Multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering

Abstract

The invention discloses a multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering. According to the method, aiming at the conditions that external disturbance is unknown and the state of the aircraft is unknown, firstly, a variable composed of the system state and the external disturbance is regarded as a new intermediate variable, an intermediate observer is established, and a state estimation value and an external disturbance estimation value of the aircraft can be output at the same time through the intermediate observer. Then, a controller is designed for the following aircraft, a dynamic event triggering mechanism is introduced to determine the updating moment of local information in the controller of the following aircraft, the information transmission frequency between the aircrafts is reduced, and it is strictly proved that no Zeno phenomenon exists. And finally, realizing the multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering under the condition that external disturbance exists and a deception attack signal exists in the action of a controller.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-aircraft control, and in particular to a multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering. Background Art

[0002] A multi-agent system is a complex large-scale system composed of a large number of distributed autonomous or semi-autonomous subsystems (agents) interconnected through a network. It is a "system of systems". Therefore, a multi-agent system has the characteristics of autonomy, distribution, and coordination. It can solve some complex problems that are difficult to solve with a single system. It has a wide range of applications in sensor networks, unmanned vehicle / aircraft formations, multi-missile attacks, intelligent transportation systems, and other fields.

[0003] In recent years, leader-follower consistency of multiple aircraft has become a hot topic. Leader-follower consistency control aims to achieve consistency of the entire system by making the follower aircraft adjust their behavior according to the behavior of the leader. In this control framework, there are usually one or more leaders whose behavior is regarded as a reference signal, and other follower aircraft achieve different mission goals by keeping consistent with the leader.

[0004] However, in solving the leader-follower consistency control problem of multiple aircraft, in actual situations, it will be affected by external interference, and in the actual operation of the controller, it may be affected by probabilistic deception attack signals. Therefore, inspired by the literature [1], the control problem of solving a single aircraft is introduced into the control problem of solving multiple aircraft, and the tracking consistency control of the leader is realized. In addition, the current situation that the traditional follower aircraft obtains the information of its neighboring follower aircraft in real time is changed. By using the dynamic event trigger mechanism, the follower aircraft does not need to continuously obtain the status information from its neighboring follower aircraft to update its own status information. Summary of the invention

[0005] The purpose of the present invention is to propose a multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering, which can effectively reduce the error between the follower aircraft and the leader and improve the stability and cohesion of the entire system.

[0006] The specific technical solution of the present invention is as follows: a multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering, comprising the following steps:

[0007] Considering the existence of various interferences in the external environment, according to reference [2], the following multi-aircraft dynamic model with external disturbances is established: In the above formula, i∈{1,...,N} represents the aircraft number, x i(t) represents the state of the following aircraft, u i (t) represents the controller to be designed for the following aircraft, ω i (t) represents the external disturbance of the follower aircraft, f(·) represents the unknown nonlinear signal, A, B, C, E, F are known system matrices with appropriate dimensions. When i = 0, it represents the navigator, and the navigator dynamic model is expressed as follows: Among them, x0(t) represents the navigator state.

[0008] First, an intermediate variable is considered for each follower aircraft: i (t) = ω i (t)-L f x i (t), where L f =αE T , after introducing the intermediate variables, the following intermediate observer is designed: In the formula, represents the estimated value of the following aircraft state, represents the estimated value of external disturbance of the following aircraft, represents the estimated value of the intermediate variable of the considered following aircraft, L x represents the observer gain.

[0009] Considering that the follower controller may be attacked by probabilistic spoofing signals during the update process, the following follower aircraft controller is designed: Where K is the feedback gain, represents the consistency error of the aircraft leader and follower, p t (t) represents the attack signal sent by the malicious attacker.

[0010] And ||P(t)|| 2 ≤p, p is a known normal number, random variable θ ij (t) can only be 0 or 1, with the following probabilities: Prob{θ ij (t) = 1} = δ ij , Prob{θ ij (t) = 0} = 1-δ ij , where δ ij ∈[0,1) is a constant, Θ(t)=[θ ij (t)] N×N , assuming θ ii (t)=0.

[0011] It should be noted that the expected matrix of Θ(t) is Δ, that is, E[Θ(t)] = Δ, where

[0012] It is iteratively updated by the following formula: In the formula, is the measurement error, Φ i is the weight matrix to be designed, Φ = diag{Φ1, Φ2, ..., Φ N}.

[0013] When the trigger condition is met,

[0014] In addition, μ i (t) is updated by decide, and

[0015] Next is to prove that there is no Zeno phenomenon: In the formula is the bound of a nonlinear function.

[0016] Solving differential equations and Be able to get According to the trigger mechanism Can get

[0017] Therefore, the lower limit of the event triggering time interval is as follows: This proves that there is no Zeno phenomenon.

[0018] Next, we define the tracking error State Estimation Error Intermediate observer estimation error

[0019] Consider when When , construct the following Lyapunov function: V(t)=E{V1(t)+V2(t)+V3(t)}, in In the formula, P1, P2, P3 represent positive definite and symmetric matrices.

[0020] Before calculating the derivative of V(t), we use the young inequality to obtain: where φ is the bound of the derivative of the nonlinear function.

[0021] By taking the derivative of the constructed Lyapunov function, we can get the following formula:

[0022] choose Can get, In the formula,

[0023] exist Substituting the trigger mechanism into the equation gives: In the formula, In the formula, represents the upper bound of the trigger threshold, and

[0024] According to Lyapunov stability theory, if The error system is ultimately bounded and stable and converges to

[0025] According to Schur's complement lemma, we can get: In the formula,

[0026] Since there are some coupling terms in the above formula, in order to solve this problem, Finsler's lemma is used to introduce P3L x =Y1, VK=Y2, P1L x =Y3, so in

[0027] Under the above conditions, we only need to ensure that: in in,

[0028] Therefore, we can get In the formula,

[0029] In summary, when time tends to infinity, the error system eventually achieves bounded stability and converges to That is, consistent bounded tracking control is achieved.

[0030] Therefore, a multi-aircraft anti-interference consistency tracking control target based on dynamic event triggering is achieved under the control law designed by the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0032] Figure 2 It is the system communication topology diagram;

[0033] Figure 3 This is a diagram showing the effect of system tracking error when the method proposed by the present invention is used in an embodiment;

[0034] Figure 4 The following is a state effect diagram of the pilot and the follower aircraft in the embodiment using the method proposed by the present invention;

[0035] Figure 5 This is a diagram showing the effect of the state estimation error of the following aircraft using the method proposed by the present invention in the embodiment;

[0036] Figure 6 This is a diagram showing the effect of interference estimation error of a following aircraft using the method proposed by the present invention in an embodiment;

[0037] Figure 7 This is an event trigger diagram of an embodiment using the method proposed by the present invention; DETAILED DESCRIPTION

[0038] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments 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, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0039] Consider a multi-vehicle system consisting of four follower aircraft, labeled 1, 2, 3, and 4, and a leader aircraft, labeled 0. Their communication topology is as follows: Figure 2 As shown;

[0040] like Figure 1 As shown, a multi-aircraft anti-interference consistency tracking control method based on dynamic event triggering consistency tracking control method comprises the following steps:

[0041] Step 1: Set the initial values ​​of various parameters and control gains;

[0042] Step 2: Update the dynamic variables in the system through the designed controller;

[0043] Step 3: Using the set dynamic event trigger function, when the dynamic variables inside the system meet the trigger conditions, the controller updates some information;

[0044] Step 4: Repeat steps 2 and 3 until the running time ends.

[0045] Figure 3 The designed control method is given, and after implementation, the tracking error between the follower aircraft and the navigator can reach bounded stability;

[0046] Figure 4 The multi-aircraft system achieves state bounded consistency under the designed controller.

[0047] Figure 5 It is given that the estimated error between the state estimated value obtained by the following aircraft through the intermediate observer and the true value has reached bounded stability;

[0048] Figure 6 It is given that the estimated error between the disturbance estimated value obtained by the following aircraft through the intermediate observer and the true value has reached bounded stability;

[0049] Figure 7 The event triggering effect diagram is shown, and it can be seen that the Zeno phenomenon is eliminated in the entire system.

[0050] References [1]Gu Y, Shen M, Ahn C K.Dynamic event-triggered fault-tolerant controlthrough a new intermediate observer[J].International Journal of Robust andNonlinear Control,2023,33(16):9804-9825. [2]Zuo Z, Zhang J, Wang Y. Adaptive fault-tolerant tracking control for linear and Lipschitz nonlinear multi-agent systems[J]. IEEE Transactions on Industrial Electronics, 2014, 62(6): 3923-3931.

Claims

1. A multi-aircraft system anti-interference consistency tracking control method based on dynamic event triggering, characterized in that: The following steps are involved: Step 1: Considering the interference in the actual environment, a nonlinear multi-aircraft dynamic model with external disturbances is established; Step 2: For the case of unknown external disturbances and unknown aircraft system states, a variable consisting of the system state and the external disturbance is first regarded as a new intermediate variable, and an intermediate observer is established, through which the state estimate of the aircraft system and the external disturbance estimate can be output simultaneously; Step 3: Introduce a dynamic event trigger mechanism to determine the update time of the local information in the follower aircraft controller. When the system meets the trigger condition, the status information of the follower aircraft can be updated at the triggering moment. Step 4: Combining steps 2 and 3, the Lyapunov stability theory is used to implement the multi-aircraft anti-interference consistency tracking control based on dynamic event triggering.

2. Consider the following dynamic model of an F-18 aircraft [2]: in, i∈{1,...,N} represents the aircraft number, α i (t) and q i (t) represent the aircraft's angle of attack and pitch rate, u i (t) represents the controller input, f(α i (t), q i (t)) represents a nonlinear function. Based on this, considering external disturbances, the above aircraft model is converted into a more general state space equation form: In the above formula, i∈{1,...,N} represents the number of the following aircraft, x i (t) represents the state of the following aircraft, u i (t) represents the controller to be designed for the following aircraft, f(·) represents the unknown nonlinear signal, ω i (t) represents the external disturbance of the follower aircraft, A, B, C, E, F are known system matrices with appropriate dimensions. When i = 0, it represents the navigator, and the navigator dynamics model is expressed as follows: Among them, x0(t) represents the navigator state.

3. According to the method of multi-aircraft anti-interference consistency tracking control based on dynamic event triggering described in claim 2, for the case of unknown external disturbance and unknown aircraft state, firstly, a variable consisting of system state and external disturbance is regarded as a new intermediate variable, and an intermediate observer is established, through which the aircraft state estimation value and external disturbance estimation value are simultaneously output, and the specific steps are as follows: First, an intermediate variable is considered for each follower aircraft: i (t) = ω i (t)-L f x i (t), where L f =αE T , after introducing the intermediate variables, the following intermediate observer is designed: In the formula, represents the estimated value of the following aircraft state, represents the estimated value of external disturbance of the following aircraft, represents the estimated value of the intermediate variable of the considered following aircraft, L x represents the observer gain.

4. According to the method of multi-aircraft anti-interference consistency tracking control based on dynamic event triggering described in claim 3, a dynamic event triggering mechanism is introduced to determine the update time of the follower aircraft controller to reduce the frequency of information transmission between aircraft. When the system meets the triggering condition, a control law that can obtain state information is designed for the follower, so as to update the state information of the follower itself, and the follower controller is considered to be subject to probabilistic deception signal attacks during the update process. The specific steps are as follows: Design the following follower aircraft controller: Where K is the feedback gain, represents the consistency error of the aircraft leader and follower, p i (t) indicates the attack signal sent by a malicious attacker. And ||P(t)|| 2 ≤p, p is a known normal number, random variable θ ij (t) can only be 0 or 1, with the following probabilities: Prob{θ ij (t)=1}=δ ij ,Prob{θ ij (t)=0}=1-δ ij , where δ ij ∈[0,1) is a constant, Θ(t)=[θ ij (t)] N×N , assuming θ ii (t) = 0. It should be noted that the expected matrix of Θ(t) is Δ, that is, E[Θ(t)] = Δ, where It is iteratively updated by the following formula: in is the measurement error, Φ i is the weight matrix to be designed, Φ = diag{Φ1, Φ2, ..., Φ N }. When the trigger condition is met, In addition, μ i (t) is updated by decide, and 0≤k≤1,α1>

0. Next is to prove that there is no Zeno phenomenon: In the formula is the bound of the nonlinear function. Solve the differential equation and Be able to get According to the trigger mechanism Can get Therefore, the lower limit of the event triggering time interval is as follows: This proves that there is no Zeno phenomenon.

5. According to the method for multi-aircraft anti-interference consistent tracking control based on dynamic event triggering according to claim 4, in combination with steps 2 and 3, Lyapunov stability theory is used to realize multi-aircraft anti-interference consistent tracking control based on dynamic event triggering, and the specific steps are as follows: B001: Define tracking error State Estimation Error Intermediate observer estimation error Consider when When , construct the Lyapunov function: V(t)=E{V1(t)+V2(t)+V3(t)}, in In the formula, P1, P2, P3 represent positive definite and symmetric matrices. B002: Use the young inequality before calculating the derivative of V(t) to obtain: where φ is the bound of the derivative of the nonlinear function. B003: Calculate the derivative of V(t): B004: Selection but in B005: Substituting the trigger mechanism into the equation gives: in In the formula, represents the upper bound of the trigger threshold, and B006: According to Lyapunov stability theory, if The error system is ultimately bounded and stable and converges to B007: According to Schur's complement lemma, we can get: in B008: Since there are some coupling terms in the above formula, in order to solve this problem, Finsler's lemma is used to introduce P3L x =Y1, VK=Y2, P1L x =Y3, so in B009: Under the above conditions, you only need to ensure that: in in, B010: Therefore, we can get in B011: In summary, when time tends to infinity, the error system eventually achieves bounded stability and converges to That is, consistent bounded tracking control is achieved. B012: Therefore, a multi-aircraft anti-interference consistency tracking control target based on dynamic event triggering can be achieved under the control law designed by the present invention.

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