Backstepping PDE design: a convex optimization approach
File(s)
Accepted version
Author(s)
Ascencio, Pedro
Astolfi, A
Parisini, T
Type
Journal Article
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. 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.
Date Issued
2018-07-01
Date Acceptance
2017-09-15
Citation
IEEE Transactions on Automatic Control, 2018, 63 (7), pp.1943-1958
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
1943
End Page
1958
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
63
Issue
7
Replaces
10044/1/51032
Copyright Statement
© 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.
Subjects
0906 Electrical And Electronic Engineering
0102 Applied Mathematics
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published
Date Publish Online
2017-09-27