A sampled-data control problem of neural-network-based systems using an improved free-matrix-based inequality

Abstract In this work, a sampled-data control problem for neural-network-based systems with an optimal guaranteed cost is investigated. By constructing suitable time-dependent functionals and utilizing an improved free-matrix-based integral inequality, a sampled-data stability criterion for neural-network-based systems is derived. Based on a first result, a sampled-data controller design method for neural-network-based systems that meets the maximum sampling period and minimum guaranteed cost performance is proposed. The superiority and validity of the results will be verified by comparing with the existing results in a numerical example.

[1]  Kazuo Tanaka,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities , 1996, IEEE Trans. Fuzzy Syst..

[2]  Yang Cao,et al.  Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays , 2018, J. Frankl. Inst..

[3]  Dragan Nesic,et al.  Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems , 2009, IEEE Transactions on Automatic Control.

[4]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Jinde Cao,et al.  Global exponential stability and dissipativity of generalized neural networks with time-varying delay signals , 2017, Neural Networks.

[6]  Dragan Nesic,et al.  Input-output stability properties of networked control systems , 2004, IEEE Transactions on Automatic Control.

[7]  Myeong-Jin Park,et al.  Weighted Consensus Protocols Design Based on Network Centrality for Multi-Agent Systems With Sampled-Data , 2017, IEEE Transactions on Automatic Control.

[8]  Ju H. Park,et al.  Further results on stabilization of neural-network-based systems using sampled-data control , 2017 .

[9]  Feng-Hsiag Hsiao,et al.  Stability analysis of neural-network interconnected systems , 2003, IEEE Trans. Neural Networks.

[10]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[11]  Youyi Wang,et al.  Stabilization for Sampled-Data Neural-Network-Based Control Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[13]  Ricardo G. Sanfelice,et al.  Hybrid Dynamical Systems: Modeling, Stability, and Robustness , 2012 .

[14]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[15]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[16]  Tae H. Lee,et al.  Improved criteria for sampled-data synchronization of chaotic Lur’e systems using two new approaches , 2017 .

[17]  Euntai Kim,et al.  A new approach to fuzzy modeling , 1997, IEEE Trans. Fuzzy Syst..

[18]  Rathinasamy Sakthivel,et al.  Advanced sampled-data synchronization control for complex dynamical networks with coupling time-varying delays , 2017, Inf. Sci..

[19]  Shengyuan Xu,et al.  Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[21]  Peng Shi,et al.  Exponential Stabilization for Sampled-Data Neural-Network-Based Control Systems , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Corentin Briat,et al.  A looped-functional approach for robust stability analysis of linear impulsive systems , 2012, Syst. Control. Lett..

[23]  Seong-Gon Choi,et al.  Betweenness Centrality-Based Consensus Protocol for Second-Order Multiagent Systems With Sampled-Data , 2017, IEEE Transactions on Cybernetics.

[24]  Jinde Cao,et al.  Design of extended dissipativity state estimation for generalized neural networks with mixed time-varying delay signals , 2018, Inf. Sci..

[25]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[26]  Dong Yue,et al.  Stabilization of Neural-Network-Based Control Systems via Event-Triggered Control With Nonperiodic Sampled Data , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[28]  Ju H. Park,et al.  Further results on sampled-data control for master–slave synchronization of chaotic Lur’e systems with time delay , 2015 .

[29]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[30]  H.K. Lam,et al.  Design and stabilization of sampled-data neural-network-based control systems , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[31]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[32]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..

[33]  Seung-Hoon Lee,et al.  Synchronization criteria for delayed Lur'e systems and randomly occurring sampled-data controller gain , 2019, Commun. Nonlinear Sci. Numer. Simul..

[34]  Jinde Cao,et al.  Stochastic sampled-data stabilization of neural-network-based control systems , 2015 .

[35]  Ju H. Park,et al.  Stability Analysis of Sampled-Data Systems via Free-Matrix-Based Time-Dependent Discontinuous Lyapunov Approach , 2017, IEEE Transactions on Automatic Control.

[36]  J. Daafouz,et al.  Stabilization of linear impulsive systems through a nearly-periodic reset , 2013 .

[37]  Jinde Cao,et al.  An Arcak-type state estimation design for time-delayed static neural networks with leakage term based on unified criteria , 2018, Neural Networks.

[38]  João Pedro Hespanha,et al.  Exponential stability of impulsive systems with application to uncertain sampled-data systems , 2008, Syst. Control. Lett..

[39]  Ricardo O. Carelli,et al.  Neural networks for advanced control of robot manipulators , 2002, IEEE Trans. Neural Networks.