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A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators (1710.03723v1)
Published 10 Oct 2017 in cs.SY
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.