Backstepping PDE Design: A Convex Optimization Approach
| Main Author: | Ascencio, Pedro; Astolfi, Alessandro; Parisini, Thomas |
|---|---|
| Format: | Article Journal |
| Terbitan: |
, 2017
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/1321752 |
Daftar Isi:
- Backstepping design for boundary linear partial differential equation (PDE) is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to nonstrict feedback structures. Based on the compactness of the Volterra- and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using sum-of-squares decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L 2 -norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.
- © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. P. Ascencio, A. Astolfi and T. Parisini, "Backstepping PDE Design: A Convex Optimization Approach," in IEEE Transactions on Automatic Control, vol. 63, no. 7, pp. 1943-1958, July 2018. doi: 10.1109/TAC.2017.2757088.