Event triggering predefined time consensus control method for high-order multi-agent under spoofing attack

Abstract

The invention provides a high-order multi-agent event triggering predefined time consensus control method under a spoofing attack, which comprises the following steps: modeling the spoofing attack as an unknown bounded nonlinear disturbance signal, and non-linearly coupling the nonlinear disturbance signal with a system state through a time-varying coefficient; through a distributed predefined time state observer, the real state of the agent masked by the attack is estimated in real time through neighborhood information interaction, and an attack signal is separated; dynamically adjusting control parameters through an adaptive law based on observer output and post-attack state difference so as to compensate state deviation caused by the attack; each agent is provided with a local control law, the input of the local control law is an observer estimation state of the agent and a neighbor, an acceleration item is introduced into the control law, and a preset convergence time upper bound is realized through preset parameters; parameters of the control law are updated based on local adjacency information of a Laplacian matrix, and distributed consensus tracking is completed only depending on states of adjacent agents.

Description

Technical Field

[0001] The present invention belongs to the technical fields of control systems, multi-agent systems, network security, etc., and particularly relates to an event-triggered predefined-time consensus control method for high-order multi-agents under deceptive attacks. Background Art

[0002] In the design of adaptive controllers and nonlinear multi-agent systems (MAS), deceptive attacks have severely damaged the availability of the accurate states of the systems, introduced significant control errors, and made it difficult to reach a consensus among multiple agents while effectively solving uncertainties. Multi-agent consensus control involves formulating coordination strategies to achieve a shared consensus state or decision in a dynamic environment. MAS applications in the real world are extensive, including robots, unmanned surface vehicles, sensor networks, etc., covering multiple fields such as intelligent transportation systems and distributed sensor networks.

[0003] The research on multi-agent consensus control mainly focuses on the following key components: First, the consensus protocol promotes continuous state updates among agents through information exchange, thus achieving convergence to a common goal or state; Second, the network topology defines the communication methods and structures among agents, such as complete graphs, local graphs, and dynamic topologies; Third, robustness is crucial for ensuring that agents can still reach a consensus in the presence of uncertainties (such as deceptive attacks). By addressing these components, the research objectives include enhancing the coordination and reliability of multi-agent systems, thereby achieving efficient task execution in complex environments.

[0004] Although finite-time consensus and fixed-time consensus have been widely studied, the convergence durations of existing methods often lack precise control and are difficult to meet the requirements of time-sensitive applications. In some practical scenarios, adjusting system parameters may not be able to reduce the upper bound below a specific constant, which highlights the need for predefined-time stability. Therefore, it is of great significance to develop a predefined-time consensus method that allows specifying the consensus time. Predefined-time control has received attention because of its ability to achieve precise and time-limited convergence, especially in applications such as swarm robotics and network control. However, existing methods rely on local scaling in theoretical proofs, resulting in overestimated upper bounds and overly conservative results, which limits their practical effectiveness. Designing a control law function that can achieve predefined-time convergence and reduce the conservativeness of the theoretical convergence time remains a major challenge.

[0005] In the context of significant control errors caused by interference and uncertainty, the main goal of consensus control is to maintain consensus among multiple agents while effectively mitigating these uncertainties. Existing methods such as adaptive methods for partial sensor attacks, dynamic event-driven adaptive dynamic programming, and security control methods have partially addressed these challenges. However, in unknown environments, there are often significant differences between the actual dynamic positions of MAS clusters and their expected formations, especially under interference. Solving this problem requires the application of advanced control theories and technologies. Despite considerable progress, there is still room for improvement in this field. For example, existing predefined-time consensus methods are mostly limited to non-interfered scenarios and do not fully consider the convergence speed of perturbations in observations. In addition, previous research on consensus under deception attacks has mainly focused on asymptotic stability or finite-time stability, with limited exploration of predefined-time stability.

[0006] In practical applications, especially in scenarios involving time-varying conditions, fast convergence is often essential. Therefore, exploring methods to achieve predefined-time consensus convergence within a specific time frame has become an important research direction. Event-triggered mechanisms have received extensive attention because they can effectively reduce communication and computational resource consumption. However, existing research has mostly not considered the situation of more general nonlinear MAS under deception attacks. With the diversification of the system's requirements for control performance, traditional control methods have become difficult to meet the requirements, so it is imperative to explore new methods to enhance system stability and convergence performance. Summary of the Invention

[0007] The problem of system state distortion caused by deceptive attacks seriously restricts the reliability of MAS, specifically manifested as: 1) The nonlinear interference introduced by the attack significantly amplifies the control error; 2) It is difficult to synchronously achieve state consensus and interference suppression in an uncertain environment.

[0008] Considering the following technical bottlenecks in existing consensus control methods: First, although traditional finite-time consensus and fixed-time consensus control methods have made some progress, their upper bounds of convergence time are often difficult to accurately define, resulting in difficulty in meeting real-time requirements in time-sensitive scenarios. Research shows that the parameter adjustment of existing algorithms cannot compress the upper bound of convergence time below a specific constant threshold, which essentially stems from the conservative scaling method used in Lyapunov stability analysis. Second, in the scenario of the coupled action of deception attacks and external interference, existing methods (including adaptive dynamic programming, event-driven control, etc.) have not effectively solved the dynamic coupling problem between the observation perturbations induced by the attack and the convergence speed, resulting in a significant deviation between the actual pose and the expected configuration of the MAS cluster. Notably, current research on attacked MAS is mostly limited to the framework of asymptotic stability or finite-time stability, and there is still a gap in the theoretical exploration of predefined-time stability.

[0009] Literature research shows that there are three key defects in the existing technical solutions: 1) The convergence time estimation under dynamic topology networks is overly conservative, resulting in a magnitude difference between the theoretical boundary and the actual performance; 2) The existing predefined time control laws do not consider the non-linear observation error propagation characteristics caused by attacks; 3) The traditional periodic triggering mechanism generates a large amount of redundant communication in attack scenarios, exacerbating network resource consumption and security risks. Although recent research has introduced a predefined time framework in formation tracking control, the design of its control function is still based on the local linearization assumption and fails to fully explore the global dynamic characteristics of non-linear MAS. These technical defects severely restrict the practical deployment of MAS in safety-critical scenarios such as unmanned system formations and industrial Internet of Things.

[0010] Therefore, it is urgent to construct a new type of predefined time consensus control architecture, which should simultaneously meet: precise prior setting of convergence time, quantitative compensation for attack-induced calculation errors, and resource optimization allocation driven by an event-triggered mechanism. This technological breakthrough will significantly improve the coordination reliability and task execution efficiency of attacked MAS in complex dynamic environments.

[0011] To this end, in view of the challenge that deceptive attacks make the true system state unavailable for controller design, the present invention proposes a predefined time consensus control method for deceptive attacks, aiming to solve the control problem of high-order non-linear multi-agent systems (MAS) under deceptive attacks. The present invention develops a predefined time state observer to compensate for the impact of deceptive attacks on the system state, thereby achieving accurate estimation of the system state. The controller of each subsystem utilizes the estimation information of itself and adjacent estimators and combines the designed adaptive law to achieve state compensation after the attack.

[0012] The core of the present invention lies in proposing a predefined time method containing an acceleration term. By avoiding the use of complex calculations such as exponential functions or trigonometric functions, the calculation process is significantly simplified and the calculation resource requirements are reduced. After adding the acceleration term, the theoretical upper bound of the convergence time is more accurate and the conservativeness is reduced. In addition, the present invention adopts a flexible formation task strategy based on neighborhood information, further improving the tracking and coordination performance of the system. Through the event-triggered mechanism, the amount of calculation and the number of information exchanges are reduced, thereby improving the efficiency and practicality of the system.

[0013] The present invention models deceptive attacks as unknown but bounded signals and designs an observer to compensate for these attack signals. The controller of each subsystem utilizes the estimation information of itself and neighboring observers, combined with an adaptation law, to achieve state compensation after the attack. A distributed adaptive predefined-time consensus control algorithm is proposed, and it is proven by Lyapunov stability analysis that the algorithm can achieve convergence within a predefined time. The designed consensus controller achieves enhanced performance in a multi-agent system, enabling agents to autonomously adjust their states and supporting dynamic adaptation and automatic reconfiguration.

[0014] The consensus strategy of the present invention has remarkable adaptability. By collecting static and dynamic data of agents, it updates its behavior in real time. Each agent only needs to know the states of its neighboring agents and the leader, without global state information, thus reducing communication and computational complexity. Specifically, the agent only needs to know the Laplacian matrix and the state information of its neighboring agents, further simplifying the implementation of the system. The present invention provides an efficient and reliable solution for predefined-time consensus control of high-order nonlinear MAS under deceptive attacks, with broad application prospects.

[0015] The technical solution specifically adopted by the present invention to solve its technical problems is:

[0016] An event-triggered predefined-time consensus control method for high-order multi-agents under deceptive attacks:

[0017] Model the deceptive attack as an unknown bounded nonlinear perturbation signal, and the nonlinear perturbation signal is nonlinearly coupled with the system state through time-varying coefficients;

[0018] Through a distributed predefined-time state observer, the true state of the agent masked by the attack is estimated in real time with neighborhood information interaction, and the attack signal is separated;

[0019] Through an adaptation law based on the difference between the observer output and the state after the attack, dynamically adjust the control parameters to compensate for the state deviation caused by the attack;

[0020] Each agent is provided with a local control law, whose input is the estimated states of itself and its neighbors. An acceleration term is introduced into the control law, and a preset upper bound of the convergence time is achieved through preset parameters;

[0021] Update the control law parameters based on the local adjacency information of the Laplacian matrix, and complete distributed consensus tracking only relying on the states of neighboring agents.

[0022] Further, the adaptation law uses the sign power function sig p , which is defined as the combination of the sign function and the absolute value power operation for each element of the vector v, where the power exponent satisfies 0 < p < 1.

[0023] Furthermore, the adaptation law is specifically as follows:

[0024]

[0025] where T c > 0, for sig p (v) = [sgn(v1)|v1| p , sgn(v2)|v2| p ,..., sgn(v n )|v n | p T , the sgn function represents the sign function, F i,l represents the estimation error, k2 is the positive efficiency.

[0026] Furthermore, the acceleration term is the nonlinear acceleration term sig p .

[0027] Furthermore, the communication frequency is dynamically controlled through the threshold condition based on the event-triggering mechanism to reduce redundant information exchange.

[0028] Furthermore, the threshold condition based on the event-triggering mechanism is specifically as follows:

[0029]

[0030] where u i is the final control input of the i-th agent, w i is the control input of the i-th agent, c > 0, representing the threshold amplitude coefficient, 0 < ε < 1, representing the attenuation rate coefficient, represents the time of the next event trigger of the i-th agent.

[0031] Furthermore, the control law is specifically as follows:

[0032]

[0033] where k i,n represents the nonlinear acceleration term gain, a i,n represents the robust term gain, s i,n represents the sliding mode surface of the i-th agent.

[0034] And, a multi-agent system includes: a distributed observer module, a nonlinear control law module, and an event-triggered communication module, adopting the method described above.

[0035] ​An electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the method described above are implemented.

[0036] A non-transitory computer-readable storage medium stores a computer program thereon. When the computer program is executed by a processor, the steps of the method described above are implemented.

[0037] Compared with the prior art, the present invention and its preferred solutions have the following prominent innovation points and advantages:

[0038] I. Nonlinear modeling and dynamic compensation mechanism for spoofing attacks. Different from the limitation of traditional methods that simplify attacks as linear noise, the present invention models spoofing attacks as unknown bounded nonlinear coupled perturbations. By the collaborative work of a distributed observer and an adaptive law, the attack signals are estimated and compensated in real time, effectively solving the nonlinear interference problem of the attack propagation path and improving the reliability of the system in complex attack scenarios. II. Predefined time collaborative control architecture. Breaking through the limitation that the convergence time of traditional methods depends on system parameters or initial states, through the joint design of a nonlinear observer and a sign power function control law, user-programmable convergence time control is achieved, allowing the direct setting of the maximum convergence time of the system to meet the high-precision real-time control requirements. III. Low-complexity nonlinear control design. Using a sign power function to replace traditional exponential or trigonometric operations, eliminating complex floating-point calculations, reducing the computational resources consumed by a single agent while ensuring predefined time convergence, and avoiding singularity problems caused by high-order terms, significantly improving the engineering applicability of the algorithm. IV. Dynamic event-triggered communication mechanism. Designing an adaptive triggering strategy based on an exponentially decaying threshold, intelligently adjusting the communication frequency under attack interference, reducing redundant communication volume, and achieving the best balance between real-time performance and resource consumption in scenarios with limited communication resources. V. Local topology adaptation and strong scalability. Based on the local adjacency information update strategy of the Laplacian matrix, only relying on the states of neighbor nodes to dynamically adjust control parameters, supporting dynamic topology changes such as the random joining or leaving of agents in the network, shortening the convergence recovery time after network structure adjustment, and being applicable to large-scale scalable systems.

[0039] Verification tests of the present invention in test scenarios such as unmanned aerial vehicle clusters and intelligent transportation systems show that it can provide a solution with strong anti-interference ability, high real-time performance, and low resource consumption for safety-critical scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention will be further described in detail below with reference to the drawings and specific embodiments:

[0041] Figure 1 It is a schematic diagram of the overall framework of the solution of the embodiment of the present invention;

[0042] Figure 2It is a flowchart for implementing the solution of the embodiment of the present invention;

[0043] Figure 3 It is a topology diagram of Scenario 1 of the embodiment of the present invention;

[0044] Figure 4 It is the state diagram of x in Scenario 1 of the embodiment of the present invention 1,l ;

[0045] Figure 5 It is a test result diagram of Scenario 1 of the embodiment of the present invention. The upper figure is the output of the observer, and the lower figure is the event trigger time;

[0046] Figure 6 It is a topology diagram of Scenario 2 of the embodiment of the present invention;

[0047] Figure 7 It is the state diagram of x in Scenario 2 of the embodiment of the present invention (upper figure), and the state diagram of x 1,i ; (lower figure) 2,i ;

[0048] Figure 8 It is a schematic diagram of the event trigger time in Scenario 2 of the embodiment of the present invention.

[0049] Figure 9 It is a topology diagram of Scenario 3 of the embodiment of the present invention.

[0050] Figure 10 It is the state diagrams in Scenario 3 of the embodiment of the present invention: a. x 1,2 with different p; b. x 2,2 with different p; c. x 3,2 with different p; d. x 4,2 with different p;

[0051] Figure 11 It is the state diagram of x with different p in Scenario 3 of the embodiment of the present invention 5,2 ;

[0052] Figure 12 It is the state diagram of x with different F in Scenario 3 of the embodiment of the present invention (upper figure), and the state diagram of x 1,2 with different F (lower figure); 2,2 ;

[0053] Figure 13 It is the state diagrams in Scenario 3 of the embodiment of the present invention: a. x 3,2 with different F; b. x 4,2 with different Fc; x 5,2 with different F. Detailed implementation manners

[0054] To make the features and advantages of this patent more obvious and understandable, specific embodiments are hereinafter given and described in detail as follows:

[0055] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by those of ordinary skill in the technical field to which this application belongs.

[0056] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0057] As Figure 1 、 Figure 2 shown, in order to overcome the challenge that the controller design cannot obtain the true system state due to spoofing attacks in the embodiments of the present invention, a predefined-time state observer is provided for high-order nonlinear MAS to compensate for the impact of spoofing attacks. The controller of each individual subsystem utilizes the estimates of its own and neighboring estimators. And an innovative predefined-time method including an acceleration term is adopted to avoid complex calculations such as exponential functions or trigonometric functions. This method simplifies the calculation and reduces the computational resource requirements. After adding the acceleration term, the theoretical upper bound of the convergence time is more accurate, reducing conservatism. This embodiment utilizes a flexible formation task strategy based only on neighborhood information, thereby improving the tracking and coordination performance. This event-triggered mechanism method reduces both the required computational amount and the number of required information exchanges.

[0058] Specifically, in the solution of this embodiment, the spoofing attacks affecting the state of each agent are modeled as unknown bounded signals. To mitigate the impact of these attacks, an observer is designed to compensate for the spoofing signals. The controller of each individual subsystem utilizes the estimates from its own and neighboring observers. Using the state and output of the observer after the attack, a corresponding adaptive law is developed. A distributed adaptive predefined-time consensus control algorithm is proposed. Through Lyapunov stability analysis, it is proved that the proposed controller including attack compensation converges within a predefined time. The designed consensus controller achieves enhanced performance in a multi-agent system, enabling the agents to autonomously adjust their states and supporting dynamic adaptation and automatic reconfiguration. Through an effective distributed control strategy, the agents can autonomously adjust their states. This strategy combines behaviors tailored for individual agents, allowing for dynamic adaptation and automatic reconfiguration. The proposed consensus strategy exhibits significant adaptability. Static and dynamic data of the agents are collected, allowing for real-time updates of their behaviors. Subsequently, the state of each agent is adjusted according to the generalized difference between each agent and a specified agent. Therefore, asFigure 1 , 2 as shown. Each agent only needs to know the states of its neighboring agents and the leader, rather than the global state of all agents. Each agent needs to know the Laplacian matrix and the states of its neighboring agents. For agent i, if (i, j) ∈ E and a ij = 1, agent i needs to know the state of agent j; otherwise, when a ik = 0, agent i does not need to know the state of agent k.

[0059] The following specifically introduces the design process of the overall solution of this embodiment:

[0060] The first step is to construct a system model.

[0061] Consider a set of N agents, and each agent is modeled as an N - order system. The dynamics of the i - th agent are:

[0062]

[0063] where is the state of the agent, is the control input, d i,l is the disturbance, which represents a deception attack in this embodiment, and f i,l is the non - linear dynamic function corresponding to the non - linear dynamics;. The present invention innovatively models the deception attack as an unknown bounded signal, described as follows:

[0064]

[0065] where is the true state after the attack signal is injected into the sensor. μ i,l and a i,l are time - varying coefficients, and a i,l ≠0.

[0066] The derivative of

[0067]

[0068] The second step is to construct an observer.

[0069] To estimate the uncertain model and disturbance after the deception attack, that is, construct an observer The estimation error quantifies the accuracy of the observer and is crucial for ensuring the convergence within a predefined time. In this case, the observer is used for the robustness against deception attacks. The definition of the estimation error is as follows:

[0070]

[0071] Let where k2 is the positive efficiency, the adaptation law is designed as follows

[0072]

[0073] where 0 < p < 1, T c > 0. For sig p (v) = [sgn(v1)|v1| p , sgn(v2)|v2| p ,..., sgn(v n )|v n | p T , where the sgn function represents the signum function.

[0074] Some existing methods for dealing with theoretical proofs adopt local scales, and the current upper bounds have been overestimated, resulting in highly conservative and overestimated theoretical results. Compared with common functions, the proposed solution of the present invention uses an acceleration term, and the theoretical convergence time T requires less conservatism. Since 0 < p < 1, the occurrence of singularities can be effectively avoided. Therefore, the algorithm proposed by the present invention has a relatively low computational cost, does not require complex calculations such as exponential functions or trigonometric functions, and reduces the demand for computing resources. Therefore, compared with traditional adaptive methods, the computational load of the controller can be significantly reduced. In addition, the designed control scheme is easy to implement.

[0075] Step 3: Define the consensus error of the i-th agent as follows:

[0076]

[0077] where s1 = [s i1 , s i2 , …, s iN T , B = [b1, b2, …, b N T x r,1 represents the desired state. b i is the coefficient. s1 can be written in the following form:

[0078]

[0079] L represents the Laplacian matrix.

[0080] The derivative of s1 is as follows:

[0081]

[0082] Define:​​​

[0083] s i,2 = x 1,2 - α i,1 (12)

[0084] where α i,1 is designed as:

[0085]

[0086] where 0 < p < 1, k i,1 > 0.

[0087] Step 4, when 2 ≤ l ≤ n - 1, define:

[0088]

[0089] α i,l is the solution of the filter, which satisfies the following conditions:

[0090]

[0091] where k i,l > 0.

[0092] Step 5, define:

[0093]

[0094] Construct a trigger condition to minimize unnecessary communication:

[0095]

[0096] where c > 0, 0 < ε < 1.

[0097] Finally, the continuous control law is obtained as follows:

[0098]

[0099]

[0100] The strategy designed above in this embodiment ensures that the agents maintain accurate consensus within a predefined time, which guarantees that the agents can not only maintain formation but also reach the expected state within the preset time.

[0101] The advantages of the solution of the present invention are further illustrated by verification tests in the following three scenarios:

[0102] Scenario 1 and its results

[0103] To further verify the solution of the present invention, a first test example is provided: The perturbation is d i,1= cos(t), d i,2 = cos(t). The initial position of the agent is at x0 = [1.3, 0.1, -0.1] T The main parameters include p = 0.8, N = 3, N = 2, k1 = 3.5. The desired state in the first case is x r = [0, 0, 0] T , as shown in the topology of Figure 3 . The test results are as shown in Figure 4 and Figure 5 .

[0104] From Figure 4 and Figure 5 it can be seen that the states of the three followers are consistent with the state of the leader. When the deceptive attacks increase, this method mitigates their impact on the system. The designed control algorithm can reduce the impact of deceptive attacks while ensuring the consensus of the multi-agent system.

[0105] Scenario 2 and results

[0106] Consider another system with five followers and one leader: The initial state of the agents is [6, 12, 18, 24, 30] T , and the initial velocity of the agents is [1, 2, 10, 3, 4, 5] T . The initial state of the leader is 5, and the Laplacian matrix is The attack is d n = (n + 1) + 0.5n(n + 1) + (n + 1) / 3.5, t n = (n + 1) / 3.5, The initial velocity is 1.3. The main parameters are p = 0.7, N = 5, N = 2, k1 = 5.5, as shown in Figure 6 . The results are as shown in Figures 7 - 8 .

[0107] Referring to the results of Figures 7 - 8 , the proposed solution of the present invention has high precision, smooth operation, excellent performance, transient enhancement, and over time, the error gradually converges to 0, and the state of each follower in the system can be aligned with the state of the leader. The event trigger times and release intervals of each agent are given in the figure. When the state converges, the threshold will automatically increase to save bandwidth resources. Under the consensus control protocol, it can be seen that the MAS can reach consensus even under deceptive attacks. The simulation results show that the designed event-triggered control protocol is effective and the MAS can reach consensus.

[0108] Scenario 3 and its results

[0109] To further verify the algorithm without an event-triggering mechanism, another experiment was conducted: F = 2. The initial positions of the agents in the first cluster are located at x0 = [-8 -2, 2, 6, 9] T . The initial velocities are [2, 1, 3, 2, 1] T . The Laplacian matrix is p = 0.7, N = 5, n = 2, k1 = 4.x r = [0, 0, 0, 0, 0]T, as Figure 9 shown.

[0110] The influence of p is discussed, as Figures 10 - 11 shown. Figures 10 - 11 It shows that when the value of p is small, the system exhibits obvious overshoot; similarly, the settling time is relatively short. On the contrary, it is just the opposite. The safety consensus goal is achieved within three seconds.

[0111] Figures 12 - 13 The influence of F is discussed. It can be seen from Figures 12 - 13 that when the disturbance is large, the consistency of the compensation mechanism with the predefined time

[0112] control method exhibits obvious overshoot and a long settling time. The safety consensus goal is achieved within 3 seconds.

[0113] In summary, the embodiment of the present invention designs a predefined-time consensus tracking protocol with a disturbance suppression term. The control protocol uses a dynamic event-triggering method, where the selection of the triggering moment is intelligently defined by the dynamic event-triggering condition. Theoretically, it is proved that this triggering mechanism does not exhibit Zeno behavior. The results show that it is superior to other traditional predefined-time controllers.

[0114] Based on the same inventive concept, the present invention further provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is configured to execute the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is used to implement one or more instructions. Specifically, it is used to load and execute one or more instructions in the computer storage medium to implement the above method.

[0115] It should be further noted that, based on the same inventive concept, the present invention further provides a computer storage medium, on which a computer program is stored, and the computer program, when run by a processor, executes the above method. The storage medium may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may, for example, but not be limited to, an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a Random Access Memory (RAM), a Read-Only Memory (ROM), an Erasable Programmable Read-Only Memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, the computer-readable storage medium may be any tangible medium that contains or stores a program, and the program can be used by or combined with an instruction execution system, apparatus, or device.

[0116] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those with ordinary skills in the field to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. Words such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "linked" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right", etc. are only used to indicate relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0117] As described above, these are only the preferred embodiments of the present invention, and are not intended to limit the present invention in other forms. Any person skilled in the art may use the technical content disclosed above to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

[0118] This patent is not limited to the above best implementation mode. Anyone inspired by this patent can come up with various other forms of ship tracking control methods with predefined time-regulated performance. All equal changes and modifications made according to the scope of the patent application of the present invention shall fall within the coverage scope of this patent.

Claims

1. A method for controlling high-order multi-agent event-triggered predefined time consensus under deception attacks, characterized by: The deception attack is modeled as an unknown bounded nonlinear disturbance signal, wherein the nonlinear disturbance signal is nonlinearly coupled with the system state through a time-varying coefficient; Through the distributed predefined time state observer, the real state of the agent masked by the attack is estimated in real time through neighborhood information interaction, and the attack signal is separated; Through the adaptive law based on the difference between the observer output and the state after the attack, the control parameters are dynamically adjusted to compensate for the state deviation caused by the attack; Each agent is set with a local control law, whose input is the observer estimated state of itself and its neighbors. An acceleration term is introduced into the control law, and the preset upper bound of the convergence time is achieved through preset parameters. The control law parameters are updated based on the local adjacency information of the Laplace matrix, and distributed consensus tracking is completed only by relying on the states of neighboring agents.

2. The event-triggered predefined time consensus control method for high-order multi-agents under deception attacks according to claim 1, characterized in that: The adaptive law uses the symbolic power function sig p , which is defined as a combination of a sign function and an absolute value power operation on each element of vector v, where the power exponent satisfies 0 <p<1。 3. The event-triggered predefined time consensus control method for high-order multi-agents under deception attacks according to claim 2 is characterized in that: The adaptive law is specifically: in T c >0, for sig p (v) = [sgn(v1)|v1| p ,sgn(v2)|v2| p ,...,sgn(v n )|v n |p] T , sgn function represents the signal function, F i,l represents the estimation error, k2 is the positive efficiency.

4. The event-triggered predefined time consensus control method for high-order multi-agents under deception attacks according to claim 1, characterized in that: The acceleration term is the nonlinear acceleration term sig p .

5. The event-triggered predefined time consensus control method for high-order multi-agents under deception attacks according to claim 1, characterized in that: The communication frequency is dynamically controlled through threshold conditions based on event-triggered mechanisms to reduce redundant information exchange.

6. The event-triggered predefined time consensus control method for high-order multi-agents under deception attacks according to claim 5, characterized in that: The threshold conditions based on the event trigger mechanism are specifically: In the formula, u i is the final control input of the ith agent, w i is the control input of the ith agent, c>0, represents the threshold amplitude coefficient, 0<ε<1, represents the attenuation rate coefficient, Indicates the time when the next event of the i-th agent is triggered.

7. The event-triggered predefined time consensus control method for high-order multi-agents under deception attacks according to claim 6, characterized in that: The control law is specifically: Among them, k i,n represents the nonlinear acceleration gain, a i,n represents the robust term gain, s i,n represents the sliding surface of the i-th agent.

8. A multi-agent system, characterized in that: include: The distributed observer module, the nonlinear control law module and the event-triggered communication module adopt the method according to any one of claims 1 to 7.

9. 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, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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