A distributed optimization method for second-order intelligent robots under DoS attacks

Abstract

This paper discloses a new method for distributed optimization of a second-order intelligent robot under DoS attacks. This method first establishes a dynamic model of the second-order intelligent robot based on second-order multi-agent distributed optimization theory. Next, considering time-series DoS attacks, appropriate detection and communication recovery mechanisms are established to address the distributed optimization of the second-order intelligent robot under DoS attacks. A second-order homogeneous feedback filter is then designed to estimate the original state of the system. A new coordinate transformation formula is introduced to reconstruct the system's controller. Finally, based on Lyapunov stability analysis, a new method for distributed optimization of the second-order intelligent robot is proposed.

Description

Technical Field

[0001] The present invention relates to a method for distributed optimization of a second-order intelligent robot, and in particular to a new method for distributed optimization of a second-order intelligent robot under DoS attack. Background Art

[0002] Multi-agent systems consist of multiple autonomous agents, each with its own goals and decision-making capabilities, collaborating to complete complex tasks. Distributed optimization, unlike centralized optimization, decomposes a problem into multiple subproblems, with different agents optimizing each subproblem in parallel, ultimately collaborating to achieve a global optimal solution. Agents exchange information and coordinate with each other through a communication network. The structure of the communication topology affects the performance of the entire system. Multi-agent systems are vulnerable to various attacks, such as denial-of-service attacks, which can disrupt the communication topology and impact system performance. Therefore, adaptive mechanisms are needed to mitigate these attacks and improve system robustness and security.

[0003] The core technologies involved in multi-agent distributed optimization include multi-agent system modeling, distributed optimization algorithms, communication topology analysis, and security assurance. Multi-agent system modeling focuses on describing the agents, their objective functions, and the mechanisms for their interactions. Distributed optimization algorithms study how to decompose a global optimization problem into multiple sub-problems, which are solved in parallel by different agents and ultimately achieve a coordinated global optimum. Communication topology analysis focuses on the structural characteristics of the communication network between agents, such as connectivity and stability, which affect system performance. Security assurance addresses the various cyber attacks to which multi-agent systems are susceptible, designing corresponding detection, defense, and adaptive mechanisms to improve system robustness.

[0004] These core technologies provide crucial support for the coordinated execution of complex tasks and for improving system reliability and robustness. With the continuous advancement of technologies like artificial intelligence and network communications, multi-agent distributed optimization holds broad application prospects in smart cities, industrial automation, and unmanned systems. Future research into key technologies such as distributed optimization algorithms, adaptive communication topologies, and security defense mechanisms will ensure that multi-agent distributed optimization plays an even more crucial role in the coordinated control of complex systems. Summary of the Invention

[0005] The purpose of this invention is to propose a new method for distributed optimization of second-order intelligent robots under DoS attacks, which can improve the optimization efficiency and computing performance while ensuring system security, and provide effective technical support for the optimization control of multi-agent systems.

[0006] The specific technical solution of the present invention is as follows: A new method for distributed optimization of a second-order intelligent robot under DoS attack, comprising the following steps:

[0007] Based on the distributed optimization theory of second-order multi-agent, the following dynamic model is established for the high-order multi-agent model in reference [1]:

[0008]

[0009] Where, as well as are the system state, control input, and output of the i-th agent respectively.

[0010] Further considering the DoS attack based on time series, by establishing appropriate detection mechanism and attack mechanism, we can solve the distributed optimization method of the second-order intelligent robot under DoS attack. The specific steps are as follows:

[0011] DoS attacks are a common attack method that can prevent the target computer or network from providing normal services or accessing resources. Attackers can launch DoS attacks by blocking communication channels, damaging devices, preventing devices from sending information, or attacking routing protocols. Depending on the attack target, DoS attacks can be divided into link attacks and node attacks. Link attacks destroy communication lines and prevent communication between nodes. Node attacks may cause one or more nodes to lose communication functions, resulting in the complete collapse of the entire communication topology. Both types of attacks can have serious impacts on the system:

[0012] Attack Detection: First, when each agent exchanges information with its neighbors, if the neighboring agent successfully receives the information, it will reply with a confirmation signal. If the neighboring agent does not receive the confirmation signal within a certain period of time, it means that the agent is under attack. In addition, to ensure security and reliability, each agent uses different protocols and secure channels to transmit information to avoid interference from attackers.

[0013] Communication recovery: To ensure security, each agent uses a different protocol to transmit information. Once an attack is detected, the affected area will send information to the intelligent management center through a secure channel. The center will then make decisions and initiate actions to repair the communication topology. A secure channel is a way to ensure the security of information transmission through encryption or other security measures. It can prevent attackers from stealing or tampering with information, ensuring the confidentiality and integrity of the information.

[0014] In short, the essence of DoS attack is to destroy the communication between agents, thus causing the change of communication topology. Where ρ i Indicates whether agent i is attacked, when ρ i = 0, which means that agent i is under attack, otherwise ρ i=1 means agent i is not attacked, time interval Δ i represents the time of the i-th DoS attack, so the total DoS attack time is

[0015]

[0016] further,

[0017]

[0018] Where, Represents the period of time when the agents are not attacked, that is, the period when they can communicate normally.

[0019] Next, we design a second-order homogeneous feedback filter to estimate the original state of the system, introduce a new coordinate change formula, and reconstruct the system controller. The specific steps are as follows:

[0020] For a second-order dual integrator system, a second-order homogeneous filter is designed as follows:

[0021]

[0022] Where, is x i，1 The estimated state, v i is an auxiliary variable and α, β are the coupling gains to be designed;

[0023] Consider the following coordinate transformation:

[0024]

[0025] Using the filtered state Construct the following virtual controller

[0026]

[0027] Where c i，j >0 is a parameter to be designed;

[0028] For the i-th agent, the controller is as follows

[0029] u i =α i，2

[0030] This part is designed.

[0031] Finally, based on the Lyapunov stability theory analysis, the distributed optimization method of the second-order intelligent robot was solved. The specific steps are as follows:

[0032] C001: Select the following Lyapunov function:

[0033]

[0034] in, and

[0035] C002: For Calculate V i，1 The derivative of

[0036]

[0037] C003: According to (7), we can get

[0038]

[0039] C004: Substituting formula (8) into formula (12), we can get the result

[0040]

[0041] C005: Similarly, by applying formula (7), V i，2 The derivative of

[0042]

[0043] C006: Combining formulas (1), (8) and (14), we can obtain:

[0044]

[0045] C007: Substituting equations (7), (8), and (9) into equation (15) completes the derivation

[0046]

[0047] C008: Further

[0048]

[0049] C009: Based on formula (1), we can finally get:

[0050]

[0051] C010: Based on the above analysis, it is not difficult to see

[0052]

[0053] C011: For

[0054] C012: When the system is attacked by DoS, it indicates the adjacency weight And the corresponding Laplace matrix is According to hypothesis (4), it can be inferred that during the attack, The communication topology described by Based on this, we have The theory has been proven. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0056] Figure 2 It is a DoS attack model;

[0057] Figure 3 This is the network topology diagram of the second-order intelligent robot;

[0058] Figure 4 is the output trajectory map of the robot;

[0059] Figure 5 Trajectory diagram of cost function and optimization variables;

[0060] Figure 6 is the trajectory diagram of the controller;

[0061] Figure 7 is the error trajectory diagram of the first dimension;

[0062] Figure 8 is the error trajectory diagram of the second dimension; DETAILED DESCRIPTION

[0063] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0064] like Figure 1 As shown in FIG, a new method for distributed optimization of second-order intelligent robots under DoS attacks includes the following steps:

[0065] Step 1: Select four cost functions and calculate their first-order derivatives and second-order derivatives;

[0066] Step 2: Introduce coordinate transformation;

[0067] Step 3: Use the filter to estimate the original state;

[0068] Step 4: Use the estimated state to build a virtual controller;

[0069] Step 5: Use the controller to update the system status.

[0070] An embodiment of the present invention is described below;

[0071] Consider the following cost function:

[0072]

[0073] The filter parameters are designed as α = 0.4, β = 0.2;

[0074] The virtual control parameter is designed as c 11 =0.5, c 21 =0.4, c 31 =0.7, c 41 =0.5, c 12 =0.4, c 22 =0.6, c 32 =0.3 and c 42 =0.4.

[0075] Figure 1 is a flow chart of a method according to an embodiment of the present invention; Figure 2 It is a DoS attack model; Figure 3 This is the network topology diagram of the second-order intelligent robot; Figure 4 is the output trajectory map of the robot; Figure 5 Trajectory diagram of cost function and optimization variables; Figure 6 is the trajectory diagram of the controller;

[0076] Figure 7 is the error trajectory diagram of the first dimension; Figure 8 is the error trajectory diagram of the second dimension.

[0077] References

[0078] [1]Zhang L, Deng C, An L.Asymptotic Tracking Control of NonlinearStrict-Feedback Systems With State / Output Triggering: A Homogeneous FilteringApproach[J]. IEEE Transactions on Automatic Control, 2024.

[0079] [2]Zhang X,Liu X,Ding T,et al.On resilience and distributed fixed-time control of MTDC systems under DoS attacks[J].IEEE Transactions onAutomation Science and Engineering,2022.

Claims

1. A method for distributed optimization of second-order intelligent robots under DoS attacks, characterized in that: The following steps are involved: Based on the second-order multi-agent distributed optimization theory, a dynamic model of the second-order intelligent robot is established; the specific steps are as follows: Based on the distributed optimization theory of second-order multi-agent, the following dynamic model is established for the high-order multi-agent model: Where, as well as are the system state, control input, and output of the i-th agent respectively; Considering DoS attacks based on time series, we establish a suitable detection mechanism and communication recovery mechanism to solve the distributed optimization method of the second-order intelligent robot under DoS attacks. The specific steps are as follows: (1) Attack detection: First, when each agent exchanges information with its neighbors, if the neighboring agent successfully receives the information, it will reply with a confirmation signal. If no confirmation signal is received within a certain period of time, it means that the agent is under attack. In addition, to ensure security and reliability, each agent uses different protocols and secure channels to transmit information, thereby avoiding interference from attackers. (2) Communication recovery: To ensure security, each intelligent agent uses a different protocol to transmit information. Once an attack is detected, the affected area will send information to the intelligent management center through a secure channel. The center will then make a decision and initiate an operation to repair the communication topology. A secure channel is a way to ensure the security of information transmission through encryption or other security measures. It can prevent attackers from stealing or tampering with information, ensuring the confidentiality and integrity of the information. definition Where ρ i Indicates whether agent i is attacked, when ρ i = 0, which means that agent i is under attack, otherwise ρ i =1 means agent i is not attacked, time interval Δ i represents the time of the i-th DoS attack, so the total DoS attack time is: further, Where, represents the period of time when the agents are not attacked, that is, the period when they can communicate normally; Design a second-order homogeneous feedback filter to estimate the original state of the system, introduce a new coordinate transformation formula, and reconstruct the system controller. The specific steps are as follows: For a second-order dual integrator system, a second-order homogeneous filter is designed as follows: Where, is x i，1 The estimated state, v i is an auxiliary variable and α, β are the coupling gains to be designed; consider the following coordinate transformation: Using the filtered state, the following virtual controller is constructed: Where c i，j >0 is a parameter to be designed; For the i-th agent, the controller is as follows: u i ＝α i，2 ； This part is designed; Based on the Lyapunov stability theory analysis, a distributed optimization method for second-order intelligent robots is proposed; the specific steps are as follows: B001: Select the following Lyapunov function: Where, and B002: For Calculate V i，1 The derivative of : B003: Available: B004: You can get the result: B005: Similarly, calculate V i，2 The derivative of can be obtained: B006: Then we can get: B007: Complete derivation: B008: Further: B009: Based on the above formula, we can finally get: B010: Based on the above analysis, it is not difficult to see B011: For B012: When the system is attacked by DoS, it indicates the adjacency weight And the corresponding Laplace matrix is It can be deduced During the attack, The communication topology described has at least one non-zero eigenvalue, which means that Based on this, we have The proof is complete.

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