Name
Abstract | ||
|---|---|---|
We consider a control problem of an unstable reaction-diffusion parabolic PDE cascaded with a heat equation through a boundary, where the heat influx of the heat equation is fed into the temperature of the reaction-diffusion equation, and the control actuator is designed at the other boundary of the heat equation. A backstepping invertible transformation is used to design a suitable boundary feedback control so that the closed-loop system is equivalent to a target system of PDE-PDE cascades, which is shown to be exponentially stable in some Hilbert space. With the boundary input from the heat equation, the reaction-diffusion PDE is shown to be exponentially stable in H-1(0, 1), and the stability of the heat equation is shown to be characterized in terms of a subspace of H1(0, 1) rather than the usual L2(0, 1). © 2013 AACC American Automatic Control Council. |
Year | DOI | Venue |
|---|---|---|
2013 | null | ACC |
Keywords | Field | DocType |
stability analysis,partial differential equations,exponential stability,heating,backstepping,heat equation,parabolic equations,asymptotic stability,actuators,feedback,kernel | Parabolic partial differential equation,Backstepping,Control theory,Heat kernel,FTCS scheme,Control engineering,Exponential stability,Heat equation,Reaction–diffusion system,Partial differential equation,Mathematics | Conference |
Volume | Issue | ISSN |
null | null | null |
Citations | PageRank | References |
0 | 0.34 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jun-Min Wang | 1 | 219 | 29.95 |
| Ling-Ling Su | 2 | 11 | 2.62 |
| Hanxiong Li | 3 | 2519 | 157.48 |