International Journal of Nonlinear Analysis and Applications
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
- R. Anbuvithya 1
- S. Dheepika Sri 1
- R. Vadivel 2
- P. Hammachukiattikul 2
- Choonkil Park 3
- Gunasekaran Nallappan 4
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 coeffcients,
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. Lindstrm, 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.
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 coeffcients,
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. Lindstrm, 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 2022Pages 2801-2820
- Receive Date: 01 September 2021
- Revise Date: 12 October 2021
- Accept Date: 14 November 2021
- First Publish Date: 01 January 2022