A multi-agent system output compensation control method under aperiodic DoS attack

Abstract

The application discloses a kind of multi-agent system output compensation control methods under non-periodic DoS attack, first construct follower fuzzy approximation system model and non-periodic DoS attack model;When attack activation causes output loss, trigger attack compensation mechanism to keep last output to provide continuous compensation signal;Switch fuzzy state observer is constructed to estimate agent state, and adaptive law in attack activation and dormancy stage is designed using Lyapunov function;Global preset performance function is constructed to establish dynamic performance boundary, and consistency tracking error and normalized conversion error are calculated to construct barrier function;Distributed adaptive security control law is obtained by combining backstepping method.The application overcomes the defect that observation performance decreases due to output loss in attack stage and traditional performance function depends on error initial value, guarantees global preset performance and high-precision state estimation, solves the cooperative control problem under non-periodic DoS attack.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent control technology, specifically relating to a method for output compensation control of a multi-agent system under aperiodic DoS attack. Background Technology

[0002] Currently, research on the control of multi-agent systems under DoS attacks still has the following shortcomings: Aperiodic DoS attacks cause blockage of the agent's sensor-controller channel, disrupting system consistency: When an aperiodic DoS attack occurs, the agent's sensor-controller channel is blocked, and the output signal cannot be fed back to the controller, resulting in a severe decline in system control performance or even instability.

[0003] Aperiodic DoS attacks increase control difficulty: DoS attacks in real-world networks often exhibit aperiodic characteristics. Although their activation time, duration, and frequency are bounded by energy constraints, they are random and unpredictable. Traditional control strategies are mostly based on the assumption of periodic attacks, which makes it difficult to cope with the uncertainty of timing, posing a serious challenge to the real-time response and stability of the system.

[0004] Traditional preset performance control relies on the initial state and cannot achieve global performance guarantee: Although preset performance control can pre-set the convergence speed and overshoot of the error variable, the construction of its performance function usually depends on the initial value of the error variable, which means that the control scheme is only effective when the initial state is known or limited, and cannot be applied to systems with unknown or arbitrarily changing initial states, lacking global preset performance guarantee.

[0005] The system state is unpredictable during an attack, and the accuracy of state estimation is difficult to guarantee: the output signal is lost when a DoS attack is activated. Existing methods often set the output signal directly to zero during the attack phase, which leads to a decrease in observer performance, an increase in observation error, and difficulty in guaranteeing the convergence of observation error during the switch between attack activation and dormancy, thus affecting system stability.

[0006] In light of this, in an environment where aperiodic DoS attacks are frequent, how to construct a consistency control scheme that takes into account both global preset performance indicators and high-precision state estimation has become a topic with both theoretical challenges and engineering value in the field of distributed collaboration. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, this invention provides a method for output compensation control of a multi-agent system under non-periodic DoS attacks.

[0008] This invention is achieved through the following technical solution: A method for output compensation control of a multi-agent system under aperiodic DoS attack includes the following steps: S1: The multi-agent system includes one leader agent and several follower agents. Construct the communication topology and leader reference signal of the multi-agent system. For a single follower agent, construct a follower agent differential equation model including unknown nonlinear functions. Use the universal approximation principle of fuzzy logic system to approximate the unknown nonlinear functions in the follower agent differential equation model, and convert the follower agent differential equation model into a fuzzy approximation system model. S2: Construct an aperiodic DoS attack model to describe the temporal characteristics of the DoS attack activation and dormancy phases; output the DoS attack temporal state signal representing the current phase of the multi-agent system through the aperiodic DoS attack model. S3: When the current stage of the multi-agent system is the attack activation stage, the output signal of the follower agent will be lost. When the controller of the follower agent cannot receive its output signal, the attack compensation mechanism is triggered. The attack compensation mechanism receives the DoS attack timing status signal, extracts the last output signal before the interruption, retains the data, and outputs continuous compensation output signals. S4: Combining the compensation output signal, the DoS attack timing state signal and the fuzzy approximation system model, construct a switching fuzzy state observer, estimate the state of the follower agent by switching the fuzzy state observer and output the estimated state value of the follower agent. S5: Define the observation error of the switching fuzzy state observer. For the switching fuzzy state observer, use the Lyapunov function to construct adaptive laws for the active and dormant phases of the DoS attack respectively. S6: Construct a monotonically decreasing global preset performance function to establish the dynamic performance boundary of each follower agent; S7: Given the leader reference signal, and combined with the follower agent state estimate and dynamic performance boundary, the consistency tracking error is obtained, and the normalized transformation error is obtained based on the consistency tracking error; then the barrier function is constructed using the normalized transformation error. S8: Based on Lyapunov stability theory, the distributed adaptive security control law under the active and dormant phases of the DoS attack is obtained by taking the DoS attack timing state signal, follower agent state estimate, adaptive law, and barrier function, and using the backstepping method.

[0009] Furthermore, in step S1, the communication topology of the multi-agent system is as follows: definition These are elements of the adjacency matrix, used to represent the first... The follower agent and the first The communication connection state between the following intelligent agents; if the first The follower agent and the first If there is a communication connection between the follower agents, then ,otherwise , If there is information exchange between the leader agent and the follower agents, then there exists ,on the contrary, ;definition , ;definition For the operation phase indication of a multi-agent system, when When this occurs, it indicates that the multi-agent system is in the DoS attack activation phase. This indicates that the multi-agent system is in a dormant phase during a DoS attack. The leader reference signal is ; The differential equation model of the follower agent is as follows: (1); in, It is the first The first state of each follower agent to the second state A state vector consisting of 10 states. ; , The first The first, second, and third follower agents. , No. A state, for dimensional vector; for The first derivative with respect to time Indicates the first The first follower agent's first One state, Indicates the first A state vector consisting of all states of each follower agent. , For the first The number of states of each follower agent. Indicates the first The first agent of the intelligent agent n The first derivative of each state variable with respect to time; and The first The control input of the follower agent and the first The output signal of a follower agent It is a real number; It is the first The first follower agent Unknown nonlinear functions in the state equations Indicates the first The first intelligent agent n Unknown nonlinear functions in the state equations; The total number of follower agents. It is a positive integer; The fuzzy approximation system model is as follows: (2); in, For the first The first follower agent's first The ideal parameter vector of the fuzzy logic system corresponding to each state equation; For the first The first follower agent's first The ideal parameter vector of the fuzzy logic system corresponding to each state equation; For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector; For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector; For the first The first agent of the intelligent agent The approximation error of the fuzzy logic system corresponding to each state equation. For the first The first follower agent's first The approximation error of the fuzzy logic system corresponding to each state equation.

[0010] Further, in step S2, the aperiodic DoS attack model is as follows: Definition of the first The time interval between DoS attacks is ,in The moment the attack begins. The moment the attack ends. This represents the sequence number of the DoS attack that occurred. ,in Time interval The total number of attacks within, of which The end time, At the starting time, ; In time interval within, no. The total duration of a DoS attack on each follower agent. for: (3); Meanwhile, the total duration of the dormancy interval in a DoS attack is defined as follows: (4); in, Indicates from time interval Remove total attack duration The remaining time set; Assumption 1: Assume there exists a constant. So that in the time interval Total attack duration The following constraints must be met: (5); Assumption 2: Assume there exists a constant constraint on the number of attacks. Attack average dwell time constant This makes the time interval Total number of attacks within The following constraints must be met: (6); definition As a time variable, when When the DoS attack timing status signal is high, it indicates that the DoS attack is in the active phase; when When the DoS attack timing status signal is low, it indicates that the attack is in a dormant phase. Indicates the first The start time of the DoS attack.

[0011] Furthermore, in step S3, the attack compensation mechanism is as follows: (7); in, It is the first The output signal after compensation by the follower agent The time when the m-th attack occurs The left limit, This is the last output signal before the interruption occurs at the time of the m-th attack.

[0012] Further, in step S4, the switching fuzzy state observer is: (8); in, For the first The estimate of the first state of the follower agent. For the first The first follower agent's first The estimated value of each state, It is the first The first follower agent's first The first derivative of the estimate of each state with respect to time, It is the first The first follower agent's first The estimated value of the state; It is the first The first follower agent's first The estimated value of each state, It is the first The first follower agent's first The first derivative of the estimate of each state with respect to time; It is the first The first follower agent's first Gain coefficients of a switching fuzzy state observer It is the first The first follower agent's first Gain coefficients of a switching fuzzy state observer; For the first The first to the second of the follower agents A state vector consisting of the estimated values ​​of each state. For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. Let be the input basis function vector. For the first The first to the second of the follower agents A state vector consisting of the estimated values ​​of each state. For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector.

[0013] Further, in step S5, the observation error is: (9); when During the active phase of a DoS attack, construct the Lyapunov function. : (10); in, For the first The observation error vector of each follower agent and It is a symmetric positive definite matrix and its dimension is 1 / 2. match, It is the attack activation phase. The fuzzy parameter estimation error vector of a follower agent; Find the time derivative of equation (10) and construct an adaptive law for the activation phase of a DoS attack. : (11); in, For the coefficients of the adaptive law correction term during the activation phase of a DoS attack, For the first The extended output estimation error vector of a follower agent during the activation phase of a DoS attack. ; It is a diagonal matrix composed of fuzzy basis functions during the activation phase of a DoS attack. Phase 1 of DoS attack activation Fuzzy parameter estimation vector of a follower agent ; Phase 1 of DoS attack activation The transpose of the parameter estimation vector of the fuzzy logic system corresponding to the first state equation of the follower agent. Phase 1 of DoS attack activation The first follower agent's first Transpose of the parameter estimation vector of the fuzzy logic system corresponding to each state equation; when During the dormant phase of a DoS attack, construct the Lyapunov function. : (12); in, and It is a symmetric positive definite matrix and its dimension is 1 / 2. match, It is the dormant phase of a DoS attack. The fuzzy parameter estimation error vector of a follower agent; Find the time derivative of equation (12) and construct an adaptive law for the dormant phase of a DoS attack. : (13); in, For the coefficients of the adaptive law correction term during the dormant phase of a DoS attack, Estimate the error vector for the extended output during the dormant phase of a DoS attack; It is a diagonal matrix composed of fuzzy basis functions during the dormant phase of a DoS attack. The hibernation phase of a DoS attack Fuzzy parameter estimation vector of a follower agent ; The hibernation phase of a DoS attack The transpose of the parameter estimation vector of the fuzzy logic system corresponding to the first state equation of the follower agent. The hibernation phase of a DoS attack The first follower agent's first Transpose of the parameter estimation vector of the fuzzy logic system corresponding to each state equation; definition For the first The gain coefficient vector of the switching fuzzy state observer during the attack phase of each follower agent is used to ensure that the observation error of the switching fuzzy state observer asymptotically converges under a DoS attack. The following set of matrix inequalities must be satisfied: (14); in, for An identity matrix of dimension 1 It is a positive number. For a dimension The constant matrix, , For dimension is The The system matrix of the error dynamic equation of a follower agent It is a positive number; It is a diagonal matrix.

[0014] Furthermore, in step S6, the globally preset performance function is a positive monotonically decreasing function, and its construction process is as follows: Define the existence of a smooth function , Defined as a smooth function of First derivative, , The requirement is that it is bounded and piecewise continuous; at the same time, define... It is a monotonically increasing function with an initial value of 1, and when , ; The globally preset performance function is: (15); in, , ,because It exhibits strict monotonically decreasing properties and satisfies the initial boundary conditions. and ;because It tends to infinity at the initial moment, thus allowing any finite initial error to fall within the dynamic performance boundary; The dynamic performance boundary includes an upper bound and a lower bound, where the upper bound is... The lower bound of the dynamic performance boundary is .

[0015] Further, in step S7, the consistency tracking error is: (16); in, Representing the The estimate of the first state of each follower agent; Differentiating equation (16) yields: (17); in, For the first The output signal after compensation by the follower agent For the first A follower agent in the stage The gain coefficient of the first switched fuzzy state observer; The normalization transformation error is: (18); The barrier function is: (19).

[0016] Furthermore, in step S8, to facilitate the construction of the distributed adaptive security control law, the barrier function in formula (19) is modified. Find the time derivative: (20); in, (twenty one); Then we get: (twenty two); Construct the following coordinate transformation: (twenty three); if ,but ;if ,but ; in, For the first A follower agent in the stage The next level of coordinate transformation error, For the first A follower agent in the stage Below Level coordinate transformation error, For the first A follower agent in the stage Below Level virtual control law; The construction process of the distributed adaptive security control law during the DoS attack activation phase is as follows: S801: When Based on Lyapunov stability theory, a Lyapunov function is constructed. : (twenty four); Differentiating equation (24) and constructing the first... A first-level virtual control law for a follower agent during the activation phase of a DoS attack. : (25); in, For the first The first-level error feedback gain of a follower agent during the DoS attack activation phase. The first derivative of the leader's reference signal with respect to time; S802: Constructing Lyapunov functions based on Lyapunov stability theory. : (26); Differentiating equation (26) and constructing the first... Secondary virtual control law of a follower agent during the activation phase of a DoS attack : (27); in, For the first Second-order error feedback gain of a follower agent during the DoS attack activation phase. For the first The first-order time derivative of the first-level virtual control law of a follower agent during the activation phase of a DoS attack. S803: Constructing Lyapunov functions based on Lyapunov stability theory. : (28); Differentiating equation (28) and constructing the first... A follower agent during the DoS attack activation phase Level Virtual Control Law as follows: (29); in, For the first A follower agent during the DoS attack activation phase Level error feedback gain, For the first A follower agent during the DoS attack activation phase The first derivative of the virtual control law with respect to time; S804: When hour, For the first A follower agent during the DoS attack activation phase Level virtual control law: (30); in, A distributed adaptive security control law during the activation phase of a DoS attack; The construction process of the distributed adaptive security control law under the dormant phase of the DoS attack is as follows: S805: When Based on Lyapunov stability theory, a Lyapunov function is constructed. : (31); Differentiating equation (31) and constructing the first... A first-level virtual control law for a follower agent during the dormant phase of a DoS attack. : (32); in, For the first The first-level error feedback gain of a follower agent during the dormant phase of a DoS attack; ; S806: Constructing Lyapunov functions based on Lyapunov stability theory. : (33); Differentiating equation (33) and constructing the first... Secondary virtual control law of a follower agent during the dormant phase of a DoS attack : (34); in, For the first Second-order error feedback gain of a follower agent during the dormant phase of a DoS attack. For the first The first-order time derivative of the first-level virtual control law of a follower agent during the dormant phase of a DoS attack. S807: Constructing Lyapunov functions based on Lyapunov stability theory. : (35); Differentiating equation (35) and constructing the first... A follower agent in the dormant phase during a DoS attack Level Virtual Control Law : (36); in, For the first A follower agent in the dormant phase during a DoS attack Level error feedback gain, For the first A follower agent in the dormant phase during a DoS attack The first derivative of the virtual control law with respect to time; S808: When hour, For the first A follower agent in the dormant phase during a DoS attack Level virtual control law: (37); in, For the distributed adaptive security control law during the attack dormant phase; The distributed adaptive security control law is: (38).

[0017] The beneficial effects that this invention can achieve are as follows: 1. This invention introduces an attack compensation mechanism that receives the DoS attack timing status signal. When a DoS attack occurs and causes the output signal to be lost, the last output signal before the interruption is extracted, the data is preserved, and a continuous compensation signal is output, which reduces the adverse effects of channel blockage caused by the DoS attack to a certain extent.

[0018] 2. This invention constructs a switching fuzzy state observer and uses the compensated output signal for state estimation. Compared with the traditional method of directly setting the agent's output signal to zero during the attack phase, this method overcomes the defects of decreased observer performance and increased observation error caused by this, and ensures the convergence of observation error during the attack activation and dormancy switching process.

[0019] 3. This invention constructs a global preset performance function. The construction of this function eliminates the dependence and limitation of the initial value of consistency tracking error on the traditional preset performance method, so that the control scheme is still effective when the initial state is unknown or changes arbitrarily, and realizes the preset performance guarantee in a global sense.

[0020] 4. This invention combines the backstepping method to construct a distributed adaptive security control law, and makes targeted designs in the activation and dormancy phases of DoS attacks, ensuring the Lyapunov stability of the multi-agent system under non-periodic DoS attacks, effectively realizing the consistency of the output signals of the follower agent and the leader agent, and solving the problem of collaborative control of multi-agent systems in the face of non-periodic DoS attacks. Attached Figure Description

[0021] Figure 1 This is a control block diagram of an embodiment of the method of the present invention.

[0022] Figure 2 This is a communication topology diagram between the follower agent and the leader agent in the simulation example of this invention.

[0023] Figure 3 This is a timing state signal diagram of an aperiodic DoS attack in the simulation example of this invention.

[0024] Figure 4 This is a graph showing the changes in the consistency tracking error of each follower agent in the simulation example of this invention.

[0025] Figure 5 This is a diagram showing the changes in the output signals of each follower agent in a simulation example of the present invention.

[0026] Figure 6 This is a graph showing the changes in the observation errors of each follower agent in the simulation example of this invention.

[0027] Figure 7 This is a distributed adaptive safety control law diagram of each follower agent in the simulation example of this invention. Detailed Implementation

[0028] A method for output compensation control of a multi-agent system under aperiodic DoS attack includes the following steps: S1: The multi-agent system includes one leader agent and several follower agents. Construct the communication topology and leader reference signal of the multi-agent system. For a single follower agent, construct a follower agent differential equation model including unknown nonlinear functions. Use the universal approximation principle of fuzzy logic system to approximate the unknown nonlinear functions in the follower agent differential equation model, and convert the follower agent differential equation model into a fuzzy approximation system model.

[0029] definition These are elements of the adjacency matrix, used to represent the first... The follower agent and the first The communication connection state between the following intelligent agents; if the first The follower agent and the first If there is a communication connection between the follower agents, then ,otherwise , If there is information exchange between the leader agent and the follower agents, then there exists ,on the contrary, ;definition , ;definition For the operation phase indication of a multi-agent system, when hour( (This is an indicator of the DoS attack activation phase), indicating that the multi-agent system is in the DoS attack activation phase. hour( (This is an indicator of the DoS attack dormancy phase, indicating that the multi-agent system is in the DoS attack dormancy phase.) The leader reference signal is ; The differential equation model of the follower agent is as follows: (1); in, It is the first The first state of each follower agent to the second state A state vector consisting of 10 states. ; , The first The first, second, and third follower agents. , No. One state, for dimensional vector; for The first derivative with respect to time Indicates the first The first follower agent's first One state, It indicates the first A state vector consisting of all states of each follower agent. , For the first The number of states of each follower agent. Indicates the first The first agent of the intelligent agent n The first derivative of each state variable with respect to time; and The first The control input of the follower agent and the first The output signal of a follower agent It is a real number; It is the first The first follower agent Unknown nonlinear functions in the state equations Indicates the first The first intelligent agent n Unknown nonlinear functions in the state equations; The total number of follower agents. It is a positive integer; Lemma 1 (Universal Approximation Theorem): For any expression defined on a compact set... Arbitrary smooth nonlinear function on Fuzzy logic system exists Make in, For state vectors, , These represent the ideal parameter vector and the basis function vector of the fuzzy logic system, respectively, and the approximation error of the fuzzy logic system. .in, , The upper bound of the approximation error is a positive real number.

[0030] The unknown nonlinear function in the differential equation model of the follower agent is approximated by using the universal approximation theorem of fuzzy systems, and the differential equation model of the follower agent (1) is transformed into a fuzzy approximation system model in the following form: (2); in, For the first The first follower agent's first The ideal parameter vector of the fuzzy logic system corresponding to each state equation; For the first The first follower agent's first The ideal parameter vector of the fuzzy logic system corresponding to each state equation; For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector; For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector; For the first The first agent of the intelligent agent The approximation error of the fuzzy logic system corresponding to each state equation. For the first The first follower agent's first The approximation error of the fuzzy logic system corresponding to each state equation.

[0031] S2: Construct an aperiodic DoS attack model to describe the temporal characteristics of the DoS attack activation and dormancy phases; output the DoS attack temporal state signal representing the current phase of the multi-agent system through the aperiodic DoS attack model.

[0032] Definition of the first The time interval between DoS attacks is ,in The moment the attack begins. The moment the attack ends. This represents the sequence number of the DoS attack that occurred. ,in Time interval The total number of attacks within, of which The end time, At the starting time, ; In time interval within, no. The total duration of a DoS attack on each follower agent. for: (3); Meanwhile, the total duration of the dormancy interval in a DoS attack is defined as follows: (4); in, Indicates from time interval Remove total attack duration The remaining time set; Assumption 1: Assume there exists a constant. So that in the time interval Total attack duration The following constraints must be met: (5); Assumption 2: Assume there exists a constant constraint on the number of attacks. Attack average dwell time constant This makes the time interval Total number of attacks within The following constraints must be met: (6); definition As a time variable, when When the DoS attack timing status signal is high, it indicates that the DoS attack is in the active phase; when When the DoS attack timing status signal is low, it indicates that the attack is in a dormant phase. Indicates the first The start time of the DoS attack.

[0033] S3: When the multi-agent system is currently in the attack activation phase, the output signal of the follower agent will be lost. When the controller of the follower agent cannot receive its output signal, the attack compensation mechanism is triggered. The attack compensation mechanism receives the DoS attack timing status signal, extracts the last output signal before the interruption, retains the data, and outputs continuous compensation output signals.

[0034] When the DoS attack timing status signal indicates that the DoS attack is in the active phase, the controller of the follower agent will not receive its output signal and will trigger the attack compensation mechanism. The attack compensation mechanism will extract the last output signal before the interruption, retain the data, and output continuous compensation output signals. When the DoS attack timing status signal indicates that the DoS attack is in the dormant phase, the controller of the follower agent will receive its output signal normally and the attack compensation mechanism will stop working and directly output the output signal of the follower agent.

[0035] The attack compensation mechanism is constructed as follows: (7); in, It is the first The output signal after compensation by the follower agent The time when the m-th attack occurs The left limit, This is the last output signal before the interruption occurs at the time of the m-th attack.

[0036] S4: Combining the compensation output signal, the DoS attack timing state signal, and the fuzzy approximation system model, construct a switching fuzzy state observer. Estimate the state of the follower agent by switching the fuzzy state observer and output the estimated state value of the follower agent.

[0037] Switch the fuzzy state observer to: (8); in, For the first The estimate of the first state of the follower agent. For the first The first follower agent's first The estimated value of each state, It is the first The first follower agent's first The first derivative of the estimate of each state with respect to time, It is the first The first follower agent's first The estimated value of the state; It is the first The first follower agent's first The estimated value of each state, It is the first The first follower agent's first The first derivative of the estimate of each state with respect to time; It is the first The first follower agent's first Gain coefficients of a switching fuzzy state observer It is the first The first follower agent's first Gain coefficients of a switching fuzzy state observer; For the first The first to the second of the follower agents A state vector consisting of the estimated values ​​of each state. For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. Let be the input basis function vector. For the first The first to the second of the follower agents A state vector consisting of the estimated values ​​of each state. For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector.

[0038] S5: Define the observation error of the switching fuzzy state observer. For the switching fuzzy state observer, use the Lyapunov function to construct adaptive laws for the active and dormant phases of a DoS attack, respectively.

[0039] The observation error is: (9); when During the active phase of a DoS attack, construct the Lyapunov function. : (10); in, For the first The observation error vector of each follower agent and It is a symmetric positive definite matrix and its dimension is 1 / 2. match, It is the attack activation phase. The fuzzy parameter estimation error vector of a follower agent; Find the time derivative of equation (10) and construct an adaptive law for the activation phase of a DoS attack. : (11); in, For the coefficients of the adaptive law correction term during the activation phase of a DoS attack, For the first The extended output estimation error vector of a follower agent during the activation phase of a DoS attack. ; It is a diagonal matrix composed of fuzzy basis functions during the activation phase of a DoS attack. Phase 1 of DoS attack activation Fuzzy parameter estimation vector of a follower agent ; Phase 1 of DoS attack activation The transpose of the parameter estimation vector of the fuzzy logic system corresponding to the first state equation of the follower agent. Phase 1 of DoS attack activation The first follower agent's first The transpose of the parameter estimation vector of the fuzzy logic system corresponding to each state equation.

[0040] when During the dormant phase of a DoS attack, construct the Lyapunov function. : (12); in, and It is a symmetric positive definite matrix and its dimension is 1 / 2. match, It is the dormant phase of a DoS attack. The fuzzy parameter estimation error vector of a follower agent; Find the time derivative of equation (12) and construct an adaptive law for the dormant phase of a DoS attack. : (13); in, For the coefficients of the adaptive law correction term during the dormant phase of a DoS attack, Estimate the error vector for the extended output during the dormant phase of a DoS attack; It is a diagonal matrix composed of fuzzy basis functions during the dormant phase of a DoS attack. The hibernation phase of a DoS attack Fuzzy parameter estimation vector of a follower agent ; The hibernation phase of a DoS attack The transpose of the parameter estimation vector of the fuzzy logic system corresponding to the first state equation of the follower agent. The hibernation phase of a DoS attack The first follower agent's first The transpose of the parameter estimation vector of the fuzzy logic system corresponding to each state equation.

[0041] definition For the first The gain coefficient vector of the switching fuzzy state observer during the follower agent attack phase is used to ensure that the observation error of the switching fuzzy state observer asymptotically converges under a DoS attack. The following set of matrix inequalities must be satisfied: (14); in, for An identity matrix of dimension 1 It is a positive number. For a dimension The constant matrix, , For dimension is The The system matrix of the error dynamic equation of a follower agent It is a positive number; It is a diagonal matrix.

[0042] S6: Construct a monotonically decreasing global preset performance function to establish the dynamic performance boundary for each follower agent.

[0043] The globally preset performance function is a positive, monotonically decreasing function, and its construction process is as follows: Define the existence of a smooth function , Defined as a smooth function of First derivative, , It satisfies the conditions of being bounded and piecewise continuous, and at the same time, defines... It is a monotonically increasing function with an initial value of 1, and when , For designable parameters, their value range satisfies ; The globally preset performance function is: (15); in, , ,because It exhibits strict monotonically decreasing properties and satisfies the initial boundary conditions. and ;because It tends to infinity at the initial moment, thus allowing any finite initial error to fall within the dynamic performance boundary; The dynamic performance boundary includes an upper bound and a lower bound, where the upper bound is... The lower bound of the dynamic performance boundary is .

[0044] S7: Given the leader reference signal, and combined with the follower agent state estimate and dynamic performance boundary, the consistency tracking error is obtained. The normalized transformation error is obtained based on the consistency tracking error. Then, the barrier function is constructed using the normalized transformation error.

[0045] To effectively address the impact of aperiodic DoS attacks on multi-agent systems, a consensus tracking error is constructed as follows: (16); in, Representing the The estimate of the first state of each follower agent; Differentiating equation (16) yields: (17); in, For the first The output signal after compensation by the follower agent For the first A follower agent in the stage The gain coefficient of the first switched fuzzy state observer; The normalization transformation error is: (18); The barrier function is: (19).

[0046] S8: Based on Lyapunov stability theory, the distributed adaptive security control law under the active and dormant phases of the DoS attack is obtained by taking the DoS attack timing state signal, follower agent state estimate, adaptive law, and barrier function, and using the backstepping method.

[0047] To facilitate the construction of the distributed adaptive security control law, the barrier function in formula (19) is modified. Find the time derivative: (20); in, (twenty one); Then we get: (twenty two); Define the following coordinate transformation: (twenty three); if ,but ;if ,but ; in, For the first A follower agent in the stage The next level of coordinate transformation error, For the first A follower agent in the stage Below Level coordinate transformation error, For the first A follower agent in the stage Below Level virtual control law; The construction process of the distributed adaptive security control law during the DoS attack activation phase is as follows: S801: When Based on Lyapunov stability theory, a Lyapunov function is constructed. : (twenty four); Differentiating equation (24) and constructing the first... A first-level virtual control law for a follower agent during the activation phase of a DoS attack. : (25); in, For the first The first-level error feedback gain of a follower agent during the DoS attack activation phase. The first derivative of the leader's reference signal with respect to time; S802: Constructing Lyapunov functions based on Lyapunov stability theory. : (26); Differentiating equation (26) and constructing the first... Secondary virtual control law of a follower agent during the activation phase of a DoS attack : (27); in, For the first Second-order error feedback gain of a follower agent during the DoS attack activation phase. For the first The first-order time derivative of the first-level virtual control law of a follower agent during the activation phase of a DoS attack. S803: Constructing Lyapunov functions based on Lyapunov stability theory. : (28); Differentiating equation (28) and constructing the first... A follower agent during the DoS attack activation phase Level Virtual Control Law as follows: (29); in, For the first A follower agent during the DoS attack activation phase Level error feedback gain, For the first A follower agent during the DoS attack activation phase The first derivative of the virtual control law with respect to time; S804: When hour, For the first A follower agent during the DoS attack activation phase Level virtual control law: (30); in, A distributed adaptive security control law during the activation phase of a DoS attack; The construction process of the distributed adaptive security control law under the dormant phase of the DoS attack is as follows: S805: When Based on Lyapunov stability theory, a Lyapunov function is constructed. : (31); Differentiating equation (31) and constructing the first... A first-level virtual control law for a follower agent during the dormant phase of a DoS attack. : (32); in, For the first The first-level error feedback gain of a follower agent during the dormant phase of a DoS attack; ; S806: Constructing Lyapunov functions based on Lyapunov stability theory. : (33); Differentiating equation (33) and constructing the first... Secondary virtual control law of a follower agent during the dormant phase of a DoS attack : (34); in, For the first Second-order error feedback gain of a follower agent during the dormant phase of a DoS attack. For the first The first-order time derivative of the first-level virtual control law of a follower agent during the dormant phase of a DoS attack. S807: Constructing Lyapunov functions based on Lyapunov stability theory. : (35); Differentiating equation (35) and constructing the first... A follower agent in the dormant phase during a DoS attack Level Virtual Control Law : (36); in, For the first A follower agent in the dormant phase during a DoS attack Level error feedback gain, For the first A follower agent in the dormant phase during a DoS attack The first derivative of the virtual control law with respect to time; S808: When hour, For the first A follower agent in the dormant phase during a DoS attack Level virtual control law: (37); in, For the distributed adaptive security control law during the attack dormant phase; The distributed adaptive security control law is: (38).

[0048] Simulation example: To demonstrate the effectiveness of the proposed global preset performance output compensation control method for multi-agent systems under aperiodic DoS attacks, a simulation example of follower-leader consistency is presented below using this control method.

[0049] Figure 1 A block diagram of the overall control scheme of the method of the present invention is shown. In this scheme, information exchange between the leader agent and the follower agents, as well as among the individual follower agents, is achieved through an inter-agent communication network. Furthermore, information transmission between the sensors and controllers within each follower agent is also achieved through a communication network. Let... and Representing the first The follower agent and the first The state information of each follower agent.

[0050] This scheme first addresses the signal blocking problem caused by DoS attacks in the communication network between the agent's sensors and controllers. When a DoS attack occurs, the attack compensation mechanism receives the DoS attack timing state signal, extracts the last output signal before the interruption, preserves the data, and outputs a continuous compensation output signal. The compensation output signal serves as the input to the switching fuzzy state observer. Simultaneously, the consistency tracking error is input to the globally preset performance function module. A barrier function ensures that the consistency tracking error meets transient and steady-state performance constraints globally, eliminating the dependence on the initial value of the tracking error. Finally, based on the DoS attack timing state signal, state estimate, adaptive law, and globally preset performance function, a distributed adaptive safety control law is obtained through backstepping and applied to the follower agent, ensuring that the multi-agent system can still achieve stable and efficient consistency tracking under aperiodic DoS attack environments.

[0051] Figure 2 This is a communication topology diagram between follower agents and leader agents in a simulation example. The leader agent is represented by 0 in the diagram, and the arrows indicate that a node sends information to its neighbor (e.g., follower agent 1 can obtain information from leader agent 0). Therefore, in this topology, only some follower agents can obtain information from the leader agent.

[0052] Figure 3 This diagram illustrates the timing state signals of an aperiodic DoS attack in a simulation example, based on the present invention. The horizontal axis represents simulation time, and the vertical axis represents the DoS attack state. The diagram reflects the distribution characteristics of the attack over time: when the signal is high, it indicates the DoS attack is in the active phase, during which the communication network between the follower agent's sensor and controller is blocked, and the follower agent's controller cannot receive its output signal; when the signal is low, it indicates the DoS attack is in the dormant phase, and communication returns to normal. The aperiodic characteristics in the diagram verify that the attack model constructed in this invention can simulate unpredictable network environments, providing a foundation for verifying the effectiveness of subsequent attack compensation mechanisms and distributed adaptive security control laws in responding to DoS attacks.

[0053] Simulation parameters: To verify the effectiveness of the proposed method, consider a multi-agent system comprising one leader agent and four follower agents, wherein the mathematical model of a single follower agent is as follows: Communication topology diagram as follows Figure 2 As shown in the diagram. Here, 0 represents the leader agent, and 1-4 represent the four follower agents. The leader reference signal is... The total system sampling time is The sampling time interval is set to For non-periodic DoS attacks, the parameters are selected as follows: , , , The relevant parameters for the global preset performance function are: Select... , , This section presents the initial information of the four follower agents. , , , , , Select parameters Solving equation (14) using the Matlab LMI toolbox yields the following result. Select parameters , From the matrix , We can obtain, , , The first and second level error feedback gains during the attack activation phase are: The first and second level error feedback gain during the attack dormancy phase is: The symmetric positive definite matrix has the following form: , It is a two-dimensional identity matrix. The coefficients of the adaptive law correction term during the attack activation and dormancy phases. Furthermore, the DoS attack range is set in this section. .

[0054] Simulation analysis: Figure 4 The graph shows the variation of the consistency tracking error of the follower agent. The consistency tracking error fluctuates slightly around zero and asymptotically converges to zero. It always changes within the dynamic performance boundary and does not exceed the dynamic performance boundary, which shows the effectiveness of the method of the present invention.

[0055] Figure 5 The plot shows the trajectory of the output signals of the follower agents and the reference signal of the leader. It indicates that although there is a brief deviation during the DoS attack phase, the tracking can be restored, and the output signals of the four follower agents gradually become consistent with the reference signal of the leader.

[0056] Figure 6The observation error diagrams for the four follower agents are presented. The results show that the observation error only has a peak at the moment of switching, but then decays rapidly. This indicates that even under aperiodic DoS attacks, the switching fuzzy state observer constructed in this invention can accurately estimate the system state, obtain a small state estimation error, and achieve high estimation accuracy.

[0057] Figure 7 The simulation demonstrates the variation of control inputs of each follower agent over time. It can be seen that the control inputs of each follower agent remain stable and generally bounded throughout the simulation, exhibiting only brief oscillations at the moment of DoS attack switching. This proves that the distributed adaptive security control law designed in this invention can maintain system stability under attack switching conditions.

Claims

1. A method for output compensation control of a multi-agent system under aperiodic DoS attack, characterized by: Includes the following steps: S1: The multi-agent system includes one leader agent and several follower agents. Construct the communication topology and leader reference signal of the multi-agent system. For a single follower agent, construct a follower agent differential equation model including unknown nonlinear functions. Use the universal approximation principle of fuzzy logic system to approximate the unknown nonlinear functions in the follower agent differential equation model, and convert the follower agent differential equation model into a fuzzy approximation system model. S2: Construct an aperiodic DoS attack model to describe the temporal characteristics of the DoS attack activation and dormancy phases; output the DoS attack temporal state signal representing the current phase of the multi-agent system through the aperiodic DoS attack model. S3: When the current stage of the multi-agent system is the attack activation stage, the output signal of the follower agent will be lost. When the controller of the follower agent cannot receive its output signal, the attack compensation mechanism is triggered. The attack compensation mechanism receives the DoS attack timing status signal, extracts the last output signal before the interruption, retains the data, and outputs continuous compensation output signals. S4: Combining the compensation output signal, the DoS attack timing state signal and the fuzzy approximation system model, construct a switching fuzzy state observer, estimate the state of the follower agent by switching the fuzzy state observer and output the estimated state value of the follower agent. S5: Define the observation error of the switching fuzzy state observer. For the switching fuzzy state observer, use the Lyapunov function to construct adaptive laws for the active and dormant phases of the DoS attack respectively. S6: Construct a monotonically decreasing global preset performance function to establish the dynamic performance boundary of each follower agent; S7: Given the leader reference signal, and combined with the follower agent state estimate and dynamic performance boundary, the consistency tracking error is obtained, and the normalized transformation error is obtained based on the consistency tracking error; then the barrier function is constructed using the normalized transformation error. S8: Based on Lyapunov stability theory, the distributed adaptive security control law under the active and dormant phases of the DoS attack is obtained by taking the DoS attack timing state signal, follower agent state estimate, adaptive law, and barrier function, and using the backstepping method.

2. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 1, characterized in that: In step S1, the communication topology of the multi-agent system is as follows: definition These are elements of the adjacency matrix, used to represent the first... The follower agent and the first The communication connection state between the following intelligent agents; if the first The follower agent and the first If there is a communication connection between the follower agents, then ,otherwise , ; If there is information exchange between the leader agent and the follower agents, then there exists ,on the contrary, ;definition , ;definition For the operation phase indication of a multi-agent system, when When this occurs, it indicates that the multi-agent system is in the DoS attack activation phase. This indicates that the multi-agent system is in a dormant phase during a DoS attack. The leader reference signal is ; The differential equation model of the follower agent is as follows: (1)； in, It is the first The first state of each follower agent to the second state A state vector consisting of 10 states. ; , The first The first, second, and third follower agents. , No. One state, for dimensional vector; for The first derivative with respect to time Indicates the first The first follower agent's first One state, Indicates the first A state vector consisting of all states of each follower agent. , For the first The number of states of each follower agent. Indicates the first The first agent of the intelligent agent n The first derivative of each state variable with respect to time; and The first The control input of the follower agent and the first The output signal of a follower agent It is a real number; It is the first The first follower agent Unknown nonlinear functions in the state equations Indicates the first The first intelligent agent n Unknown nonlinear functions in the state equations; The total number of follower agents. It is a positive integer; The fuzzy approximation system model is as follows: (2)； in, For the first The first follower agent's first The ideal parameter vector of the fuzzy logic system corresponding to each state equation; For the first The first follower agent's first The ideal parameter vector of the fuzzy logic system corresponding to each state equation; For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector; For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector; For the first The first agent of the intelligent agent The approximation error of the fuzzy logic system corresponding to each state equation. For the first The first follower agent's first The approximation error of the fuzzy logic system corresponding to each state equation.

3. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 2, characterized in that: In step S2, the aperiodic DoS attack model is as follows: Definition of the first The time interval between DoS attacks is ,in The moment the attack begins. The moment the attack ends. This represents the sequence number of the DoS attack that occurred. ,in Time interval The total number of attacks within, of which The end time, At the starting time, ; In time interval within, no. The total duration of a DoS attack on each follower agent. for: (3)； Meanwhile, the total duration of the dormancy interval in a DoS attack is defined as follows: (4)； in, Indicates from time interval Remove total attack duration The remaining time set; Assumption 1: Assume there exists a constant. So that in the time interval Total attack duration The following constraints must be met: (5)； Assumption 2: Assume there exists a constant constraint on the number of attacks. Attack average dwell time constant This makes the time interval Total number of attacks within The following constraints must be met: (6)； definition As a time variable, when When the DoS attack timing status signal is high, it indicates that the DoS attack is in the active phase; when When the DoS attack timing status signal is low, it indicates that the attack is in a dormant phase. Indicates the first The start time of the DoS attack.

4. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 3, characterized in that: In step S3, the attack compensation mechanism is as follows: (7)； in, It is the first The output signal after compensation by the follower agent The time when the m-th attack occurs The left limit, This is the last output signal before the interruption occurs at the time of the m-th attack.

5. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 4, characterized in that: In step S4, the switching fuzzy state observer is: (8)； in, For the first The estimate of the first state of the follower agent. For the first The first follower agent's first The estimated value of each state, It is the first The first follower agent's first The first derivative of the estimate of each state with respect to time, It is the first The first follower agent's first The estimated value of the state; It is the first The first follower agent's first The estimated value of each state, It is the first The first follower agent's first The first derivative of the estimate of each state with respect to time; It is the first The first follower agent's first Gain coefficients of a switching fuzzy state observer It is the first The first follower agent's first Gain coefficients of a switching fuzzy state observer; For the first The first to the second of the follower agents A state vector consisting of the estimated values ​​of each state. For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. Let be the input basis function vector. For the first The first to the second of the follower agents A state vector consisting of the estimated values ​​of each state. For the first The first follower agent's first The fuzzy logic system corresponding to each state equation is represented by a vector. The input basis function vector.

6. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 5, characterized in that: In step S5, the observation error is: (9)； when During the active phase of a DoS attack, construct the Lyapunov function. : (10)； in, For the first The observation error vector of each follower agent and It is a symmetric positive definite matrix and its dimension is 1 / 2. match, It is the attack activation phase. The fuzzy parameter estimation error vector of a follower agent; Find the time derivative of equation (10) and construct an adaptive law for the activation phase of a DoS attack. : (11)； in, For the coefficients of the adaptive law correction term during the activation phase of a DoS attack, For the first The extended output estimation error vector of a follower agent during the activation phase of a DoS attack. ; It is a diagonal matrix composed of fuzzy basis functions during the activation phase of a DoS attack. Phase 1 of DoS attack activation Fuzzy parameter estimation vector of a follower agent ; Phase 1 of DoS attack activation The transpose of the parameter estimation vector of the fuzzy logic system corresponding to the first state equation of the follower agent. Phase 1 of DoS attack activation The first follower agent's first Transpose of the parameter estimation vector of the fuzzy logic system corresponding to each state equation; when During the dormant phase of a DoS attack, construct the Lyapunov function. : (12)； in, and It is a symmetric positive definite matrix and its dimension is 1 / 2. match, It is the dormant phase of a DoS attack. The fuzzy parameter estimation error vector of a follower agent; Differentiate equation (12) and construct an adaptive law for the dormant phase of a DoS attack. : (13)； in, For the coefficients of the adaptive law correction term during the dormant phase of a DoS attack, Estimate the error vector for the extended output during the dormant phase of a DoS attack; It is a diagonal matrix composed of fuzzy basis functions during the dormant phase of a DoS attack. The hibernation phase of a DoS attack Fuzzy parameter estimation vector of a follower agent ; The hibernation phase of a DoS attack The transpose of the parameter estimation vector of the fuzzy logic system corresponding to the first state equation of the follower agent. The hibernation phase of a DoS attack The first follower agent's first Transpose of the parameter estimation vector of the fuzzy logic system corresponding to each state equation; definition For the first The gain coefficient vector of the switching fuzzy state observer during the follower agent attack phase is used to ensure that the observation error of the switching fuzzy state observer asymptotically converges under a DoS attack. The following set of matrix inequalities must be satisfied: (14)； in, for An identity matrix of dimension 1 It is a positive number. For a dimension The constant matrix, , For dimension is The The system matrix of the error dynamic equation of a follower agent It is a positive number; It is a diagonal matrix.

7. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 6, characterized in that: In step S6, the globally preset performance function is a positive monotonically decreasing function, and its construction process is as follows: Define the existence of a smooth function , Defined as a smooth function of First derivative, , It satisfies the conditions of being bounded and piecewise continuous; at the same time, it defines... It is a monotonically increasing function with an initial value of 1, and when , ; The globally preset performance function is: (15)； in, , ,because It exhibits strict monotonically decreasing properties and satisfies the initial boundary conditions. and ;because It tends to infinity at the initial moment, thus allowing any finite initial error to fall within the dynamic performance boundary; The dynamic performance boundary includes an upper bound and a lower bound, where the upper bound is... The lower bound of the dynamic performance boundary is .

8. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 7, characterized in that: In step S7, the consistency tracking error is: (16)； in, Representing the The estimate of the first state of each follower agent; Differentiating equation (16) yields: (17)； in, For the first The output signal after compensation by the follower agent For the first A follower agent in the stage The gain coefficient of the first switched fuzzy state observer; The normalization transformation error is: (18)； The barrier function is: (19)。 9. The multi-agent system output compensation control method under aperiodic DoS attack as described in claim 8, characterized in that: In step S8, to facilitate the construction of the distributed adaptive security control law, the barrier function in formula (19) is modified. Find the time derivative: (20)； in, (21)； Then we get: (22)； Construct the following coordinate transformation: (23)； if ,but ;if ,but ; in, For the first A follower agent in the stage The next level of coordinate transformation error, For the first A follower agent in the stage Below Level coordinate transformation error, For the first A follower agent in the stage Below Level virtual control law; The construction process of the distributed adaptive security control law during the DoS attack activation phase is as follows: S801: When Based on Lyapunov stability theory, a Lyapunov function is constructed. : (24)； Differentiating equation (24) and constructing the first... A first-level virtual control law for a follower agent during the activation phase of a DoS attack. : (25)； in, For the first The first-level error feedback gain of a follower agent during the DoS attack activation phase. The first derivative of the leader's reference signal with respect to time; S802: Constructing Lyapunov functions based on Lyapunov stability theory. : (26)； Differentiating equation (26) and constructing the first... Secondary virtual control law of a follower agent during the activation phase of a DoS attack : (27)； in, For the first Second-order error feedback gain of a follower agent during the DoS attack activation phase. For the first The first-order time derivative of the first-level virtual control law of a follower agent during the activation phase of a DoS attack. S803: Constructing Lyapunov functions based on Lyapunov stability theory. : (28)； Differentiating equation (28) and constructing the first... A follower agent during the DoS attack activation phase Level Virtual Control Law as follows: (29)； in, For the first A follower agent during the DoS attack activation phase Level error feedback gain, For the first A follower agent during the DoS attack activation phase The first derivative of the virtual control law with respect to time; S804: When hour, For the first A follower agent during the DoS attack activation phase Level virtual control law: (30)； in, A distributed adaptive security control law during the activation phase of a DoS attack; The construction process of the distributed adaptive security control law under the dormant phase of the DoS attack is as follows: S805: When Based on Lyapunov stability theory, a Lyapunov function is constructed. : (31)； Differentiating equation (31) and constructing the first... A first-level virtual control law for a follower agent during the dormant phase of a DoS attack. : (32)； in, For the first The first-level error feedback gain of a follower agent during the dormant phase of a DoS attack; ; S806: Constructing Lyapunov functions based on Lyapunov stability theory. : (33)； Differentiating equation (33) and constructing the first... Secondary virtual control law of a follower agent during the dormant phase of a DoS attack : (34)； in, For the first Second-order error feedback gain of a follower agent during the dormant phase of a DoS attack. For the first The first-order time derivative of the first-level virtual control law of a follower agent during the dormant phase of a DoS attack. S807: Constructing Lyapunov functions based on Lyapunov stability theory. : (35)； Differentiating equation (35) and constructing the first... A follower agent in the dormant phase during a DoS attack Level Virtual Control Law : (36)； in, For the first A follower agent in the dormant phase during a DoS attack Level error feedback gain, For the first A follower agent in the dormant phase during a DoS attack The first derivative of the virtual control law with respect to time; S808: When hour, For the first A follower agent in the dormant phase during a DoS attack Level virtual control law: (37)； in, For the distributed adaptive security control law during the attack dormant phase; The distributed adaptive security control law is: (38)。

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