Late-lumping backstepping control of partial differential equations. (English) Zbl 1411.93158
Summary: We consider in this paper three different Partial Differential Equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. The backstepping controllers are approximated and it is proven that the finite-dimensional approximated controller stabilizes the original system if the order is high enough. This approach is known as late-lumping. The other approach to controller design for PDEs first approximates the PDE and then a controller is designed; this is known as early-lumping. Simulation results comparing the performance of late-lumping and early-lumping controllers are provided.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
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