A neural network for linear matrix inequality problems

Author

Lin, Chun-Liang ; Lai, Chi-Chih ; Huang, Teng-Hsien

Author_Institution

Dept. of Autom. Control Eng., Feng Chia Univ., Taichung, Taiwan

Volume

11

Issue

5

fYear

2000

fDate

9/1/2000 12:00:00 AM

Firstpage

1078

Lastpage

1092

Abstract

Gradient-type Hopfield networks have been widely used in optimization problems solving. The paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities (LMIs), which are commonly encountered in the robust control system analysis and design. The solution process is parallel and distributed in neural computation. The proposed networks are proven to be stable in the large. Representative LMIs such as generalized Lyapunov matrix inequalities, simultaneous Lyapunov matrix inequalities, and algebraic Riccati matrix inequalities are considered. Several examples are provided to demonstrate the proposed results. To verify the proposed control scheme in real-time applications, a high-speed digital signal processor is used to emulate the neural-net-based control scheme

Keywords

Hopfield neural nets; Lyapunov matrix equations; Riccati equations; gradient methods; matrix algebra; robust control; algebraic Riccati matrix inequalities; generalized Lyapunov matrix inequalities; gradient-type Hopfield networks; high-speed digital signal processor; linear matrix inequality problems; matrix oriented gradient approach; neural-net-based control scheme; simultaneous Lyapunov matrix inequalities; Concurrent computing; Digital signal processors; Distributed computing; Linear matrix inequalities; Matrices; Neural networks; Problem-solving; Riccati equations; Robust control; System analysis and design;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.870041

Filename

870041