Extended dissipativity synchronization for Markovian jump recurrent neural networks via memory sampled-data control and its application to circuit theory

Document Type : Research Paper

Authors

1 Department of Mathematics, Sri Sarada College for Women (Autonomous), Salem 636016, India

2 Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket-83000, Thailand

3 Research Institute of Natural Science, Hanyang University, Seoul 04763, Korea

4 Intelligence Laboratory, Toyota Technological Institute, Nagoya, 468-8511, Japan

Abstract

 The problem of synchronization with extended dissipativity for Markovian Jump Recurrent Neural Networks (MJRNNs) is investigated. For MJRNNs, a new memory sampled-data extended dissipative control approach is suggested here. Some sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are acquired by suitably establishing a relevant Lyapunov - Krasovskii functional (LKF), wherein the master and the slave system of MJRNNs are quadratically stable. At last, a numerical section is provided, along with one of the applications in circuit theory that clearly illustrates the efficacy of the proposed method's performance.

Keywords

[1] C.K. Ahn, State estimation for T-S fuzzy Hopfield neural networks via strict output passivation of the error system, Int. J. Gen. Syst. 11 (2013) 503—518.
[2] M.S. Ali, R. Vadivel, A. Alsaedi and B. Ahmed, Extended dissipativity and event-triggered synchronization for T–S fuzzy Markovian jumping delayed stochastic neural networks with leakage delays via fault-tolerant control, Soft Comput. 24 (2020) 3675-–3694.
[3] M.S. Ali, N. Gunasekaran and R. Saravanakumar, Design of passivity and passification for delayed neural networks with Markovian jump parameters via non-uniform sampled-data control, Neural Computing and Applications, 30 (2018) 595-605.
[4] M. Syed Ali, N. Gunasekaran, M. Esther Rani, Robust stability of Hopfield delayed neural networks via an augmented LK functional, Neurocomput. 234 (2017) 198–204.
[5] N. Gunasekaran, N.M. Thoiyab, P. Muruganantham, G. Rajchakit and B. Unyong, Novel results on global robust stability analysis for dynamical delayed neural networks under parameter uncertainties, IEEE Access 8 (2020) 178108–178116.
[6] R. Anbuvithya, S. Dheepika Sri, R. Vadivel, N. Gunasekaran and P. Hammachukiattikul, Extended dissipativity and non-fragile synchronization for recurrent neural networks with multiple time-varying delays via sampled-data control, IEEE Access 9 (2021) 31454–31466.
[7] S. Arik, An improved robust stability result for uncertain neural networks with multiple time delays, Neural Networks 54 (2014) 1-–10.
[8] P. Baldi and A.F. Atiya, How delays affect neural dynamics and learning, IEEE Trans. Neural Netw. 5 (1994) 612—621.
[9] J. Cao, G. Chen and P. Li, Global synchronization in an array of delayed neural networks with hybrid coupling, IEEE Trans. Syst. ManCybernet. Part B 38 (2008) 488—498.
[10] J. Cao, A. Chen and X. Huang, Almost periodic attractor of delayed neural networks with variable coefficients, Phys. Lett. A 340 (2005) 104—120.
[11] L. Chao and L. Hong, Controllability of Boolean control networks under asynchronous stochastic update with time delay, J. Vib. Control 22 (2016) 235-–246.
[12] W.H. Chen and X. Lu, Mean square exponential stability of uncertain stochastic delayed neural networks, Phys. Lett. A 372 (2008) 1061—1069.
[13] Y. Ephraim and N. Merhav, Hidden Markov processes, IEEE Trans. Inform. Theory 48 (2002) 1518-–1569.
[14] M. Gupta, L. Jin and N. Homma, Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory, Wiley IEEE Press, 2013.
[15] G. Joya, M.A. Atencia and F. Sandoval, Hopfield neural networks for optimization: study of the different dynamics, Neurocomput. 43 (2012) 219—237.
[16] W. Jun, S. Kaibo, Q. Huang, S. Zhong and D. Zhang, Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout, Appl. Math. Comput., 335 (2018) 211-230.
[17] W.J. Li and T. Lee, Hopfield neural networks for affine invariant matching, IEEE Trans. Neural Netw. 12 (2001) 1400-–1410.
[18] T. Li, L. Guo and C. Sun, Robust stability for neural networks with time-varying delays and linear fractional uncertainties, Neurocomput. 71 (2017) 421—427.
[19] T.H. Lee and J.H. Park, Stability analysis of sampled-data systems via free-matrix-based time-dependent discontinuous Lyapunov approach, IEEE Trans. Autom. Control 62 (2017) 3653—3657.
[20] S. Long, Q. Song, X. Wang and D. Li, Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations, J. Franklin Inst. 349 (2012) 2461—2479.
[21] W. Lu and T. Chen, Global synchronization of discrete-time dynamical network with a directed graph, IEEE Trans. Circuits Syst. II 54 (2017) 136-–140.
[22] H. Lu, Chaotic attractors in delayed neural networks, Phys. Lett. 298 (2002) 109—116.
[23] P. Nystrup, H. Madsen and E. Lindstrom, Long memory of financial time series and hidden Markov models with time-varying parameters, J. Forecast. 36 (2016).
[24] P. Park, J. Ko and C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica 47 (2011) 235—238.
[25] J.H. Park, C.H. Park, O.M. Kwon and S.M. Lee, A new stability criterion for bidirectional associative memory neural networks of neutral-type, Neurocomput. (2008) 716-–722.
[26] H. Shen, Y. Zhu, L. Zhang and J.H. Park, Extended dissipative state estimation for Markov jump neural networks with unreliable links, IEEE Trans. Neural Netw. Learn. Syst. 28 (2017) 346-–358.
[27] L. Sun, Y. Tang, W. Wang, and S. Shen, Stability analysis of time-varying delay neural networks based on new integral inequalities, J. Franklin Inst. 357 (2020) 10828–10843.
[28] D. Tong, Q. Zhu, W. Zhou, Y. Xu and J. Fang, Adaptive synchronization for stochastic T-S fuzzy neural networks with time-delay and Markovian jumping parameters, Neurocomput. 117 (2013) 91-–97.
[29] R. Vadivel, P. Hammachukiattikul, N. Gunasekaran, R. Saravanakumar and H. Dutta, Strict dissipativity synchronization for delayed static neural networks: An event-triggered scheme, Chaos, Solitons & Fractals 150 (2021) 111212.
[30] R. Vadivel, S. Srinivasan, Y. Wu and N. Gunasekaran, Study on bifurcation analysis and TakagiSugeno fuzzy sampled-data stabilization of PMSM systems, Math. Meth. Appl. Sci. (2021) DOI: 10.22541/au.162220248.86155430/v1.
[31] R. Vadivel, R. Suresh, P. Hammachukiattikul, B. Unyong and N. Gunasekaran, Event-triggered L2–L∞ filtering for network-based Neutral systems with time-varying delays via T-S fuzzy approach, IEEE Access 9 (2021) 145133–145147.
[32] R. Vadivel, M. Syed Ali and H.J. Young, Drive-response synchronization of uncertain Markov jump generalized neural networks with interval time-varying delays via decentralized event-triggered communication scheme, J. Franklin Inst. 357(11) (2020) 6824–6857.
[33] H. Wei, R. Li, C. Chen and Z. Tu, Extended dissipative analysis for memristive neural networks with two additive time-varying delay components, Neurocomput. 216 (2016) 429–438.
[34] J. Zhang and C. Peng, Synchronization of master-slave neural networks with a decentralized event-triggered communication scheme, Neurocomput. 173 (2016) 1824—1831.
[35] M. Manigandan, S. Muthaiah, T. Nandhagopal, R. Vadivel, B. Unyong and N. Gunasekaran, Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order, AIMS Math. 1 (2022) 723–755.
[36] S. Elango, A. Tamilselvan, R. Vadivel, N. Gunasekaran, H. Zhu, J. Cao and X. Li, Finite difference scheme for singularly perturbed reaction-diffusion problem of partial delay differential equation with nonlocal boundary condition, Adv. Difference Equ. 1 (2021) 1–20.
[37] B. Unyong, A. Mohanapriya, A. Ganesh, G. Rajchakit, V. Govindan, R. Vadivel, N. Gunasekaran and C.P. Lim, Fractional Fourier transform and stability of fractional differential equation on Lizorkin space, Adv. Difference Equ. 1 (2021) 1–23.
[38] P. Hammachukiattikul, E. Sekar, A. Tamilselvan, R. Vadivel, N. Gunasekaran and P. Agarwal, Comparative study on numerical methods for singularly perturbed advanced-delay differential equations, J. Math. 2021 (2021) 6636607.
[39] M. Syed Ali, R. Vadivel and K. Murugan, Finite-time decentralized event-triggered communication scheme for neutral-type Markovian jump neural networks with time-varying delays, Chinese J. Phys. 56 (2018) 2448–2464.
[40] M. Syed Ali and R. Vadivel, Decentralized event-triggered exponential stability for uncertain delayed genetic regulatory networks with Markov jump parameters and distributed delays, Neural Process. Lett. 47 (2018) 1219–1252.
Volume 13, Issue 1
March 2022
Pages 2801-2820
  • Receive Date: 01 September 2021
  • Revise Date: 12 October 2021
  • Accept Date: 14 November 2021