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Pu H, Li F, Wang Q, Li P. Preassigned-time projective synchronization of delayed fully quaternion-valued discontinuous neural networks with parameter uncertainties. Neural Netw 2023; 165:740-754. [PMID: 37406427 DOI: 10.1016/j.neunet.2023.06.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Revised: 05/19/2023] [Accepted: 06/08/2023] [Indexed: 07/07/2023]
Abstract
This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.
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Affiliation(s)
- Hao Pu
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China
| | - Fengjun Li
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
| | - Qingyun Wang
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China; School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China
| | - Pengzhen Li
- Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, 60607, USA
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Zhang Y, Yang L, Kou KI, Liu Y. Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays. Neural Netw 2023; 165:274-289. [PMID: 37307669 DOI: 10.1016/j.neunet.2023.05.045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Revised: 04/22/2023] [Accepted: 05/23/2023] [Indexed: 06/14/2023]
Abstract
In this paper, the fixed-time synchronization (FXTSYN) of unilateral coefficients quaternion-valued memristor-based neural networks (UCQVMNNs) with mixed delays is investigated. A direct analytical approach is suggested to obtain FXTSYN of UCQVMNNs utilizing one-norm smoothness in place of decomposition. When dealing with drive-response system discontinuity issues, use the set-valued map and the differential inclusion theorem. To accomplish the control objective, innovative nonlinear controllers and the Lyapunov functions are designed. Furthermore, some criteria of FXTSYN for UCQVMNNs are given using inequality techniques and the novel FXTSYN theory. And the accurate settling time is obtained explicitly. Finally, in order to show that the obtained theoretical results are accurate, useful, and applicable, numerical simulations are presented at the conclusion.
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Affiliation(s)
- Yanlin Zhang
- Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, 999078, China.
| | - Liqiao Yang
- Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, 999078, China.
| | - Kit Ian Kou
- Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, 999078, China.
| | - Yang Liu
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, China.
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Wang X, Cao J, Zhou X, Liu Y, Yan Y, Wang J. A novel framework of prescribed time/fixed time/finite time stochastic synchronization control of neural networks and its application in image encryption. Neural Netw 2023; 165:755-773. [PMID: 37418859 DOI: 10.1016/j.neunet.2023.06.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Revised: 05/27/2023] [Accepted: 06/19/2023] [Indexed: 07/09/2023]
Abstract
In this paper, we investigate a novel framework for achieving prescribed-time (PAT), fixed-time (FXT) and finite-time (FNT) stochastic synchronization control of semi-Markov switching quaternion-valued neural networks (SMS-QVNNs), where the setting time (ST) of PAT/FXT/FNT stochastic synchronization control is effectively preassigned beforehand and estimated. Different from the existing frameworks of PAT/FXT/FNT control and PAT/FXT control (where PAT control is deeply dependent on FXT control, meaning that if the FXT control task is removed, it is impossible to implement the PAT control task), and different from the existing frameworks of PAT control (where a time-varying control gain such as μ(t)=T/(T-t) with t∈[0,T) was employed, leading to an unbounded control gain as t→T- from the initial time to prescribed time T), the investigated framework is only built on a control strategy, which can accomplish its three control tasks (PAT/FXT/FNT control), and the control gains are bounded even though time t tends to the prescribed time T. Four numerical examples and an application of image encryption/decryption are given to illustrate the feasibility of our proposed framework.
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Affiliation(s)
- Xin Wang
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China; Huai'an Key Laboratory of Big Data Intelligent Computing and Analysis, Huaiyin Normal University, Huaian 223300, Jiangsu, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
| | - Xianghui Zhou
- School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China
| | - Ying Liu
- School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, Jiangsu, China
| | - Yaoxi Yan
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China; Huai'an Key Laboratory of Big Data Intelligent Computing and Analysis, Huaiyin Normal University, Huaian 223300, Jiangsu, China
| | - Jiangtao Wang
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China; Huai'an Key Laboratory of Big Data Intelligent Computing and Analysis, Huaiyin Normal University, Huaian 223300, Jiangsu, China
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Wei R, Cao J, Alsaadi FE. Fixed/Prescribed-Time Bipartite Synchronization of Coupled Quaternion-Valued neural Networks with Competitive Interactions. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11225-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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Peng T, Wu Y, Tu Z, Alofi AS, Lu J. Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions. Neural Netw 2023; 160:108-121. [PMID: 36630738 DOI: 10.1016/j.neunet.2022.12.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Revised: 11/26/2022] [Accepted: 12/19/2022] [Indexed: 01/05/2023]
Abstract
A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.
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Affiliation(s)
- Tao Peng
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China; Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Yanqiu Wu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China.
| | - Zhengwen Tu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China.
| | - A S Alofi
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
| | - Jianquan Lu
- Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China; School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China.
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Finite-time stabilization of quaternion-valued neural networks with time delays: An implicit function method. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.09.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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