Local Stabilization of an Unstable Parabolic Equation via Saturated Controls
Andrii Mironchenko, Christophe Prieur, Fabian Wirth
Abstract
We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control, and with different types of saturations. The efficiency of the proposed method is demonstrated by means of numerical simulations.
Topics & Concepts
MathematicsScalar (mathematics)Control theory (sociology)Lyapunov functionLyapunov equationLinear systemBilinear interpolationBoundary (topology)Stability (learning theory)Applied mathematicsMathematical analysisNonlinear systemControl (management)Computer sciencePhysicsGeometryArtificial intelligenceQuantum mechanicsMachine learningStatisticsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods for differential equations