A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators
Systems and Control
2017-10-11 v1
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.
Keywords
Cite
@article{arxiv.1710.03723,
title = {A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators},
author = {Pedro Ascencio and Alessandro Astolfi and Thomas Parisini},
journal= {arXiv preprint arXiv:1710.03723},
year = {2017}
}