Resource-aware self-triggered hierarchical dithering pulse synchronization control method and system

Abstract

The embodiment of the application provides a resource perception-based self-triggered hierarchical pinning pulse synchronization control method and system, and relates to the technical field of automation control. The method first establishes a complex dynamic network model of a target system, and generates hierarchical network structures of a leader layer and an interactive following layer based on an invariable pinning mechanism. Then, control inputs are designed according to the complex dynamic network model and the hierarchical network structures, and then the pinning pulse synchronization control is performed on the target system according to the control inputs. For the leader layer, self-triggered driven pulse pinning control is designed, a constrained node set containing multiple nodes is determined in advance, the proportion of effective control nodes is improved, the required pulse frequency is reduced while the synchronization performance is ensured; for the interactive following layer, self-triggered control is designed, the controlled nodes determine the control application time according to the local state, global error information and centralized scheduling are not required, and the occupation amount of communication and calculation resources is reduced.

Description

Technical Field

[0001] This application relates to the field of automation control technology, and in particular to a resource-aware self-triggering hierarchical restraint pulse synchronization control method and system. Background Technology

[0002] The regulation of cooperative behavior in complex dynamic networks can be applied to fields such as engineering, biological systems, and social sciences. For example, in the process of controlling UAV formation flight, by designing appropriate external control inputs for the UAVs, multiple UAVs can execute flight control according to the control inputs, thereby regulating the flight strategy of the entire UAV system to achieve the expected cooperative behavior among the multiple UAVs. In some practical applications, since discontinuous control inputs are more reasonable, and methods such as state feedback, output feedback, or adaptive control are difficult to apply directly, discontinuous control methods such as strafe pulse control can be used to achieve system stability with a smaller pulse gain.

[0003] The strait control strategy can include single-point strait control and switching strait control. Single-point strait control applies a pulse input to only a single node in the network, while switching strait control allows the leader to strait multiple nodes. However, switching strait control requires reselecting the strait-controlled node at each pulse time based on the real-time errors of all nodes. Furthermore, the set of strait-controlled nodes for switching strait control is time-varying, resulting in high implementation costs and requiring the leader to obtain error information from all nodes, making it unsuitable for specific real-world scenarios.

[0004] While single-point control strategies can avoid node reselection issues, they always control only a single node. When the network is large, the proportion of controlled nodes becomes too small, requiring extremely high pulse frequencies to ensure system convergence. This makes it difficult for some devices to support such rapid control updates, resulting in high communication and computing resource consumption and poor system scalability. Therefore, designing an effective pulse control strategy while keeping the set of controlled nodes constant has become a pressing technical problem in this field. Summary of the Invention

[0005] In view of this, embodiments of this application provide a resource-aware self-triggering hierarchical restraint pulse synchronization control method and system to solve the problem of excessively high pulse frequency required by the restraint pulse control strategy.

[0006] According to a first aspect of this application, a resource-aware, self-triggering hierarchical restraint pulse synchronization control method is provided, the method comprising:

[0007] A complex dynamic network model of a target system is established, wherein the target system comprises a complex dynamic network consisting of multiple neural networks; the complex dynamic network model comprises a set of dynamic behavioral differential equations constructed for each node in the target system.

[0008] A hierarchical network structure for the target system is generated based on an invariant constraint mechanism. The hierarchical network structure includes a leader layer and a follower layer. The leader layer includes at least one constraint node. The constraint node is configured to directly receive constraint control input information for synchronizing the target trajectory. The follower layer includes multiple follower nodes. The follower nodes are configured to interact with neighboring nodes.

[0009] The control input is designed based on the complex dynamic network model and the hierarchical network structure. The control input includes a hierarchical controller and a self-triggering function designed based on the hierarchical network structure. The hierarchical controller includes a self-triggering pulse controller designed for the restraining nodes in the leadership layer and a self-triggering distributed controller designed for the following nodes in the following layer. The self-triggering function is used to calculate the interval of the next pulse control based on the synchronization error at the current moment.

[0010] The target system is subjected to self-triggering driven restraint pulse synchronization control according to the control input.

[0011] In some embodiments, establishing a complex dynamic network model of the target system includes:

[0012] Traverse the neural network nodes of the target system;

[0013] A dynamic behavior differential equation is constructed for each node; the dynamic behavior differential equation is used to characterize the functional relationship between the derivatives of the dynamic network state variables and the state variables, nonlinear vector functions, and control inputs;

[0014] Obtain the dynamic model of the virtual synchronization target node, wherein the virtual synchronization target node is at least one of the following: an equilibrium point, a chaotic orbit, and a periodic orbit;

[0015] A complex dynamic network model of the target system is established based on the differential equations of the nodes and the dynamic model of the virtual synchronous target nodes.

[0016] In some embodiments, the method further includes:

[0017] The network size and network type of the target system are determined by traversing the neural network nodes of the target system.

[0018] A directed topology graph is constructed based on the network size and network type. The directed topology graph includes a vertex set, an edge set, and an adjacency matrix. The matrix elements in the adjacency matrix are used to represent the connection weight between two nodes in the target system. When both nodes belong to the vertex set and the edge set, the matrix element value is greater than 0.

[0019] Key analysis tools are defined based on the directed topological structure graph, and these key analysis tools include the Laplace matrix.

[0020] In some embodiments, generating the hierarchical network structure of the target system based on an invariant constraint mechanism includes:

[0021] Obtain the information interaction status between nodes in the target system; the information interaction status is a first state or a second state; the first state indicates that there is a direct connection between nodes; the second state indicates that there is no direct connection between nodes.

[0022] If the information interaction state of the node is in the first state, the node is assigned to the leadership layer;

[0023] If the information interaction state of the node is in the second state, the node is assigned to the following layer.

[0024] In some embodiments, generating the hierarchical network structure of the target system based on the invariant constraint mechanism further includes:

[0025] Count the number of nodes in the leadership layer and the following layer;

[0026] The hierarchical network structure is generated based on the number of nodes;

[0027] The Laplace matrix is ​​decomposed into block matrices according to the hierarchical network structure. The block matrices include a first block matrix, a second block matrix, a third block matrix, and a fourth block matrix. The first block matrix describes the connection relationship between restraining nodes within the leadership layer; the second block matrix describes the connection relationship between following nodes within the following layer; the third block matrix describes the connection relationship from the following layer to the leadership layer; and the fourth block matrix describes the connection relationship from the leadership layer to the following layer.

[0028] In some embodiments, generating the hierarchical network structure based on the number of nodes includes:

[0029] Initialize the ring network according to the stated number of nodes;

[0030] Add random long-range edges to the nodes in the regular ring network; the random long-range edges are used to shorten the average distance between the nodes and maintain a high clustering coefficient.

[0031] Obtain the network generation parameters and initial state range;

[0032] Based on the network generation parameters, the node is randomly assigned an initial state within the initial state interval.

[0033] In some embodiments, the control input is designed based on the complex dynamic network model and the hierarchical network structure, including:

[0034] Define a synchronization error variable, which is used to characterize the synchronization error between the constrained dynamic network and the target network;

[0035] Based on the complex dynamic network model, the leadership pulse control gain is set according to the synchronization error variable;

[0036] The triggering time is determined through a self-triggering mechanism;

[0037] The self-triggering pulse controller is constructed based on the leadership pulse control gain, the synchronization error variable, the triggering time, and the Dirac function.

[0038] In some embodiments, the triggering time is determined by a self-triggering mechanism, including:

[0039] A triggering time determination condition is set for the restraining node; the determination condition is used to characterize the occurrence of the triggering time when the synchronization error variable reaches the exponential decay boundary;

[0040] Obtain the combined matrix; the combined matrix is ​​the result of a combination operation of a preset diagonal matrix, an input real matrix, and a constant matrix;

[0041] An error representation term is calculated based on the exponential decay boundary and the synchronization error variable; the error representation term is obtained based on the natural logarithm of the ratio of the exponential decay boundary to the synchronization error variable.

[0042] The self-triggering function is defined based on the error representation term and the combination matrix;

[0043] The triggering time is generated according to the self-triggering function and the determination condition.

[0044] In some embodiments, when designing control inputs based on the complex dynamic network model and the hierarchical network structure, the self-triggering pulse controller executes the control inputs according to the following formula:

[0045]

[0046] in, For the first i The control input of a dynamic network node self-triggering pulse controller; The first in the leadership i Pulse control gain of each dynamic network node; For synchronization error variables; t For time; Represents the Dirac function; For the first i The first dynamic network node k The next trigger moment;

[0047] The self-triggering distributed controller executes the control input according to the following formula:

[0048]

[0049] in, For the first i The control input of a dynamic network node to a self-triggered distributed controller; The coupling strength between the dynamic networks in the follower layer; These are the matrix elements of the adjacency matrix; For the first i The first following node j The state of each neighboring node; For the first i The state of each following node; t For time.

[0050] According to a second aspect of this application, a resource-aware self-triggering hierarchical restraint pulse synchronization control system is provided, the system comprising:

[0051] The model building module is used to build a complex dynamic network model of the target system, which includes a complex dynamic network composed of multiple neural networks; the complex dynamic network model includes a set of dynamic behavior differential equations constructed for each node in the target system.

[0052] The structure setting module is used to generate a hierarchical network structure of the target system based on an invariant constraint mechanism. The hierarchical network structure includes a leader layer and a follower layer. The leader layer includes at least one constraint node. The constraint node is configured to directly receive constraint control input information for synchronizing the target trajectory. The follower layer includes multiple follower nodes. The follower nodes are configured to interact with neighboring nodes.

[0053] A control input module is used to design control inputs based on the complex dynamic network model and the hierarchical network structure. The control inputs include a hierarchical controller and a self-triggering function designed based on the hierarchical network structure. The hierarchical controller includes a self-triggering pulse controller designed for the restraining nodes in the leadership layer and a self-triggering distributed controller designed for the following nodes in the follower layer. The self-triggering function is used to calculate the interval of the next pulse control based on the synchronization error at the current moment.

[0054] The synchronization control module is used to perform self-trigger driven restraint pulse synchronization control on the target system according to the control input.

[0055] Based on the above technical solutions, this application provides a resource-aware, self-triggered hierarchical restraint pulse synchronization control method and system. The method first establishes a complex dynamic network model of the target system and generates a hierarchical network structure of a leader layer and an interactive follower layer based on an invariant restraint mechanism. Then, control inputs are designed according to the complex dynamic network model and the hierarchical network structure, and restraint pulse synchronization control is executed on the target system according to the control inputs. The method constructs a hierarchical network structure containing an invariant restraint leader layer and an interactive follower layer. For the leader layer, a self-triggered pulse restraint control is designed, pre-determining a set of constrained nodes containing multiple nodes to increase the proportion of effective control nodes and reduce the required pulse frequency while ensuring synchronization performance. For the interactive follower layer, a self-triggered control is designed, enabling the controlled nodes to self-trigger and determine the control application time based on their local state, eliminating the need for global error information and centralized scheduling, thus reducing the consumption of communication and computing resources.

[0056] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0057] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0058] Figure 1 A schematic flowchart of a resource-aware self-triggering hierarchical restraint pulse synchronization control method provided in an embodiment of this application;

[0059] Figure 2 This is a schematic diagram of the restraint pulse synchronization control process provided in the embodiments of this application;

[0060] Figure 3This is a schematic diagram of the process of dividing a hierarchical network structure according to an embodiment of this application;

[0061] Figure 4 This is a schematic diagram of the control input design process provided in an embodiment of this application;

[0062] Figure 5 A schematic diagram of the structure of a resource-aware self-triggering hierarchical restraint pulse synchronization control system provided in an embodiment of this application. Detailed Implementation

[0063] The present application will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present application can be combined with each other.

[0064] In this embodiment, pulse synchronization control is an automated control method used to regulate the cooperative behavior of complex dynamic networks. Pulse synchronization control can be applied to fields such as engineering technology, biological systems, and social sciences. For example, in the process of controlling UAV formation flight, by designing appropriate external control inputs for the UAVs, multiple UAVs can execute flight control according to the control inputs, thereby regulating the flight strategy of the entire UAV system to achieve the expected cooperative behavior among multiple UAVs.

[0065] Pinning pulse control, as a pulse synchronization control method, can include single-point pinning strategies and switching pinning strategies. Single-point pinning applies a pulse input to only a single node in the network, while switching pinning allows the leader to pin multiple nodes. However, switching pinning requires reselecting the pinned node at each pulse time based on the real-time errors of all nodes. Furthermore, the set of pinned nodes in switching pinning is time-varying, resulting in high implementation costs and requiring the leader to obtain error information from all nodes, making it unsuitable for specific real-world scenarios.

[0066] While the single-point restraint strategy can avoid the node reselection problem, it only restrains a single node. When the network is large, the proportion of restrained nodes is too small, requiring an extremely high pulse frequency to ensure system convergence. This makes it difficult for some devices to support such rapid control updates, resulting in high consumption of communication and computing resources and poor system scalability.

[0067] Pulse control also involves the control execution process, that is, the control execution method of nodes in the controlled network. The result of pulse control requires that each node executes the pulse control input synchronously, which is difficult to achieve for self-triggered pulse control methods. Since distributed characteristics are a basic requirement of event-driven protocols in complex networks, and synchronous triggering is a global constraint, each node needs to independently generate its own pulse timing.

[0068] In some embodiments, synchronization of heterogeneous coupled neural networks can be achieved by designing a pulse-coupled controller, realizing invariant constraint, but the pulse sequence still needs to remain synchronized. Although edge-based event-triggered communication protocols can achieve asynchronous information sharing on each edge of the network, a unified pulse triggering time is still required. While some progress has been made in asynchronous pulse control for linear multi-agent systems, the relevant conclusions require that the system possess asymptotic stability even without control input, and pulse control only plays a role in accelerating convergence.

[0069] In summary, how to achieve a truly distributed self-triggered pulse control strategy that enables each node to independently generate control moments based on its own state while ensuring the synchronization performance of complex networks, while keeping the set of restraining nodes unchanged, has become an urgent technical problem to be solved.

[0070] To address the issue of excessively high pulse frequencies required by the tethered pulse control strategy, this application provides a resource-aware, self-triggering hierarchical tethered pulse synchronization control method in some embodiments. This method constructs a two-layer control architecture consisting of a leader layer and a follower layer. Tethered nodes in the leader layer only receive leader information and do not participate in neighbor communication. Each tethered node is equipped with a self-triggering pulse controller, which predicts the next pulse time and applies the pulse input through a self-triggering mechanism. Follower layer nodes only receive neighbor information and are equipped with self-triggering coupling drivers, avoiding continuous monitoring of local interactions. The set of tethered nodes remains unchanged during the control process, and the pulse time of each node is independently generated by self-triggering rules, requiring no global synchronization. Furthermore, based on Lyapunov stability theory and algebraic graph theory, it is proven that this framework can achieve asymptotic synchronization of complex dynamic networks. Simultaneously, the self-triggering mechanism effectively avoids Zeno behavior, significantly reducing communication and computing resource consumption and improving engineering feasibility and flexibility.

[0071] The resource awareness mentioned here refers to the ability of the restraining node to monitor, evaluate, and utilize the state information of the limited communication, computing, and energy resources in the network in real time based on a configured self-triggering pulse controller. It also involves predicting the next pulse time and applying the pulse input through a self-triggering mechanism to dynamically optimize the triggering and execution of the control strategy, rather than operating according to a fixed cycle or ignoring resource constraints. Based on this, the execution time of the next control action (pulse) of the restraining and following nodes is not fixed by an external clock, but is calculated jointly by the current state and the current resource level. Combined with the hierarchical restraint principle, in complex networks, restraint control only needs to control a subset of key nodes, thereby adjusting the amplitude, width, or frequency of the pulse through resource awareness to optimize the energy consumption and efficiency of pulse control.

[0072] The method can be applied to electronic devices with data processing capabilities. These electronic devices include, but are not limited to, computers, servers, mobile terminals, smart wearable devices, and industrial control machines. For ease of description, this application embodiment uses an electronic device as the execution subject of the method. It should be understood that the method can also be applied to other types of execution subjects, which are not illustrated in this application embodiment. Figure 1 As shown, the method includes:

[0073] S101. Establish a complex dynamic network model of the target system.

[0074] When performing traction pulse synchronization control, a complex dynamic network model of the target system can be established based on the network characteristics of the target system. The target system comprises a complex dynamic network consisting of multiple neural networks. This complex dynamic network model includes a set of dynamic behavioral differential equations constructed for each node in the target system.

[0075] like Figure 2 As shown, in order to establish a complex dynamic network model, in some embodiments, when establishing a complex dynamic network model of the target system, the neural network nodes of the target system can be traversed first, and a dynamic behavior differential equation can be constructed for each node. The dynamic behavior differential equation is used to characterize the functional relationship between the derivatives of the dynamic network state variables and the state variables, nonlinear vector functions, and control inputs.

[0076] For example, the target system is based on N The hierarchical restraint pulse synchronization control problem of a follower network consisting of dynamic network nodes can be formulated as follows: by calculating the control input of each node through model calculation, the state of the nodes in the network can be asymptotically synchronized to the target state. Then the... i ( i =1, 2, , N The dynamic network model using 10 nodes can be represented as:

[0077]

[0078] In the formula, Indicates the first i Derivatives of the state variables of a dynamic network node; Indicates the first i The state vectors of each dynamic network node, and , express n A set of 3D real-valued vectors; Represents a nonlinear function; This represents the control input, i.e., the controller that needs to be designed; Represents a diagonal matrix; This represents the input real matrix, i.e. express N × N A real matrix of the form.

[0079] After establishing the differential equations of the nodes, the dynamic model of the virtual synchronization target node can also be obtained, where the virtual synchronization target node is at least one of the following: an equilibrium point, a chaotic orbit, and a periodic orbit. Then, based on the differential equations of the nodes and the dynamic model of the virtual synchronization target node, a complex dynamic network model of the target system is established.

[0080] For example, after establishing the differential equations of the nodes, a synchronization objective function can be introduced. This serves as a virtual synchronization target node for dynamic network synchronization. The synchronization target function... The synchronization objective function can be used to represent a virtual synchronization target node in an equilibrium point, a chaotic state, or a periodic orbit. The rate of change of satisfies the following relationship:

[0081]

[0082] in, Represents the state derivative of the target network; Indicates the state of the target network, i.e. ; Represents a diagonal matrix; Indicates an input real matrix; This represents a nonlinear function.

[0083] In some embodiments, a specific, computable underlying network model can also be defined based on the constructed complex dynamic network model to define key analytical tools. Therefore, when establishing a large-scale complex dynamic network model, the network size and type of the target system can be determined by traversing the neural network nodes of the target system. A directed topology graph can then be constructed based on the network size and type, and key analytical tools, including the Laplacian matrix, can be defined based on this directed topology graph. The directed topology graph includes a vertex set, an edge set, and an adjacency matrix; the matrix elements in the adjacency matrix represent the connection weights between two nodes in the target system; when both nodes belong to both the vertex set and the edge set, the matrix element values ​​are greater than 0.

[0084] For a target system containing N nodes, the network size and type can be determined by traversing the nodes in the target system; that is, the target system is a small-world network containing N nodes. Then, a directed topology graph is constructed based on the network size and type. The directed topology graph can be represented as:

[0085]

[0086] in, Represents the vertex set, i.e. ; Represents the edge set, i.e. ; Represents the adjacency matrix, i.e. , its first The elements are .

[0087] For nodes in the vertex set, If and only if hour, ,otherwise And, if Then it is called a diagram. It is an undirected graph.

[0088] Furthermore, based on the directed topological structure graph, key analytical tools including the Laplace matrix are defined, where the Laplace matrix... It is a core matrix in graph theory and network science, used to represent the connectivity of the entire network, and can be derived from the adjacency matrix. That is, in hour, = ;when hour, .

[0089] For example, consider a complex dynamic network target system containing 50 neural networks, where the dynamic behavior of each node is described by the following differential equation:

[0090]

[0091] In the formula, Indicates the first i Derivatives of the state variables of a dynamic network node; Indicates the first i The state of a dynamic network node i =1, 2, 50; The input to be designed represents the control input to be designed, while the controller to be designed represents the controller to be designed. It is a nonlinear vector function; Represents a diagonal matrix. This represents the input real matrix, i.e. It is a constant matrix.

[0092] To achieve network synchronization, a virtual synchronization target node can be introduced. It can be one of the following: an equilibrium point, a chaotic orbit, or a periodic orbit. Its dynamic model is expressed as:

[0093]

[0094] in, Represents the state derivative of the target network; Indicates the state of the target network, i.e. ; Represents a diagonal matrix; Indicates an input real matrix; This represents a nonlinear function.

[0095] Then the diagonal matrix can be represented as:

[0096]

[0097] The input real matrix can be represented as:

[0098]

[0099] in, Therefore, based on the nonlinear function, it can be calculated that:

[0100]

[0101] Where j represents the first... j A constraint node. That is... j =1, 2, 3. Based on the above calculations, the initial conditions can be determined as follows: Accordingly, the control objective is to design control inputs for each node. This allows the state of all nodes to asymptotically synchronize with the virtual target, that is:

[0102]

[0103] in, Indicates the first i Each node t Synchronization error at specific times.

[0104] For a small-world network consisting of 50 nodes, a directed topology graph can be constructed. ,in Represents the vertex set, i.e. , Represents an edge set. Let be the corresponding adjacency matrix. Correspondingly, the Laplace matrix is... Similarly, when hour, = ;when hour, .

[0105] S102. Generate the hierarchical network structure of the target system based on the invariant constraint mechanism.

[0106] After establishing a complex dynamic network model of the target system, a hierarchical network structure for the target system can be generated based on an invariant constraint mechanism. This hierarchical network structure includes a leader layer and a follower layer. The leader layer includes at least one constraint node, which can directly receive constraint control input information to synchronize the target trajectory. The follower layer includes multiple follower nodes, and these follower nodes can interact with their neighboring nodes.

[0107] To determine the leadership and followers, such as Figure 3 As shown, in some embodiments, when generating the hierarchical network structure of the target system based on the invariant constraint mechanism, the information interaction state between nodes in the target system can be obtained first. The information interaction state can be a first state or a second state. The first state indicates that there is a direct connection between the leader and the follower nodes; the second state indicates that there is no direct connection between the leader and the follower nodes.

[0108] The node's affiliation is then determined based on the information interaction status. If the node's information interaction status is in the first state, the node is assigned to the leadership layer; if the node's information interaction status is in the second state, the node is assigned to the follower layer.

[0109] Based on whether there is direct information exchange between network nodes and the leader node, the vertex set can be... It is divided into two levels, namely the leadership level. , and following layer Among them, the leadership The nodes included are called restraint nodes, which can directly receive restraint control input information from the target trajectory and assume the role of leadership in synchronization guidance. Follower layer The included nodes are called follower nodes, which can interact with neighboring nodes and achieve synchronization with the leadership through distributed control.

[0110] For example, by reading the information interaction status, it can be determined whether there is direct information interaction between network nodes and the leader node. If there is a direct connection between the leader node and network node i, then that node can be assigned to the leadership level. Otherwise, assign the node to the follower layer, i.e. .

[0111] After dividing the nodes into layers, the Laplace matrix can be further divided into blocks according to the layered structure. That is, in some embodiments, when generating the layered network structure of the target system based on the invariant constraint mechanism, the number of nodes in the leader layer and the follower layer can be counted first, and the layered network structure can be generated according to the number of nodes.

[0112] When generating a hierarchical network structure based on the number of nodes, a regular ring network can be initialized according to the number of nodes, and random long-range edges can be added to the nodes in the regular ring network. These random long-range edges are used to shorten the average distance between nodes and maintain a high clustering coefficient. Then, network generation parameters and an initial state interval are obtained, and based on the network generation parameters, initial states are randomly assigned to nodes within the initial state interval.

[0113] The Laplace matrix is ​​then decomposed into block matrices according to the hierarchical network structure. These block matrices include a first block matrix, a second block matrix, a third block matrix, and a fourth block matrix. The first block matrix describes the connections between restraining nodes within the leadership layer; the second block matrix describes the connections between following nodes within the following layer; the third block matrix describes the connections from the following layer to the leadership layer; and the fourth block matrix describes the connections from the leadership layer to the following layer.

[0114] For example, when constructing a hierarchical network structure induced by invariant constraint control, a hierarchical network structure can be constructed first. Assuming that in a dynamic network... Each node is directly constrained by the leader node, i.e., the constraining layer. All other nodes belong to the follower layer, denoted as .

[0115] If the 50-node dynamic network is divided into two layers according to the constant constraint mechanism, namely the leader layer and the follower layer, then for the leader layer... Network nodes 1-3 can be selected from 50 network nodes as control nodes, directly receiving control input information for the synchronized target trajectory and undertaking the leadership role in synchronization guidance. For the follower layer... Of the 50 network nodes, the remaining 47 nodes, excluding the three leadership nodes which are controlled by the target node, can be classified into the follower layer. Follower nodes only interact with their neighboring nodes and achieve synchronization with the leadership layer through distributed control.

[0116] Then, the Newman-Watts (NW) small-world network algorithm is used to generate a network topology containing 50 nodes. Nodes 1 to 3 are designated as the leadership layer. The remaining 47 nodes constitute the follower layer. By setting the network generation parameters to... =0.7763. Therefore, the initial state of all nodes can be found in the initial state interval [...]. Randomly generated within [10, 10].

[0117] Then, based on the hierarchical network structure, the Laplacian matrix is ​​divided into blocks. The resulting Laplacian matrix after the hierarchical structure... This corresponds to four partitioned matrices, namely:

[0118]

[0119] in, Represents the Laplace matrix; This represents the first block matrix, i.e. OK A block matrix of columns; This represents the second block matrix, i.e. OK A block matrix of columns; This represents the third block matrix, i.e. OK A block matrix of columns; This represents the fourth block matrix, i.e. OK A block matrix of columns.

[0120] S103. Design control inputs based on complex dynamic network models and hierarchical network structures.

[0121] After generating the hierarchical network structure of the target system based on the invariant restraint mechanism, control inputs can be designed according to the complex dynamic network model and the hierarchical network structure. The control inputs include a hierarchical controller and a self-triggering function designed based on the hierarchical network structure. The hierarchical controller executes the control inputs according to the control characteristics of the corresponding level to achieve coordinated control of the restraint pulses. The self-triggering function calculates the interval of the next pulse control based on the synchronization error at the current moment, enabling each controlled node to self-trigger and determine the pulse application time based on its local state using a self-triggering driven asynchronous restraint pulse control mechanism.

[0122] Since the hierarchical network structure includes two levels, the leader level and the follower level, and the control pulse synchronization methods of the two levels are different, the hierarchical controller in the control input designed according to the complex dynamic network model and the hierarchical network structure also includes two types of controllers: a self-triggering pulse controller designed for the control nodes in the leader level and a self-triggering distributed controller designed for the follower nodes in the follower level.

[0123] like Figure 4 As shown, in order to determine the invariant restraint pulse control input driven by the leader layer, in some embodiments, when designing the control input based on the complex dynamic network model and hierarchical network structure, a synchronization error variable can be defined first. This synchronization error variable characterizes the synchronization error between the restrained dynamic network and the target network. Then, based on the complex dynamic network model, the leader layer pulse control gain is set according to the synchronization error variable.

[0124] For example, the first can be defined iThe synchronization error variable between the constrained dynamic network and the target network is:

[0125]

[0126] in, Indicates the first i Each node t Synchronization error at time, ; For the first i The state of each node; This indicates the state of the target network.

[0127] The dynamics satisfied by the synchronization error variable are:

[0128]

[0129] in, Indicates the first i Each node t The derivative of the synchronization error at time t, ; Represents a diagonal matrix; Indicates the first i Each node t Synchronization error at any given moment; Indicates an input real matrix; Represents a nonlinear function; For the first i The state of each node; Indicates the state of the target network; This represents the control input of the checkpoints in the leadership structure.

[0130] Based on this hierarchical structure, targeting the leadership level A constant restraint pulse control input with self-triggering function can be designed, specifically as follows:

[0131]

[0132] In the formula, Indicates the pulse control gain of the leadership layer; Represents the Dirac function; Indicates the first i Each node t Synchronization error at specific times. Indicates the first i The k-th trigger time of a dynamic network node is generated by a self-triggering mechanism.

[0133] The triggering time is then determined through a self-triggering mechanism. Specifically, when determining the triggering time, a triggering condition can be set for the restraining node. This condition characterizes the occurrence of a triggering time when the synchronization error variable reaches the exponential decay boundary.

[0134] Next, a combination matrix is ​​obtained, which is the result of combining a preset diagonal matrix, an input real matrix, and a constant matrix. Then, an error representation term is calculated based on the exponential decay boundary and the synchronization error variable. This error representation term is obtained by calculating the natural logarithm of the ratio of the exponential decay boundary and the synchronization error variable. Based on the error representation term and the combination matrix, a self-triggering function is defined, and a trigger time is generated according to the self-triggering function and the judgment conditions.

[0135] For example, for the leadership The dynamic triggering time of the i-th restraining node in the equation can be determined by the following formula:

[0136]

[0137] in, Indicates the first i The first dynamic network node k+ One trigger time; It is a constant, satisfying and ; For synchronization error variables; The attenuation rate parameters to be designed for the leadership team. The infimum of a set is the largest lower bound of the set.

[0138] It can be seen that for any The self-triggering mechanism guarantees This holds true consistently, meaning the synchronization error of the restraint layer nodes converges exponentially. A self-triggered pulse controller is then constructed based on the leader pulse control gain, synchronization error variable, triggering time, and Dirac function. Therefore, the self-triggered pulse controller can execute the control input according to the following formula:

[0139]

[0140] in, For the first i The control input of a dynamic network node self-triggering pulse controller; As the first in the leadership i Pulse control gain of each dynamic network node; For synchronization error variables; t For time; Represents the Dirac function; For the first i The first dynamic network node kThe next trigger moment;

[0141] Accordingly, the self-triggering function of the leadership layer is:

[0142]

[0143] in, It is a diagonal matrix; D It is a constant matrix, such as the Lipschitz constant matrix; Input a real matrix; This is the boundary of exponential decay; Synchronization error at the trigger moment; For the first i The first dynamic network node k+ One trigger time; For the first i The first dynamic network node k The next trigger moment.

[0144] For example, when designing a hierarchical controller and self-triggering mechanism, differentiated control inputs can be designed for nodes at different levels to achieve efficient synchronization. Therefore, for the design of the leadership controller, different control inputs can be designed for the leadership level... Nodes in The design maintains the constant constraint pulse control input:

[0145]

[0146] In the formula, the pulse control gain of the leadership layer is designed as follows: , Represents the Dirac function, This indicates synchronization error. Indicates the first The trigger time of the k-th pulse at each node. To avoid continuous monitoring state errors, a self-triggering mechanism can be introduced to generate the trigger time, i.e.:

[0147]

[0148] Among them, design , Therefore, a self-trigger function can be defined as:

[0149]

[0150] in, The Lipschitz constant matrix is:

[0151]

[0152] By designing a hierarchical controller and self-triggering function for the leadership layer, the invariant restraint pulse control input for the leadership layer's self-triggering drive can be realized, so that subsequent execution of restraint pulse synchronous control can be achieved.

[0153] Similarly, to determine the control input of a distributed controller driven by a self-triggering layer, in some embodiments, when designing the control input based on a complex dynamic network model and hierarchical network structure, a synchronization error variable can be defined first. This synchronization error variable characterizes the synchronization error between the constrained dynamic network and the target network. The control gain is then set based on the synchronization error variable according to the complex dynamic network model.

[0154] For example, for a distributed controller driven by a self-triggering follower layer, the first... i The synchronization error variable between each dynamic network node in the follower layer and the target network is:

[0155]

[0156] in, Indicates the first i Each node t Synchronization error at time, ; For the first i The state of each node; This indicates the state of the target network.

[0157] The kinetics satisfied by the synchronization error variable are:

[0158]

[0159] in, Indicates the first i Each node t The derivative of the synchronization error at time t, ; Represents a diagonal matrix; Indicates the first i Each node t Synchronization error at any given moment; Indicates an input real matrix; Represents a nonlinear function; For the first i The state of each node; Indicates the state of the target network; This represents the control input of the restraining node in the follow layer.

[0160] For the follower layer It is possible to design distributed control inputs with self-triggering function. ,Right now:

[0161]

[0162] in, This represents the control input variable of the follower layer, i.e., the first... i The control input of a dynamic network node to a self-triggered distributed controller; This indicates the coupling strength between dynamic networks in the follower layer. These are the matrix elements of the adjacency matrix; Indicates the first i The state of each following node; Indicates the first i The first following node j The state of each neighboring node.

[0163] Then, by defining the measurement error, that is:

[0164]

[0165] in, This represents the measurement error of the i-th node at time t; Indicates the i-th node at the driving moment Control input; This represents the control input variables of the follow layer.

[0166] For each following network node Driving Moment It can be generated by the following event triggering mechanism, namely:

[0167]

[0168] in, No. i The state vector of each node; Indicates the first i Transpose of the state vectors of each node; This is the event trigger matrix; Represents a constant. and ; Indicates the first i Each node t Synchronization error at any given moment; No. i Each node t The transpose of the synchronization error vector at time t.

[0169] Accordingly, based on the following layer The event triggering condition can be defined by defining the self-trigger function of the follower layer as follows:

[0170]

[0171] in, For the first i The node of the first k+ One trigger time, ; For the first i The node of the first k The next trigger moment; Indicates the synchronization error at the trigger moment; , , These represent three different design constants.

[0172] Here, the design constant M can represent the initial value of the boundary conditions or the upper bound of the error. Related to the Lipschitz constant or matrix norm of the system dynamics. Design constants. It can be used as a scaling factor, that is:

[0173]

[0174]

[0175]

[0176] in, and These are two constants; express 3D identity matrix and event triggering matrix The Kronecker product; Representation matrix The Kronecker product with the n-dimensional identity matrix; D This represents the Lipschitz constant matrix.

[0177] For example, for a hierarchical controller in a follower layer, it can be targeted at the follower layer. In the following nodes, design a distributed control input with self-triggering function. , is represented as:

[0178]

[0179] in, For the first i The control input of a dynamic network node to a self-triggered distributed controller; For the first i The first following node j The state of each neighboring node; For the first i The state of each following node; t For time; The coupling strength between the dynamic networks in the follower layer, such as coupling strength ; These are the matrix elements of the adjacency matrix, which can be automatically generated using the NW small-world network algorithm. Define the measurement error. Then for each follower network You can configure the event triggering mechanism. The event trigger matrix is ​​as follows:

[0180]

[0181] Based on the above event triggering mechanism, the driving moment can be determined. Then, the self-trigger function of the follower layer is determined by combining the distributed control input. The self-trigger function of the follower layer can be set during the calculation process. and .

[0182] S104. Perform self-triggering driven restraint pulse synchronization control on the target system according to the control input.

[0183] After designing the control input, the target system can be subjected to restraint pulse synchronization control according to the control input. That is, restraint pulse synchronization control is performed based on the aforementioned leader controller and self-triggering conditions, as well as the follower controller and self-triggering conditions. During the control process, the error states of the nonlinear error systems of the target network and the leader dynamic network, and the error systems of the target network and the follower dynamic network tend to zero. That is, the target node pulls the leader node to achieve synchronization, and the leader node pulls the follower node, ultimately achieving global synchronization.

[0184] By applying the technical solutions of the above embodiments, the resource-aware self-triggering hierarchical restraint pulse synchronization control method described in the above embodiments can adapt to different network characteristics and realize an invariant restraint pulse synchronization control scheme. For any invariant restraint strategy, when applied to a large-scale complex dynamic network, a hierarchical network topology can be spontaneously formed. Based on the above-mentioned hierarchical network structure characteristics, the method can design differentiated control mechanisms for the leader layer nodes and follower layer nodes in the network, that is, for the leader layer nodes, a self-triggering pulse control mechanism is designed; for the follower layer nodes, a self-triggering distributed control mechanism is designed. Through the design of a multi-level collaborative controller architecture, it can adapt to the large-scale complex dynamic network, and by adopting a composite control scheme combining invariant restraint pulse control and distributed control, the entire network can achieve synchronous stability. At the same time, relying on the self-triggering control mechanism, a pulse controller based on self-triggering events is configured for each restrained node. The controller operates stably and reliably, preventing Zeno's phenomenon. In addition, the method described in this paper can also abandon the rigid requirement of synchronous triggering of all nodes, allowing each node to trigger independently, greatly improving the flexibility of the control strategy. Compared to event-triggered pulse control strategies, the proposed method significantly improves the practicality and engineering adaptability of the control scheme in key aspects such as trigger mechanism design and restraint node selection.

[0185] Compared to single-pin and switching pin pulse synchronization control methods, the proposed method achieves innovation in pin control mechanism. Addressing the shortcomings of single-pin control (applying pulses to only a single node with high pulse frequency requirements), switching pin control (lacking error information when detached from the leader node), and reliance on neighborhood, topology, or leader-related information, the proposed method utilizes only leader information without requiring any network topology information, thus circumventing the inherent weaknesses of pin control.

[0186] The method can also be optimized through interaction layer trigger control. A self-trigger control scheme is designed for the interaction layer, and control input is generated based on the current state of the node itself and neighboring nodes, which greatly saves information transmission costs and has better performance than existing event-triggered control strategies.

[0187] The method also achieves a breakthrough in asynchronous pulse control. Pulse self-triggering control does not require continuous state monitoring and is suitable for application scenarios without additional hardware. Furthermore, the asynchronous self-triggering pulse scheme does not require continuous state monitoring, is suitable for hardware-constrained scenarios, and can deduce the next trigger time based on the real-time error state, solving engineering and computational challenges.

[0188] In some embodiments, as a specific implementation of the resource-aware self-triggering hierarchical restraint pulse synchronization control method described in the above embodiments, some embodiments of this application also provide a resource-aware self-triggering hierarchical restraint pulse synchronization control system, such as... Figure 5 As shown, the system includes:

[0189] The model building module is used to build a complex dynamic network model of the target system, which includes a complex dynamic network composed of multiple neural networks; the complex dynamic network model includes a set of dynamic behavior differential equations constructed for each node in the target system.

[0190] The structure setting module is used to generate a hierarchical network structure of the target system based on an invariant constraint mechanism. The hierarchical network structure includes a leader layer and a follower layer. The leader layer includes at least one constraint node. The constraint node is configured to directly receive constraint control input information for synchronizing the target trajectory. The follower layer includes multiple follower nodes. The follower nodes are configured to interact with neighboring nodes.

[0191] A control input module is used to design control inputs based on the complex dynamic network model and the hierarchical network structure. The control inputs include a hierarchical controller and a self-triggering function designed based on the hierarchical network structure. The hierarchical controller includes a self-triggering pulse controller designed for the restraining nodes in the leadership layer and a self-triggering distributed controller designed for the following nodes in the follower layer. The self-triggering function is used to calculate the interval of the next pulse control based on the synchronization error at the current moment.

[0192] The synchronization control module is used to perform self-trigger driven restraint pulse synchronization control on the target system according to the control input.

[0193] By applying the technical solutions of the above embodiments, the resource-aware self-triggering hierarchical restraint pulse synchronization control system described in the above embodiments can establish a complex dynamic network model of the target system and generate a hierarchical network structure of the target system based on an invariant restraint mechanism. Then, control inputs are designed according to the complex dynamic network model and the hierarchical network structure, and restraint pulse synchronization control is executed on the target system according to the control inputs. The system constructs a hierarchical network structure including an invariant restraint leader layer and an interactive follower layer. For the leader layer, a self-triggering pulse restraint control is designed, pre-determining a set of constrained nodes containing multiple nodes to increase the proportion of effective control nodes and reduce the required pulse frequency while ensuring synchronization performance. For the interactive follower layer, a self-triggering control is designed so that the controlled nodes self-trigger to determine the control application time based on their local state, eliminating the need for global error information and centralized scheduling, thus reducing the consumption of communication and computing resources.

[0194] It should be noted that other corresponding descriptions of the functional units involved in the resource-aware self-triggering hierarchical restraint pulse synchronization control system provided in the embodiments of this application can be found in the corresponding descriptions in the resource-aware self-triggering hierarchical restraint pulse synchronization control method provided in the above embodiments, and will not be repeated here.

[0195] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0196] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A resource-aware, self-triggering hierarchical restraint pulse synchronization control method, characterized in that, The method includes: A complex dynamic network model of a target system is established, wherein the target system comprises a complex dynamic network consisting of multiple neural networks; the complex dynamic network model comprises a set of dynamic behavioral differential equations constructed for each node in the target system. A hierarchical network structure for the target system is generated based on an invariant constraint mechanism. The hierarchical network structure includes a leader layer and a follower layer. The leader layer includes at least one constraint node. The constraint node is configured to directly receive constraint control input information for synchronizing the target trajectory. The follower layer includes multiple follower nodes. The follower nodes are configured to interact with neighboring nodes. The control input is designed based on the complex dynamic network model and the hierarchical network structure. The control input includes a hierarchical controller and a self-triggering function designed based on the hierarchical network structure. The hierarchical controller includes a self-triggering pulse controller designed for the restraining nodes in the leadership layer and a self-triggering distributed controller designed for the following nodes in the following layer. The self-triggering function is used to calculate the interval duration of the next pulse control based on the synchronization error at the current moment. The design of the control input based on the complex dynamic network model and the hierarchical network structure includes: defining a synchronization error variable, which characterizes the synchronization error between the restrained dynamic network and the target network; setting the leadership pulse control gain based on the synchronization error variable according to the complex dynamic network model; and determining the trigger time through a self-triggering mechanism. This includes: setting a triggering time determination condition for the restraining node; the determination condition being used to characterize the generation of the triggering time when the synchronization error variable touches the exponential decay boundary; obtaining a combination matrix; the combination matrix being the result of a combination operation of a preset diagonal matrix, an input real matrix, and a constant matrix; calculating an error representation term based on the exponential decay boundary and the synchronization error variable; the error representation term being calculated based on the natural logarithm of the ratio of the exponential decay boundary to the synchronization error variable; defining the self-triggering function based on the error representation term and the combination matrix; generating the triggering time according to the self-triggering function and the determination condition; constructing the self-triggering pulse controller based on the leadership pulse control gain, the synchronization error variable, the triggering time, and the Dirac function; the self-triggering pulse controller executing the control input according to the following formula: in, As the first in the leadership i The control input of a dynamic network node self-triggering pulse controller; The first in the leadership i Pulse control gain of each dynamic network node; For synchronization error variables; t For time; Represents the Dirac function; For the first i The first dynamic network node k The next trigger moment; The self-triggering distributed controller executes the control input according to the following formula: in, To follow the first layer i The control input of a dynamic network node to a self-triggered distributed controller; The coupling strength between the dynamic networks in the follower layer; These are the matrix elements of the adjacency matrix; For the first i The first following node j The state of each neighboring node; For the first i The state of each following node; t For time; The target system is subjected to self-triggering driven restraint pulse synchronization control according to the control input.

2. The method according to claim 1, characterized in that, Establish a complex dynamic network model of the target system, including: Traverse the neural network nodes of the target system; A dynamic behavior differential equation is constructed for each node; the dynamic behavior differential equation is used to characterize the functional relationship between the derivatives of the dynamic network state variables and the state variables, nonlinear vector functions, and control inputs; Obtain a dynamic model of a virtual synchronization target node, wherein the virtual synchronization target node is at least one of an equilibrium point, a chaotic orbit, and a periodic orbit; A complex dynamic network model of the target system is established based on the differential equations of the nodes and the dynamic model of the virtual synchronous target nodes.

3. The method according to claim 2, characterized in that, The method further includes: The network size and network type of the target system are determined by traversing the neural network nodes of the target system. A directed topology graph is constructed based on the network size and network type. The directed topology graph includes a vertex set, an edge set, and an adjacency matrix. The matrix elements in the adjacency matrix are used to represent the connection weight between two nodes in the target system. When both nodes belong to the vertex set and the edge set, the matrix element value is greater than 0. Key analysis tools are defined based on the directed topological structure graph, and these key analysis tools include the Laplace matrix.

4. The method according to claim 1, characterized in that, The hierarchical network structure of the target system is generated based on an invariant constraint mechanism, including: Obtain the information interaction status between nodes in the target system; the information interaction status is a first state or a second state; the first state indicates that there is a direct connection between nodes; the second state indicates that there is no direct connection between nodes. If the information interaction state of the node is in the first state, the node is assigned to the leadership layer; If the information interaction state of the node is in the second state, the node is assigned to the following layer.

5. The method according to claim 4, characterized in that, The hierarchical network structure of the target system generated based on the invariant constraint mechanism also includes: Count the number of nodes in the leadership layer and the following layer; The hierarchical network structure is generated based on the number of nodes; The Laplace matrix is ​​decomposed into block matrices according to the hierarchical network structure. The block matrices include a first block matrix, a second block matrix, a third block matrix, and a fourth block matrix. The first block matrix describes the connection relationship between restraining nodes within the leadership layer; the second block matrix describes the connection relationship between following nodes within the following layer; the third block matrix describes the connection relationship from the following layer to the leadership layer; and the fourth block matrix describes the connection relationship from the leadership layer to the following layer.

6. The method according to claim 5, characterized in that, The hierarchical network structure is generated based on the number of nodes, including: Initialize the ring network according to the stated number of nodes; Add random long-range edges to the nodes in the regular ring network; the random long-range edges are used to shorten the average distance between the nodes and maintain a high clustering coefficient. Obtain the network generation parameters and initial state range; Based on the network generation parameters, the node is randomly assigned an initial state within the initial state interval.

7. A resource-aware, self-triggering, hierarchical restraint pulse synchronization control system, characterized in that, The system includes: The model building module is used to build a complex dynamic network model of the target system, which includes a complex dynamic network composed of multiple neural networks; the complex dynamic network model includes a set of dynamic behavior differential equations constructed for each node in the target system. The structure setting module is used to generate a hierarchical network structure of the target system based on an invariant constraint mechanism. The hierarchical network structure includes a leader layer and a follower layer. The leader layer includes at least one constraint node. The constraint node is configured to directly receive constraint control input information for synchronizing the target trajectory. The follower layer includes multiple follower nodes. The follower nodes are configured to interact with neighboring nodes. A control input module is used to design control inputs based on the complex dynamic network model and the hierarchical network structure. The control inputs include a hierarchical controller and a self-triggering function designed based on the hierarchical network structure. The hierarchical controller includes a self-triggering pulse controller designed for the restraining nodes in the leadership layer and a self-triggering distributed controller designed for the following nodes in the following layer. The self-triggering function is used to calculate the interval duration of the next pulse control based on the synchronization error at the current moment. Designing the control inputs based on the complex dynamic network model and the hierarchical network structure includes: defining a synchronization error variable, which characterizes the synchronization error between the restrained dynamic network and the target network; setting the leadership pulse control gain based on the synchronization error variable according to the complex dynamic network model; and determining the triggering mechanism. The triggering time includes: setting a triggering time determination condition for the restraining node; the determination condition is used to characterize the generation of the triggering time when the synchronization error variable touches the exponential decay boundary; obtaining a combination matrix; the combination matrix is ​​the result of a combination operation of a preset diagonal matrix, an input real matrix, and a constant matrix; calculating an error representation term based on the exponential decay boundary and the synchronization error variable; the error representation term is calculated based on the natural logarithm of the ratio of the exponential decay boundary to the synchronization error variable; defining the self-triggering function based on the error representation term and the combination matrix; generating the triggering time according to the self-triggering function and the determination condition; constructing the self-triggering pulse controller based on the leadership pulse control gain, the synchronization error variable, the triggering time, and the Dirac function; the self-triggering pulse controller executes the control input according to the following formula: in, As the first in the leadership i The control input of a dynamic network node self-triggering pulse controller; The first in the leadership i Pulse control gain of each dynamic network node; For synchronization error variables; t For time; Represents the Dirac function; For the first i The first dynamic network node k The next trigger moment; The self-triggering distributed controller executes the control input according to the following formula: in, To follow the first layer i The control input of a dynamic network node to a self-triggered distributed controller; The coupling strength between the dynamic networks in the follower layer; These are the matrix elements of the adjacency matrix; For the first i The first following node j The state of each neighboring node; For the first i The state of each following node; t For time; The synchronization control module is used to perform self-trigger driven restraint pulse synchronization control on the target system according to the control input.

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