Circulation Design for Eigenvalue Replacement: Minimizing Gain Magnitude

Duan, Guang-Ren1,2

2023-08-01

10.1109/TSMC.2023.3300905

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS   Impact Factor & Quartile

2168-2216

2168-2232

Based on a complete parametric partial eigenstructure assignment (ESA) approach, a circulation design for ESA in a stabilizable linear system via state feedback is proposed. It is shown that, in those rounds where a real open-loop eigenvalue of order 1 is replaced, a type of very general indices can be globally minimized, which include those for general eigenvector configuration and gain magnitude minimization as special cases. When all the open-loop eigenvalues to be replaced are real and are of order 1, the proposed circulation design turns out to be extremely simple and efficient, and also possesses good numerical reliability since the globally optimal solution is established in a simple, direct, and explicit form, and the proposed circulation algorithms remove completely matrix inverse operations. An illustrative example demonstrates the simplicity and effect of the proposed approach.

Eigenvalues and eigenfunctions Indexes Linear systems State feedback Programming Minimization Control theory Circulation designs globally optimal solutions minimum gain feedback multivariable linear systems partial eigenstructure assignment (ESA)

SCI

English

First ; Corresponding

Shenzhen Key Laboratory of Control Theory and Intelligent Systems[ZDSYS20220330161800001] ; Science Center Program of the National Natural Science Foundation of China[62188101] ; Major Program of National Natural Science Foundation of China["61690210","61690212"] ; National Natural Science Foundation of China[61333003]

Automation & Control Systems ; Computer Science

Automation & Control Systems ; Computer Science, Cybernetics

WOS:001060581300001

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

Web of Science

1.Southern Univ Sci & Technol, Shenzhen Key Lab Control Theory & Intelligent Syst, Shenzhen 518055, Peoples R China
2.Harbin Inst Technol, Ctr Control Theory & Guidance Technol, Harbin 150001, Peoples R China

Duan, Guang-Ren. Circulation Design for Eigenvalue Replacement: Minimizing Gain Magnitude[J]. IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS,2023.

Duan, Guang-Ren.(2023).Circulation Design for Eigenvalue Replacement: Minimizing Gain Magnitude.IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS.

Duan, Guang-Ren."Circulation Design for Eigenvalue Replacement: Minimizing Gain Magnitude".IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS (2023).