Premium
Finite‐dimensional approximation for optimal fixed‐order compensation of distributed parameter systems
Author(s) -
Bernstein Dennis S.,
Rosen I. Gary
Publication year - 1990
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660110102
Subject(s) - optimal projection equations , linear quadratic gaussian control , finite element method , projection (relational algebra) , distributed parameter system , optimal control , controller (irrigation) , mathematics , model order reduction , control theory (sociology) , mathematical optimization , convergence (economics) , galerkin method , reduction (mathematics) , computer science , partial differential equation , mathematical analysis , algorithm , control (management) , engineering , artificial intelligence , structural engineering , agronomy , geometry , economic growth , biology , economics
In controlling distributed parameter systems it is often desirable to obtain low‐order, finite‐dimensional controllers in order to minimize real‐time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite‐dimensional approximation of the infinite‐dimensional Bernstein/Hyland optimal projection theory. Our approach yields fixed‐finite‐order controllers which are optimal with respect to high‐order, approximating, finite‐dimensional plant models. We illustrate the technique by computing a sequence of first‐order controllers for one‐dimensional, single‐input/single‐output parabolic (heat/diffusion) and hereditary systems using a spline‐based, Ritz‐Galerkin, finite element approximation. Our numerical studies indicate convergence of the feedback gains with less than 2% performance degradation over full‐order LQG controllers for the parabolic system and 10% degradation for the hereditary system.