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arXiv · 1710.03723

A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators

Pedro Ascencio·Alessandro Astolfi·Thomas Parisini
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Abstract

Backstepping design for boundary linear 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 non-strict 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(SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.

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Pedro Ascencio, Alessandro Astolfi, Thomas Parisini. 2017-10-10. A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators. https://arxiv.org/abs/1710.03723

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