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EnglishThis paper deals with backstepping design for boundary PDE control/observer as a convex optimization problem. Both Volterra and Fredholm operators are analysed for a class of parabolic and hyperbolic PDEs. The resulting Kernel-PDEs are formulated in terms of polynomial functions, the parameters of which are optimized using Sum-of-Squares (SOS) techniques and solved via semidefinite programming. Uniqueness and invertibility of the Fredholm-type transformation are proven for polynomial Kernels in the space of real-analytic functions. The inverse kernels are approximated as the optimal solution of a SOS and moment problem. The effectiveness of this approach is illustrated by numerical simulations.
| Titolo: | Backstepping PDE Design, Volterra and Fredholm Operators: a Convex Optimization Approach |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Abstract: | This paper deals with backstepping design for boundary PDE control/observer as a convex optimization problem. Both Volterra and Fredholm operators are analysed for a class of parabolic and hyperbolic PDEs. The resulting Kernel-PDEs are formulated in terms of polynomial functions, the parameters of which are optimized using Sum-of-Squares (SOS) techniques and solved via semidefinite programming. Uniqueness and invertibility of the Fredholm-type transformation are proven for polynomial Kernels in the space of real-analytic functions. The inverse kernels are approximated as the optimal solution of a SOS and moment problem. The effectiveness of this approach is illustrated by numerical simulations. |
| Handle: | http://hdl.handle.net/11368/2851520 |
| ISBN: | 9781479978854 9781479978861 |
| URL: | http://ieeexplore.ieee.org/document/7403330/ |
| Appare nelle tipologie: | 4.1 Contributo in Atti Convegno (Proceeding) |
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| Ascencio_Astolfi_Parisini_CDC2015.pdf | pdf editoriale | Publisher-Version | Digital Rights Management non definito | Administrator Richiedi una copia |
http://hdl.handle.net/11368/2851520
