Distributed game Nash equilibrium search algorithm for unbounded attack

Abstract

The invention discloses a distributed game Nash equilibrium search algorithm for unbounded attacks. The method has the beneficial effects that the algorithm effectively reduces the negative influence of the unbounded FDI attack on the network search process and the information exchange between the users through the accurate estimation of the adjacent dynamics and the fine adjustment of the parameters of the unmanned aerial vehicle, deals with the FDI attack through the deployment of the distributed observer, guarantees the convergence performance of the unmanned aerial vehicle target through the optimization of the gradient function, and improves the reliability of the unmanned aerial vehicle. And the influence of attacks is resisted. And finally, a Lyapunov stability analysis method is utilized to describe the convergence of a distributed Nash equilibrium strategy of the proposed algorithm in resisting the unbounded attack in detail, and the strategy guides all participants to enter a Nash equilibrium neighborhood by controlling adjustment of gain, so that the robustness of the distributed Nash equilibrium strategy is improved. Therefore, the distributed Nash equilibrium can be realized even if the actuator and the sensor are subjected to unbounded attacks at the same time.

Description

Technical Field

[0001] The present invention relates to the field of distributed algorithms, and in particular to a distributed game Nash equilibrium search algorithm under unbounded attacks. Background Art

[0002] In recent years, with the remarkable development of efficient embedded computing, agile and lightweight hardware solutions, and a variety of telecommunication technologies with complementary advantages, multi-unmanned aerial systems (MUSs) have achieved remarkable success in various application scenarios. Game theory is widely used in the control and optimization problems of network systems, where each participant (user) is modeled as an independent and selfish decision maker who strives to optimize their individual but interdependent cost functions. Distributed Nash equilibrium search describes the optimal strategy configuration of multiple participants in a distributed environment, where the goal of the participants is to maximize their own utility (or minimize cost), and their decisions are affected by the choices of other participants. The game reaches a Nash equilibrium in a certain stable state.

[0003] In the actual application scenarios of drones, attacks against drones are also increasing, which can be mainly divided into two categories: point attacks and edge attacks. Point attacks mainly target the drone itself, such as injecting false data into the drone's controller and sensor, which damages the system stability and makes the drone unable to fly according to the predetermined trajectory. These data attacks can be divided into unbounded and bounded data attacks, and actuator attacks are also a common form. Edge attacks mainly target multi-drone networks, such as denial of service (DoS) attacks. Malicious actors interrupt the normal functions of drone equipment, making the target drone unable to use communications or other equipment, and ultimately causing the system to be unable to handle normal traffic, thereby affecting the services of other users. In order to deal with unbounded attacks, a distributed Nash equilibrium search algorithm under unbounded attacks is proposed. Summary of the invention

[0004] The purpose of the present invention is to provide a distributed game Nash equilibrium search algorithm for unbounded attacks in view of the shortcomings and defects in the prior art. The algorithm effectively reduces the negative impact of unbounded FDI attacks on the network search process and information exchange between users by accurately estimating neighboring dynamics and fine-tuning drone parameters. It also responds to FDI attacks by deploying distributed observers and ensures the convergence performance of drone targets by optimizing gradient functions to resist the impact of attacks. Finally, the convergence of the distributed Nash equilibrium strategy of the proposed algorithm in countering unbounded attacks is described in detail using the Lyapunov stability analysis method. The strategy guides all participants into the neighborhood of Nash equilibrium by adjusting the control gain, thereby ensuring that distributed Nash equilibrium can be achieved even when the actuators and sensors are simultaneously subjected to unbounded attacks.

[0005] To achieve the above purpose, the present invention adopts the following technical solution: a distributed game Nash equilibrium search algorithm for unbounded attacks, characterized in that the dynamic equation of the drone is described by the following equation: When the attack is not considered, the UAV's Nash equilibrium algorithm uses gradient descent and state feedback. At this time, the input u of the system is:

[0006]

[0007] Where k is the control parameter, represents the cost function of multiple drones, Represents the pseudo gradient function of the current UAV and neighboring UAVs, where represents the dynamic estimation of the current UAV’s neighbor information status in the communication network under partial information game, S i is a coefficient matrix. Under the action of u, multiple drones can realize Nash equilibrium search. By exploring the multi-drone system receiving unbounded false data injection attack sensors and actuators, when the actuator of the drone i system is attacked, Among them, u i represents the input of the original UAV system, ρ i Represents the state of the actuator. A value of 1 indicates that there is an attack on the actuator by a malicious attacker, and a value of 0 indicates that there is no attack. represents an unbounded false data injection attack launched by a malicious attacker on the actuator of the drone; when the sensor of drone i is attacked, in, represents the unbounded false sensor data injected into the i-th UAV by a malicious attacker, where N i represents the set of neighbors of the i-th UAV. Although the attacks of sensors are unbounded, it is assumed that their derivatives are bounded. This property provides a key potential solution. The extended state observer (ESO) method has been adjusted to handle scenarios involving unbounded attacks. ESO can estimate unknown elements of the system state, including unknown attacks caused by such attacks. By adjusting the control parameter r, ESO enables users to maintain their pursuit of Nash equilibrium in the presence of attacks and minimize the interference of attacks on the dynamic estimates of UAVs within the UAV communication link network in the graph. Based on the actuator attack observer and the sensor attack observer, the following distributed game Nash equilibrium search algorithm is proposed to resist unbounded FDI attacks:

[0008]

[0009] Furthermore, it is worth noting that an attacker may choose a more sophisticated approach to evade certain detection and identification methods focused on sensor measurements. Instead of launching an independent and relatively large false measurement attack, which is easily detectable, an attacker may simultaneously inject and correlate sensor attacks. If a sensor attack occurs, then ρ xi is equal to 1, otherwise, ρ xi =0; Traditional distributed Nash control algorithms are not sufficient to solve the problem of unbounded FDI attacks. In order to solve this problem, a distributed Nash equilibrium search algorithm is designed. The main goal of these algorithms is to ensure the stability of the entire user system and promote its distributed search for targets. Even in the presence of malicious, unbounded FDI attacks, the control algorithm can effectively maintain the system. In addition, it also ensures the stability of the drone control system and the distributed search for Nash equilibrium.

[0010] Furthermore, the observer design for the actuator attack: To address the actuator attack, an observer is designed to compensate for the unknown and potentially infinite FDI attacks. The main goal of the observer is to adjust the control input to effectively counter the impact of the attack and thus keep the system

[0011] Stability: in, represents the observation of the unbounded executor attack, is an auxiliary variable, r1 and r2 are control parameters.

[0012] Furthermore, the observer design of the sensor attack: For sensor attacks that affect the dynamic estimation between drones and neighbors in a partial information game, a specific observer is designed for the unbounded FDI attack. The observer aims to mitigate the unbounded sensor attack by ensuring accurate estimation between users.

[0013]

[0014] Impact of the attack: in, represents the observation of sensor attack, is an auxiliary variable.

[0015] After adopting the above technical solution, the beneficial effects of the present invention are as follows: the algorithm effectively reduces the negative impact of unbounded FDI attacks on the network search process and information exchange between users by accurately estimating the neighboring dynamics and fine-tuning the drone parameters, and also responds to FDI attacks by deploying distributed observers, and ensures the convergence performance of drone targets by optimizing the gradient function to resist the impact of attacks. Finally, the convergence of the distributed Nash equilibrium strategy of the proposed algorithm in countering unbounded attacks is described in detail using the Lyapunov stability analysis method. The strategy guides all participants into the neighborhood of Nash equilibrium by adjusting the control gain, thereby ensuring that distributed Nash equilibrium can be achieved even when the actuators and sensors are simultaneously subjected to unbounded attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0017] Figure 1 It is a schematic diagram of the drone node and the malicious attacker in the present invention.

[0018] Figure 2 It is the overall design framework diagram for implementing verification in the present invention.

[0019] Figure 3 It is a Nash equilibrium search graph of the UAV control system in the present invention when it is not subjected to any attack.

[0020] Figure 4 It is a schematic diagram of the state of the drone under the unbounded attack in the present invention.

[0021] Figure 5 It is a schematic diagram of the speed of the UAV under the unbounded attack in the present invention. DETAILED DESCRIPTION

[0022] The technical solution adopted in this specific implementation is: It is characterized in that the dynamic equation of the drone is described by the following equation:

[0023]

[0024] When the attack is not considered, the UAV's Nash equilibrium algorithm uses gradient descent and state feedback. At this time, the input u of the system is:

[0025]

[0026] Where k is the control parameter, represents the cost function of multiple drones, Represents the pseudo gradient function of the current UAV and neighboring UAVs, where represents the dynamic estimation of the current UAV’s neighbor information status in the communication network under partial information game, S i is a coefficient matrix. At this time, multiple drones can realize Nash equilibrium search under the action of u;

[0027] By exploring the multi-UAV system receiving unbounded false data injection attack sensors and actuators, when the actuator of the UAV i system is attacked, Among them, u i represents the input of the original UAV system, ρ i Represents the state of the actuator. A value of 1 indicates that there is an attack on the actuator by a malicious attacker, and a value of 0 indicates that there is no attack. It represents an unbounded false data injection attack on the actuator of the drone launched by a malicious attacker;

[0028] When the sensor of drone i is attacked, in, represents the unbounded false sensor data injected into the i-th UAV by a malicious attacker, where N i represents the set of neighbors of the ith drone.

[0029] See also Figure 1 As shown, it is worth noting that the attacker may choose a more sophisticated approach to evade certain detection and identification methods that focus on sensor measurements. The attacker may not launch an independent and relatively large false measurement attack, which is easy to detect, but rather inject and correlate sensor attacks at the same time. If a sensor attack occurs, then ρ xi is equal to 1, otherwise, ρ xi is equal to 0;

[0030] Traditional distributed Nash control algorithms are not sufficient to solve the problem of unbounded FDI attacks. In order to solve this problem, a distributed Nash equilibrium search algorithm is designed. The main goal of these algorithms is to ensure the stability of the entire user system and promote its distributed search for targets. Even in the presence of malicious, unbounded FDI attacks, the control algorithm can effectively maintain the system. In addition, it also ensures the stability of the drone control system and the distributed search for Nash equilibrium.

[0031] Observer Design for Actuator Attacks: To address the actuator attack, an observer is designed to compensate for unknown and potentially infinite FDI attacks. The main goal of the observer is to adjust the control input to effectively counter the impact of the attack and thus maintain the stability of the system:

[0032]

[0033] in, represents the observation of the unbounded executor attack, is an auxiliary variable, r1 and r2 are control parameters.

[0034] Observer Design for Sensor Attacks: For sensor attacks that affect the dynamic estimation between drones and their neighbors in a partial information game, a specific observer is designed for the unbounded FDI attack. The observer aims to mitigate the impact of unbounded sensor attacks by guaranteeing accurate estimation between users:

[0035]

[0036] in, represents the observation of sensor attack, is an auxiliary variable.

[0037] Although the attacks on sensors are unbounded, their derivatives are assumed to be bounded. This property provides a key potential solution. The Extended State Observer (ESO) approach has been adapted to handle scenarios involving unbounded attacks. ESO can estimate unknown elements of the system state, including those caused by such attacks. By adjusting the control parameter r, ESO enables users to maintain their pursuit of Nash equilibrium in the presence of attacks and minimize the interference of attacks on the dynamic estimates of the UAVs within the UAV communication link network in the graph.

[0038] Based on the actuator attack observer and the sensor attack observer, the following distributed game Nash equilibrium search algorithm is proposed to resist unbounded FDI attacks:

[0039]

[0040] The following are the experimental verification related data and steps of the present invention:

[0041] The overall framework of experimental verification can be found in Figure 2 shown.

[0042] The designed control algorithm is verified by using drones. The cost of designing five drones is as follows:

[0043]

[0044] For parameter f a =0.8,f b =1,fc =0.01, among which malicious attacks are:

[0045]

[0046] And sensor attacks are: First, when the system is not attacked, the Nash equilibrium search of the drone is as follows: Figure 3 As shown:

[0047] pass Figure 3 It can be seen that when not under any attack, the five drones searched for the corresponding Nash equilibrium according to the predetermined cost function design.

[0048] Next, under unbounded attack, using the control algorithm designed above, the drone can still search for the Nash equilibrium designed by the cost function, such as Figure 4-5 As shown;

[0049] pass Figure 4-5 It can be seen that even if the drone is attacked by malicious unbounded false data injection from a malicious attacker, using the designed control algorithm, the drone can still successfully search for the corresponding Nash equilibrium according to the predetermined cost function.

[0050] The above description is only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in this field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A distributed game Nash equilibrium search algorithm for unbounded attacks, characterized by: The dynamic equation of the drone is described by the following equation: When the attack is not considered, the UAV's Nash equilibrium algorithm uses gradient descent and state feedback. At this time, the input u of the system is: Where k is the control parameter, represents the cost function of multiple drones, Represents the pseudo gradient function of the current UAV and neighboring UAVs, where represents the dynamic estimation of the current UAV’s neighbor information status in the communication network under partial information game, S i is a coefficient matrix. At this time, multiple drones can realize Nash equilibrium search under the action of u; By exploring the multi-UAV system receiving unbounded false data injection attack sensors and actuators, when the actuator of the UAV i system is attacked, Among them, u i represents the input of the original UAV system, ρ i Represents the state of the actuator. A value of 1 indicates that there is an attack on the actuator by a malicious attacker, and a value of 0 indicates that there is no attack. It represents an unbounded false data injection attack on the actuator of the drone launched by a malicious attacker; When the sensor of drone i is attacked, in, represents the unbounded false sensor data injected into the i-th UAV by a malicious attacker, where N i represents the set of neighbors of the i-th drone; Although the attacks on sensors are unbounded, their derivatives are assumed to be bounded. This property provides a key potential solution. The Extended State Observer (ESO) approach has been adapted to handle scenarios involving unbounded attacks. ESO can estimate unknown elements of the system state, including those caused by such attacks. By adjusting the control parameter r, ESO enables users to maintain their pursuit of Nash equilibrium in the presence of attacks and minimize the interference of attacks on the dynamic estimates of the UAVs within the UAV communication link network in the graph. Based on the actuator attack observer and the sensor attack observer, the following distributed game Nash equilibrium search algorithm is proposed to resist unbounded FDI attacks:

2. The distributed game Nash equilibrium search algorithm for unbounded attacks according to claim 1, characterized in that: It is worth noting that the attacker may choose a more sophisticated approach to evade certain detection and identification methods focused on sensor measurements. The attacker may not launch an independent and relatively large false measurement attack, which is easy to detect, but rather a simultaneous injection and related sensor attack. If a sensor attack occurs, then ρ xi is equal to 1, otherwise, ρ xi is equal to 0; Traditional distributed Nash control algorithms are not sufficient to solve the problem of unbounded FDI attacks. In order to solve this problem, a distributed Nash equilibrium search algorithm is designed. The main goal of these algorithms is to ensure the stability of the entire user system and promote its distributed search for targets. Even in the presence of malicious, unbounded FDI attacks, the control algorithm can effectively maintain the system. In addition, it also ensures the stability of the drone control system and the distributed search for Nash equilibrium.

3. The distributed game Nash equilibrium search algorithm for unbounded attacks according to claim 1, characterized in that: The observer design of the actuator attack: To address the actuator attack, an observer is designed to compensate for the unknown and potentially infinite FDI attacks. The main goal of the observer is to adjust the control input to effectively counter the impact of the attack and thus maintain the stability of the system: in, represents the observation of the unbounded executor attack, is an auxiliary variable, r1 and r2 are control parameters.

4. The distributed game Nash equilibrium search algorithm for unbounded attacks according to claim 1, characterized in that: The observer design of the sensor attack: For sensor attacks that affect the dynamic estimation between drones and their neighbors in a partial information game, a specific observer is designed for the unbounded FDI attack. The observer aims to mitigate the impact of unbounded sensor attacks by guaranteeing accurate estimation between users: in, represents the observation of sensor attack, is an auxiliary variable.

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