stokes Equations

Given a nonstationary trajectory of the Navier–Stokes system, a finite-dimensional feedback boundary control stabilizing locally the system to the given trajectory is derived. Moreover the control is

Internal stabilization of Navier-Stokes equations with finite-dimensional controllers

The steady-state solutions to Navier-Stokes equations on Ω ⊂ R d , d = 2, 3, with no-slip boundary conditions, are locally exponentially stabilizable by a finite-dimensional feedback controller with

A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations

The stability and suboptimality of the unconstrained receding horizon framework is studied, which leads to a nonsmooth infinite-horizon problem which provides stabilizing optimal controls with a low number of active actuators over time.

Learning an Optimal Feedback Operator Semiglobally Stabilizing Semilinear Parabolic Equations

Stabilizing feedback operators are presented which depend only on the orthogonal projection of the state onto the finite-dimensional control space. A class of monotone feedback operators mapping the

Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier-Stokes Equations

It is shown that the control constructed for the linear problem stabilizes locally also the full Navier–Stokes system, based on a truncated observability inequality, the regularizing property for thelinearized equation, and some standard techniques of the optimal control theory.