Guaranteed cost synchronous control of time-varying delay cellular neural networks

• Published in: Neural computing & applications Vol. 22; no. 1; pp. 103 - 110
• Main Authors: Tu, Jianjun, He, Hanlin, Xiong, Ping
• Format: Journal Article
• Language: English
• Published: London Springer-Verlag 01.01.2013; Springer
• Subjects: Applied sciences; Artificial Intelligence; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Computer science; control theory; systems; Data Mining and Knowledge Discovery; Exact sciences and technology; Global analysis, analysis on manifolds; Image Processing and Computer Vision; Learning and adaptive systems; Mathematical analysis; Mathematics; Ordinary differential equations; Original Article; Probability and Statistics in Computer Science; Sciences and techniques of general use; Sequences, series, summability; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Guaranteed cost control; Time-varying delay; Saturation; Cellular neural network; Synchronous control; Cost minimization; Neural computation; Solving; Cellular neural nets; Optimization method; Interior point method; Neural network; Controller; Synchronization; Algorithm; Optimization; Synthesis; Experimental design; Linear matrix inequality; Lyapunov stability; Matrix method; Delay time; Chaotic systems
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-011-0667-6

This paper deals with the synchronization of time-varying delay cellular neural networks. Based on the Lyapunov stability analysis and the zoned discussion and maximax synthesis (ZDMS) method, the quadratic matrix inequality (QMI) criterion for the guaranteed cost synchronous controller is designed to synchronize the given chaotic systems. For the convenience to solve, using a generalized result of Schur complement, the criterion in the form of QMI is turned into the linear matrix inequality (LMI) form, which can be used efficiently via existing numerical convex optimization algorithms such as the interior-point algorithms for solving LMIs. The minimization of the guaranteed cost is further studied, and the corresponding LMI criterion for getting the controller is given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost synchronous control and its corresponding minimization problem.