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| Feedback Stabilization for a Scalar Conservation Law with PID Boundary Control |
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Citation： |
Jean Michel CORON,Simona Oana TAMASOIU.Feedback Stabilization for a Scalar Conservation Law with PID Boundary Control[J].Chinese Annals of Mathematics B,2015,36(5):763~776 |
| Page view： 1227
Net amount： 983 |
Authors： |
Jean Michel CORON; Simona Oana TAMASOIU |
Foundation： |
This work was supported by the ERC Advanced Grant 266907
(CPDENL) of the 7th Research Framework Programme (FP7), FIRST,
Initial Training Network of the European Commission (No.238702)
and PITN-GA-2009-238702. |
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| Abstract： |
This paper deals with a scalar conservation law in 1-D space
dimension, and in particular, the focus is on the stability analysis
for such an equation. The problem of feedback stabilization under
proportional-integral-derivative (PID for short) boundary control is
addressed. In the proportional-integral (PI for short) controller
case, by spectral analysis, the authors provide a complete
characterization of the set of stabilizing feedback parameters, and
determine the corresponding time delay stability interval. Moreover,
the stability of the equilibrium is discussed by Lyapunov function
techniques, and by this approach the exponential stability when a
damping term is added to the classical PI controller scheme is
proved. Also, based on Pontryagin results on stability for
quasipolynomials, it is shown that the closed-loop system subject to
PID control is always unstable. |
Keywords： |
Boundary feedback, PID controllers, Linear scalar conservation law |
Classification： |
93B52, 93D15, 35L50 |
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