Stabilization of Reaction-Diffusion PDE Distributed Actuation and Input Delay | IEEE Conference Publication | IEEE Xplore

Stabilization of Reaction-Diffusion PDE Distributed Actuation and Input Delay


Abstract:

This paper pursuits control design for an unstable reaction-diffusion equation with arbitrarily large input delay affecting the in-domain actuator. A transport PDE whose ...Show More

Abstract:

This paper pursuits control design for an unstable reaction-diffusion equation with arbitrarily large input delay affecting the in-domain actuator. A transport PDE whose solution captures the effect of the time delay is introduced resulting in an extended spatial domain in which two PDEs are in cascade. More precisely, a coupled system containing the considered system without explicit delay and a transport PDE is derived. We apply the PDE backstepping method to design a controller which compensates the effect of the delay, for the coupled system. A Dirac delta function is employed as an initial condition of the kernel functions which are the control gains weighting the state feedback, so that the in domain input delay can be compensated. The compensated feedback control achieves exponential stability in H1 norm for the system. A numerical simulation illustrates the effectiveness of the control design.
Date of Conference: 17-19 December 2018
Date Added to IEEE Xplore: 20 January 2019
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Conference Location: Miami, FL, USA

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