Distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process, electronic equipment and readable storage medium thereof

Abstract

The invention provides a distributed fault-tolerant consistency control method based on chord decomposition and a semi-Markov process, and the method comprises the steps: building a unified error dynamic model based on a chord decomposition theory and a semi-Markov random process by comprehensively considering the influence of multiple factors, such as physical coupling, topological random reconstruction, an actuator multiplicative fault and external disturbance; converting a global high-dimensional control problem into a low-dimensional sub-problem in combination with chordal graph decomposition by taking system asymptotic stability and robust performance as a control target; a Lyapunov stability theory, a Schur complementary lemma and a linear matrix inequality (LMI) technology are utilized, a local distributed controller of the maximum clique of each chordal graph is designed firstly, then the overlapping state between subsystems is coordinated, and finally extensible fault-tolerant control under multi-fault concurrency is achieved. According to the method, the limitation of dimension disasters is broken through, and the control reliability and the calculation efficiency of industrial systems such as microgrids and continuous casting and rolling in random topology and mixed fault scenes are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of industrial automation and intelligent control technology, in particular to a fault-tolerant consensus control method for large-scale interconnected multi-agent systems (IMAS), and more particularly to a distributed fault-tolerant consensus control method based on chordal decomposition and semi-Markov process, an electronic device and a computer readable storage medium thereof. BACKGROUND

[0002] In the next-generation industrial internet architecture, large-scale interconnected multi-agent systems, such as interconnected microgrids and large-scale continuous casting and rolling units, are the core foundation for achieving high coordination and high flexibility operation. Robust, scalable and fault-tolerant collaborative control has important theoretical and engineering value. However, the inherent physical coupling and distributed characteristics of such systems make the design of their collaborative controllers face severe challenges, especially when dealing with multiple concurrent uncertainties such as semi-Markov random topology changes, actuator multiplicative faults and external disturbances. The existing technologies have obvious limitations in dealing with the above problems. Some methods use Markov jump models to handle random topologies, but do not fully consider the joint effects of physical coupling and actuator faults. Some distributed fault-tolerant architectures can handle partial faults, but often rely on ideal communication conditions or fixed topology assumptions, making it difficult to adapt to semi-Markov random restructuring coupled with disturbances. Other methods design collaborative protocols based on performance, but are mostly limited to centralized optimization frameworks, lacking practical scalability. In addition, some general distributed control methods are difficult to directly apply to high-dimensional, strongly coupled actual systems due to insufficient consideration of system structure sparsity and concurrent fault characteristics.

[0003] Therefore, the existing technologies still have significant deficiencies in model separability, structural flexibility and computational complexity, and there is an urgent need for a distributed control framework that can systematically integrate and efficiently handle the above multiple concurrent problems. SUMMARY

[0004] In view of the dimension disaster and collaborative control problems faced by large-scale interconnected multi-agent systems (IMAS) in the industrial internet under random topology restructuring and mixed actuator faults, the present application provides a distributed fault-tolerant consensus control method based on chordal decomposition and semi-Markov process, an electronic device and a computer readable storage medium thereof. First, considering multiple sources of uncertainty such as physical coupling, semi-Markov random communication topology, probabilistic actuator multiplicative faults and external disturbances, a unified error dynamic model is established. Second, based on chordal decomposition theory, the global high-dimensional control problem is decomposed into low-dimensional sub-problems. Using Lyapunov stability theory, Schur complement lemma and linear matrix inequality (LMI) techniques, local distributed consensus controllers for the maximum clique of the chordal graph are designed first, and then the global consensus controller is obtained by solving a convex optimization problem. Finally, the semi-Markov random topology changes, actuator faults and external disturbances are considered in the design of the global consensus controller, and the stability of the system is guaranteed by the Lyapunov stability theory. ​The controller, coordinating the overlapping state between subsystems, finally realizes the scalable fault-tolerant consistent control under the concurrent multiple faults. The application breaks through the bottleneck of the centralized method in the calculation complexity and scalability, and significantly improves the control reliability and real-time performance of the micro-grid, continuous casting and rolling and other industrial systems in the complex dynamic environment.

[0005] The application provides a distributed fault-tolerant consistent control method suitable for semi-Markov random topology and concurrent mixed faults. The semi-Markov communication graph An information-physical fusion topology is constructed. Then, based on chord decomposition, the global error dynamic system is split into local sub-problems of the maximum group of chord graphs. Finally, combined with the fault probability boundary And the semi-Markov transition rate The distributed controller gain that meets the performance is designed. The application discloses a distributed fault-tolerant consistent control method suitable for an industrial internet based on chord decomposition and a semi-Markov process. S1, physical quantity, information quantity coupling and fault parameters of an interconnected multi-agent system are collected. S2, a unified model of the multi-agent system considering physical coupling, semi-Markov random communication topology, actuator multiplicative fault and external disturbance is established. S3, based on the unified model, a consistent error state of the system is defined, and a global closed-loop error dynamic system is constructed. S4, based on chord decomposition theory, the control problem of the global closed-loop error dynamic system is decomposed into a series of low-dimensional sub-problems corresponding to the maximum groups in a chord graph. S5, for each low-dimensional sub-problem corresponding to the maximum group, a local distributed fault-tolerant controller is designed by using Lyapunov stability theory, Schur complement lemma and linear matrix inequality technology. S6, the overlapping state between the maximum group subsystems is coordinated, all local distributed fault-tolerant controllers are integrated, and finally, scalable fault-tolerant consistent control of the multi-agent system under concurrent multiple faults is realized.

[0006] Preferably, in the step S1, the interconnected multi-agent system unified model is that the multi-agent system comprises N interconnected agents, the physical coupling is defined by a graph , wherein the dynamic model of the a-th agent is: ; wherein, is the state vector, is the control input vector, is the output vector, is the external disturbance vector, denotes the neighborhood set of agent a in the physical topology ; the communication topology is driven by a semi-Markov process with time-varying transition probability: ; Each agent adopts the following distributed control law: ; wherein, is the mode-dependent feedback gain, is the edge weight in the communication topology .

[0007] Preferably, in step S2, the actuator fault model with probability severity is adopted to model the fault of the dth actuator of the ath agent as a multiplicative attenuation: ; and the fault model is specifically: ; wherein, ; and is the threshold value for distinguishing between severe and slight faults.

[0008] wherein, is the efficiency coefficient representing the single actuator severe fault, used to depict the fault degree of the actuator, is the lower limit value of , i.e. the “worst-case boundary” of the actuator efficiency coefficient, is the upper limit value of , i.e. the “best-case boundary” of the actuator efficiency coefficient, is the ideal fault-free control input signal representing the single actuator, i.e. the expected control input assigned by the system to the actuator when the actuator has not occurred any fault, is the indicator function (taking only values 0 or 1) of the actuator fault level, used to distinguish the “severity type” of the actuator fault, which is the core variable of the Bernoulli distribution fault model, is the efficiency coefficient representing the single actuator slight fault.

[0009] It can be preferred that in said step S3, said global closed-loop error dynamic system is represented as: ; ; wherein, is the global consensus error state vector of the system, is the controlled output vector, is the disturbance input matrix of the global error system, is the disturbance input matrix of the global system, is the global external disturbance vector, is the global output matrix, is the closed-loop system matrix comprising the nominal matrix and the uncertainty matrix , in particular: ; wherein, is the projection matrix, is the n-dimensional identity matrix, is the state matrix of the global system, is the control input matrix of the global system, is the mode variable of the semi-Markov process, is the global actuator severe fault probability matrix, is the global severe fault nominal efficiency matrix, is the global slight fault nominal efficiency matrix, is the mode Laplacian matrix of the communication topology, is the distributed controller feedback gain matrix in the mode , is the global actuator actual fault matrix, is the global severe fault efficiency uncertainty matrix, is the global slight fault efficiency uncertainty matrix.

[0010] It can be preferred that in said step S4, the cyber-physical integrated graph is extended to a chordal graph based on chordal decomposition theory and decomposed into p maximal cliques , for each maximal clique , the following are defined: 1) a clique selection matrix , whose elements are defined as: ; 2) a local error state vector: ; 3) and a clique qualification matrix: ; The global closed-loop error dynamic system is decomposed into: ; The local dynamics matrix of the clique is: ; in, Let be the local state matrix of clique k. Let k be the local control input matrix for clique k. For pattern The Laplace matrix of the local communication topology of the lower clique k. For pattern The local controller feedback gain matrix of the lower group k, Let k be the local actuator fault matrix. Let be the local projection matrix of clique k. Let be the local error disturbance matrix of clique k. Let be the local disturbance input matrix of clique k.

[0011] Preferably, in step S5, the distributed system is designed. The fault-tolerant controller specifically includes: for each mode and each largest group Solve the following system of linear matrix inequalities to ensure the asymptotic stability of the clique local system and performance: ; in, Let the clique local system matrix and the Lyapunov matrix be to be determined. Controller gain matrix Disturbance suppression level and failure probability parameters The resulting block matrix. Then, variable substitution is used. The bilinear terms in the linear matrix inequalities are transformed into linear terms, thereby transforming the system of inequalities into a solvable convex optimization problem.

[0012] Preferably, in step S6, each clique is obtained by solving the system of linear matrix inequalities. In each mode Local controller gain The derivation of the linear matrix inequality is based on the clique local dynamics, the fault uncertainty boundary, and the representation of the semi-Markov transition rate using a polyhedral shape. The convexity process is achieved by coordinating the clique constraint matrix. and the overlap state , the obtained local controller gains of each local controller are integrated to form a global distributed control strategy applied to the multi-agent system, so that the system realizes asymptotic consistency under the concurrent multiple faults, that is: ; and meets the predetermined robust performance index, wherein is the state vector of agent a at time t, is the state vector of agent b at time t.

[0013] The application also provides a computer readable storage medium, which mainly comprises a computer program stored thereon, and the computer program realizes the steps of the distributed fault-tolerant consistency control method based on chordal decomposition and semi-Markov process when executed by a processor.

[0014] The application also provides a computer device, which mainly comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor realizes the steps of the distributed fault-tolerant consistency control method based on chordal decomposition and semi-Markov process when executing the computer program.

[0015] Compared with the prior art, the application has the following advantages: A multi-factor unified error model considering semi-Markov random topology reconfiguration, probability type actuator mixed fault and physical coupling is established, a high-dimensional global control problem is converted into a low-dimensional distributed optimization problem based on chordal decomposition theory, a hierarchical design method is used to design local distributed fault-tolerant controllers of each chord diagram maximum clique, and a global control strategy is integrated through a state coordination mechanism to realize scalable fault-tolerant consistent control of a large-scale interconnected multi-agent system under multiple concurrent faults, and the control reliability, calculation efficiency and convergence performance of microgrids, continuous casting and rolling and other industrial systems in a dynamic random environment are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 A flowchart of a distributed fault-tolerant consistency control method based on chordal decomposition and semi-Markov process suitable for a large-scale interconnected multi-agent system (IMAS) in a next-generation industrial internet architecture.

[0017] Figure 2 A topology processing framework diagram of a distributed fault-tolerant consistency control method based on chordal decomposition and semi-Markov process suitable for a large-scale interconnected multi-agent system.

[0018] Figure 3Fig. 1 is a schematic diagram of a random reconfigurable topology based on string decomposition theory and a maximum clique decomposition of the present application.

[0019] Figure 4 Fig. 2 is a schematic diagram of the first state tracking error convergence process of an intelligent agent in performance verification of the present application.

[0020] Figure 4 Fig. 3 is a schematic diagram of the second state tracking error convergence process of an intelligent agent in performance verification of the present application.

[0021] Figure 4 Fig. 4 is a schematic diagram of a semi-Markov communication topology switching sequence in performance verification of the present application.

[0022] Figure 4 Fig. 5 is a schematic diagram of the system consistency error evolution process in performance verification of the present application.

[0023] Figure 5 Fig. 6 is a schematic diagram of the external disturbance amplitude setting in the test environment setting of the present application under the condition of concurrent external disturbance and actuator failure.

[0024] Figure 5 Fig. 7 is a schematic diagram of the actuator time-varying failure efficiency simulation in the test environment setting of the present application under the condition of concurrent external disturbance and actuator failure. DETAILED DESCRIPTION

[0025] In order to more clearly describe the technical content of the present application, further description will be made below in combination with specific embodiments.

[0026] The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process of the present application is shown in Figs. 1-7. Figure 1 and Figure 2 First, according to the dynamic characteristics of the multi-agent system, the information-physical fusion topology is constructed by fusing the physical coupling graph and the semi-Markov communication graph Then, based on string decomposition, the global error dynamic system is split into local sub-problems of the maximum clique of the string graph Finally, combined with the fault probability boundary and the semi-Markov transition rate , the distributed controller gain satisfying the performance is designed, and the specific design method steps of the controller are as follows: S1, collect the physical quantity, information quantity coupling and fault parameters of the interconnected multi-agent system; S2, establish a unified model of the multi-agent system considering physical coupling, semi-Markov random communication topology, actuator multiplicative failure and external disturbance; S3, design the distributed controller gain based on the semi-Markov process and the string decomposition theory; and S4, design the distributed controller gain based on the semi-Markov process and the string decomposition theory.S3, defining a consistency error state of the system based on the unified model, constructing a global closed-loop error dynamic system; S4, decomposing the control problem of the global closed-loop error dynamic system into a series of low-dimensional sub-problems corresponding to the maximum cliques in the chordal graph based on the chordal decomposition theory; S5, for each low-dimensional sub-problem corresponding to the maximum clique, using Lyapunov stability theory, Schur complement lemma and linear matrix inequality technique to design a local distributed fault-tolerant controller; S6, coordinating the overlapping states between each maximum clique subsystem, integrating all local distributed fault-tolerant controllers, and finally realizing the scalable fault-tolerant consensus control of the multi-agent system under concurrent faults.

[0027] In the step S1, the established unified model of the interconnected multi-agent system is: the multi-agent system comprises N interconnected agents, the physical coupling of which is defined by a graph , wherein the dynamic model of the a-th agent is: ; wherein, is a state vector, is a control input vector, is an output vector, is an external disturbance vector, denotes the neighbor set of agent a in the physical topology ; the communication topology evolves driven by a semi-Markov process , and the time-varying transition probability thereof is: ; Each agent adopts the following distributed control law: ; wherein, is a mode-dependent feedback gain, is an edge weight in the communication topology .

[0028] In the step S2, an actuator fault model with probability severity is designed, and the fault of the d-th actuator of the a-th agent is modeled as a multiplicative attenuation: ; And based on the Bernoulli distribution, the severe fault and the slight fault are distinguished, and the fault model is specifically: ; wherein, ; and Threshold for distinguishing between severe and minor faults. Efficiency coefficient for representing a single actuator severe fault, used to characterize the degree of fault of an actuator, Lower limit value of , i.e. "worst-case boundary" of the actuator efficiency coefficient, Upper limit value of , i.e. "best-case boundary" of the actuator efficiency coefficient, Ideal fault-free control input signal for a single actuator, i.e. the desired control input assigned by the system to the actuator when it is not subject to any fault, Indicator function of the actuator fault level (taking values only 0 or 1), used to distinguish between "severity types" of actuator faults, is the core variable of the Bernoulli distribution fault model, Efficiency coefficient for representing a single actuator minor fault.

[0029] In said step S3, the global closed-loop error dynamic system is then represented as: ; ; wherein, is the global uniform error state vector of the system, is the controlled output vector, is the disturbance input matrix of the global error system, is the disturbance input matrix of the global system, is the global external disturbance vector, is the global output matrix, is the closed-loop system matrix containing the nominal matrix and the uncertainty matrix , in particular: ; wherein, is the projection matrix, is the n-dimensional identity matrix, is the state matrix of the global system, is the control input matrix of the global system, is the mode variable of the semi-Markov process, is the global actuator severe fault probability matrix, is the global severe fault nominal efficiency matrix, is the global minor fault nominal efficiency matrix, is the Laplacian matrix of the communication topology for the mode , is the Laplacian matrix of the communication topology for the mode The distributed controller feedback gain matrix under the following conditions This is the actual fault matrix of the global actuator. The efficiency uncertainty matrix for global severe faults. This represents the global minor fault efficiency uncertainty matrix.

[0030] In step S4, the cyber-physical fusion graph is then applied based on string decomposition theory. Expanded into a chord diagram And decomposed into p maximal cliques For each largest group definition: 1) Clique selection matrix Its elements are defined as: ; 2) Local error state vector: ; 3) And the group-limited matrix: ; The global closed-loop error dynamic system is decomposed into: ; The local dynamics matrix of the clique is: ; in, Let be the local state matrix of clique k. Let k be the local control input matrix for clique k. For pattern The Laplace matrix of the local communication topology of the lower clique k. For pattern The local controller feedback gain matrix of the lower group k, Let k be the local actuator fault matrix. Let be the local projection matrix of clique k. Let be the local error disturbance matrix of clique k. Let be the local disturbance input matrix of clique k.

[0031] In step S5, the distributed system is designed. The fault-tolerant controller specifically includes: for each mode and each largest group Solve the following system of linear matrix inequalities to ensure the asymptotic stability of the clique local system and performance: ; in, , which is the clique local system matrix and the Lyapunov matrix to be determined. , controller gain matrix , disturbance rejection level , and failure probability parameter The block matrix is formed. Then the bilinear term in the linear matrix inequality is converted into a linear term by variable substitution , thereby converting the inequality set into a solvable convex optimization problem.

[0032] In the step S6, each team The local controller gain under each mode The linear matrix inequality derivation is based on the team local dynamics, the failure uncertainty boundary, and the convex processing of the semi-Markov transition rate by polyhedral representation. By coordinating the team defining matrix and the overlapping state , the obtained local controller gain is integrated to form a global distributed control strategy applied to the multi-agent system, ensuring that the system realizes asymptotic consistency under the concurrent multiple failures, that is: ; and meets the predetermined robust performance index, wherein is the state vector of agent a at time t, is the state vector of agent b at time t.

[0033] By applying the distributed fault-tolerant consistency control method based on chordal decomposition and semi-Markov process designed by the present application, Figures 3 to 5 The system performance test results under multiple uncertainty conditions such as random topology reconstruction, external disturbance, and concurrent actuator failure are given respectively. From Figure 3 It can be seen that the chordal decomposition method used in the present application can effectively handle random reconfigurable topologies of different structures such as complex connection type, grid type and star ring mixed type, and convert the high-dimensional global control problem into a series of low-dimensional sub-problems through maximum team decomposition, which significantly reduces the complexity of system design and provides a structural basis for the realization of distributed controller. Figure 4 (a-b) shows the convergence process of the two state tracking errors of the multi-agent system. Figure 4 (a) is the convergence of the first state; Figure 4(b) represents the convergence of the second state; the state can refer to velocity, acceleration, etc. in reality. As can be seen from the figure, although the initial errors of each agent are large and dispersed, under the action of the controller proposed in this invention, the tracking errors of all agents converge rapidly to a very small interval near zero within 5 seconds, indicating that the system has excellent dynamic response performance and consistent coordination ability. Figure 5 The external disturbance signal used in the test and the time-varying fault efficiency setting of the actuator are given. Combined with... Figure 4 The convergence result of (ab) shows that even with continuous external disturbances ( Figure 5 (a) and the actuators of Agent 3 and Agent 6 exhibit severe efficiency degradation. Figure 5 Under the harsh operating conditions of (b), the system can still maintain stability and achieve the consistency control target, which fully verifies the fault tolerance and robustness of the method of the present invention under multiple concurrent faults.

[0034] For the specific implementation scheme of this embodiment, please refer to the relevant descriptions in the above embodiments, which will not be repeated here.

[0035] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0036] It should be noted that in the description of this invention, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, in the description of this invention, unless otherwise stated, "a plurality of" means at least two.

[0037] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0038] It should be understood that portions of the application can be implemented in hardware, software, firmware, or combinations thereof. In the embodiments described above, the various steps or methods can be implemented, in part, or in whole, by software or firmware stored in memory and executed by suitable instruction execution devices. For example, if implemented in hardware, and in another embodiment, any of the following techniques, which are well known in the art, can be used to implement the application: a hybrid of the techniques mentioned above; a combination of one or more of the techniques mentioned above; or a combination of one or more of the techniques mentioned above with other techniques.

[0039] Those skilled in the art can understand that all or part of the steps carried out by the above-mentioned embodiment method can be completed by programs instructing related hardware, and the corresponding programs can be stored in a computer readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0040] In addition, each functional unit in each embodiment of the present application can be integrated into one processing module, or each unit can exist physically separately, or two or more units can be integrated into one module. The integrated module can be realized in the form of hardware or in the form of a software function module. If the integrated module is realized in the form of a software function module and sold or used as an independent product, it can also be stored in a computer readable storage medium.

[0041] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0042] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0043] By using the distributed fault-tolerant consensus control method based on chordal decomposition and semi-Markov process, a multi-factor unified error model considering semi-Markov random topology reconfiguration, probability type actuator mixed fault and physical coupling is established. Based on chordal decomposition theory, the high-dimensional global control problem is converted into a low-dimensional distributed optimization problem. By using the hierarchical design method, the local distributed control of the maximum clique of each chord diagram is designed first, and then the global control of the chord diagram is designed by using the local control of the maximum clique of each chord diagram. The fault-tolerant controller integrates the global control strategy through a state coordination mechanism, realizes the scalable fault-tolerant consensus control of the large-scale interconnected multi-agent system under multiple concurrent faults, and significantly improves the control reliability, calculation efficiency and convergence performance of the micro-grid, continuous casting and rolling and other industrial systems in the dynamic random environment.

[0044] In this specification, the application has been described with reference to particular embodiments thereof. However, it is apparent that various modifications and changes can be made without departing from the spirit and scope of the application. Therefore, the specification and drawings should be considered in an illustrative, and not a restrictive sense.

Claims

1. A distributed fault-tolerant consistency control method based on string decomposition and semi-Markov processes, characterized in that, Includes the following steps: S1. Collect physical quantities, information coupling, and fault parameters of interconnected multi-agent systems; S2. Establish a unified model of a multi-agent system that considers physical coupling, semi-Markov random communication topology, actuator multiplicative faults and external disturbances. S3. Based on the unified model, define the consistency error state of the system and construct a global closed-loop error dynamic system; S4. Based on string decomposition theory, the control problem of the global closed-loop error dynamic system is decomposed into a low-dimensional subproblem corresponding to the maximal clique in the string diagram. S5. For the low-dimensional subproblems corresponding to each maximal clique, design locally distributed [problems] using Lyapunov stability theory, Schur's complement lemma, and linear matrix inequality techniques. Fault-tolerant controller; S6. Coordinate the overlapping states between the largest cluster subsystems and integrate all local distributed systems. The fault-tolerant controller ultimately enables the multi-agent system to achieve scalable, fault-tolerant, and consistent control under multiple concurrent faults.

2. The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process according to claim 1, characterized in that: In step S1, the multi-agent system comprises N interconnected agents, whose physical coupling is shown in the figure. Defined, where the dynamic model of agent a is: ； in, For state vectors, To control the input vector, For the output vector, This represents the external disturbance vector. Indicates physical topology The neighbor set of agent a; the communication topology From a semi-Markov process The driving evolution, its time-varying transition probability is: ； Each agent employs the following distributed control law: ； in, For modality-dependent feedback gain, For communication topology Edge weights in the equation.

3. The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process according to claim 2, characterized in that, In step S2, an actuator failure model with probabilistic severity is used to model the failure of the d-th actuator of the a-th agent as multiplicative decay: ； Based on the Bernoulli distribution, a fault model is used to distinguish between severe and minor faults. ； in, ； and A threshold for distinguishing between serious and minor faults. The efficiency coefficient, representing a severe failure of a single actuator, is used to characterize the degree of actuator failure. for The lower limit of the actuator efficiency coefficient is the "worst-case boundary". for The upper limit of the actuator efficiency coefficient is the "best-case boundary". To represent the ideal fault-free control input signal for a single actuator, that is, the desired control input assigned to that actuator by the system when no fault occurs, This is an indicator function for the actuator fault level, taking only 0 or 1. It is used to distinguish the "severity type" of actuator faults and is a core variable in the Bernoulli distribution fault model. The efficiency coefficient represents the efficiency of a single actuator in the event of a minor malfunction.

4. The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process according to claim 3, characterized in that, In step S3, the global closed-loop error dynamic system is represented as follows: ； ； in, This is the global consistency error state vector of the system. For the controlled output vector, The disturbance input matrix of the global error system. The interference input matrix of the global system. This is the global external disturbance vector. This is the global output matrix. For including nominal matrix and uncertainty matrix The closed-loop system matrix is ​​as follows: ； in, For the projection matrix, It is an n-dimensional identity matrix. The state matrix of the global system. This is the control input matrix for the global system. For the pattern variables of a semi-Markov process, This is the global actuator severe failure probability matrix. This is the nominal efficiency matrix for global severe faults. This is the nominal efficiency matrix for global minor faults. For pattern The Laplace matrix of the communication topology, For pattern The distributed controller feedback gain matrix under the following conditions This is the actual fault matrix of the global actuator. The efficiency uncertainty matrix for global severe faults. This represents the global minor fault efficiency uncertainty matrix.

5. The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process according to claim 4, characterized in that, In step S4, the cyber-physical fusion graph is based on string decomposition theory. Expanded into a chord diagram And decomposed into p maximal cliques For each largest group definition: 1) Clique selection matrix Its elements are defined as: ； 2) Local error state vector: ； 3) And the group-limited matrix: ； The global closed-loop error dynamic system is decomposed into: ； The local dynamics matrix of the clique is: ； in, Let be the local state matrix of clique k. Let k be the local control input matrix for clique k. For pattern The Laplace matrix of the local communication topology of the lower clique k. For pattern The local controller feedback gain matrix of the lower group k, Let k be the local actuator fault matrix. Let be the local projection matrix of clique k. Let be the local error disturbance matrix of clique k. Let be the local disturbance input matrix of clique k.

6. The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process according to claim 5, characterized in that, In step S5, the distributed system is designed. Fault-tolerant controllers specifically include: For each mode and each largest group Solve the following system of linear matrix inequalities to ensure the asymptotic stability of the clique local system and performance: ； in, , which is the clique local system matrix and the Lyapunov matrix to be determined. Controller gain matrix Disturbance suppression level and failure probability parameters The constructed block matrix is ​​then processed through variable substitution. The bilinear terms in the linear matrix inequalities are transformed into linear terms, thereby transforming the system of inequalities into a solvable convex optimization problem.

7. The distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process according to claim 6, characterized in that, In step S6, each clique is obtained by solving the system of linear matrix inequalities. In each mode Local controller gain The derivation of the linear matrix inequality is based on the clique local dynamics, the fault uncertainty boundary, and the representation of the semi-Markov transition rate using a polyhedral shape. Convexation processing; by coordinating the clique constraint matrix and the overlapping state The obtained local controller gains will be calculated. The systems are integrated to form a globally distributed control strategy applied to the multi-agent system, ensuring that the system achieves asymptotic consistency under multiple concurrent faults, i.e.: ； And meet the predetermined Robust performance metrics, among which Let be the state vector of agent a at time t. Let be the state vector of agent b at time t.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the distributed fault-tolerant consistency control method based on string decomposition and semi-Markov process as described in any one of claims 1 to 7.

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