CN116449701A - Synchronous control method of second-order CG neural network - Google Patents
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Abstract
The invention belongs to the technical field of new generation information, and particularly relates to a synchronous control method of a second-order CG neural network. The method specifically comprises the following steps: step S1: constructing a master system and a slave system of a second-order CG neural network; step S2: setting a synchronization error and establishing a synchronization error system; step S3: designing a proper synchronous controller; step S4: and (3) acting the synchronous controller designed in the step (S3) on the slave system so that the slave system is synchronous with the master system in a synchronous stopping time with limited time. The invention combines the Lyapunov functional and the inequality technology, and provides a control method for master-slave finite time synchronization of the second-order CG neural network.
Description
Technical Field
The invention relates to the technical field of new generation information, in particular to a synchronous control method of a second-order CG neural network.
Background
Artificial neural networks have been widely used in the field of new generation information technology in recent decades, such as pattern recognition, associative memory, and image processing. From a model structure perspective, CG neural networks can be transformed into many other neural network models, such as cellular neural network models, hopfield neural network models, and recurrent neural network models, so CG neural networks are more versatile neural networks.
Notably, the results of the study demonstrate that the introduction of inertial terms in neural networks is considered an effective method of producing chaotic and complex bifurcation behavior [ see, for details, the documents Mauro a, conti F, dodge F, et al, subthreshold behavior and phenomenological impedance of the squid giant axon [ J ]. The Journal of general physiology,1970,55 (4): 497-523 ]. Therefore, a class expressed as a second order CG neural network is an important research topic.
In many applications of neural networks, its dynamic behavior is critical. Among them, synchronization is one of the hot spots studied in neural network dynamics behavior. For example, in documents [ Wang Limei, hao Zhongyang, fang Xin, zhang Kang ] H-type platform fuzzy neural network synchronization control based on active-disturbance-rejection [ J ]. Electrical engineering journal, 2022,17 (03): 122-129 ], authors have studied H-type platform fuzzy neural network synchronization control based on active-disturbance-rejection; in literature [ Tian Jiaping, xie Lidian, wang Chunzhu, wang Jiawei, ge Chao ] sample synchronization control study based on markov hopping neural networks [ J ] modern computer, 2021 (02): 8-13 ], authors have studied the synchronization control of a class of neural networks based on markov hopping using a control strategy; in the literature [ Cai Qingrui, huang Zhenkun, binghua. Control of the pinning synchronization of the time-lapse neural network on a time scale [ J ]. Spring society of education, 2021,39 (02): 52-59.], authors studied the pinning synchronization of the time-lapse neural network on a time scale.
However, the results of these synchronicity correlations are exponential or progressive, and the synchronization time of exponential or progressive synchronization may be infinite. In practical applications, it is often required that the synchronization time of the system is limited, i.e. that the synchronization of the system is performed within a limited time interval.
Disclosure of Invention
Therefore, the invention aims to provide a synchronous control method of a second-order CG neural network, which can realize the limited time synchronous control of the second-order CG neural network.
The invention is realized by adopting the following scheme: a synchronous control method of a second order CG neural network comprises the following steps:
step S1: the method for constructing the master system and the slave system of the second-order CG neural network comprises the following steps of:
step S11: establishing a second-order CG neural network dynamics equation:
wherein, the time t is more than or equal to 0; n represents the number of neurons in the second order CG neural network; i=1, 2, …, n; j=1, 2, …, n; x is x i (t) represents a state variable of an ith neuron of the second-order CG neural network at time t; alpha i (x i (t)) represents an i-th neuron differentiable amplification function that satisfies: for any real number u, there isAnd |alpha' i (u) | is less than or equal to q i Wherein i α、/>And q i >0 are constants; beta i Is a positive constant; h is a i (x i (t)) represents the differentiable behavior function of the ith neuron and let ψ i (c)＝α i (c)h i (c) There is a positive constant P i And Q i So that 0<P i ≤Ψ′ i (c)≤Q i And beta is i -Q i >0, wherein c is any real number; a, a ij (t) and b ij (t) represents a connection weight between neurons; f (f) j (. Cndot.) represents the activation function of the second order CG neural network and satisfies the Lipohsh condition, i.e. there is a positive constant M j So that |f j (·)|≤M j And for any real number a and b, there is a positive constant l j So that |f j (a)-f j (b)|≤l j |a-b|；τ j (t) represents a discrete time lag; i i (t) represents an external input to an i-th neuron of the second-order CG neural network;
step S12: a main system for constructing the second-order CG neural network:
performing variable replacement and order reduction processing on the second-order CG neural network in the step S11, and constructing a main system as follows:
wherein y is i (t)＝(dx i (t)/dt)+x i (t)；x i (t) represents a state variable of an ith neuron of the host system at time t;
step S13: a slave system for constructing the second-order CG neural network:
the slave system corresponding to the master system in the construction step S12 is:
in the formula, v i (t)＝(du i (t)/dt)+u i (t)；u i (t) represents a state variable of an ith neuron of the slave system at time t; u (U) i (t) andis a synchronous controller which needs to be designed in the slave system; the definition of other parameters of the slave system is the same as that of the master system;
step S2: setting a synchronization error according to the master system and the slave system constructed in the step S1, and establishing a synchronization error system, wherein the method comprises the following specific steps:
step S21: setting the synchronization errors of the master system and the slave system constructed according to the step S1 as follows:
step S22: according to the master system, the slave system and the synchronization error set in the step S21, a synchronization error system is established as follows:
step S3: according to the synchronization error established in the step S2, a proper synchronization controller U is designed i (t) and
step S4: the synchronous controller U designed in the step S3 i (t) andacting on the slave system such that the slave system is synchronized with the master system within a synchronization dwell time T of limited time.
Further, the synchronous controller U i (t) andthe method comprises the following steps:
wherein lambda is>0 represents a synchronization controller adjustable constant; the synchronous controller parameter eta is a normal number and satisfies 0<η<1；k 1 、k 2 And delta j Representing the synchronous controller parameters to be determined.
Further, the synchronous controller parameters to be determined respectively satisfy:
in the method, in the process of the invention, is a real set.
Further, the finite time synchronous rest time T is:
wherein,,
the invention provides a synchronous control method of a second-order CG neural network, which has the beneficial effects that compared with the prior art:
1. the variable transformation method is based on the variable transformation method, the second-order CG neural network is converted into the first-order CG neural network, and the finite time synchronization between the master system and the slave system is realized.
2. According to the invention, by designing a special synchronous controller, the parameter conditions are given in algebraic form, so that the complexity of parameter calculation of the synchronous controller is greatly reduced.
3. The invention provides the synchronous stopping time of the limited time, and meanwhile, the synchronous stopping time of the limited time can be flexibly regulated through two parameters lambda and eta in the synchronous controller designed by the invention, thereby greatly improving the flexibility and the application range of the synchronous control method.
Drawings
FIG. 1 is a flow chart of a method for synchronous control of a second order CG neural network according to the invention;
FIG. 2 shows a main system x without the synchronous controller in embodiment 2 of the present invention 1 (t) and slave System u 1 A trace map of (t);
FIG. 3 shows a master system x without a synchronous controller in embodiment 2 of the present invention 2 (t) and slave System u 2 A trace map of (t);
FIG. 4 shows a master system y without a synchronous controller in embodiment 2 of the present invention 1 (t) and slave System v 1 A trace map of (t);
FIG. 5 shows an embodiment 2 of the present invention without synchronization controlMain system y under action of controller 2 (t) and slave System v 2 A trace map of (t);
FIG. 6 is a graph showing the trace of the synchronization error without the synchronization controller in embodiment 2 of the present invention;
FIG. 7 shows a main system x under the action of a synchronous controller in embodiment 2 of the present invention 1 (t) and slave System u 1 A trace map of (t);
FIG. 8 shows a main system x under the action of a synchronous controller in embodiment 2 of the present invention 2 (t) and slave System u 2 A trace map of (t);
FIG. 9 shows a master system y under the action of a synchronous controller in embodiment 2 of the present invention 1 (t) and slave System v 1 A trace map of (t);
FIG. 10 shows a master system y under the action of a synchronous controller in embodiment 2 of the present invention 2 (t) and slave System v 2 A trace map of (t);
FIG. 11 is a trace comparison chart of a synchronization error under the action of a synchronization controller in embodiment 2 of the present invention;
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.
Example 1:
as shown in fig. 1, the present embodiment provides a synchronous control method of a second-order CG neural network, including the following steps:
step S1: the method for constructing the master system and the slave system of the second-order CG neural network comprises the following steps of:
step S11: establishing a second-order CG neural network dynamics equation:
wherein, the time r is more than or equal to 0; n represents the number of neurons in the second order CG neural network; i=1, 2, …, n; j=1, 2, …, n; x is x i (t) represents a state variable of an ith neuron of the second-order CG neural network at time t; alpha i (x i (t)) represents an i-th neuron differentiable amplification function that satisfies: for any real number u, there isAnd |alpha' i (u)|≤q i Wherein i α、/>And q i >0 are constants; beta i Is a positive constant; h is a i (x i (t)) represents the differentiable behavior function of the ith neuron and let ψ i (c)＝α i (c)h i (c) There is a positive constant P i And Q i So that 0<P i ≤Ψ′ i (c)≤Q i And beta is i -Q i >0, wherein c is any real number; a, a ij (t) and b ij (t) represents a connection weight between neurons; f (f) j (. Cndot.) represents the activation function of the second order CG neural network and satisfies the Lipohsh condition, i.e. there is a positive constant M j So that |f j (·)|≤M j And for any real number a and b, there is a positive constant l j So that |f j (a)-f j (b)|≤l j |a-b|；τ j (t) represents a discrete time lag; i i (t) represents an external input to an i-th neuron of the second-order CG neural network;
step S12: a main system for constructing the second-order CG neural network:
performing variable replacement and order reduction processing on the second-order CG neural network in the step S11, and constructing a main system as follows:
wherein y is i (t)＝(dx i (t)/dt)+x i (t)；x i (t) represents a state variable of an ith neuron of the host system at time t;
step S13: a slave system for constructing the second-order CG neural network:
the slave system corresponding to the master system in the construction step S12 is:
in the formula, v i (t)＝(du i (t)/dt)+u i (t)；u i (t) represents a state variable of an ith neuron of the slave system at time t; u (U) i (t) andis a synchronous controller which needs to be designed in the slave system; the definition of other parameters of the slave system is the same as that of the master system;
step S2: setting a synchronization error according to the master system and the slave system constructed in the step S1, and establishing a synchronization error system, wherein the method comprises the following specific steps:
step S21: setting the synchronization errors of the master system and the slave system constructed according to the step S1 as follows:
step S22: according to the master system, the slave system and the synchronization error set in the step S21, a synchronization error system is established as follows:
step S3: according to the steps ofS2, establishing a synchronous error, and designing a proper synchronous controller U i (t) and
step S4: the synchronous controller U designed in the step S3 i (t) andacting on the slave system such that the slave system is time-synchronized to the master system.
In this embodiment, the synchronization controller U i (t) andthe method comprises the following steps:
wherein lambda is>0 represents a synchronization controller adjustable constant; the synchronous controller parameter eta is a normal number and satisfies 0<η<1；k 1 、k 2 And delta j Representing the synchronous controller parameters to be determined.
In this embodiment, the parameters of the synchronization controller to be determined respectively satisfy:
in the method, in the process of the invention, is a real set.
In this embodiment, the finite time synchronization downtime T is:
wherein,,
example 2:
the embodiment mainly comprises two parts of contents:
one is to carry out theoretical demonstration of the effectiveness of the synchronous control method of the second-order CG neural network proposed in example 1.
Secondly, the synchronous performance of the master system and the slave system of the second-order CG neural network constructed in the embodiment 1 is verified in a simulation way by a numerical simulation method.
(neither theoretical demonstration nor simulation experiment is intended to limit the invention, in other embodiments, simulation experiments may be omitted, or other experimental schemes may be used to verify the performance of the neural network system.)
1. Proof of theory
The quotation that will be adopted in the certification process is given below:
lemma 1: if z 1 、z 2 、…、z n Are all non-negative numbers, 1 is greater than or equal to a 1 >0，a 2 >1, the following two inequalities hold:
and (4) lemma 2: if the continuous positive definite function V (t) satisfies the inequalityWherein 0 is<η<1、γ>0, then V (t) satisfies the following inequality:
V 1-η (t)≤V 1-η (0)-γ(1-η)t,0<t<T
V(t)＝0,t≥T
wherein,,
according to the differential median theorem, it is possible to:
α i (u i (t))-α i (x i (t))＝α′ i (ξ i )e i (t)
wherein the parameter ζ i Andis located at u i (t) and x i A number between (t);
due to the presence of positive constant P i And Q i So that 0<P i ≤Ψ′ i (c)≤Q i And beta is i -Q i >0, wherein c is any real number, then it is possible to obtain: beta i -Ψ′ i (ξ i )≥β i -Q i >0，0<P i β i -Ψ′ i (ξ i )≤β i -P i >0；
From the error system, it can be seen that:
further, it is possible to obtain:
also because for any real number a and b there is an inequality:then:
therefore, there are:
further can be obtained:
consider the lyapunov functional as:
the derivative of V (t) is:
again because:
then:further, according to the lemma 1, it is possible to obtain:
wherein,,then according to lemma 2, it is possible to:
V(t)＝0，t≥T
wherein,,
thus, V (T) converges to zero within a finite time T, i.e. the master system and the slave system are time-synchronized, and the rest time is synchronized
It is worth to say that, the invention converts the second order CG neural network into the first order CG neural network based on the variable transformation method, has realized the finite time synchronization between the main system and slave system; according to the invention, by designing a special synchronous controller, the parameter conditions are given in algebraic form, so that the complexity of parameter calculation of the synchronous controller is greatly reduced; the invention provides the synchronous stopping time of the limited time, and meanwhile, the synchronous stopping time of the limited time can be flexibly regulated through two parameters lambda and eta in the synchronous controller designed by the invention, thereby greatly improving the flexibility and the application range of the synchronous control method.
2. Numerical simulation
In this embodiment, taking a two-dimensional second-order CG neural network as an example:
wherein i=1, 2;
and then, variable replacement and order reduction processing is carried out on the two-dimensional second-order CG neural network, and a main system is constructed as follows:
the slave system corresponding to the master system is:
the parameters are set as follows:β 1 ＝β 2 ＝3；h i (x i (t))＝x i (t)；I 1 (t)＝I 2 (t)＝0；τ 1 (t)＝τ 2 (t)＝0.2cos 2 (t)；f 1 (·)＝f 2 (·)＝tanh(·)；
then, according to the above parameter settings, it is possible to:2<α i (u)≤2.5；M j ＝l i ＝1； i α＝0.5、/>for any real number u, there is |α '' i (u)|<0.5, q is preferable i ＝0.5；/>1.9<Ψ′ i (u) is less than or equal to 2.5, P can be selected i ＝1.9、Q i =2.5; obviously, the parameters taken satisfy beta i -Q i >0; further, when i is taken as 1 and 2, respectively, there are:
further, according to the above range, the controller parameter k is synchronized 1 、k 2 And delta j The values can be respectively: k (k) 1 ＝2.2、k 2 ＝0.95、δ 1 =0.8 and δ 2 =0.9; in addition, λ=0.8; η=0.6.
And the master system, the slave system and the synchronous controller carry out numerical simulation experiments on the master system, the slave system and the synchronous controller under the set parameters. The initial values of the master system and the slave system are set as follows: x is x 1 (0)＝-2.6，x 2 (0)＝2.8，y 1 (0)＝-2.3，y 2 (0)＝-2.9，u 1 (0)＝-3.8，u 2 (0)＝-3，v 1 (0)＝3.2，v 2 (0) =1.3, the specific simulation experiment results are as follows: FIG. 2 shows the state x of the main system without the synchronous controller 1 (t) and slave System State u 1 A trace map of (t); FIG. 3 shows the state x of the main system without the synchronous controller 2 (t) and slave System State u 2 Track of (t)A control chart; FIG. 4 shows the state y of the main system without the synchronous controller 1 (t) and slave System State v 1 A trace map of (t); FIG. 5 shows the state y of the main system without the synchronous controller 2 (t) and slave System State v 2 A trace map of (t); FIG. 6 is a graph of trace contrast of synchronization errors of a master system and a slave system without the action of a synchronization controller; FIG. 7 shows the state x of the main system under the action of the synchronous controller 1 (t) and slave System State u 1 A trace map of (t); FIG. 8 shows the state x of the main system under the action of the synchronous controller 2 (t) and slave System State u 2 A trace map of (t); FIG. 9 shows the state y of the main system under the action of the synchronous controller 1 (t) and slave System State v 1 A trace map of (t); FIG. 10 shows the state y of the main system under the action of the synchronous controller 2 (t) and slave System State v 2 A trace map of (t); FIG. 11 is a graph of trace contrast of synchronization errors of a master system and a slave system under the influence of a synchronization controller. From fig. 2 to fig. 6 of the simulation experiment results, it can be seen that: under the action of a synchronous controller, the master system and the slave system cannot realize synchronization; from fig. 7 to fig. 11, which show simulation results, it can be seen that: the slave system is synchronous with the master system for a limited time under the action of the synchronous controller, and the correctness and the effectiveness of the synchronous performance are verified.
Finally, it should be noted that: the foregoing is merely a preferred example of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. The synchronous control method of the second-order CG neural network is characterized by comprising the following steps:
step S1: the method for constructing the master system and the slave system of the second-order CG neural network comprises the following steps of:
step S11: establishing a second-order CG neural network dynamics equation:
wherein, the time t is more than or equal to 0; n represents the number of neurons in the second order CG neural network; i=1, 2, …, n; j=1, 2, …, n; x is x i (t) represents a state variable of an ith neuron of the second-order CG neural network at time t; alpha i (x i (t)) represents an i-th neuron differentiable amplification function that satisfies: for any real number u, there isAnd |alpha' i (u)|≤q i Wherein i α、/>And q i >0 are constants; beta i Is a positive constant; h is a i (x i (t)) represents the differentiable behavior function of the ith neuron and let ψ i (c)＝α i (c)h i (c) There is a positive constant P i And Q i So that 0<P i ≤Ψ′ i (c)≤Q i And beta is i -Q i >0, wherein c is any real number; a, a ij (t) and b ij (t) represents a connection weight between neurons; f (f) j (. Cndot.) represents the activation function of the second order CG neural network and satisfies the Lipohsh condition, i.e. there is a positive constant M j So that |f j (·)|≤M j And for any real number a and b, there is a positive constant l j So that |f j (a)-f j (b)|≤l j |a-b|；τ j (t) represents a discrete time lag; i i (t) represents an external input to an i-th neuron of the second-order CG neural network;
step S12: a main system for constructing the second-order CG neural network:
performing variable replacement and order reduction processing on the second-order CG neural network in the step S11, and constructing a main system as follows:
wherein y is i (t)＝(dx i (t)/dt)+x i (t)；x i (t) represents a state variable of an ith neuron of the host system at time t;
step S13: a slave system for constructing the second-order CG neural network:
the slave system corresponding to the master system in the construction step S12 is:
in the formula, v i (t)＝(du i (t)/dt)+u i (t)；u i (t) represents a state variable of an ith neuron of the slave system at time t; u (U) i (t) andis a synchronous controller which needs to be designed in the slave system; the definition of other parameters of the slave system is the same as that of the master system;
step S2: setting a synchronization error according to the master system and the slave system constructed in the step S1, and establishing a synchronization error system, wherein the method comprises the following specific steps:
step S21: setting the synchronization errors of the master system and the slave system constructed according to the step S1 as follows:
step S22: according to the master system, the slave system and the synchronization error set in the step S21, a synchronization error system is established as follows:
step S3: according to the synchronization error established in the step S2, a proper synchronization controller U is designed i (t) and
step S4: the synchronous controller U designed in the step S3 i (t) andacting on the slave system such that the slave system is synchronized with the master system within a synchronization dwell time T of limited time.
2. The synchronous control method of the second-order CG neural network as claimed in claim 1 wherein said synchronous controller U i (t) andthe method comprises the following steps:
wherein lambda is>0 represents a synchronization controller adjustable constant; the synchronous controller parameter eta is a normal number and satisfies 0<η<1；k 1 、k 2 And delta j Representing the synchronous controller parameters to be determined.
3. The synchronous control method of a second-order CG neural network according to claim 2, wherein the synchronous controller parameters to be determined respectively satisfy:
in the method, in the process of the invention, is a real set.
4. A synchronous control method of a second order CG neural network as claimed in claim 3 wherein the finite time synchronous rest time T is:
wherein,,
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Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110266217A (en) * | 2019-02-27 | 2019-09-20 | 齐鲁工业大学 | A kind of improved permanent magnet synchronous motor Control of Chaotic Synchronization method |
| CN111077776A (en) * | 2019-12-16 | 2020-04-28 | 重庆航天职业技术学院 | Optimal synchronous control method of coupled fractional order chaotic electromechanical device |
| CN112621759A (en) * | 2020-12-28 | 2021-04-09 | 燕山大学 | Teleoperation system fractional order sliding mode synchronous control method based on event trigger mechanism |
| CN113824361A (en) * | 2021-10-26 | 2021-12-21 | 贵州大学 | Fuzzy finite time optimal synchronous control method of fractional order permanent magnet synchronous generator |
| CN114442483A (en) * | 2022-01-18 | 2022-05-06 | 曲阜师范大学 | Self-adaptive non-periodic intermittent boundary control method |
| CN115169539A (en) * | 2022-07-28 | 2022-10-11 | 盐城工学院 | Secret communication method based on inertia complex value memristor neural network |
| CN115544542A (en) * | 2022-09-29 | 2022-12-30 | 盐城工学院 | Image encryption method based on memristor neural network synchronous control |
| CN115760837A (en) * | 2022-12-06 | 2023-03-07 | 泉州装备制造研究所 | Crystal quality evaluation method and system based on deep neural network |
| CN115860075A (en) * | 2022-12-08 | 2023-03-28 | 盐城工学院 | Synchronous control method of fractional order memristor neural network |
| CN115860096A (en) * | 2022-12-08 | 2023-03-28 | 盐城工学院 | Index synchronization control method of inertial neural network with mixed time-varying time lag |
-
2023
- 2023-04-07 CN CN202310368738.2A patent/CN116449701B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110266217A (en) * | 2019-02-27 | 2019-09-20 | 齐鲁工业大学 | A kind of improved permanent magnet synchronous motor Control of Chaotic Synchronization method |
| CN111077776A (en) * | 2019-12-16 | 2020-04-28 | 重庆航天职业技术学院 | Optimal synchronous control method of coupled fractional order chaotic electromechanical device |
| CN112621759A (en) * | 2020-12-28 | 2021-04-09 | 燕山大学 | Teleoperation system fractional order sliding mode synchronous control method based on event trigger mechanism |
| CN113824361A (en) * | 2021-10-26 | 2021-12-21 | 贵州大学 | Fuzzy finite time optimal synchronous control method of fractional order permanent magnet synchronous generator |
| US11616460B1 (en) * | 2021-10-26 | 2023-03-28 | Guizhou University | Fuzzy finite-time optimal synchronization control method for fractional-order permanent magnet synchronous generator |
| CN114442483A (en) * | 2022-01-18 | 2022-05-06 | 曲阜师范大学 | Self-adaptive non-periodic intermittent boundary control method |
| CN115169539A (en) * | 2022-07-28 | 2022-10-11 | 盐城工学院 | Secret communication method based on inertia complex value memristor neural network |
| CN115544542A (en) * | 2022-09-29 | 2022-12-30 | 盐城工学院 | Image encryption method based on memristor neural network synchronous control |
| CN115760837A (en) * | 2022-12-06 | 2023-03-07 | 泉州装备制造研究所 | Crystal quality evaluation method and system based on deep neural network |
| CN115860075A (en) * | 2022-12-08 | 2023-03-28 | 盐城工学院 | Synchronous control method of fractional order memristor neural network |
| CN115860096A (en) * | 2022-12-08 | 2023-03-28 | 盐城工学院 | Index synchronization control method of inertial neural network with mixed time-varying time lag |
Non-Patent Citations (5)
| Title |
|---|
| ALI MOHAMED ALSHAWISH: "Sensorless Control for Permanent Magnet Synchronous Motor (PMSM) Using the Mechanical Model of the Motor with a Reduced Order Observe", 《2022 IEEE KANSAS POWER AND ENERGY CONFERENCE (KPEC)》 * |
| XIANQING CAO: "Real-time IP controller based on neural network for permanent magnet synchronous motors", 《2009 4TH IEEE CONFERENCE ON INDUSTRIAL ELECTRONICS AND APPLICATIONS》 * |
| XIAOFAN LI HUIYUAN LI: "Event-Triggered Synchronization of Multiple Discrete-Time Markovian Jump Memristor- Based Neural Networks With Mixed Mode-Dependent Delays", 《IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS》 * |
| 何佳昊，李小凡: "无边界分布时滞惯性忆阻神经网络的反同步控制研究", 《盐城工学院学报》 * |
| 蒋文芳: "基于状态估计的分数阶线性系统同步控制", 《南通大学学报（自然科学版）》 * |
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