838 research outputs found

    A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances

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    This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers' equation. The developed approach is a combination of the method of De~Giorgi iteration and the technique of Lyapunov functionals by adequately splitting the original problem into two subsystems. The ISS properties in L2L^2-norm for Burgers' equation have been established using this method. Moreover, as an application of De~Giorgi iteration, ISS in L∞L^\infty-norm w.r.t. in-domain disturbances and actuation errors in boundary feedback control for a 1-DD {linear} {unstable reaction-diffusion equation} have also been established. It is the first time that the method of De~Giorgi iteration is introduced in the ISS theory for infinite dimensional systems, and the developed method can be generalized for tackling some problems on multidimensional spatial domains and to a wider class of nonlinear {partial differential equations (PDEs)Comment: This paper has been accepted for publication by IEEE Trans. on Automatic Control, and is available at http://dx.doi.org/10.1109/TAC.2018.2880160. arXiv admin note: substantial text overlap with arXiv:1710.0991

    Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Time-dependent Reactivity

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    This paper presents an event-triggered boundary control strategy for a class of reaction-diffusion PDEs with time-varying reactivity under Robin actuation. The control approach consists of a backstepping full-state feedback boundary controller and a dynamic event-triggering condition, which determines the time instants when the control input needs to be updated. It is proved that under the proposed event-triggered boundary control approach, there is a uniform minimal dwell-time between two event times. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to zero in L2L^2-sense are established. A simulation is conducted to validate the theoretical developments
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