Backstepping PDE Design: A Convex Optimization Approach

Autor: Alessandro Astolfi, Thomas Parisini, Pedro Ascencio
Přispěvatelé: Ascencio, P., Astolfi, A., Parisini, T.
Rok vydání: 2018
Předmět:
0209 industrial biotechnology
Polynomial
Mathematical optimization
Backstepping control
MathematicsofComputing_NUMERICALANALYSIS
02 engineering and technology
01 natural sciences
symbols.namesake
020901 industrial engineering & automation
Settore ING-INF/04 - Automatica
0102 Applied Mathematics
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Applied mathematics
0101 mathematics
Electrical and Electronic Engineering
Mathematics
Semidefinite programming
Partial differential equation
010102 general mathematics
0906 Electrical And Electronic Engineering
Hilbert space
Computer Science Applications
Industrial Engineering & Automation
Control and Systems Engineering
Backstepping
Convex optimization
symbols
Convex function
Hyperbolic partial differential equation
0913 Mechanical Engineering
Zdroj: IEEE Transactions on Automatic Control
ISSN: 2334-3303
0018-9286
DOI: 10.1109/tac.2017.2757088
Popis: Backstepping design for boundary linear partial differential equation (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 nonstrict 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 decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the $\mathcal{L}^2$ -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.
Databáze: OpenAIRE
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