A matrix-scale safety consistency control method for unmanned swarm systems

Abstract

The present invention discloses a matrix-scale safety consistency control method for an unmanned cluster system, which belongs to the technical field of unmanned autonomous system control, and includes the following steps: step S1, using graph theory to construct the communication relationship in the unmanned cluster system; step S2, constructing a dynamic model of a heterogeneous unmanned cluster system; step S3, designing a matrix-scale safety consistency fault-tolerant algorithm based on a security kernel method, and using an event-triggered communication mechanism to update the state; step S4, establishing the necessary and sufficient conditions for the network topology to solve the matrix-scale safety consistency problem; step S5, verifying the effectiveness of the proposed algorithm through a simulation example of a heterogeneous unmanned cluster system containing malicious nodes. The present invention adopts the above-mentioned matrix-scale safety consistency control method for an unmanned cluster system, which can make the application of multiple autonomous agents more flexible and effectively handle the safety consistency problem in the multi-dimensional state space.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned cluster system control, and in particular to a matrix-scale safety consistency control method for an unmanned cluster system. Background Art

[0002] Unmanned swarm systems utilize a group of relatively limited autonomous agents to work together to complete complex tasks in a distributed manner. Unmanned swarm system cooperative control has wide applications in many fields, including consensus, formation control, clock synchronization, etc. In recent years, with the rapid development of network and information technology, researchers have paid significant attention to network security. In an unstable network environment, some vulnerable autonomous agents may be vulnerable to attacks by malicious autonomous agents. These malicious autonomous agents may not comply with the predetermined protocol and try to mislead normal autonomous agents, preventing them from converging or entering an unsafe range. Therefore, it is of great significance to design appropriate security algorithms to enable the system to recover from malicious attacks and ensure protocol consistency between normal autonomous agents.

[0003] In the past years of research on safety consistency, the state of the autonomous agent was assumed to be a scalar value. This assumption limits the applicability of these schemes in multidimensional state spaces. For example, when performing vehicle platoon control on a two-dimensional plane, scalar values ​​cannot fully describe the multidimensional dynamic characteristics of the autonomous agent. Inspired by this, recent research has focused on extending the MSR algorithm to more general high-dimensional systems. Yan proposed a safety consistency algorithm based on the Tverberg method and used the intersection of multiple convex sets to find the safety points of high-dimensional unmanned cluster systems. The algorithm uses convex combinations of safety points to update the state of the autonomous agent. The difficulty of the algorithm lies in how to ensure that the safety point is taken from the convex hull of the normal autonomous agent subset. In addition, the existence of the safety point is closely related to the number of normal autonomous agents, the number of malicious autonomous agents, and the dynamic order.

[0004] At present, all the work on multi-agent security consistency focuses on the study of general security consistency. However, in many practical applications, for the security consistency control problem of unmanned cluster systems with multi-dimensional state space and complex dynamic characteristics under malicious attack environments, traditional malicious attack defense mechanisms are difficult to deal with the security consistency problem of heterogeneous multi-dimensional systems. Most of the existing consensus problem research is limited to one-dimensional state space and fails to effectively deal with the independence between multi-dimensional states. Therefore, we urgently need to expand the analysis perspective from the traditional scalar scale under malicious attacks to matrix scale security consistency control, so as to fully characterize the interdependence of normal multi-dimensional autonomous states under malicious attacks. Summary of the invention

[0005] The purpose of the present invention is to provide a matrix-scale safety consistency control method for an unmanned cluster system, which can make the application of multiple autonomous agents more flexible and effectively handle the safety consistency problem in a multi-dimensional state space.

[0006] To achieve the above object, the present invention provides a matrix-scale safety consistency control method for an unmanned cluster system, comprising the following steps:

[0007] Step S1: Use graph theory to construct the communication relationship in the unmanned cluster system, and define r-robustness and (r,s)-robustness to describe the fault tolerance of the network topology; the unmanned cluster system consists of normal autonomous agents and malicious autonomous agents, which may have first-order or second-order dynamic characteristics, thus forming a heterogeneous unmanned cluster system. On this basis, two robustness indicators are defined to describe the fault tolerance of the network topology;

[0008] Step S2: construct a dynamic model of a heterogeneous unmanned swarm system, where the heterogeneous unmanned swarm system includes a first-order autonomous agent and a second-order autonomous agent;

[0009] Step S3, design a matrix-scale security consistency fault-tolerant algorithm based on the security kernel method, each normal autonomous subject collects the matrix-scale position information of its neighbors at each sampling time, sorts the collected information in ascending order, and selects a specific number of points from the sorted sequence according to the limit on the number of malicious autonomous subjects to construct a security kernel, calculates auxiliary points using a linear programming method, and updates the state of the autonomous subject based on the auxiliary points, and the autonomous subject checks whether the event triggering condition is met, and does not send the state information to the neighbor if it is not met;

[0010] Step S4: Based on step S3, by analyzing the robustness of the network topology, sufficient and necessary conditions for solving the matrix-scale safety consistency problem are established. The sufficient and necessary conditions involve the r-robustness or (r, s)-robustness of the network topology, as well as the specific value ranges of the sampling period and the control gain. Through theoretical derivation, it is proved that when these conditions are met, the heterogeneous unmanned cluster system can achieve matrix-scale safety consistency.

[0011] Step S5: Use a simulation example of a heterogeneous unmanned cluster system containing malicious nodes to verify the effectiveness of the proposed algorithm. The simulation results show that even in the presence of malicious autonomous agents, by applying the matrix-scale safety consistency fault-tolerant algorithm and event-triggered communication mechanism proposed by us, normal autonomous agents can still reach a consensus within a safe range and significantly reduce the communication burden. This verifies the effectiveness and robustness of the algorithm.

[0012] Preferably, the r-robustness in step S1 is specifically:

[0013] r-Robustness: Given a directed graph G = (V, E, A) with |V| ≥ 2, for any two non-empty and disjoint subsets V1 and V2 of V, the graph G is called r-robust if at least one of the following conditions is satisfied:

[0014] 1) There is at least one node in V1 whose at least r in-degree neighbors are not in V1;

[0015] 2) There is at least one node in V2 whose at least r in-degree neighbors are not in V2.

[0016] r-Robustness measures the redundancy of each subset (V1 or V2) in the network topology with external connections. Here "r" represents a threshold, indicating how many connections each subset needs to maintain with the outside world to consider the network robust.

[0017] Preferably, the (r, s)-robustness in step S1 is specifically:

[0018] Given a directed graph G = (V, E, A) with |V| ≥ 2, for any two non-empty and disjoint subsets V1 and V2 of V, the graph G is called an (r,s)-robust graph if at least one of the following conditions is satisfied:

[0019] 1) All nodes in V1 have at least r in-degree neighbors from outside V1;

[0020] 2) All nodes in V2 have at least r in-degree neighbors from outside V2;

[0021] 3) There are at least s nodes in V1∪V2, and each node has at least r in-degree neighbors from outside the subset (V1 or V2) to which it belongs.

[0022] (r,s)-robustness is an extension of r-robustness. It not only considers the number of connections (r) between each subset and the outside world, but also introduces another parameter s to measure the number of nodes that meet this connection condition. Compared with r-robustness, (r,s)-robustness provides stronger fault tolerance for network topology. It requires that at least a certain number of nodes (s) maintain sufficient external connections, which helps maintain the stability of the system when the network suffers a larger-scale attack.

[0023] Preferably, in step S2, a dynamic model of a heterogeneous unmanned swarm system is constructed as follows:

[0024] The heterogeneous unmanned swarm system composed of first-order and second-order autonomous agents is:

[0025] (1);

[0026] in, , indicating the self-subject location, Representing the subject The dimensional status of each position; , indicating the self-subject speed, Representing the subject Dimensional status of each speed; , indicating the self-subject The control input, Representing the subject The dimensional status of each control input; represents a first-order autonomous subject; represents a second-order autonomous subject; t represents continuous time; express d dimensional real number space.

[0027] Preferably, the dynamic characteristics of each second-order autonomous body in discrete time are as follows:

[0028] (2);

[0029] in, , , Represents the second-order autonomous At sampling time , Position, velocity and control inputs, represents a natural number; h represents a discrete time interval;

[0030] The dynamic characteristics of each first-order autonomous body in discrete time are as follows:

[0031] (3);

[0032] in, , Represent the first-order autonomous entity At sampling time , position and control inputs.

[0033] Preferably, for formula (1), the following matrix scale consistency algorithm is designed:

[0034] (4);

[0035] in, is the edge weight; and Self-subject and neighbors The matrix weight of ; sign represents the sign function; Representing the subject The dimensional state of each position at the sampling time; Representing the subject Dimensional status of each speed at sampling time; Indicates neighbors In time Location status; , is the control gain to be determined.

[0036] Preferably, the matrix-scale safety consistency fault-tolerant algorithm constructed in step S3 is specifically as follows:

[0037] 1) Collect matrix scale position information of neighbors;

[0038] Each normal autonomous subject (marked as ) at each sampling time t k Collect the matrix scale position information of its neighbors, sampling time t k Denoted as:

[0039] (5);

[0040] in k is an integer; T is the sampling period;

[0041] For the self-subject , represents a normal autonomous set, and its neighbor set is , each neighbor The matrix scale position information of , store the matrix scale position information value of each neighbor to ;

[0042] 2) Sort the collected information in ascending order and build a security kernel;

[0043] Self-subject The collected neighbor matrix scale position information By each dimension (marked ,in ) to sort in ascending order;

[0044] Then, select the initial The last point points, stored in collections and , these points are used to build a secure kernel , security kernel (Here is and ) is for the point set All The intersection of the convex hulls of the subsets, where It is a point set The base number, is the maximum number of malicious agents, where Is a subset The convex hull of

[0045] 3) Calculate auxiliary points using linear programming methods;

[0046] To find the auxiliary points in the security kernel, a linear programming method is used. Specifically, a point is found by solving the following linear programming problem (for )and (for ), so that it is located within the security kernel. The linear programming problem can be expressed as:

[0047] (6);

[0048] in, is a circulant matrix, Is the set of points or The matrix of the midpoints, is the decision variable, is any positive vector (used to maximize the objective function, but its value is not important in the actual solution), represents the Kronecker product, and They are dimensional identity matrix and dimension all 1 vector, and They are Peacekeeping dimensional all-zero vector; represents the d×d identity matrix;

[0049] After solving this linear programming problem, we get , then calculate the point or :

[0050] (7);

[0051] in, and The calculation formula is the same, but they are based on different point sets. and ; represents the optimal decision variable.

[0052] 4) Update the state of the autonomous subject based on the auxiliary point;

[0053] Self-subject Use the calculated auxiliary points to update its state. For the second-order autonomous agent and first-order autonomous agents The update rule is as follows:

[0054] Second-order autonomous body:

[0055] (8);

[0056] in, , represents the auxiliary points calculated by linear programming; ;

[0057] First-order autonomous agent:

[0058] (9);

[0059] 5) Check event triggering conditions;

[0060] The event triggering condition is defined as:

[0061] (10);

[0062] in, is the position measurement error, It is an autonomous subject In time The latest broadcast status value of represents a constant; represents a term that decays over time;

[0063] Self-subject Check whether the event triggering conditions are met. If the triggering conditions are not met, , then no status information is sent to the neighbor; otherwise, the updated status is sent to neighbors, which helps reduce the communication burden.

[0064] Preferably, step S5 is specifically:

[0065] For any initial state, if and only if formula (1) satisfies the following two conditions, it is called matrix-scale safety consistency:

[0066] C1) Security condition: There is a secure kernel , so that for all normal autonomous agents , its status At t ≥ 0, it is in the safety kernel The security condition ensures that even if there are malicious nodes in the network, the state of the normal autonomous entity will not exceed the security range, thus maintaining the security of the system.

[0067] C2) Matrix scale consistency: For ,have ,in, Indicates the error level; matrix scale consistency requires that after a long period of operation, the states of normal autonomous entities can be consistent under the matrix scale, that is, their state differences fluctuate within a small range.

[0068] Therefore, the present invention adopts the above-mentioned matrix-scale safety consistency control method based on safety core for unmanned swarm systems, which deeply integrates graph theory, network malicious attack analysis and multi-agent control theory. By applying matrix scale to characterize the interdependence between the multidimensional states of individuals in a group, the present invention breaks through the limitations of traditional scalar consistency and expands the state space of the multi-agent system from a straight line to a wider open subspace.

[0069] In a complex network environment with malicious autonomous entities, the event-triggered matrix scale security consistency protocol designed by the present invention aims to effectively save communication resources while ensuring that normal autonomous entities can achieve matrix scale consistency. The protocol introduces the concept of security core and uses linear programming methods to efficiently calculate auxiliary points to update the state of the autonomous entity. This innovative mechanism not only significantly reduces the computational complexity, but also ensures that the state of the autonomous entity is always kept within a safe and permissible convex hull with its respective matrix scale during the change process.

[0070] The protocol proposed in the present invention allows communication between autonomous entities only when the trigger function meets the conditions. This strategy greatly reduces unnecessary communication overhead and improves the energy efficiency of the system. In summary, the present invention has shown significant advantages in both theoretical innovation and technical application, and provides a new solution for the safety consistency control of unmanned cluster systems in complex network environments.

[0071] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a flowchart of an embodiment of a matrix-scale safety consistency control method for an unmanned cluster system of the present invention;

[0073] Figure 2 is a network communication topology diagram of the present invention;

[0074] Figure 3 The present invention Figure 2 Longitudinal position trajectories of multiple agents under the communication topology graph;

[0075] Figure 4 The present invention Figure 2 The lateral position trajectories of multiple agents under the communication topology;

[0076] Figure 5 The present invention Figure 2 Dynamic trajectories in the two-dimensional state space of multiple agents under the communication topology graph;

[0077] Figure 6 It is the specific triggering moment of multiple autonomous subjects under the event triggering mechanism. DETAILED DESCRIPTION

[0078] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0079] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0080] Embodiment 1

[0081] like Figure 1 As shown, the present invention provides a matrix-scale safety consistency control method for an unmanned cluster system, comprising the following steps:

[0082] Step S1, use graph theory to construct the communication relationship in the unmanned cluster system, define r-robustness and (r,s)-robustness to describe the fault tolerance of the network topology; the unmanned cluster system is composed of normal autonomous agents and malicious autonomous agents, which may have first-order or second-order dynamic characteristics, thus forming a heterogeneous unmanned cluster system. On this basis, two robustness indicators are defined to describe the fault tolerance of the network topology; Figure 2 As shown, 1 is a malicious subject and the others are normal subjects.

[0083] The r-robustness in step S1 is specifically:

[0084] r-Robustness: Given a directed graph G = (V, E, A) with |V| ≥ 2, for any two non-empty and disjoint subsets V1 and V2 of V, the graph G is called r-robust if at least one of the following conditions is satisfied:

[0085] 1) There is at least one node in V1 whose at least r in-degree neighbors are not in V1;

[0086] 2) There is at least one node in V2 whose at least r in-degree neighbors are not in V2.

[0087] r-Robustness measures the redundancy of each subset (V1 or V2) in the network topology with external connections. Here "r" represents a threshold, indicating how many connections each subset needs to maintain with the outside world to consider the network robust.

[0088] The (r,s)-robustness is specifically:

[0089] Given a directed graph G = (V, E, A) with |V| ≥ 2, for any two non-empty and disjoint subsets V1 and V2 of V, the graph G is called an (r,s)-robust graph if at least one of the following conditions is satisfied:

[0090] 1) All nodes in V1 have at least r in-degree neighbors from outside V1;

[0091] 2) All nodes in V2 have at least r in-degree neighbors from outside V2;

[0092] 3) There are at least s nodes in V1∪V2, and each node has at least r in-degree neighbors from outside the subset (V1 or V2) to which it belongs.

[0093] (r,s)-robustness is an extension of r-robustness. It not only considers the number of connections (r) between each subset and the outside world, but also introduces another parameter s to measure the number of nodes that meet this connection condition. Compared with r-robustness, (r,s)-robustness provides stronger fault tolerance for network topology. It requires that at least a certain number of nodes (s) maintain sufficient external connections, which helps maintain the stability of the system when the network suffers a larger-scale attack.

[0094] The communication topology model is used to describe the heterogeneous unmanned cluster system as follows:

[0095] Using directed graph It indicates that, is a series of autonomous sets, including normal autonomous sets and malicious agent collection , (That is, the total set of autonomous entities in the system is the union of normal autonomous entities and malicious autonomous entities), and (That is, normal autonomous entities and malicious autonomous entities have no intersection.) Some have first-order dynamics, while others have second-order dynamics, where is a collection of normal autonomous entities with first-order dynamics, is a collection of normal autonomous entities with second-order dynamics, ,in It is a point set The base number, is an edge set; , express Matrix of It is a directed graph The adjacency matrix of .

[0096] In a directed graph middle, The definition is from the subject Towards the subject The direction of the edge; The neighbor is defined as ;

[0097] If the subject Can directly receive from the main body information, then ,otherwise .

[0098] Step S2: construct a dynamic model of a heterogeneous unmanned swarm system, where the heterogeneous unmanned swarm system includes a first-order autonomous agent and a second-order autonomous agent;

[0099] In step S2, a dynamic model of a heterogeneous unmanned swarm system is constructed, as follows:

[0100] The heterogeneous unmanned swarm system composed of first-order and second-order autonomous agents is:

[0101] (1);

[0102] in, , indicating the self-subject location, Representing the subject The dimensional status of each position; , indicating the self-subject speed, Representing the subject Dimensional status of each speed; , indicating the self-subject The control input, Representing the subject The dimensional status of each control input; represents a first-order autonomous subject; represents a second-order autonomous subject; t represents continuous time; express d dimensional real number space.

[0103] The dynamic characteristics of each second-order autonomous body in discrete time are as follows:

[0104] (2);

[0105] in, , , Represents the second-order autonomous At sampling time , Position, velocity and control inputs, represents a natural number; h represents a discrete time interval;

[0106] The dynamic characteristics of each first-order autonomous body in discrete time are as follows:

[0107] (3);

[0108] in, , Represent the first-order autonomous entity At sampling time , position and control inputs. Figure 3 , Figure 4 They are the longitudinal position trajectory and lateral position trajectory of multiple agents respectively. Figure 5 is the dynamic trajectory of multiple agents in the two-dimensional state space.

[0109] For formula (1), the following matrix scale consistency algorithm is designed:

[0110] (4);

[0111] in, is the edge weight; and Self-subject and neighbors The matrix weight of ; sign represents the sign function; Representing the subject The dimensional state of each position at the sampling time; Representing the subject Dimensional status of each speed at sampling time; Indicates neighbors In time Location status; , is the control gain to be determined.

[0112] On the basis of step S2, an event-triggered communication rule is introduced, and an event trigger condition is designed based on the difference between the current broadcast value and the latest measured value of the autonomous body. Communication is performed only when the state value of the autonomous body changes significantly, that is, the event trigger condition is met. A matrix scale consistency control algorithm based on the event trigger mechanism is designed for the first-order and second-order autonomous bodies, respectively, so that the final state of the autonomous body is no longer limited to a fixed value or a specific proportion, but is extended to a wider state space subspace; the matrix scale consistency control algorithm based on event triggering is designed for the first-order and second-order autonomous bodies respectively as follows:

[0113] In order to save communication resources, a communication mechanism based on event triggering is considered, in which the autonomous Only at the sampling instant that meets the event triggering condition, its state value is sent to its external neighbors. Representing the subject In time of The latest broadcast value of the dimension state, that is, the self-agent At the last event trigger time Dimension status value; Defined as ,in Representing the subject The transmission time is determined by formula (5); definition Position measurement error , trigger function for:

[0114] ;

[0115] in, and These are constants predefined according to actual needs;

[0116] Based on the above event-triggered communication mechanism and combined with formula (4), the following event-triggered matrix scale control protocol is proposed:

[0117] ;

[0118] in, express exist The most recent broadcast value at . Figure 6 The figure shows the specific triggering moments of eight autonomous entities under the event triggering mechanism. This figure shows the time points when different autonomous entities reach specific triggering conditions. Specifically, Figure 6The horizontal axis represents time, and the vertical axis represents the autonomous agent number, which corresponds to autonomous agents 1-8 respectively. Different colors are used to distinguish different autonomous agents in the figure. The position of each mark on the horizontal axis indicates the specific moment when the corresponding autonomous agent triggers the event. As can be seen from the figure, the triggering moments of different autonomous agents are scattered, which means that they are not triggered at the same time, but at different time points according to their respective state changes and needs. Compared with the traditional time-triggered mechanism, this event-triggered mechanism can significantly reduce unnecessary communication and calculation, thereby saving system resources.

[0119] Step S3, design a matrix-scale security consistency fault-tolerant algorithm based on the security kernel method, each normal autonomous subject collects the matrix-scale position information of its neighbors at each sampling time, sorts the collected information in ascending order, and selects a specific number of points from the sorted sequence according to the limit on the number of malicious autonomous subjects to construct a security kernel, calculates auxiliary points using a linear programming method, and updates the state of the autonomous subject based on these auxiliary points, and the autonomous subject checks whether the event triggering condition is met, and does not send the state information to the neighbor if it is not met;

[0120] The matrix-scale safety consistency fault-tolerant algorithm constructed in step S3 is as follows:

[0121] 1) Collect matrix scale position information of neighbors;

[0122] Each normal autonomous subject (marked as ) at each sampling time t k Collect the matrix scale position information of its neighbors, sampling time t k Denoted as:

[0123] (5);

[0124] in k is an integer; T is the sampling period;

[0125] For the self-subject , represents a normal autonomous set, and its neighbor set is , each neighbor The matrix scale position information of , store the matrix scale position information value of each neighbor to ;

[0126] 2) Sort the collected information in ascending order and build a security kernel;

[0127] Self-subject The collected neighbor matrix scale position information By each dimension (marked ,in ) to sort in ascending order;

[0128] Then, select the initial The last point points, stored in collections and , these points are used to build a secure kernel , security kernel (Here is and ) is for the point set All The intersection of the convex hulls of the subsets, is the maximum number of malicious agents, where It is a point set All A collection of subsets, Is a subset The convex hull of

[0129] 3) Calculate auxiliary points using linear programming methods;

[0130] To find the auxiliary points in the security kernel, a linear programming method is used. Specifically, a point is found by solving the following linear programming problem (for )and (for ), so that these points are within the safety kernel. The linear programming problem can be expressed as:

[0131] (6);

[0132] in, is a circulant matrix, Is the set of points or The matrix of the midpoints, is the decision variable, is any positive vector (used to maximize the objective function, but its value is not important in the actual solution), represents the Kronecker product, and They are dimensional identity matrix and dimension all 1 vector, and They are Peacekeeping dimensional all-zero vector; represents the d×d identity matrix;

[0133] After solving this linear programming problem, we can get , then calculate the point or :

[0134] (7);

[0135] in, and The calculation formula is the same, but they are based on different point sets. and ; represents the optimal decision variable.

[0136] 4) Update the state of the autonomous subject based on the auxiliary point;

[0137] Self-subject Use the calculated auxiliary points to update its state. For the second-order autonomous agent and first-order autonomous agents The update rule is as follows:

[0138] Second-order autonomous body:

[0139] (8);

[0140] in, , represents the auxiliary points calculated by linear programming; ;

[0141] First-order autonomous agent:

[0142] (9);

[0143] in, ;

[0144] 5) Check event triggering conditions;

[0145] The event triggering condition is defined as:

[0146] (10);

[0147] in, is the position measurement error, It is an autonomous subject At sampling time The latest broadcast status value of

[0148] Self-subject Check whether the event triggering conditions are met. If the triggering conditions are not met, , then no status information is sent to the neighbor; otherwise, the updated status is sent to neighbors, which helps reduce the communication burden.

[0149] Step S4: Based on step S3, by analyzing the robustness of the network topology, the necessary and sufficient conditions for solving the matrix-scale safety consistency problem are established. The necessary and sufficient conditions involve the r-robustness or (r, s)-robustness of the network topology, as well as the specific value ranges of the sampling period and the control gain. Through theoretical derivation, it is proved that when these conditions are met, the heterogeneous unmanned cluster system can achieve matrix-scale safety consistency.

[0150] Step S5: Use a simulation example of a heterogeneous unmanned cluster system containing malicious nodes to verify the effectiveness of the proposed algorithm. The simulation results show that even in the presence of malicious autonomous agents, by applying the matrix-scale safety consistency fault-tolerant algorithm and event-triggered communication mechanism proposed by us, normal autonomous agents can still reach a consensus within a safe range and significantly reduce the communication burden. This verifies the effectiveness and robustness of the algorithm.

[0151] For any initial state, if and only if formula (1) satisfies the following two conditions, it is called matrix-scale safety consistency:

[0152] C1) Security condition: There is a secure kernel , so that for all normal autonomous agents , its status At t ≥ 0, it is in the safety kernel The security condition ensures that even if there are malicious nodes in the network, the state of the normal autonomous entity will not exceed the security range, thus maintaining the security of the system.

[0153] C2) Matrix scale consistency: For ,have ,in, Indicates the error level; matrix scale consistency requires that after a long period of operation, the states of normal autonomous entities can be consistent under the matrix scale, that is, their state differences fluctuate within a small range.

[0154] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0155] Therefore, the present invention adopts the above-mentioned matrix-scale safety consistency control method of an unmanned cluster system. The present invention adopts the above-mentioned matrix-scale safety consistency control method of an unmanned cluster system, which can make the application of multiple autonomous agents more flexible and effectively deal with safety consistency problems in multi-dimensional state space.

[0156] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A matrix-scale safety consistency control method for an unmanned cluster system, characterized in that: The following steps are involved: Step S1, using graph theory to construct the communication relationship in the unmanned cluster system, defining r-robustness and (r,s)-robustness to describe the fault tolerance of the network topology; The specific r-robustness is: Given a directed graph G = (V, E, A) with |V| ≥ 2, for any two non-empty and disjoint subsets V1 and V2 of V, the graph G is called r-robust if at least one of the following conditions is satisfied: 1) There is at least one node in V1 whose at least r in-degree neighbors are not in V1; 2) There is at least one node in V2 whose at least r in-degree neighbors are not in V2; r-Robustness measures the redundancy of each subset in the network topology with external connections; The (r,s)-robustness is specifically: Given a directed graph G = (V, E, A) with |V| ≥ 2, for any two non-empty and disjoint subsets V1 and V2 of V, the graph G is called an (r,s)-robust graph if at least one of the following conditions is satisfied: 1) All nodes in V1 have at least r in-degree neighbors from outside V1; 2) All nodes in V2 have at least r in-degree neighbors from outside V2; 3) There are at least s nodes in V1∪V2, and each node has at least r in-degree neighbors from outside the subset to which it belongs; (r,s)-robustness is an extension of r-robustness, which introduces the parameter s to measure the number of nodes that meet the connection condition; Step S2, constructing a dynamic model of a heterogeneous unmanned swarm system, where the heterogeneous unmanned swarm system includes a first-order autonomous agent and a second-order autonomous agent; Step S3, design a matrix-scale security consistency fault-tolerant algorithm based on the security kernel method, each normal autonomous subject collects the matrix-scale position information of its neighbors at each sampling time, sorts the collected information in ascending order, and selects a specific number of points from the sorted sequence according to the limit on the number of malicious autonomous subjects to construct a security kernel, calculates auxiliary points using a linear programming method, and updates the state of the autonomous subject based on the auxiliary points, and the autonomous subject checks whether the event triggering condition is met, and does not send the state information to the neighbor if it is not met; The matrix-scale safety consistency fault-tolerant algorithm based on the safety kernel method is as follows: 1) Collect matrix scale position information of neighbors; Each normal autonomous agent at each sampling time t k Collect the matrix scale position information of its neighbors, sampling time t k Denoted as: （5）； in k is an integer; T is the sampling period; For the self-subject , represents a normal autonomous set, and its neighbor set is , each neighbor The matrix scale position information of , store the matrix scale position information value of each neighbor to ; 2) Sort the collected information in ascending order and build a security kernel; Self-subject The collected neighbor matrix scale position information Sort by each dimension in ascending order; Then, select the initial The last point points, stored in collections and ,in, Indicates Dimensions; Indicates k sampling time; used to build a safety kernel , security kernel For the point set All The intersection of the convex hulls of the subsets, where It is a point set The base number, is the maximum number of malicious agents, where Is a subset The convex hull of 3) Calculate auxiliary points using linear programming methods; To find the auxiliary point in the safety kernel, a linear programming method is used to find a point by solving the following linear programming problem: and , so that it is located within the security kernel, the linear programming problem is expressed as: （6）； in, is a circulant matrix, Is the set of points or The matrix of midpoints, is the decision variable, is any positive vector, represents the Kronecker product, and They are dimensional identity matrix and dimension all 1 vector, and They are Peacekeeping dimensional all-zero vector; represents the d×d identity matrix; After solving this linear programming problem, we get , then calculate the point or : （7）； in, and The calculation formula is the same, but they are based on different point sets. and ; represents the optimal decision variable; 4) Update the state of the autonomous subject based on the auxiliary point; Self-subject Use the calculated auxiliary points to update its state. For the second-order autonomous agent and first-order autonomous agents The update rule is as follows: Second-order autonomous body: （8）； in, , represents the auxiliary points calculated by linear programming; ; First-order autonomous agent: （9）； 5) Check event triggering conditions; The event triggering condition is defined as: （10）； in, is the position measurement error, It is an autonomous subject At sampling time The latest broadcast status value of represents a constant; represents a term that decays over time; Self-subject Check whether the event triggering conditions are met. If the triggering conditions are not met, , then no status information is sent to the neighbor; otherwise, the updated status is sent to neighbors; Step S4: According to step S3, by analyzing the robustness of the network topology, sufficient and necessary conditions for solving the matrix scale safety consistency problem are established, and the sufficient and necessary conditions involve the r-robustness and (r, s)-robustness of the network topology, as well as the specific value ranges of the sampling period and the control gain; Step S5: verify the effectiveness of the proposed algorithm through a simulation example of a heterogeneous unmanned cluster system containing malicious nodes.

2. The matrix-scale safety consistency control method for an unmanned cluster system according to claim 1, characterized in that: In step S2, a dynamic model of a heterogeneous unmanned swarm system is constructed, as follows: The heterogeneous unmanned swarm system composed of first-order and second-order autonomous agents is: （1）； in, , indicating the self-subject location, Represents the dimensional state of each position of subject i; , indicating the self-subject speed, Represents the dimensional state of each speed of subject i; , indicating the self-subject The control input, Represents the dimensional state of each control input of agent i; represents a first-order autonomous subject; represents a second-order autonomous subject; t represents continuous time; express d dimensional real number space.

3. The matrix-scale safety consistency control method for an unmanned cluster system according to claim 2, characterized in that: The dynamic characteristics of each second-order autonomous body in discrete time are as follows: （2）； in, , , Represents the second-order autonomous At sampling time , Position, velocity and control inputs, N represents a natural number; , Represents a second-order autonomous entity At sampling time Position and speed; h represents a discrete time interval; The dynamic characteristics of each first-order autonomous body in discrete time are as follows: （3）； in, , Represent the first-order autonomous entity At sampling time , Position and control inputs; Represents a first-order autonomous entity At sampling time location.

4. The matrix-scale safety consistency control method for an unmanned cluster system according to claim 3, characterized in that: For formula (1), the following matrix scale consistency algorithm is designed: （4）； in, is the edge weight; and Self-subject and neighbors The matrix weight of ; sign represents the sin function; Represents the dimensional state of each position at the sampling time of subject i; Represents the dimensional state of each speed at the sampling time of subject i; Indicates neighbors In time Location status; , is the control gain to be determined.

5. The matrix-scale safety consistency control method for an unmanned cluster system according to claim 4, characterized in that: Step S5 is specifically as follows: For any initial state, if and only if formula (1) satisfies the following two conditions, it is called matrix-scale safety consistency: C1) Security condition: There is a secure kernel , so that for all normal autonomous agents , its status At t ≥ 0, it is in the safety kernel Inside; C2) Matrix scale consistency: For ,have ,in, Indicates the error level.

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