Method and device for analyzing strong structural controllability of complex network with same subsystems

Abstract

The application discloses a complex network strong structure controllability analysis method and device with same subsystems, and the method comprises the following steps: firstly, establishing a structured system model of the complex network system with same subsystems to determine whether the related system is strong structure controllable, if not, the complex network system is not strong structure controllable; if yes, determining whether the subsystem is a single-input single-output subsystem, if not a single-input single-output subsystem, determining whether the subsystem is strong structure input state observable, if yes, the complex network system is strong structure controllable; if not, the strong structure controllability of the complex network system cannot be determined. If it is a single-input single-output subsystem, determining whether the subsystem is strong structure controllable and observable, if yes, the complex network system is strong structure controllable; if not, the complex network system is not strong structure controllable.

Description

Technical Field

[0001] This invention relates to the field of complex network system control technology, and in particular to a method and apparatus for analyzing the strong structure controllability of complex networks with identical subsystems. Background Technology

[0002] In the context of the network age, complex network systems are ubiquitous in nature and human society, such as social networks, brain neural networks, the internet, and transportation networks. The depth of our understanding of natural or technological systems is often reflected in our ability to control them. However, how to effectively manage and control these complex network systems remains a pressing challenge. In this field, strong structure controllability analysis and optimization, as key indicators for evaluating control performance, have attracted widespread attention and significant progress has been made in research.

[0003] In many cases, due to the sheer size and complexity of network dynamics, it is difficult to accurately understand the connections and their weights in complex network systems. This has spurred the development of a new research area focused on simplifying complex network systems into structured network systems by utilizing information about the existence of connections between subsystems (rather than actual connection weights), and studying their controllability. In structured systems theory, this information about the existence of connections between subsystems is typically represented as zero / non-zero subsystems. If at least one system in the set of subsystems is controllable, then the set of systems is considered weakly structured and controllable. If all systems in the set are controllable, then the network system is considered strongly structured and controllable.

[0004] Current research in this field largely relies on idealized assumptions that neglect subsystem dynamics. These assumptions are difficult to satisfy in many scenarios or can lead to inaccurate conclusions. Therefore, research on the strong structural controllability of complex network systems that comprehensively considers subsystem dynamics has gradually attracted researchers' attention. Existing strong structural controllability analysis techniques mainly target heterogeneous network structures, where node systems can exhibit different dynamic behaviors. However, the problem of strong structural controllability in complex network systems with identical subsystems remains unsolved. Therefore, there is an urgent need to propose a strong structural controllability analysis method for complex network systems with identical subsystems to overcome the aforementioned technical shortcomings of existing techniques. Summary of the Invention

[0005] This invention aims to at least partially solve one of the technical problems in related technologies. To this end, the first objective of this invention is to propose a method for analyzing the strong structural controllability of complex networks with identical subsystems. By establishing a structured system model adapted to complex network systems with identical subsystems, this method can solve the problem of inaccurate strong structural controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods. Furthermore, it proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two aspects: having single-input single-output (SISO) subsystems and having multiple-input multiple-output (MIMO) subsystems.

[0006] The second objective of this invention is to provide a device for analyzing the strong structure controllability of complex networks with identical subsystems.

[0007] To achieve the above objectives, a first aspect of the present invention proposes a method for analyzing the strong structure controllability of complex networks with identical subsystems, comprising: S1: establishing a structured system model of a complex network system with identical subsystems. in, As a subsystem, S2: Determine the interaction structure between subsystems and between external inputs and subsystems; S3: If the complex network system is strongly structured and controllable, then determine whether the subsystem is strongly structured and controllable. Is it a single-input single-output subsystem? If not, proceed to step S4; if yes, proceed to step S5. S4: Determine if the subsystem is single-input single-output. S5: Determine whether the input state is strongly structured and observable. If yes, the complex network system is strongly structured and controllable; otherwise, the strong structured and controllable nature of the complex network system cannot be determined. Whether the complex network system is strongly structure-controllable and observable; if so, then the complex network system is strongly structure-controllable; if not, then the complex network system is not strongly structure-controllable.

[0008] According to the strong structure controllability analysis method for complex networks with identical subsystems according to embodiments of the present invention, a structured system model of the complex network system with identical subsystems is first established. Determine the related system Is the structure strongly controllable? If not, the complex network system is not strongly controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem... Is the input state observable with a strong structure? If yes, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input, single-output subsystem, then determine the subsystem... The method determines whether a complex network system is strongly structurally controllable and observable. If so, the complex network system is strongly structurally controllable; otherwise, it is not. Therefore, this method establishes a structured system model adapted to complex network systems with identical subsystems, thus solving the problem of inaccurate strong structural controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods. Furthermore, it proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two perspectives: single-input single-output (SISO) subsystems and multiple-input multiple-output (MIMO) subsystems.

[0009] Furthermore, the method for analyzing the strong structure controllability of complex networks with identical subsystems according to the above embodiments of the present invention may also have the following additional technical features:

[0010] According to one embodiment of the present invention, the structured system model includes several identical subsystems. A system with m external inputs and the interaction structure between subsystems and between external inputs and subsystems. .

[0011] According to an embodiment of the present invention, in step S2, the associated system is determined. Whether it has strong structural controllability includes: network structure information based on structured system models. Extracting the Partner Matrix ; Verify the system's association with directed graphs using a directed graph coloring mechanism. and Whether it can be colored; if not, then the complex network system is not strongly structured and controllable.

[0012] According to one embodiment of the present invention, a coloring mechanism of a directed graph is used to verify an association system. Associative directed graph and Whether a coloring is possible requires verification of the associated directed graph. and Can it be stained?

[0013] According to an embodiment of the present invention, in step S4, the subsystem is determined. Whether the input state is strongly structured includes: network structure information based on a structured system model. Extracting the Partner Matrix Verify the association of directed graphs using the coloring mechanism of directed graphs. and Is it colorable? If so, then the subsystem... It is a strongly structured input state observable; otherwise, the subsystem... It is not a strong structure input state observable.

[0014] According to an embodiment of the present invention, in step S5, the subsystem is determined. Whether the structure is strongly controllable and observable includes: network structure information based on a structured system model. and Extract the partner matrix separately and The subsystems were verified using a directed graph coloring mechanism. Whether the structure is controllable and observable.

[0015] According to one embodiment of the present invention, the subsystem is verified using a directed graph coloring mechanism. Whether the structure is strongly controllable includes: verifying the subsystem using a directed graph coloring mechanism. Associative directed graph and Can it be stained? If not, then the subsystem... It is not strongly structure-controllable; if it is, then the subsystem... It is strongly structured and controllable.

[0016] According to one embodiment of the present invention, the subsystem is verified using a directed graph coloring mechanism. Whether it is a strong structure observable includes: verifying the subsystem using a directed graph coloring mechanism. The associated directed graph and Can it be stained? If not, then the subsystem It is not a strongly structured observable; if it is, then the subsystem... It is a strong structure energy observation.

[0017] According to an embodiment of the present invention, the partner matrix is ​​extracted using the following formula. and ::

[0018]

[0019]

[0020] in, Represent matrices respectively The ij-th matrix block in Represent matrices respectively , The ii-th matrix block in the matrix.

[0021] To achieve the above objectives, a second aspect of the present invention provides a strongly structured controllability analysis device for complex networks with identical subsystems. The device includes: a network system establishment module, used to establish a structured system model of the complex network system with identical subsystems. ,in, As a subsystem, The system comprises an interaction structure between subsystems and between external inputs and subsystems; a strong structure controllability analysis module is used to determine the interaction structure of the system. Whether it has strong structural controllability; if not, then the complex network system is not strongly structurally controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem. If the input state is observable, then the complex network system is strongly structured and controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input single-output subsystem, then the subsystem is determined... Whether the complex network system is strongly structure-controllable and observable; if so, then the complex network system is strongly structure-controllable; if not, then the complex network system is not strongly structure-controllable.

[0022] According to an embodiment of the present invention, a strongly structured controllability analysis device for complex networks with identical subsystems is provided, wherein the network system establishment module establishes a structured system model of the complex network system with identical subsystems. Strong structure energy control analysis module judges the related system Is the structure strongly controllable? If not, the complex network system is not strongly controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem... Is the input state observable with a strong structure? If yes, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input, single-output subsystem, then determine the subsystem... Whether a complex network system is strongly structurally controllable and observable is a key factor in determining its structural controllability. If it is, then the complex network system is strongly structurally controllable; otherwise, it is not. Therefore, this device addresses the problem of inaccurate strong structural controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods by establishing a structured system model adapted to complex network systems with identical subsystems. Furthermore, it proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two perspectives: single-input single-output (SISO) subsystems and multiple-input multiple-output (MIMO) subsystems.

[0023] The technical solution of the present invention has the following advantages compared with the prior art:

[0024] 1. The present invention provides a method and apparatus for analyzing the strong structure controllability of complex network systems with identical subsystems. It establishes a structured system model adapted to complex network systems with identical subsystems, and solves the problem of inaccurate strong structure controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods.

[0025] 2. The present invention provides a method and apparatus for analyzing the strong structural controllability of complex network systems with identical subsystems, which proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two aspects: having a single-input single-output (SISO) subsystem and having a multiple-input multiple-output (MIMO) subsystem.

[0026] 3. This method employs a directed graph coloring mechanism to perform strong structure controllability analysis, enabling it to adapt to the large scale and other complex characteristics of complex network systems.

[0027] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0028] Figure 1 A flowchart of a method for analyzing the strong structure controllability of complex networks with identical subsystems according to an embodiment of the present invention;

[0029] Figure 2 One embodiment of the present invention comprises two complex network systems (A,B,C,W,H) and (A',B',C',W,H) with the same associated system structure, wherein (a) is a schematic diagram of the associated system structure, (b) is a schematic diagram of a multi-input multi-output subsystem (A,B,C), and (c) is a schematic diagram of a single-input single-output subsystem (A',B',C').

[0030] Figure 3 Verification of Association Systems via Directed Graph Coloring Mechanism in One Embodiment of the Present Invention A schematic diagram of strong structure controllability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process;

[0031] Figure 4 This is a verification subsystem using a directed graph coloring mechanism according to an embodiment of the present invention. This is a schematic diagram of the strong structure input state observability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process;

[0032] Figure 5 This is a verification subsystem using a directed graph coloring mechanism according to an embodiment of the present invention. A schematic diagram of strong structure controllability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process;

[0033] Figure 6 This is a verification subsystem using a directed graph coloring mechanism according to an embodiment of the present invention. A schematic diagram of strong structure observability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. staining process

[0034] Figure 7 This is a block diagram of a complex network strong structure controllability analysis device with identical subsystems according to an embodiment of the present invention. Detailed Implementation

[0035] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0036] The following description, with reference to the accompanying drawings, describes the method and apparatus for analyzing the strong structure controllability of complex networks with identical subsystems, as proposed in embodiments of the present invention.

[0037] Figure 1 This is a flowchart of a method for analyzing the strong structure controllability of complex networks with identical subsystems according to an embodiment of the present invention.

[0038] like Figure 1 As shown, the method for analyzing the strong structure controllability of complex networks with identical subsystems according to embodiments of the present invention may include the following steps:

[0039] S1: Establish a structured system model for complex network systems with identical subsystems. ,in, As a subsystem, It is a system of interaction structures between subsystems and between external inputs and subsystems.

[0040] S2: Determine the related system Whether it is strongly structured and controllable; if not, then complex network systems are not strongly structured and controllable.

[0041] S3: If so, then determine the subsystem. Is it a single-input single-output subsystem? If not, proceed to step S4; if yes, proceed to step S5.

[0042] S4: Judgment Subsystem Whether the input state is observable is a strong structure; if so, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined.

[0043] S5: Judgment Subsystem Whether the complex network system is strongly structure-controllable and observable depends on whether it is. If so, the complex network system is strongly structure-controllable; otherwise, the complex network system is not strongly structure-controllable.

[0044] According to the strong structure controllability analysis method for complex networks with identical subsystems according to embodiments of the present invention, a structured system model of the complex network system with identical subsystems is first established. Determine the related system Is the structure strongly controllable? If not, the complex network system is not strongly controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem... Is the input state observable with a strong structure? If yes, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input, single-output subsystem, then determine the subsystem... The method determines whether a complex network system is strongly structurally controllable and observable. If so, the complex network system is strongly structurally controllable; otherwise, it is not. Therefore, this method establishes a structured system model adapted to complex network systems with identical subsystems, thus solving the problem of inaccurate strong structural controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods. Furthermore, it proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two perspectives: single-input single-output (SISO) subsystems and multiple-input multiple-output (MIMO) subsystems.

[0045] According to one embodiment of the present invention, the structured system model includes several identical subsystems. A system with m external inputs and the interaction structure between subsystems and between external inputs and subsystems. .

[0046] Specifically, in step S1, a structured system model of a complex network system with identical subsystems is established. ,include:

[0047] (1) Introducing the pattern matrix To represent zero / non-zero / arbitrary structures, the pattern matrix The elements are composed of the symbol set {0, ,?} represents, where 0 represents zero, * represents non-zero, and ? represents any real number; each pattern matrix There is a corresponding pattern set P(M), which represents the set of all real matrices that satisfy a specific structure:

[0048] Among them, M ij Let represent the ij-th element in the pattern matrix M, and p and q represent the number of rows and columns of the pattern matrix M, respectively;

[0049] (2) By connecting a series of structured systems through the structured interconnection principle, a system model of a complex network system with the same subsystems is established; a complex network with N identical subsystems is represented by the following formula:

[0050]

[0051] Where, k∈{1,…,N}, x& (k) x represents (k) The derivative of and

[0052] The interconnection rules between subsystems and between external inputs and subsystems are expressed by the following formula:

[0053]

[0054] Among them, y (j) u represents the output of the j-th subsystem. (l) Let l represent the l-th external input, where l∈{1,…,N}. and

[0055] Through the transformation of equation (2), N identical subsystems are interconnected to form a global system with a state dimension of nN×nN and m control signals, which can then be expressed in a compact form as follows:

[0056]

[0057] in, and Complex network systems with identical subsystems, i.e., satisfying Complex network systems are represented by (A, B, C, W, H). It is understandable that a family of systems with the same pattern as equation (3) can be derived from... express.

[0058] According to an embodiment of the present invention, in step S2, the associated system is determined. Whether it has strong structural controllability includes: network structure information based on structured system models. Extracting the Partner Matrix ; Verify the system's association with directed graphs using a directed graph coloring mechanism. and Whether it can be colored; if not, then the complex network system is not strongly structured and controllable.

[0059] Furthermore, according to one embodiment of the present invention, the association system is verified using a coloring mechanism of a directed graph. Associative directed graph and Whether a coloring is possible requires verification of the associated directed graph. and Can it be stained?

[0060] Specifically, the partner matrix can be extracted using the following formula. :

[0061]

[0062] in, Representation matrix The ij-th matrix block in Representation matrix The ii-th matrix block in the matrix.

[0063] Then we can determine that the system's associated directed graph is... and Then, the coloring mechanism of directed graphs is used to verify the system's associated directed graphs. and Can it be colored? If the system is an associated directed graph. and If coloring is not possible, it indicates that the complex network system is not strongly structured and controllable; if the system is an associated directed graph... and If staining is possible, continue with step S3 above.

[0064] It is important to understand that the above verification process involves the coloring mechanism of directed graphs, for example, for directed association graphs. Where V:={1,2,…,q} is the set of nodes in the association graph. It is the set of edges in the associated graph, E * and E ？ These are the sets of solid edges and dashed edges in the directed graph, respectively. The specific steps of the coloring mechanism are as follows:

[0065] (1) First, color all nodes in V white;

[0066] (2) If node i has one and only one white outward neighbor j, and the edge between the two nodes is a solid line edge, then color node j black.

[0067] (3) Repeat step (2) until no new nodes are colored;

[0068] (4) After the coloring is complete, if nodes 1, 2, ..., p are all colored black, then the association graph... It is dyeable, and conversely, it is not dyeable.

[0069] According to an embodiment of the present invention, in step S4, the determination subsystem Whether the input state is strongly structured includes: network structure information based on a structured system model. Extracting the Partner Matrix Verify the association of directed graphs using the coloring mechanism of directed graphs. and Is it colorable? If so, then the subsystem... It is a strongly structured input state observable; otherwise, the subsystem... It is not a strong structure input state observable.

[0070] According to an embodiment of the present invention, in step S5, the determination subsystem Whether the structure is strongly controllable and observable includes: network structure information based on a structured system model. and Extract the partner matrix separately and The subsystems were verified using a directed graph coloring mechanism. Whether the structure is controllable and observable.

[0071] According to an embodiment of the present invention, the partner matrix is ​​extracted using the following formula. and ::

[0072]

[0073]

[0074] in, Represent matrices respectively The ij-th matrix block in Represent matrices respectively The ii-th matrix block in the matrix.

[0075] According to one embodiment of the present invention, a coloring mechanism of a directed graph is used to verify the subsystem. Whether the structure is strongly controllable includes: verifying the subsystem using a directed graph coloring mechanism. Associative directed graph and Can it be stained? If not, then the subsystem It is not strongly structure-controllable; if it is, then the subsystem... It is strongly structure-controllable. Specifically, the verification subsystem utilizes a directed graph coloring mechanism. Associative directed graph and Whether a coloring is possible requires verification of the associated directed graph. and Can it be stained?

[0076] According to one embodiment of the present invention, a coloring mechanism of a directed graph is used to verify the subsystem. Whether it is a strong structure observable includes: verifying the subsystem using a directed graph coloring mechanism. The associated directed graph and Can it be stained? If not, then the subsystem It is not a strongly structured observable; if it is, then the subsystem... It exhibits strong structure observability. Specifically, the subsystem is verified using a directed graph coloring mechanism. Associative directed graph and Whether a coloring is possible requires verification of the associated directed graph. and Can it be stained?

[0077] The following examples illustrate in detail the strong structure controllability analysis method for complex network systems with identical subsystems proposed in this invention.

[0078] A method for analyzing the strong structure controllability of complex network systems with identical subsystems includes the following steps:

[0079] 1. For example Figure 2 The diagram shows two complex network systems (A,B,C,W,H) and (A',B',C',W,H) with the same associated system structure. (a) is a schematic diagram of the associated system structure, (b) is a schematic diagram of the multi-input multi-output subsystem (A,B,C), and (c) is a schematic diagram of the single-input single-output subsystem (A',B',C').

[0080] The expression for the association system (W,H) of the complex network system shown in (a) is:

[0081]

[0082] (b) shows a subsystem (A,B,C) that is a multiple-input multiple-output subsystem, and its expression is:

[0083]

[0084] (c) shows a subsystem (A', B', C') that is a single-input single-output subsystem, and its expression is:

[0085]

[0086] Where w ij ,h i ,λ i ,u i ,o i ≠0; μ i ≠0, i∈{2,4,5}, that is, except for μ1 and μ3 which are arbitrary values, all other parameter values ​​are non-zero.

[0087] 2. First, the complex network system (A,B,C,W,H) with multiple input and multiple output subsystems is discriminated, and its structured system model is extracted using the methods defined in equations (1), (2), and (3).

[0088]

[0089]

[0090] 3. Extract the partner matrix using the methods defined in equations (4) and (5). and as follows:

[0091]

[0092] 4. According to step S2, through Figure 3 The method shown utilizes a directed graph coloring mechanism to verify directed graphs. and All can be stained, i.e., related systems It is strongly structured and controllable, and the subsystem Since this is a multiple-input multiple-output subsystem, step S4 is executed. It should be noted that... Figure 3 This invention uses a directed graph coloring mechanism to verify the association system. A schematic diagram of strong structure controllability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process.

[0093] 5. Through Figure 4 The method shown utilizes a directed graph coloring mechanism to verify directed graphs. and It is colorable, i.e., a subsystem. It has strong structured input state observability, therefore complex network systems It is strongly structure-controllable. It should be noted that... Figure 4 This invention verifies the subsystem using a directed graph coloring mechanism. This is a schematic diagram of the strong structure input state observability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process.

[0094] 6. Next, the complex network system (A', B', C', W, H) with a single-input single-output subsystem is discriminated, and its structured system model is extracted using the methods defined in equations (1), (2), and (3).

[0095]

[0096] 7. Extract the partner matrix using the methods defined in equations (4) and (5). and as follows:

[0097]

[0098] 8. As can be seen from the above, the system of association... It is controllable, and the subsystem Since it is a single-input single-output subsystem, step S5 is executed.

[0099] 9. Through Figure 5 and Figure 6 The method shown utilizes a directed graph coloring mechanism to verify directed graphs. and as well as and All can be stained, i.e., subsystems It is a strongly structured, controllable, and observable complex network system. It is strongly structure-controllable. It should be noted that... Figure 5 This is a verification subsystem using a directed graph coloring mechanism, as described in an embodiment of the present invention. A schematic diagram of strong structure controllability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process; Figure 6 This is a verification subsystem using a directed graph coloring mechanism, as described in an embodiment of the present invention. A schematic diagram of strong structure observability, where (a) is an associated directed graph. The coloring process, (b) is an associated directed graph. The staining process.

[0100] In summary, the strongly structured controllability analysis method for complex networks with identical subsystems according to embodiments of the present invention first establishes a structured system model of the complex network system with identical subsystems. Determine the related system Is the structure strongly controllable? If not, the complex network system is not strongly controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem... Is the input state observable with a strong structure? If yes, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input, single-output subsystem, then determine the subsystem... The method determines whether a complex network system is strongly structurally controllable and observable. If so, the complex network system is strongly structurally controllable; otherwise, it is not. Therefore, this method establishes a structured system model adapted to complex network systems with identical subsystems, thus solving the problem of inaccurate strong structural controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods. Furthermore, it proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two perspectives: single-input single-output (SISO) subsystems and multiple-input multiple-output (MIMO) subsystems.

[0101] Corresponding to the above embodiments, the present invention also proposes a strong structure controllability analysis device for complex networks with identical subsystems.

[0102] Figure 7 This is a block diagram of a strong structure controllability analysis device for complex networks with identical subsystems according to an embodiment of the present invention.

[0103] like Figure 7 As shown, the strong structure controllability analysis device 100 for complex networks with the same subsystems in this embodiment of the invention may include: a network system establishment module 110 and a strong structure controllability analysis module 120.

[0104] Among them, the network system establishment module 110 is used to establish a structured system model of a complex network system with the same subsystems. ,in, As a subsystem, This refers to the structural relationships between subsystems and between external inputs and subsystems. The strong structure controllability analysis module 120 is used to determine the relationships within the system. Is the structure strongly controllable? If not, the complex network system is not strongly controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem... Is the input state observable with a strong structure? If yes, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input, single-output subsystem, then determine the subsystem... Whether the complex network system is strongly structure-controllable and observable depends on whether it is. If so, the complex network system is strongly structure-controllable; otherwise, the complex network system is not strongly structure-controllable.

[0105] According to one embodiment of the present invention, the structured system model includes several identical subsystems. A system with m external inputs and the interaction structure between subsystems and between external inputs and subsystems. .

[0106] According to one embodiment of the present invention, the strong structure energy control analysis module 120 determines the associated system. Whether it has strong structural controllability, specifically for network structure information based on structured system models. Extracting the Partner Matrix ; Verify the system's association with directed graphs using a directed graph coloring mechanism. and Whether it can be colored; if not, then the complex network system is not strongly structured and controllable.

[0107] According to one embodiment of the present invention, the strong structure controllability analysis module 120 verifies the correlation system using a directed graph coloring mechanism. Associative directed graph and Whether a coloring is possible requires verification of the associated directed graph. and Can it be stained?

[0108] According to one embodiment of the present invention, the strong structure energy control analysis module 120 determines the subsystem. Whether the input state is strongly structured and observable, specifically used for network structure information based on structured system models. Extracting the Partner Matrix Verify the association of directed graphs using the coloring mechanism of directed graphs. and Is it colorable? If so, then the subsystem... It is a strongly structured input state observable; otherwise, the subsystem... It is not a strong structure input state observable.

[0109] According to one embodiment of the present invention, the strong structure energy control analysis module 120 determines the subsystem. Whether it is strongly structured, controllable, and observable, specifically for network structure information based on structured system models. and Extract the partner matrix separately and The subsystems were verified using a directed graph coloring mechanism. Whether the structure is controllable and observable.

[0110] According to one embodiment of the present invention, the strong structure controllability analysis module 120 verifies the subsystem using a directed graph coloring mechanism. Whether it is strongly structured and controllable, specifically used for verifying subsystems using directed graph coloring mechanisms. Associative directed graph and Can it be stained? If not, then the subsystem It is not strongly structure-controllable; if it is, then the subsystem... It is strongly structured and controllable.

[0111] According to one embodiment of the present invention, the strong structure controllability analysis module 120 verifies the subsystem using a directed graph coloring mechanism. Whether it is a strong structure observable, specifically used to verify the subsystem using the coloring mechanism of directed graphs. The associated directed graph and Can it be stained? If not, then the subsystem It is not a strongly structured observable; if it is, then the subsystem... It is a strong structure energy observation.

[0112] According to one embodiment of the present invention, the strong structure controllability analysis module 120 extracts the partner matrix using the following formula. and :

[0113]

[0114]

[0115] in, , Represent matrices respectively , The ij-th matrix block in , Represent matrices respectively , The ii-th matrix block in the array.

[0116] It should be noted that for details not disclosed in the strong structure controllability analysis device for complex networks with the same subsystem in the embodiments of the present invention, please refer to the details disclosed in the strong structure controllability analysis method for complex networks with the same subsystem in the embodiments of the present invention, which will not be repeated here.

[0117] According to an embodiment of the present invention, a strongly structured controllability analysis device for complex networks with identical subsystems is provided, wherein the network system establishment module establishes a structured system model of the complex network system with identical subsystems. Strong structure energy control analysis module judges the related system Is the structure strongly controllable? If not, the complex network system is not strongly controllable; if so, then determine the subsystem. Is it a single-input single-output subsystem? If it is not a single-input single-output subsystem, then determine the subsystem... Is the input state observable with a strong structure? If yes, the complex network system is strongly structure controllable; otherwise, the strong structure controllability of the complex network system cannot be determined. If it is a single-input, single-output subsystem, then determine the subsystem... Whether a complex network system is strongly structurally controllable and observable is a key factor in determining its structural controllability. If it is, then the complex network system is strongly structurally controllable; otherwise, it is not. Therefore, this device addresses the problem of inaccurate strong structural controllability analysis results caused by the independent dynamics of subsystems in traditional analysis methods by establishing a structured system model adapted to complex network systems with identical subsystems. Furthermore, it proposes sufficient and necessary conditions for the strong structural controllability of complex network systems with identical subsystems from two perspectives: single-input single-output (SISO) subsystems and multiple-input multiple-output (MIMO) subsystems.

[0118] It should be noted that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0119] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0120] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0121] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0122] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0123] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for analyzing the strong structure controllability of complex networks with identical subsystems, characterized in that, include: S1: Establish a structured system model for complex network systems with identical subsystems. ,in, As a subsystem, A system of interconnected structures for interactions between subsystems and between external inputs and subsystems; S2: Determine the associated system Whether it is strongly structure controllable; if not, then the complex network system is not strongly structure controllable. S3: If so, then determine the subsystem. Is it a single-input single-output subsystem? If not, proceed to step S4; if yes, proceed to step S5. S4: Determine the subsystem Whether the input state is strongly structured observable; if so, the complex network system is strongly structured controllable; if not, the strong structured controllability of the complex network system cannot be determined. S5: Determine the subsystem Whether the complex network system is strongly structure-controllable and observable; if so, then the complex network system is strongly structure-controllable; if not, then the complex network system is not strongly structure-controllable; wherein, in step S2, the associated system is determined. Whether it is strongly structurally controllable includes: Network structure information based on structured system model Extracting the Partner Matrix ; Verification of system associations using directed graph coloring mechanisms and Whether it can be colored; if not, then the complex network system is not strongly structured and controllable. In step S4, the subsystem is determined. Whether the input state is strongly structured observable includes: Network structure information based on structured system model Extracting the Partner Matrix ; Verifying Associated Directed Graphs Using Coloring Mechanisms and Is it colorable? If so, then the subsystem... It is a strongly structured input state observable; otherwise, the subsystem It is not a strongly structured input state observable; In step S5, the subsystem is determined. Whether a strong structure is controllable and observable includes: Network structure information based on structured system model and Extract the partner matrix separately and ; The subsystems were verified using a directed graph coloring mechanism. Whether the structure is controllable and observable.

2. The method for analyzing the strong structure controllability of complex networks with identical subsystems according to claim 1, characterized in that, The structured system model includes several identical subsystems. A system with m external inputs and the interaction structure between subsystems and between external inputs and subsystems. .

3. The method for analyzing the strong structure controllability of complex networks with identical subsystems according to claim 1, characterized in that, Verifying Association Systems Using Coloring Mechanisms in Directed Graphs Associative directed graph and Whether a coloring is possible requires verification of the associated directed graph. and Can it be stained? 4. The method for analyzing the strong structure controllability of complex networks with identical subsystems according to claim 1, characterized in that, Verify the subsystem using a directed graph coloring mechanism. Whether it is strongly structurally controllable includes: Verify the subsystem using a directed graph coloring mechanism. Associative directed graph and Can it be stained? If not, then the subsystem... It is not strongly structure-controllable; if it is, then the subsystem... It is strongly structured and controllable.

5. The method for analyzing the strong structure controllability of complex networks with identical subsystems according to claim 1, characterized in that, Verify the subsystem using a directed graph coloring mechanism. Whether it is a strong structure observable includes: Verification of the subsystem using a directed graph coloring mechanism The associated directed graph and Can it be stained? If not, then the subsystem It is not a strongly structured observable; if it is, then the subsystem... It is a strong structure energy observation.

6. The method for analyzing the strong structure controllability of complex networks with identical subsystems according to claim 1, characterized in that, The partner matrix is ​​extracted using the following formula. and : in, , Represent matrices respectively , The ij-th matrix block in , Represent matrices respectively , The ii-th matrix block in the matrix.

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