CN107332714A - A kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node - Google Patents
A kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node Download PDFInfo
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Abstract
A kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node, is related to complex network control.According to the coupled relation between the heterogeneous multiple-input and multiple-output complex networks system topological diagram of node, nodes dynamics and each node, corresponding adjacency matrix, nodes dynamics matrix and interior coupling matrix are obtained；Utilize obtained adjacency matrix, nodes dynamics matrix and interior coupling matrix, set up the heterogeneous multiple-input and multiple-output complex networks system model of node, along with corresponding control input, the system model with control input is obtained, the form for obtaining more compact network system model is finally integrated；The network system model obtained using the inference analysis of PBH criterions, so that the fully controllable sufficient and necessary condition of whole network that must send as an envoy to；Using obtained sufficient and necessary condition as constraints, design optimization algorithm simultaneously sets up optimization problem model；Above-mentioned optimization problem is solved, the minimum driving node number obtained required for making whole network system fully controllable is calculated.
Description
Technical field
The present invention relates to complex network control, more particularly, to a kind of heterogeneous multiple-input and multiple-output complex networks system of node
Control method.
Background technology
One system is controllable, refers to by selecting suitable control input, and system can be within the limited time, from any
Original state run to arbitrary dbjective state.Traditional control theory for linear time invariant system controllability Study
There is provided Kalman orders criterion and PBH criterions two it is used for the sufficient and necessary condition that controllability judges through highly developed.But,
For this kind of scale of complex network than larger network dynamics system, if still using traditional control method, then meter
Calculating the problem of complexity is big can not solve.
The control of complex network is the focus of current complex network research, is also the final mesh of analysis and research complex network
Mark, in recent years by more and more extensive concern.Substantially, control to be to select suitable driving section the problem of complex network
Point make it that whole network system is fully controllable, and most simple directly method is to add control input to each node.So do
No doubt enable to whole network system fully controllable, but be difficult to accomplish this point in real network, examined from economic angle
Worry is also not intended to so do.Therefore, the key of control complex networks system is to find the institute for make it that whole network system is controllable
The number of the minimum driving node needed, and the position where these driving nodes.
In order to solve the above problems, in recent years, related researcher does a lot of work, and achieve it is certain into
Really.But, it is one-dimensional situation to have studied the node only considered in complex network, but under many circumstances, in network
Node can have own dynamics, and the own dynamics of node are often higher-dimension, and this causes the control of complex network to become
More complicated and difficulty.At present, for higher-dimension, the research of complex network control is also fewer, and some only researchs are most
What is considered is each identical situation of node own dynamics in network.But, in real network, node is heterogeneous
Situation is largely present, at present, also gives egress heterogeneous multiple-input and multiple-output complex networks system without related researcher
Control method, mainly have following side for the difficult point of the control of the heterogeneous multiple-input and multiple-output complex networks system of node
Face：First, influence of the network topology to controllability is not only considered, it is also contemplated that node own dynamics are to network controllability
Influence, particularly when the own dynamics of each node are different；2nd, coupled modes different between node and multi input are more
The situation of output, adds the difficulty of controllability analysis；3rd, the scale of network is than larger, the minimum control input needed for calculating
When, it is necessary to overcome the problem of computation complexity is excessive.
The content of the invention
The invention aims to solve the control problem of the heterogeneous multiple-input and multiple-output complex networks system of node there is provided
The method that whole network system can be made fully controllable, and a kind of minimum node of required driving node number is heterogeneous more
Input the control method of multi output complex networks system.
The present invention comprises the following steps：
Step 1：According to the heterogeneous multiple-input and multiple-output complex networks system topological diagram of node, nodes dynamics and each node
Between coupled relation, obtain corresponding adjacency matrix, nodes dynamics matrix and interior coupling matrix；
Step 2：Adjacency matrix, nodes dynamics matrix and the interior coupling matrix obtained using step 1, sets up node heterogeneous
Multiple-input and multiple-output complex networks system model, along with corresponding control input, obtains a system for carrying control input
Model, finally integrates the form for obtaining a kind of more compact network system model；
Step 3：Using the network system model obtained in the inference analysis step 2 of PBH criterions, so that the whole net that must send as an envoy to
The fully controllable sufficient and necessary condition of network；
Step 4：Using sufficient and necessary condition resulting in step 3 as constraints, design an optimized algorithm and simultaneously build
Vertical optimization problem model；
Step 5：Above-mentioned optimization problem is solved, the minimum driving obtained required for making whole network system fully controllable is calculated
Node number.
In step 1, the heterogeneous multiple-input and multiple-output complex networks system topological diagram of the node, is oriented weighted network,
Corresponding adjacency matrix L, node own dynamics matrix Ai(i=1,2 ..., N) and interior coupling matrix H formula are represented such as
Under：
Wherein, βijInformation channel between different nodes is represented, a line if pointing to node i from node j, then
βij≠ 0, otherwise βij=0；aijInner couplings between same node different conditions are represented, if the shape that i-th state is tieed up with jth
There is coupling between state, then aij≠ 0, otherwise aij=0；H is then the matrix for representing inner couplings relation between different nodes.
In step 2, the adjacency matrix, nodes dynamics matrix and interior coupling matrix, set up the heterogeneous multi input of node
The system model of multi output complex network, is adjacency matrix L, node own dynamics matrix Ai(i=1,2 ..., N) and it is interior
Coupling matrix H, sets up the system model of the heterogeneous multiple-input and multiple-output complex network of node：
Wherein, xi∈RnRepresent the state vector of node i, yi∈RmRepresent the output vector of node i, Ci∈Rm×nRepresent defeated
Go out matrix；After corresponding control input, the public affairs of the system model of the heterogeneous multiple-input and multiple-output complex network of node are obtained
Formula is as follows：
Wherein, ui∈RpIt is the outside control input being added in node i, Bi∈Rn×pInput matrix is represented, and for all i
=1,2 ..., N, if δi=1, then it represents that add control input in node i, otherwise δi=0；
The system model for adding the heterogeneous multiple-input and multiple-output complex network of node after control input is integrated, is expressed as
More compact form as follows：
Wherein, φ=Λ+Γ and Λ=diag (A1,...,AN)∈RNn×Nn, Γ=[βijHCj]∈RNn×Nn, ψ=diag
[δiBi]∈RNn×Np。
The controllable sufficient and necessary condition of the heterogeneous multiple-input and multiple-output complex networks system of node is equation below group：
Solution αi(i=1,2 ..., N) only has null solution, according to the inference of PBH criterions, and the heterogeneous multiple-input and multiple-output of node is answered
The controllable sufficient and necessary condition of miscellaneous network system is equation below：
Solution αT=0.Wherein αT∈R1×Nn, make αT=[α1,α2,...,αN],αi∈R1×n, then can be obtained according to above-mentioned equation
It is non trivial solution α to the controllable sufficient and necessary condition of the heterogeneous multiple-input and multiple-output complex networks system of nodei(i=1,2 ...,
N) there was only null solution.
In step 4, the sufficient and necessary condition using obtained by step 3 is defined as follows most as constraints
The mathematical modeling of optimization problem：
Solution αi(i=1,2 ..., N) only has null solution, wherein, object functionI.e. so that whole network system reaches
To it is fully controllable when required minimum driving node number, constraints ensure that whole network system can reach and completely may be used
Control, when the value of object function is global optimum, then the value of object function is so that whole network system reaches completely
The number of minimum driving node required for controllable, δiSubscript i represent the position that control input should be added.
In steps of 5, the optimization problem in the solution procedure 4, is to calculate to obtain making whole network system fully controllable
Position where required minimum driving node number and driving node.
Present invention firstly provides the control method of the heterogeneous multiple-input and multiple-output complex networks system of node, sentenced using PBH
According to the heterogeneous complex networks system of inference analysis node controllability, and give so that network system reaches fully controllable fill
Divide necessary condition.Resulting controllability sufficient and necessary condition as constraints, is devised an optimized algorithm by the present invention,
Calculate and obtained so that whole network system reaches fully controllable required minimum driving node number, and uses optimized algorithm
Method calculate required for minimum driving node number, so as to reduce computation complexity, and improve efficiency.
Compared to existing technology, advantageous effects of the invention are as follows：
(1) control method of the heterogeneous multiple-input and multiple-output complex networks system of node is proposed first.
(2) give the heterogeneous multiple-input and multiple-output complex networks system of node controllable sufficient and necessary condition.
(3) a kind of side for calculating and making whole network reach fully controllable required minimum driving node number is provided
Method.
(4) the minimum driving node number required for being calculated using the method optimized, computation complexity is low, and efficiency is more
It is high.
Embodiment
The present invention is further illustrated for following examples.
The concrete operation step of the present invention is as follows：
Step 1：The heterogeneous multiple-input and multiple-output complex networks system topological diagram of analysis node, nodes dynamics and each node
Between coupled relation, corresponding adjacency matrix, nodes dynamics matrix and interior coupling matrix are obtained, with reference to formula (1)；
Step 2：Adjacency matrix, nodes dynamics matrix and the interior coupling matrix obtained according to step 1, sets up node heterogeneous
Multiple-input and multiple-output complex networks system model, along with corresponding control input, obtains a system for carrying control input
Model, finally integrates and obtains a kind of more compact network system model form, with reference to formula (4)；
Step 3：Using the network system model (4) obtained in the inference analysis step 2 of PBH criterions, so that it is whole to send as an envoy to
The fully controllable sufficient and necessary condition of individual network, with reference to formula (5)；
Step 4：Using sufficient and necessary condition resulting in step 3 as constraints, design an optimized algorithm and simultaneously build
Vertical optimization problem model, with reference to formula (6) (7)；
Step 5：Optimization problem in solution procedure 4, calculating is obtained required for making whole network system fully controllable most
Few driving node number.
Above-mentioned steps 1 to step 5 is the concrete operation step of flow chart, the heterogeneous multiple-input and multiple-output complex network system of node
The final purpose of the control method of system is to obtain making whole network system reach fully controllable required minimum driving node
Number.Therefore, first have to set up network system model, then obtain that network system is controllable fully must according to the inference of PBH criterions
Condition is wanted, an optimized algorithm is finally designed, calculates and obtains causing whole network system reaches fully controllable required minimum
Position where driving node number and driving node.With reference to instantiation, control method of the present invention is carried out detailed
Explanation：
Consider a complex networks system being made up of N number of node.
1st step：The complex networks system of this multiple-input and multiple-output being made up of N number of node is analyzed, obtains reflecting network
The adjacency matrix L of system topological figure, the matrix A of the N number of node own dynamics of descriptioni(i=1,2 ..., N) and expression node
Between coupled relation interior coupling matrix H, formula is as follows：
Wherein, βijInformation channel between different nodes is represented, a line if pointing to node i from node j, then
βij≠ 0, otherwise βij=0.aijInner couplings between same node different conditions are represented, if the shape that i-th state is tieed up with jth
There is coupling between state, then aij≠ 0, otherwise aij=0.H is then the matrix for representing inner couplings relation between different nodes.
2nd step：According to adjacency matrix L, node own dynamics matrix A in (1)i(i=1,2 ..., N) and interior coupling
Matrix H, sets up the system model of the heterogeneous multiple-input and multiple-output complex network of node, and formula is as follows：
Wherein, xi∈RnRepresent the state vector of node i, yi∈RmRepresent the output vector of node i, Ci∈Rm×nRepresent defeated
Go out matrix.
If it is fully controllable to reach whole network system, corresponding control input need to be added, node is then obtained heterogeneous many
The system model of multi output complex network is inputted, formula is as follows：
Wherein, ui∈RpIt is the outside control input being added in node i, Bi∈Rn×pInput matrix is represented, and for all i
=1,2 ..., N, if δi=1, then it represents that add control input in node i, otherwise δi=0.
In order to write conveniently, also for being easy to controllability to analyze, the heterogeneous multi input of node added after control input is integrated
The system model of multi output complex network, is expressed as more compact form：
Wherein, φ=Λ+Γ
0 represent is matrix-block that the element with corresponding dimension is all 0 in above-mentioned matrix.
3rd step：The controllable abundant necessity of the heterogeneous multiple-input and multiple-output complex networks system of node is obtained according to theory deduction
Condition is equation below group：
Solution αi(i=1,2 ..., N) there was only null solution.According to controllability PBH inference, the heterogeneous multiple-input and multiple-output of node
The controllable sufficient and necessary condition of complex networks system (4) is equation below：
Solution αT=0.Wherein αT∈R1×Nn, make αT=[α1,α2,...,αN],αi∈R1×n, then can be obtained according to equation (5)
It is the solution α of equation (5) to the controllable sufficient and necessary condition of the heterogeneous multiple-input and multiple-output complex networks system (4) of nodei(i=1,
2 ..., N) there was only null solution.
4th step：In order to calculate obtain so that whole network system reach it is fully controllable required for minimum driving node
Position where number and driving node, can design an optimized algorithm, by sufficient and necessary condition resulting in the 3rd step
As constraints, and the mathematical modeling for the optimization problem being defined as follows：
Solution αi(i=1,2 ..., N) there was only null solution (7)
Wherein, object functionI.e. so that the minimum driving required when reaching fully controllable of whole network system
Node number, it is fully controllable that constraints (7) ensure that whole network system can reach, when the value of object function is the overall situation
When optimal, then the value of object function is minimum driving node required when making whole network system reach fully controllable
Number, δiSubscript i represent the position that control input should be added.
5th step：The optimization problem in the 4th step is solved, calculating is obtained required for making whole network system fully controllable most
Position where few driving node number and driving node；
Present invention firstly provides the control method of the heterogeneous multiple-input and multiple-output complex networks system of node, and use can
The inference of control property PBH criterions derive so that the heterogeneous multiple-input and multiple-output complex networks system of node reach it is fully controllable abundant
Necessary condition, designs an optimized algorithm, and using obtained controllability sufficient and necessary condition as constraints, calculating is caused
Whole network system reaches fully controllable required minimum driving node numberδiSubscript i then represent control it is defeated
Enter added position, the minimum driving node number required for being calculated using the method for optimized algorithm can reduce calculating multiple
Miscellaneous degree, improves computational efficiency.
Claims (6)
1. a kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node, it is characterised in that comprise the following steps：
Step 1：According between the heterogeneous multiple-input and multiple-output complex networks system topological diagram of node, nodes dynamics and each node
Coupled relation, obtain corresponding adjacency matrix, nodes dynamics matrix and interior coupling matrix；
Step 2：Adjacency matrix, nodes dynamics matrix and the interior coupling matrix obtained using step 1, sets up node heterogeneous how defeated
Enter multi output complex networks system model, along with corresponding control input, obtain a system model for carrying control input,
Finally integrate the form for obtaining a kind of more compact network system model；
Step 3：Using the network system model obtained in the inference analysis step 2 of PBH criterions, so that the whole network that must send as an envoy to is complete
Complete controllable sufficient and necessary condition；
Step 4：Using sufficient and necessary condition resulting in step 3 as constraints, design an optimized algorithm and simultaneously set up excellent
Change problem model；
Step 5：Above-mentioned optimization problem is solved, the minimum driving node obtained required for making whole network system fully controllable is calculated
Number.
2. a kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node as claimed in claim 1, its feature exists
In in step 1, the heterogeneous multiple-input and multiple-output complex networks system topological diagram of node, is oriented weighted network, accordingly
Adjacency matrix L, node own dynamics matrix Ai(i=1,2 ..., N) and interior coupling matrix H formula are expressed as follows：
Wherein, βijInformation channel between different nodes is represented, a line if pointing to node i from node j, then βij≠ 0,
Otherwise βij=0；aijInner couplings between same node different conditions are represented, if between the state of i-th state and jth dimension
In the presence of coupling, then aij≠ 0, otherwise aij=0；H is then the matrix for representing inner couplings relation between different nodes.
3. a kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node as claimed in claim 1, its feature exists
In in step 2, the adjacency matrix, nodes dynamics matrix and interior coupling matrix set up the heterogeneous multiple-input and multiple-output of node
The system model of complex network, is adjacency matrix L, node own dynamics matrix Ai(i=1,2 ..., N) and interior coupling moment
Battle array H, sets up the system model of the heterogeneous multiple-input and multiple-output complex network of node：
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Wherein, xi∈RnRepresent the state vector of node i, yi∈RmRepresent the output vector of node i, Ci∈Rm×nRepresent output square
Battle array；After corresponding control input, the formula of system model of the heterogeneous multiple-input and multiple-output complex network of node is obtained such as
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Wherein, ui∈RpIt is the outside control input being added in node i, Bi∈Rn×pInput matrix is represented, and for all i=1,
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The system model for adding the heterogeneous multiple-input and multiple-output complex network of node after control input is integrated, is expressed as
More compact form：
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4. a kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node as claimed in claim 1, its feature exists
In in step 2, the controllable sufficient and necessary condition of the heterogeneous multiple-input and multiple-output complex networks system of node is equation below
Group：
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Solution αi(i=1,2 ..., N) only has null solution, according to the inference of PBH criterions, the heterogeneous multiple-input and multiple-output complex web of node
The controllable sufficient and necessary condition of network system is equation below：
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Solution αT=0, wherein αT∈R1×Nn, make αT=[α1,α2,...,αN],αi∈R1×n, then node is obtained according to above-mentioned equation
The controllable sufficient and necessary condition of heterogeneous multiple-input and multiple-output complex networks system is non trivial solution αi(i=1,2 ..., N) only have
Null solution.
5. a kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node as claimed in claim 1, its feature exists
In in step 4, the sufficient and necessary condition using obtained by step 3 is as constraints, and the optimization being defined as follows is asked
The mathematical modeling of topic：
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<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
<mo>&NotEqual;</mo>
<mi>i</mi>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>HC</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>N</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&delta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>B</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>N</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Solution αi(i=1,2 ..., N) only has null solution, wherein, object functionI.e. so that whole network system has reached
Required minimum driving node number when complete controllable, it is fully controllable that constraints ensure that whole network system can reach,
When object function value be global optimum when, then the value of object function be so that whole network system reach it is fully controllable
The number of required minimum driving node, δiSubscript i represent the position that control input should be added.
6. a kind of control method of the heterogeneous multiple-input and multiple-output complex networks system of node as claimed in claim 1, its feature exists
In in steps of 5, the optimization problem in the solution procedure 4 is to calculate to obtain making whole network system fully controllable required
Minimum driving node number and driving node where position.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116319363A (en) * | 2023-05-16 | 2023-06-23 | 江南大学 | Structured network controllability analysis method and device with MIMO subsystem |
Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2003069846A1 (en) * | 2002-02-14 | 2003-08-21 | France Telecom | Method and system for adjusting the control parameter values of a network in an optimal manner |
| CN101730177A (en) * | 2008-10-30 | 2010-06-09 | 财团法人工业技术研究院 | Adaptive handover device and adaptive handover method for heterogeneous network |
| CN101801081A (en) * | 2010-01-19 | 2010-08-11 | 河海大学 | Cluster synchronization method of complex time delay network |
| CN101894093A (en) * | 2010-06-04 | 2010-11-24 | 哈尔滨工程大学 | Mixed-mode multi-CPU parallel computing system and control method |
| CN202261357U (en) * | 2011-11-06 | 2012-05-30 | 广东省电力调度中心 | Safety transmission system for complex network environment data |
| CN102890703A (en) * | 2012-07-20 | 2013-01-23 | 浙江工业大学 | Network heterogeneous multidimensional scaling (HMDS) method |
| CN103279032A (en) * | 2013-05-03 | 2013-09-04 | 北京航空航天大学 | Robust convergence control method of heterogeneous multi-agent system |
| CN103501235A (en) * | 2013-07-15 | 2014-01-08 | 中国航天标准化研究所 | Complex system availability determination method based on cellular automaton |
| CN105634828A (en) * | 2016-03-03 | 2016-06-01 | 厦门大学 | Method for controlling distributed average tracking of linear differential inclusion multi-agent systems |
| CN106407373A (en) * | 2016-09-12 | 2017-02-15 | 电子科技大学 | Heterogeneous network community structure and community discovery method based on the structure |
| CN106550474A (en) * | 2015-09-18 | 2017-03-29 | 中华电信股份有限公司 | heterogeneous network integration method and device |
-
2017
- 2017-08-11 CN CN201710685313.9A patent/CN107332714B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2003069846A1 (en) * | 2002-02-14 | 2003-08-21 | France Telecom | Method and system for adjusting the control parameter values of a network in an optimal manner |
| CN101730177A (en) * | 2008-10-30 | 2010-06-09 | 财团法人工业技术研究院 | Adaptive handover device and adaptive handover method for heterogeneous network |
| CN101801081A (en) * | 2010-01-19 | 2010-08-11 | 河海大学 | Cluster synchronization method of complex time delay network |
| CN101894093A (en) * | 2010-06-04 | 2010-11-24 | 哈尔滨工程大学 | Mixed-mode multi-CPU parallel computing system and control method |
| CN202261357U (en) * | 2011-11-06 | 2012-05-30 | 广东省电力调度中心 | Safety transmission system for complex network environment data |
| CN102890703A (en) * | 2012-07-20 | 2013-01-23 | 浙江工业大学 | Network heterogeneous multidimensional scaling (HMDS) method |
| CN103279032A (en) * | 2013-05-03 | 2013-09-04 | 北京航空航天大学 | Robust convergence control method of heterogeneous multi-agent system |
| CN103501235A (en) * | 2013-07-15 | 2014-01-08 | 中国航天标准化研究所 | Complex system availability determination method based on cellular automaton |
| CN106550474A (en) * | 2015-09-18 | 2017-03-29 | 中华电信股份有限公司 | heterogeneous network integration method and device |
| CN105634828A (en) * | 2016-03-03 | 2016-06-01 | 厦门大学 | Method for controlling distributed average tracking of linear differential inclusion multi-agent systems |
| CN106407373A (en) * | 2016-09-12 | 2017-02-15 | 电子科技大学 | Heterogeneous network community structure and community discovery method based on the structure |
Non-Patent Citations (6)
| Title |
|---|
| LI, X等: "Pinning a complex dynamical network to its equilibrium", 《IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS》 * |
| WANG, XF等: "Synchronization in scale-free dynamical networks: Robustness and fragility", 《IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS》 * |
| 晁永翠等: "复杂网络在路形拓扑结构下可控的充要条件", 《智能系统学报》 * |
| 聂森: "复杂网络可控性研究", 《中国优秀博士学位论文全文库》 * |
| 项林英: "复杂动态网络的建模、分析与控制研究综述", 《自然科学进展》 * |
| 项林英等: "一类异步网络控制系统的分析与建模", 《计算机工程与科学》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116319363A (en) * | 2023-05-16 | 2023-06-23 | 江南大学 | Structured network controllability analysis method and device with MIMO subsystem |
| CN116319363B (en) * | 2023-05-16 | 2023-08-25 | 江南大学 | Structured network controllability analysis method and device with MIMO subsystem |
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