A method for fault-tolerant control of multi-agent systems under actuator failures

Abstract

The application discloses a kind of multi-agent system fault-tolerant control methods under actuator failure, first construct the linear multi-agent system mathematical model of introducing actuator multiplicative fault and additive fault to describe the influence of actuator failure on control input, based on the communication topological relationship of system, construct a consistent error dynamic equation, for describing the change of each agent state error with time, finally design fixed gain fault-tolerant controller based on the multi-agent system mathematical model, realize multi-agent system fault-tolerant control.The method of the application has the advantages of simple controller structure, strong adaptability, low implementation cost, high communication efficiency, etc., can be widely applied to unmanned aerial vehicle formation, robot cooperation, sensor network and other multi-agent system fault-tolerant control scene, has good engineering application value and popularization prospect.

Description

Technical Field

[0001] This invention belongs to the field of fault-tolerant control of multi-agent systems, and specifically relates to a fault-tolerant control method for multi-agent systems under actuator failure. Background Technology

[0002] Multi-agent systems (MAS) are distributed systems composed of multiple interacting agents, possessing autonomy, distributed decision-making, and collaborative capabilities. They have wide applications in fields such as UAV swarms, robot group control, and sensor networks. To ensure the stable operation of a MAS, each agent must maintain normal functionality and communication connectivity. However, in actual operation, actuators, as components directly controlling the system, are constantly in operation and are prone to multiplicative faults (gain attenuation) or additive faults (deviation introduction). These faults can lead to local performance degradation and even propagate throughout the network, causing system failure.

[0003] Existing fault-tolerant control methods are mainly divided into passive fault-tolerant control and active fault-tolerant control. Passive methods involve designing a fault-tolerant controller before system operation, resulting in a simple structure but an inability to handle unknown or novel faults. Active methods design a compensation controller after a fault occurs through detection and diagnosis, offering high flexibility but relying on model accuracy and involving complex calculations. Furthermore, traditional fault-tolerant control often employs periodic communication and control updates, leading to bandwidth waste and actuator wear. To reduce communication burden and extend equipment lifespan, event-triggered mechanisms have become a research hotspot. These mechanisms update control signals only when triggering conditions are met, significantly reducing the number of updates. Therefore, a fault-tolerant control method for multi-agent systems that can maintain stability even under actuator failure conditions while reducing communication and control frequency is more advantageous in practical applications. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a fault-tolerant control method for multi-agent systems under actuator failure. By combining fixed-gain fault-tolerant control with an event-triggered mechanism, the method can ensure consistent system stability even when the actuator experiences partial failure or deviation, while significantly reducing the frequency of communication and control updates.

[0005] The specific technical solution for achieving the objective of this invention is as follows:

[0006] A fault-tolerant control method for a multi-agent system under actuator failure includes the following steps:

[0007] Step 1: Construct a mathematical model of a linear multi-agent system that incorporates multiplicative and additive actuator faults to describe the impact of actuator faults on control inputs;

[0008] Step 2: Based on the constructed mathematical model of the multi-agent system and its communication topology, construct a consistency error dynamic equation to describe the change of state error of each agent over time.

[0009] Step 3: Design a fixed-gain fault-tolerant controller based on the mathematical model of the multi-agent system to realize fault-tolerant control of the multi-agent system.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0011] (1) The solution of the present invention can simultaneously cope with multiplicative and additive faults of actuators by constructing a multi-agent system model that includes multiplicative faults and additive faults, and has stronger robustness.

[0012] (2) The present invention obtains the controller parameters by solving linear matrix inequalities. The calculation process is simple and the controller structure designed by this method is simple and clear, and easy to implement in engineering.

[0013] (3) The solution of the present invention introduces an event triggering mechanism on the basis of a fixed gain fault-tolerant controller, and only updates the control input when the measurement error meets the triggering condition, which effectively reduces the number of communication and control updates and improves the overall operating efficiency and lifespan of the system.

[0014] (4) The method used in the present invention supports undirected connected graphs and various topologies containing directed spanning trees, and has strong engineering applicability.

[0015] The present invention will be further described below with reference to specific embodiments. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the fault-tolerant control method for a multi-agent system under actuator failure according to the present invention.

[0017] Figure 2 This is an undirected communication topology diagram of a multi-agent system in an embodiment of the present invention.

[0018] Figure 3 This is a directed communication topology diagram of a multi-agent system in an embodiment of the present invention.

[0019] Figure 4 This is a graph showing the changes in the displacement state components of each intelligent agent in an embodiment of the present invention.

[0020] Figure 5 This is a graph showing the changes in the velocity state components of each intelligent agent in an embodiment of the present invention.

[0021] Figure 6 This is a diagram showing the control triggering times of each intelligent agent in this embodiment of the invention.

[0022] Figure 7 This is a graph showing the change in the absolute value of the measurement error of each intelligent agent in the embodiments of the present invention. Detailed Implementation

[0023] Example

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0026] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0027] Combination Figure 1 A fault-tolerant control method for a multi-agent system under actuator failure includes the following steps:

[0028] Step 1: Construct a mathematical model of a linear multi-agent system that incorporates multiplicative and additive actuator faults to describe the impact of actuator faults on control inputs;

[0029] Step 1-1, constructing from A linear system consisting of 100 intelligent agents (without a leader):

[0030]

[0031] in, Tie Time-based intelligent agent state, It means defined on the real number field 3D vector space, express Momentary intelligent agents The control input, It means defined on the real number field 3D vector space, matrix Let these represent the system's state matrix and input matrix, respectively. They respectively represent those defined on the real number field dimensional matrix vector space and 3D matrix-vector space, where it is assumed that the matrix pairs It is calming, which ensures the stability of the system.

[0032] Step 1-2: Constructing an actuator fault model:

[0033]

[0034] in, They represent the first Multiplicative and additive faults occurring in the actuators of an agent. It means that it is defined in the real number field. It means defined on the real number field dimensional vector space, when Only additive faults can occur in the actuator when Only multiplicative faults can occur in the actuator when The actuator is functioning normally. express A zero-dimensional column vector;

[0035] In addition, the multiplicative fault coefficient It is a bounded parameter that satisfies Additive fault coefficient It is also bounded; it satisfies , These represent the upper and lower bounds of the multiplicative fault coefficient, respectively. These represent the boundaries of the additive fault coefficients; these values ​​are unknown and depend on the specific circumstances.

[0036] Steps 1-3: Obtain the mathematical model of the linear multi-agent system incorporating multiplicative and additive faults in the actuators:

[0037] .

[0038] Step 2: Based on the constructed mathematical model of the multi-agent system and its communication topology, construct a dynamic equation for the consistency error to describe the change of the state error of each agent over time.

[0039]

[0040] in, Represents the Kronecker product. They represent The first-order identity matrix and An identity matrix of order 1. express A column vector of all 1s. This represents the state matrix of all agents.

[0041] matrix eigenvalues One 1 and one 0, therefore There exists a simple root 0, and the corresponding right eigenvector is Therefore, it can be concluded that if and only if When, that is, when all agents reach a consensus, there is At this point, the system consistency problem can be equivalent to the asymptotic stability problem of the dynamic equation of system consistency error, which provides specific control objectives and design basis for subsequent fault-tolerant controllers.

[0042] Step 3: Based on the mathematical model of the multi-agent system, design a fixed-gain fault-tolerant controller to realize fault-tolerant control of the multi-agent system:

[0043]

[0044] in, The communication coupling weights between agents. For the feedback gain matrix, This refers to the communication topology diagram. Middle Adjacency Matrix Corresponding intelligent agents arrive Elements of communication relationships;

[0045] Fixed gain fault-tolerant controller parameters and Each satisfies And there are those who meet the conditions The value makes: ;in Let be a symmetric positive definite matrix, and let be the unknown matrix to be solved in the design. The solution is obtained using the following linear matrix inequalities:

[0046]

[0047] The smallest non-zero positive eigenvalue of the Laplace matrix of the system communication topology is denoted as , Multiplicative Fault Matrix The smallest non-zero element in the system is found. At this point, the fixed-gain controller can ensure that the dynamic equation of the system consistency error is asymptotically stable under actuator failure conditions, which means that the control objective of system consistency is satisfied.

[0048] In addition, this embodiment introduces an event triggering mechanism on the basis of the fixed gain fault-tolerant controller to reduce the update frequency of the controller and reduce the consumption of communication and control resources.

[0049] The fixed-gain fault-tolerant controller that incorporates an event-triggered mechanism is:

[0050]

[0051] in, Intelligent agents The latest trigger time, , Intelligent agents The state value from the previous propagation;

[0052] The event triggering protocol is as follows:

[0053]

[0054]

[0055] in , It is a pending positive constant, which will be determined when the event triggers the function. At that time, it will affect the intelligent agent. An event is triggered only once; otherwise, it is not triggered. express Time-based intelligent agent The amount of error, Represents intelligent agents Based on the state value of the previous propagation The estimated state values

[0056] The parameters of the linear multi-agent system in this embodiment are:

[0057]

[0058] Assume that agents 1 and 2 malfunction, and the malfunction parameters are as follows:

[0059]

[0060] Figure 2This diagram represents the communication topology of the system. The nodes in the diagram are numbered sequentially to represent agents 1 through 5. Figure 2 The Laplace matrix of the communication topology graph is

[0061]

[0062] The smallest non-zero eigenvalue of the matrix was calculated. Then we can obtain the coupling weights. Timely satisfaction Furthermore, by solving the linear matrix inequalities, we can obtain...

[0063]

[0064] The final gain is obtained The value is

[0065]

[0066] Substituting the parameters into the designed controller, the simulation results of the system are obtained as follows: Figure 4 , Figure 5 .

[0067] Specifically Figure 4 , Figure 5 The state variables of the multi-agent system are described respectively. As time progresses, it becomes clear that under the action of the fault-tolerant controller, the state variables gradually become more consistent, indicating that the system can achieve consistency well and has accomplished the goal of fault-tolerant control.

[0068] To further verify the effectiveness of the added event-triggered protocol, another agent is added. Figure 3 This is the communication topology diagram of the system. The node numbers in the diagram represent agents 1 to 6 in sequence. Figure 3 The Laplace matrix of the communication topology graph is

[0069]

[0070] The parameters for selecting the event triggering protocol are: Thus, the event triggering function is defined as:

[0071]

[0072] Simulation results are shown below Figure 6 , Figure 7 ,in Figure 6 The event-driven approach demonstrates the moment when each agent meets the event triggering condition, at which moment the agent's controller is driven to update its state. It can be seen that the event-driven approach significantly reduces the frequency of controller state updates. Figure 7The graph represents the change in the absolute value of the measurement error for each agent. The numbers e1-e6 in the graph correspond to the absolute values ​​of the measurement errors for agents 1 to 6, respectively. As can be seen from the graph, the error gradually approaches zero over time. The blue curve represents the absolute value of the measurement error, and the fluctuation gradually decreases. The orange curve is the envelope of the fluctuation of the absolute value of the error, which describes the exponential decay trend of the error. This shows the rationality of the control method and that there is no negative impact due to the reduction in the controller update frequency.

[0073] In summary, this invention proposes a fault-tolerant control method for multi-agent systems under actuator failure. By establishing a system model incorporating multiplicative and additive faults, designing a fixed-gain fault-tolerant controller, and combining it with an event-triggered mechanism, it effectively saves communication resources while ensuring consistent stability across multiple agents. Compared with existing technologies, this invention's method has advantages such as simple controller structure, strong adaptability, low implementation cost, and high communication efficiency. It can be widely applied to fault-tolerant control scenarios in multi-agent systems such as UAV formations, robot collaboration, and sensor networks, demonstrating significant engineering application value and promising prospects for widespread adoption.

[0074] This solution also provides a fault-tolerant control system for a multi-agent system under actuator failure, including the following modules:

[0075] System Model Construction Module: This module is used to construct a linear multi-agent system mathematical model that incorporates multiplicative and additive actuator faults to describe the impact of actuator faults on control inputs. Based on the constructed multi-agent system mathematical model and its communication topology, a consistency error dynamic equation is constructed to describe the change of state error of each agent over time.

[0076] Fixed gain fault-tolerant controller module: Used to design a fixed gain fault-tolerant controller based on the mathematical model of a multi-agent system, so as to realize fault-tolerant control of the multi-agent system.

[0077] This solution also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform the following steps:

[0078] Step 1: Construct a mathematical model of a linear multi-agent system that incorporates multiplicative and additive actuator faults to describe the impact of actuator faults on control inputs;

[0079] Step 2: Based on the constructed mathematical model of the multi-agent system and its communication topology, construct a consistency error dynamic equation to describe the change of state error of each agent over time.

[0080] Step 3: Design a fixed-gain fault-tolerant controller based on the mathematical model of the multi-agent system to realize fault-tolerant control of the multi-agent system.

[0081] This solution also provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the following steps:

[0082] Step 1: Construct a mathematical model of a linear multi-agent system that incorporates multiplicative and additive actuator faults to describe the impact of actuator faults on control inputs;

[0083] Step 2: Based on the constructed mathematical model of the multi-agent system and its communication topology, construct a consistency error dynamic equation to describe the change of state error of each agent over time.

[0084] Step 3: Design a fixed-gain fault-tolerant controller based on the mathematical model of the multi-agent system to realize fault-tolerant control of the multi-agent system.

[0085] The embodiments described above are merely one implementation method of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. 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 all fall within the protection scope of this application. Therefore, the protection scope of this invention application should be determined by the appended claims.

Claims

1. A fault-tolerant control method for a multi-agent system under actuator failure, characterized in that, Includes the following steps: Step 1: Construct a mathematical model of a linear multi-agent system incorporating multiplicative and additive actuator faults to describe the impact of actuator faults on the control input: Step 1-1, constructing from A linear system composed of intelligent agents: ； in, Tie Time-based intelligent agent state, It means defined on the real number field 3D vector space, express Momentary intelligent agents The control input, It means defined on the real number field 3D vector space, matrix Let these represent the system's state matrix and input matrix, respectively. They respectively represent those defined on the real number field dimensional matrix vector space and 3D matrix vector space; Step 1-2: Constructing an actuator fault model: ； in, They represent the first Multiplicative and additive faults occurring in the actuators of an agent. The representation is defined in the real number field, when Only additive faults can occur in the actuator when Only multiplicative faults can occur in the actuator when The actuator is functioning normally. express A zero-dimensional column vector; Steps 1-3: Obtain the mathematical model of the linear multi-agent system incorporating multiplicative and additive faults in the actuators: ； Step 2: Based on the constructed mathematical model of the multi-agent system and its communication topology, construct a dynamic equation for the consistency error to describe the change of the state error of each agent over time. ； in Represents the Kronecker product. They represent The first-order identity matrix and An identity matrix of order 1. express A column vector of all 1s. This represents the state matrix of all agents; Step 3: Based on the mathematical model of the multi-agent system, design a fixed-gain fault-tolerant controller to realize fault-tolerant control of the multi-agent system: ； in, The communication coupling weights between agents. For the feedback gain matrix, This refers to the communication topology diagram. Middle Adjacency Matrix Corresponding intelligent agents arrive Elements of communication relationships; Fixed gain fault-tolerant controller parameters and Each satisfies And there are those who meet the conditions The value makes: ;in Given a symmetric positive definite matrix, solve using the following linear matrix inequality: ； The smallest non-zero positive eigenvalue of the Laplace matrix of the system communication topology is denoted as , Multiplicative Fault Matrix The smallest non-zero element in the system is found. At this point, the fixed-gain fault-tolerant controller can ensure that the dynamic equation of the system consistency error is asymptotically stable under actuator failure conditions, which means that the control objective of system consistency is satisfied.

2. The fault-tolerant control method for a multi-agent system under actuator failure as described in claim 1, characterized in that, An event-triggered mechanism is introduced based on the fixed-gain fault-tolerant controller to reduce the update frequency of the controller and reduce the consumption of communication and control resources. The fixed-gain fault-tolerant controller that incorporates an event-triggered mechanism is: ； in, Intelligent agents The latest trigger time, , Intelligent agents The state value from the previous propagation; The event triggering protocol is as follows: ； ； in , It is a normal number, when the event triggers the function. At that time, it will affect the intelligent agent. An event is triggered only once; otherwise, it is not triggered. express Time-based intelligent agent The amount of error, Represents intelligent agents Based on the state value of the previous propagation The estimated state values.

3. A fault-tolerant control system for a multi-agent system under actuator failure, characterized in that, Includes the following modules: System Model Construction Module: This module is used to construct a linear multi-agent system mathematical model that incorporates multiplicative and additive actuator faults to describe the impact of actuator faults on control inputs. Based on the constructed multi-agent system mathematical model and its communication topology, a consistency error dynamic equation is constructed to describe the change of state error of each agent over time. The process of constructing the mathematical model of the linear multi-agent system that introduces multiplicative and additive faults in the actuators includes: Build by A linear system composed of intelligent agents: ； in, Tie Time-based intelligent agent state, It means defined on the real number field 3D vector space, express Momentary intelligent agents The control input, It means defined on the real number field 3D vector space, matrix Let these represent the system's state matrix and input matrix, respectively. They respectively represent those defined on the real number field dimensional matrix vector space and 3D matrix vector space; Constructing an actuator failure model: ； in, They represent the first Multiplicative and additive faults occurring in the actuators of an agent. The representation is defined in the real number field, when Only additive faults can occur in the actuator when Only multiplicative faults can occur in the actuator when The actuator is functioning normally. express A zero-dimensional column vector; Obtain the mathematical model of the linear multi-agent system that incorporates multiplicative and additive faults in the actuators: ； Then, based on the constructed mathematical model of the multi-agent system and its communication topology, a consensus error dynamic equation is constructed to describe the change of the state error of each agent over time: ； in Represents the Kronecker product. They represent The first-order identity matrix and An identity matrix of order 1. express A column vector of all 1s. This represents the state matrix of all agents; Fixed-gain fault-tolerant controller module: Used to design a fixed-gain fault-tolerant controller based on the mathematical model of a multi-agent system, and to realize fault-tolerant control of the multi-agent system. ； in, The communication coupling weights between agents. For the feedback gain matrix, This refers to the communication topology diagram. Middle Adjacency Matrix Corresponding intelligent agents arrive Elements of communication relationships; Fixed gain fault-tolerant controller parameters and Each satisfies And there are those who meet the conditions The value makes: ;in Given a symmetric positive definite matrix, solve using the following linear matrix inequality: ； The smallest non-zero positive eigenvalue of the Laplace matrix of the system communication topology is denoted as , Multiplicative Fault Matrix The smallest non-zero element in the system is found. At this point, the fixed-gain fault-tolerant controller can ensure that the dynamic equation of the system consistency error is asymptotically stable under actuator failure conditions, which means that the control objective of system consistency is satisfied.

4. A computer 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 computer program, it implements the steps of the method according to any one of claims 1-2.

5. A computer-storable medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-2.

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