UAV air-to-ground tracking control method based on hybrid event triggering in network environment

Abstract

The present invention discloses a method for air-to-ground tracking control of an unmanned aerial vehicle (UAV) based on a hybrid event trigger mechanism in a network environment. By taking the measurement output and external input of an unmanned vehicle as transmission signals and designing a switching condition, a new hybrid event trigger scheme is proposed, which achieves a good balance between reducing the frequency of data transmission and maintaining ideal tracking performance. According to the trigger signal of the unmanned vehicle and the measurement output of the UAV, an observer is designed to estimate the states of the unmanned vehicle and the UAV, the external input of the unmanned vehicle, and the external disturbance of the UAV. Based on the above estimated values, a composite anti-interference tracking controller for the UAV is constructed to eliminate interference and track the unmanned vehicle in a bounded manner, and an augmented system consisting of an estimation error and a tracking error is established. Then, the stability criterion of the augmented system is derived, and a joint design scheme of the hybrid event trigger mechanism, the observer, and the tracking controller is established in the form of a linear matrix inequality.

Description

Technical Field

[0001] The present invention belongs to the field of control technology, and in particular relates to an air-to-ground tracking control method for an unmanned aerial vehicle (UAV) based on hybrid event triggering in a network environment. Background Art

[0002] In recent years, unmanned vehicle systems have been widely used in military and civilian fields, playing an important role in many dangerous, harsh and complex tasks. For example, aerial drones can be used for target monitoring and aerial reconnaissance, and ground unmanned vehicles can be used for ground patrols and supply transportation. Although these two types of unmanned vehicle systems have certain limitations in their respective application fields, they can achieve complementary performance in monitoring, communication and guidance. Therefore, in order to improve work efficiency and mission effectiveness, the concept of air-ground collaboration between drones and unmanned vehicles has been proposed.

[0003] Air-ground tracking control is the basis of air-ground collaboration, and many complex tasks are completed based on ideal air-ground tracking control. In environments such as battlefields or production activities, drones can be used to track unmanned vehicles to achieve specific tracking control goals. In addition, the information transmission between drones and unmanned vehicles in air-ground tracking control usually requires the help of wireless communication networks. Therefore, research on drone air-ground tracking control methods in non-ideal network environments has very important theoretical significance and application value.

[0004] Generally speaking, common factors of non-ideal network environment include network-induced delay, packet loss, limited communication resources and network attacks. From the perspective of practical application, delay is usually unavoidable in the process of data transmission through the network. It is mainly composed of computing delay, network access delay and transmission delay. The existence of network-induced delay will have a certain impact on system performance, and in severe cases, it may even cause the system to lose stability.

[0005] In the process of data communication in communication networks, time-triggered transmission often leads to problems such as network congestion and energy shortage. Therefore, event triggering mechanisms that can effectively reduce communication pressure have received continuous attention and research. As the research deepens, researchers have proposed various event triggering mechanisms for various needs and scenarios. For example, the literature “E. Tian, ​​C. Peng, Memory-Based Event-Triggering H ∞Load Frequency Controlfor Power Systems Under Deception Attacks,IEEE Transactions on Cybernetics,50(11):4610-4618,2020” proposed a memory event trigger mechanism based on multiple triggered signals, which makes the sampled data easier to be triggered at the peaks and troughs of the system state response, thereby shortening the transient process and improving the control performance. However, we can also get from the literature that when the response changes rapidly, the memory event trigger mechanism will increase the number of event triggers.

[0006] Therefore, in order to realize the air-to-ground tracking control of UAVs based on the hybrid event trigger mechanism in a network environment, the technical problems that need to be solved are:

[0007] (1) In order to solve the problem of limited communication resources between unmanned vehicles and drones, how to reasonably switch between regular event triggering and memory event triggering in order to design a hybrid event triggering mechanism;

[0008] (2) How to design the observer and composite anti-interference controller to ensure the stability of estimation error and tracking error while considering external interference, unmeasurable state and transmission delay. Summary of the invention

[0009] Purpose of the invention: In view of the actual application scenarios and the deficiencies of the above-mentioned prior art, the present invention provides a UAV air-to-ground tracking control method based on a hybrid event trigger mechanism in a network environment.

[0010] Technical solution: The air-to-ground tracking control method of a UAV based on hybrid event triggering in a network environment of the present invention comprises the following steps:

[0011] Step 1: Establish discrete models of unmanned vehicles and drones based on state space;

[0012] Step 2: According to the design of hybrid event triggering, a data transmission mechanism between the unmanned vehicle and the UAV is established, and an observer is designed on the UAV side based on the trigger signal. The observer is used to estimate the state and input signal of the unmanned vehicle and the state and external interference of the UAV.

[0013] Step 3: Based on the estimated value of the observer, the design of the UAV composite anti-interference tracking controller is constructed, and an augmented system consisting of the estimation error and the tracking error is established;

[0014] Step 4: Establish the exponential bounded stability judgment condition of the augmented system, obtain the joint design scheme of the hybrid event trigger mechanism, observer and tracking controller, and solve the feasibility problem through the Matlab LMI toolbox.

[0015] Furthermore, in step 1, the discrete models of the unmanned vehicle and the unmanned aerial vehicle based on the state space are respectively:

[0016]

[0017] in, represents the plane position vector of the unmanned vehicle, and They represent the control input of the unmanned vehicle and the given external bounded input respectively, represents the measurement output of the UAV;

[0018] represents the plane position state vector of the UAV, and represent the control input and measurement output of the UAV respectively; A represents the external bounded interference of the UAV; a ,B a ,B r ,C a and A b ,B b ,B d ,C b is a known constant matrix of appropriate dimension.

[0019] Furthermore, the external input r(k) and the external disturbance d(k) are bounded, and they satisfy ||r(k)||≤η1 and ||d(k)||≤η2, where η1 and η2 are two positive constants; the changes Δr(k)=r(k+1)-r(k) and Δd(k)=d(k+1)-d(k) are also bounded, and satisfy ||Δr(k)||≤η3 and ||Δd(k)||≤η4, where η3 and η4 are two positive constants; for the model parameters of the unmanned vehicle and the drone, rank(B b )=rank(B b ,B d ), and there exist matrices X1, X2, X3 and S that satisfy SA b +SB b X1=(A a +B a X2) S and SB b X3=B r .

[0020] Furthermore, the controller of the unmanned vehicle is u a =K a y a (k) = K a C a x a (k).

[0021] Furthermore, in step 2, the hybrid event triggering mechanism is designed as follows:

[0022]

[0023] Among them, σ n-i (k) = θ y (k)-θ y (t n-i ), δ1 and δ2 are given trigger thresholds, Ω1 and Ω2 are positive definite weighted parameter matrices, μ i ∈(0,1](i=0,…,m-1) is the given weight parameter, f(k) is the switching function used to determine the event trigger mechanism selection, and μ i The sum of (i=0, ..., m-1) is 1, and the switching function f(k) satisfies the following equation:

[0024]

[0025] Where α is a given positive constant.

[0026] Furthermore, in step 2, the observer is designed as:

[0027]

[0028] in, and Represent the state x of the unmanned vehicle respectively a (k) and the estimated value of the external input r(k), and Respectively represent the drone state x b (k) and the estimated value of external disturbance d(k), H i (i=1,2,3,4) is the observer gain matrix to be designed.

[0029] Furthermore, in step 3, the design of the composite anti-interference tracking controller is:

[0030]

[0031] Among them, the matrix satisfy Control gain matrix K b1 and K b2 Meet SA b +S b B b K b1 =(A a +B a K a C a )Sb and S b B b K b2 =B r .

[0032] Furthermore, in step 3, under the influence of transmission delay, the augmented system consisting of observation error and tracking error is:

[0033]

[0034] in,

[0035]

[0036] Furthermore, in step 4, the exponentially bounded stability criterion of the augmented system is:

[0037] For the delay upper bound τ M , positive scalars η1, η2, η3, η4, δ1, δ2, μ i (i=0,L m-1) and matrix K a ,S b ,K b1 ,K b2 , if there exist positive definite matrices P1, P2, P3, P4, Q, R1, R2, S, Ω1, Ω2 and matrices T1, T2, T3, T4 of appropriate dimensions, such that the following matrix inequality holds:

[0038]

[0039] in,

[0040]

[0041] Σ1=[0,0,T1,-T1+T2,-T2,0,0,0,0,0], Σ2=[0,0,T3,-T3+T4,-T4,0,L,0],

[0042]

[0043] Γ2=[P1E3A θ ,0,0,0,0,0,0,0,0,0],Γ3=[0,0,P2A θ ,-P2H θ C θ ,0,0,0,P2H θ ,P2E1,0],

[0044]

[0045] Γ7=[P1E3A θ,0,L,0],Γ8=[0,0,P2A θ ,-P2H θ C θ ,0,0,0,P2H θ ,0,L 0,P2E1,0],

[0046]

[0047] Under the action of hybrid event-triggered mechanism, observer and tracking controller, the augmented system is exponentially bounded and stable.

[0048] Furthermore, in step 4, the joint design scheme of the hybrid event trigger mechanism, observer and tracking controller is:

[0049] For the delay upper bound τ M , positive scalars η1, η2, η3, η4, δ1, δ2, μ i (i=0,L m-1) and matrix K a ,S b ,K b1 ,K b2 ,G, if there exist positive definite matrices P1,P2,P3,P4,Q,R1,R2,S,Ω1,Ω2, matrices T1,T2,T3,T4 of appropriate dimensions and scalars σ1>0,σ2>0, satisfying the following linear matrix inequality:

[0050]

[0051] in,

[0052]

[0053] Ψ2=[P1E3A θ ,0,0,0,0,0,0,0,0,0,0,0],Ψ3=[0,0,P2A θ ,-XC θ ,0,0,0,X,P2E1,0,0,0],

[0054]

[0055] Ψ7=[P1E3A θ ,0,L,0],Ψ8=[0,0,P2A θ ,-XC θ ,0,0,0,X,0,L,0,P2E1,0,0,0],

[0056]

[0057] Then the augmented system (16) is exponentially bounded and stable, and the controller gain K = L -1 J, observer gain

[0058] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0059] (1) The present invention comprehensively considers the influence of external interference, unpredictable state and transmission delay in the air-to-ground tracking control problem of UAVs and unmanned vehicles, which is more realistic and valuable.

[0060] (2) In order to overcome the shortcomings of the existing event trigger mechanism, the present invention utilizes the idea of ​​switching between the conventional event trigger mechanism and the memory event trigger mechanism, and proposes a new hybrid event trigger mechanism, which achieves a good balance between reducing the transmission frequency and maintaining ideal tracking performance.

[0061] (3) The present invention provides a joint design scheme for the parameters of the hybrid event trigger mechanism, observer gain and controller gain in the form of linear matrix inequalities. The scheme has no restriction on the full rank of the input matrix of the UAV system and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a block diagram of an air-to-ground tracking control structure in an embodiment of the present invention;

[0063] Figure 2 It is the trajectory motion curve of air-ground tracking control;

[0064] Figure 3 It is the curve of the X-axis position coordinate of the air-ground tracking control changing with time;

[0065] Figure 4 It is the curve of the Y-axis position coordinate of the air-ground tracking control changing with time;

[0066] Figure 5 The instantaneous and interval of data transmission for the hybrid event triggering mechanism;

[0067] Figure 6 It is the change curve of the switching function in the hybrid event trigger mechanism. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0069] like Figure 1 As shown, the present invention discloses a UAV air-to-ground tracking control method based on a hybrid event trigger mechanism in a network environment, comprising the following specific steps:

[0070] Step 1: Establish discrete models of unmanned vehicles and drones based on state space.

[0071] In the embodiment of the present invention, only the situation where the unmanned vehicle moves in a two-dimensional plane is considered, so the linear discrete time system model of the unmanned vehicle is established as follows:

[0072]

[0073] in, represents the plane position vector of the unmanned vehicle, and They represent the control input of the unmanned vehicle and the given external bounded input respectively, Represents the measurement output of the UAV; A a ,B a ,B r and C a is a known constant matrix of appropriate dimension.

[0074] Assuming that the UAV is in a hovering state near the ground, the linear discrete-time system model of the UAV can be described as:

[0075]

[0076] in, represents the position state vector of the drone, and represent the control input and measurement output of the UAV respectively; A represents the external bounded interference of the UAV; b ,B b ,B d and C b is a known constant matrix of appropriate dimension.

[0077] For the tracking control problem of unmanned vehicles and drones, the attitude control of drones is the basis of tracking control, but this embodiment mainly designs an anti-interference tracking control scheme for the adverse effects of non-ideal network environments. Therefore, the attitude control process is reasonably ignored here, and only the plane position control of unmanned vehicles and drones is considered.

[0078] Assumption 1: For external bounded input r(k) and external bounded disturbance d(k), they satisfy ||r(k)||≤η1 and ||d(k)||≤η2, where η1 and η2 are two positive constants. At the same time, by defining r(k+1)=r(k)+Δr(k) and d(k+1)=d(k)+Δd(k), it can be obtained that Δr(k) and Δd(k) are also bounded and satisfy ||Δr(k)||≤η3 and ||Δd(k)||≤η4, where η3 and η4 are two positive constants.

[0079] Assumption 2: For the model parameters of unmanned vehicles and drones, rank(B b )=rank(B b ,B d ), and there exist matrices X1, X2, X3 and S that satisfy SA b +SB b X1=(A a +B a X2) S and SB b X3=B r .

[0080] Since the state of the unmanned vehicle system is unpredictable, in order to maintain the stability of the unmanned vehicle system, an output feedback controller is designed as: a =K a y a (k) = K a C a x a (k). Substituting the output feedback controller into equation (1), the unmanned vehicle system can be rewritten as:

[0081] x a (k+1)=(A a +B a K a C a )x a (k)+B r r(k). (3)

[0082] Under the condition that the external input r(k) is bounded, if there exists a controller gain K a So that the matrix A a +B a K a C a All eigenvalues ​​of are inside the unit circle, then the system (3) is bounded and stable.

[0083] Step 2: Design a hybrid event trigger mechanism, establish a data transmission mechanism between the unmanned vehicle and the drone, and design an observer on the drone side based on the trigger signal. Use the observer to estimate the state and input signal of the unmanned vehicle as well as the state and external interference of the drone.

[0084] The data transmission mechanism considers the measurement output y of the unmanned vehicle a (k) and the known external input r(k) are sent to the drone, so we define θ y (k) = [y a T (k),r T (k)] T is the synthetic signal transmitted from the unmanned vehicle to the drone. Assume θ y(t n )for

[0085] The most recently transmitted composite signals, {0, 1, 2, …, k, …} and {0, t1, t2, …, t n , …} represent the sequence of sampling time and triggering time respectively.

[0086] Based on the advantages of the conventional event trigger mechanism and the memory event trigger mechanism, a hybrid event trigger mechanism is designed by combining the above two event trigger mechanisms:

[0087]

[0088] Among them, σ n-i (k) = θ y (k)-θ y (t n-i ), δ1 and δ2 are given trigger thresholds, Ω1 and Ω2 are positive definite weighted parameter matrices, μ i ∈(0,1](i=0,…,m-1) is the given weight parameter, and f(k) is the switching function used to determine the event trigger mechanism selection. At the same time, μ i The sum of (i=0, ..., m-1) is 1, and the switching function f(k) satisfies the following equation:

[0089]

[0090] Where α is a given positive constant.

[0091] By setting the constant α appropriately, f(k) < 0 when the composite signal is at a peak or trough, and f(k) ≥ 0 when the composite signal changes rapidly. In other words, the hybrid event trigger mechanism can select the memory event trigger at the peak or trough of the composite signal, making it easier to trigger the sampled data. At the same time, the hybrid event trigger mechanism can also select the conventional event trigger during the stage of rapid changes in the composite signal, avoiding the excessive and meaningless increase in the number of triggers caused by the use of memory event triggers. Therefore, the hybrid event trigger mechanism makes full use of the advantages of the memory event trigger mechanism and effectively avoids the disadvantages of the memory event trigger mechanism.

[0092] Assume that the transmission delay of the communication network between the unmanned vehicle and the drone is τ n ,and Due to the existence of transmission delay, the drone will n +τ n Receive event trigger output signalθ y (t n ), and the observer on the drone side will be in the interval [t n +τ n ,tn+1 +τ n+1 ) uses the trigger signal to estimate the state of the unmanned vehicle and the external input. Based on the above analysis, let j = min{l|t n +l+τ n ≥t n+1 +τ n+1}, and the interval [t n +τ n ,t n+1 +τ n+1 ) is divided into the following sub-intervals:

[0093]

[0094] At the same time, define the following function:

[0095]

[0096] From equations (7) and (8), we can get: Next, for the interval [t n +τ n ,t n+1 +τ n+1 ), the hybrid event trigger mechanism can be rewritten as follows:

[0097]

[0098] in,

[0099] To estimate the unmeasurable state x a (k),x b (k), external input r(k) and external interference d(k), and used for the UAV to suppress interference and track the unmanned vehicle, and the following observer is designed:

[0100]

[0101] in, and Represent the state x of the unmanned vehicle respectively a (k) and the estimated value of the external input r(k), and Respectively represent the drone state x b (k) and the estimated value of external disturbance d(k), H i (i=1,2,3,4) is the observer gain matrix to be designed.

[0102] For the above estimated values, four estimation errors are defined as and By combining equations (1), (2), (9) and (10), we can obtain the estimated error of the observer:

[0103]

[0104] By defining two augmented vectors as The estimated error (11) is equivalent to:

[0105]

[0106] in,

[0107]

[0108] Step 3: Based on the estimated value of the observer, construct the design of the UAV composite anti-interference tracking controller, and establish an augmented system consisting of the estimation error and the tracking error.

[0109] The control goal of the present invention is to design a composite anti-interference tracking control scheme for the UAV under the influence of external interference, unpredictable state and transmission delay, so that At the same time, assuming C b =C a S b , if you want to ensure This is equivalent to satisfying

[0110] Define tracking error as e(k)=S b x b (k)-x a (k), and further we can get

[0111] e(k+1)=S b x b (k+1)-x a (k+1)

[0112] =S b A b x b (k)+S b B b u b (k)+S b B d d(k)-[(A a +B a K a C a )x a (k)+B r r(k)]. (13)

[0113] Based on observer (10), a composite anti-disturbance tracking controller is designed as:

[0114]

[0115] According to Assumption 2, the matrix satisfy Select the gain matrix K b1 and K b2 Make SA b +S b B b K 1b =(A a +B a K a C a )S b and S b B b K b2 =B r Next, substituting equations (1), (2) and (14) into equation (13), we can obtain

[0116]

[0117] in, E3=[I2,0] 2×4 and E4=[I4,0] 4×6 Combining equations (12) and (15), we can get the augmented system as follows:

[0118]

[0119] Step 4: Establish the exponential bounded stability judgment condition of the augmented system, obtain the joint design scheme of the hybrid event trigger mechanism, observer and tracking controller, and solve the feasibility problem through the Matlab LMI toolbox.

[0120] In order to facilitate further derivation, the following definitions and lemmas are given:

[0121] Definition 1: For the augmented system (16), if there exist scalars π>0,κ>0 and 0<ρ<1 such that

[0122]

[0123] Then the system (16) is exponentially bounded and stable, where

[0124]

[0125] In addition, we define an augmented vector as

[0126]

[0127] Lemma 1: For any vector and matrix Then the following inequality holds

[0128] 2a T b≤a T Na+b T N -1 b.

[0129] Lemma 2: Consider the Lyapunov function V(ξ k ), if there exists a scalar λ ≥ 0, μ>0, ν>0 and 0<ψ<1, such that

[0130] μ||ξ k || 2 ≤V(ξ k )≤ν||ξ k || 2 ,

[0131] V(ξ k+1 )-V(ξ k )≤λ-ψV(ξ k ),

[0132] Then the vector ξ k satisfy

[0133]

[0134] Lemma 3: If the matrix F(k) satisfies F T (k)F(k)≤I, then for matrices E, G and scalar σ>0, such that EF(k)G+G T F T (k)E T ≤σEE T +σ -1 G T G.

[0135] Lemma 4: For any matrix A, the following two inequalities are equivalent

[0136] (a) There exists a matrix P>0 such that

[0137]

[0138] (b) There exist matrices Y and P>0 such that

[0139]

[0140] Where, Sym{Y}=Y+Y T .

[0141] Theorem 1: For a positive scalar τ M ,η1,η2,η3,η4,δ1,δ2,μi (i=0,L m-1) and the matrix K obtained by equation (3) and assumption 2 a ,S b ,K b1 ,K b2 , if there exist positive definite matrices P1, P2, P3, P4, Q, R1, R2, S, Ω1, Ω2 and matrices T1, T2, T3, T4 of appropriate dimensions, such that the following matrix inequality holds:

[0142]

[0143] in,

[0144]

[0145] Σ1=[0,0,T1,-T1+T2,-T2,0,0,0,0,0], Σ2=[0,0,T3,-T3+T4,-T4,0,L,0],

[0146]

[0147] Γ2=[P1E3A θ ,0,0,0,0,0,0,0,0,0],Γ3=[0,0,P2A θ ,-P2H θ C θ ,0,0,0,P2H θ ,P2E1,0],

[0148]

[0149] Γ7=[P1E3A θ ,0,L,0],Γ8=[0,0,P2A θ ,-P2H θ C θ ,0,0,0,P2H θ ,0,L 0,P2E1,0],

[0150]

[0151] Then, under the action of the hybrid event triggering mechanism (4), the observer (10) and the tracking controller (14), the augmented system (16) is exponentially bounded and stable.

[0152] Proof: Define a vector Construct the following Lyapunov function

[0153] V(k)=V1(k)+V2(k)+V3(k),(18)

[0154] in,

[0155]

[0156] For V(k) and ||ξ(k)||, there exist two scalars λ1>0 and λ2>0 satisfying λ1||ξ(k)|| 2 ≤V(k)≤λ2||ξ(k)|| 2 Next, by performing differential processing on V1(k), V2(k) and V3(k), we can obtain

[0157]

[0158] For any matrices T1, T2, T3 and T4 of appropriate dimensions, the following system of equations holds

[0159]

[0160] According to Lemma 1, we can further obtain

[0161]

[0162]

[0163] According to the hybrid event trigger mechanism (9) and assumption 1, the following inequality holds:

[0164]

[0165] When f(k)≥0, using equations (19)-(23), (26), (27), (30) and (31), we can deduce

[0166]

[0167] When f(k)<0, by combining equations (19)-(21), (24), (25), (28)-(31), we can obtain

[0168]

[0169] Based on the above two cases, by equation (17) and Schur's complement lemma, we can ensure that Φ1<0 and Φ2<0. By defining the scalar 0<β<min{λ2,-λ max (Φ1),-λ max (Φ2)}, we can get the following inequality

[0170]

[0171] According to Lemma 2, we can get

[0172] ||ξ(k)|| 2≤π+κ||ξ(0)|| 2 ρ 2 ,

[0173] in, and Therefore, the augmented system (16) is exponentially bounded and stable. The proof is complete.

[0174] For the nonlinear term S -1 ,P2H θ ,P3H bd The problem that makes equation (17) difficult to solve using the Matlab LMI toolbox is solved by Theorem 2 to obtain a feasible solution for the joint design of the hybrid event-triggered mechanism, observer, and tracking controller.

[0175] Theorem 2: For a positive scalar τ M ,η1,η2,η3,η4,e,δ1,δ2,μ i (i=0,L m-1) and matrix K a ,S b ,K b1 ,K b2 ,G, if there exist positive definite matrices P1,P2,P3,P4,Q,R1,R2,S,Ω1,Ω2, matrices T1,T2,T3,T4 of appropriate dimensions and scalars σ1>0,σ2>0, satisfying the following linear matrix inequality:

[0176]

[0177] in, Given by formula (17),

[0178]

[0179] Ψ2=[P1E3A θ ,0,0,0,0,0,0,0,0,0,0,0],Ψ3=[0,0,P2A θ ,-XC θ ,0,0,0,X,P2E1,0,0,0],

[0180]

[0181] Ψ7=[P1E3A θ ,0,L,0],Ψ8=[0,0,P2A θ ,-XC θ ,0,0,0,X,0,L,0,P2E1,0,0,0],

[0182]

[0183] Then the augmented system (16) is exponentially bounded and stable, and the controller gain K = L -1 J, observer gain

[0184]

[0185] Proof: For positive definite matrices P2 and S, there exists a scalar e>0 satisfying

[0186] -P2S -1 P2≤-2eP2+e 2 S. (33)

[0187] The following coupling terms are defined as

[0188]

[0189] Next, multiply W1=diag(I 42+w ,P2,I2,I4,I6,I2), multiply W2=diag(I 38+4m+w , P2, I2, I4, I6, I2). By substituting equations (33) and (34) into the expressions of W1Λ1W1 and W2Λ2W2, the following two inequalities can be derived to ensure that equation (17) holds:

[0190]

[0191] in,

[0192]

[0193] N1=[0,0,L -1 JE3,0,0,-L -1 JS b E4,L -1 J,0,0,0,0,0],

[0194] N2=[0,0,L -1 JE3,0,0,-L -1 JS b E4,L -1 J,0,L,0,0,0,0,0].

[0195] According to Lemma 3, there exist scalars σ1>0 and σ2>0, such that the following inequality holds

[0196]

[0197] Substituting equations (36) and (37) into equation (35), and using Schur's complement lemma and Lemma 4, we can obtain

[0198]

[0199] It can be seen that the terms in the above equation are the same as the linear matrix inequality in equation (32). Therefore, the validity of equation (32) can ensure that equation (17) is valid, that is, the exponentially bounded stability of the closed-loop system (16) is guaranteed. The proof is complete.

[0200] Compared with the commonly used singular value decomposition (SVD) method, the decoupling method used in the present invention can be used without requiring matrix The problem of nonlinear terms can be solved when the column is full rank, so the joint design scheme of trigger parameters, observer gains and controller gains has fewer restrictions and a wider range of applications.

[0201] Simulation verification:

[0202] Set gravity acceleration g = 10m / s 2 and sampling period h = 0.02s, considering the unmanned ground vehicle and unmanned helicopter model parameters are

[0203]

[0204] By assumption 2, the matrix can be obtained by assuming that:

[0205]

[0206] Set the parameters of the hybrid event trigger mechanism m = 3, μ1 = 0.7, μ2 = 0.2, μ3 = 0.1, δ1 = 0.01, δ2 = 0.007 and the delay upper bound τ M =3, set external interference to

[0207]

[0208] By solving the linear matrix inequality in Theorem 2, we can obtain the control gain K, observer gain H1, H2, H3, H4 and hybrid event trigger parameter matrix Ω1, Ω2 as follows:

[0209]

[0210] Figure 2 , Figure 3 and Figure 4 They are respectively the trajectory motion curve of air-to-ground tracking control and the curve of position coordinates changing with time. It can be concluded that under the influence of external interference, unpredictable state and transmission delay, drones and unmanned vehicles can achieve bounded tracking. In addition, Figure 5 and Figure 6 The instantaneous data transmission and transmission interval of the hybrid event trigger mechanism and the switching function f(k) curve are shown respectively. Figure 5It can be seen that the hybrid event trigger mechanism can select the memory event trigger at the peak or trough of the signal, and select the regular event trigger at the stage of rapid signal change. Figure 6 It also shows the curve of the switching function changing between greater than 0 and less than 0. Therefore, Figure 5 and Figure 6 It is proved that the hybrid event triggering mechanism can work effectively.

[0211] From the above pictures, it can be concluded that the UAV air-to-ground tracking control method based on the hybrid event trigger mechanism in a network environment proposed by the present invention can achieve bounded tracking control goals for UAVs and unmanned vehicles while taking into account external interference, unpredictable state and transmission delay.

Claims

1. A UAV air-to-ground tracking control method based on hybrid event triggering in a network environment, characterized in that: The steps include: Step 1: Establish discrete models of unmanned vehicles and unmanned aerial vehicles based on state space; the discrete models of unmanned vehicles and unmanned aerial vehicles based on state space are: in, represents the plane position vector of the unmanned vehicle, and They represent the control input of the unmanned vehicle and the given external bounded input respectively, represents the measurement output of the UAV; represents the plane position state vector of the drone, and represent the control input and measurement output of the UAV respectively; A represents the external bounded interference of the UAV; a ,B a ,B r ,C a and A b ,B b ,B d ,C b is a known constant matrix of appropriate dimensions; Step 2: According to the design of hybrid event triggering, a data transmission mechanism between the unmanned vehicle and the drone is established, and an observer is designed on the drone side based on the trigger signal, and the observer is used to estimate the state and input signal of the unmanned vehicle and the state and external interference of the drone; the design of the hybrid event triggering mechanism is: Among them, σ n-i (k) = θ y (k)-θ y (t n-i ), δ1 and δ2 are given trigger thresholds, Ω1 and Ω2 are positive definite weighted parameter matrices, μ i ∈(0,1](i=0,…,m-1) is the given weight parameter, f(k) is the switching function used to determine the event trigger mechanism selection, and μ i The sum of (i=0, ..., m-1) is 1, and the switching function f(k) satisfies the following equation: Among them, α is a given positive constant; The design of the observer is: in, and Represent the state x of the unmanned vehicle respectively a (k) and the estimated value of the external input r(k), and Respectively represent the drone state x b (k) and the estimated value of external disturbance d(k), H i (i=1,2,3,4) is the observer gain matrix to be designed; Step 3: Based on the estimated value of the observer, a composite anti-interference tracking controller design of the UAV is constructed, and an augmented system consisting of the estimation error and the tracking error is established; the design of the composite anti-interference tracking controller is: Among them, the matrix satisfy Control gain matrix K b1 and K b2 Meet SA b +S b B b K b1 =(A a +B a K a C a )S b and S b B b K b2 =B r ; Under the influence of transmission delay, the augmented system composed of observation error and tracking error is: in, Step 4: Establish the exponential bounded stability judgment condition of the augmented system, obtain the joint design scheme of the hybrid event trigger mechanism, observer and tracking controller, and solve the feasibility problem through the Matlab LMI toolbox; the exponential bounded stability judgment condition of the augmented system is: For the delay upper bound τ M , positive scalars η1, η2, η3, η4, δ1, δ2, μ i (i=0,Lm-1) and matrix K a ,S b ,K b1 ,K b2 , if there exist positive definite matrices P1, P2, P3, P4, Q, R1, R2, S, Ω1, Ω2 and matrices T1, T2, T3, T4 of appropriate dimensions, such that the following matrix inequality holds: in, Σ1=[0,0,T1,-T1+T2,-T2,0,0,0,0,0], Σ2=[0,0,T3,-T3+T4,-T4,0,L,0], <h2 style=";text-align:left;direction:ltr">Γ2=[P1E3A<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,0,0,0,0,0,0,0,0],Γ3=[0,0,P2A<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,-P2H<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> C<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,0,0,P2H<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,P2E1,0], <h2 style=";text-align:left;direction:ltr">Γ7=[P1E3A<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,L,0],Γ8=[0,0,P2A<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,-P2H<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> C<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,0,0,P2H<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,L0,P2E1,0], Under the action of hybrid event triggering mechanism, observer and tracking controller, the augmented system is exponentially bounded and stable. The joint design scheme of the hybrid event trigger mechanism, observer and tracking controller is: For the delay upper bound τ M , positive scalars η1, η2, η3, η4, δ1, δ2, μ i (i=0,Lm-1) and matrix K a ,S b ,K b1 ,K b2 ,G, if there exist positive definite matrices P1,P2,P3,P4,Q,R1,R2,S,Ω1,Ω2, matrices T1,T2,T3,T4 of appropriate dimensions and scalars σ1>0,σ2>0, satisfying the following linear matrix inequality: in, Ψ2=[P1E3A θ ,0,0,0,0,0,0,0,0,0,0,0],Ψ3=[0,0,P2A θ ,-XC θ ,0,0,0,X,P2E1,0,0,0], <h2 style=";text-align:left;direction:ltr">Ψ7=[P1E3A<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,L,0],Ψ8=[0,0,P2A<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,-XC<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> ,0,0,0,X,0,L,0,P2E1,0,0,0], Then the augmented system is exponentially bounded and stable, and the controller gain K = L -1 J, observer gain H θ =P2 -1 X,H bd =P3 -1 Y.

2. The method for controlling UAV air-to-ground tracking based on hybrid event triggering in a network environment according to claim 1 is characterized in that: The external input r(k) and external disturbance d(k) are bounded, they satisfy r(k)≤η1 and d(k)≤η2, where η1 and η2 are two positive constants; the variation Δr(k)=r(k+1)-r(k) and Δd(k)=d(k+1)-d(k) are also bounded, and satisfy Δr(k)≤η3 and Δd(k)≤η4, where η3 and η4 are two positive constants; for the model parameters of unmanned vehicles and drones, rank(B b )=rank(B b ,B d ), and there exist matrices X1, X2, X3 and S that satisfy SA b +SB b X1=(A a +B a X2) S and SB b X3=B r .

3. The method for controlling UAV air-to-ground tracking based on hybrid event triggering in a network environment according to claim 1 is characterized in that: The controller of the unmanned vehicle is u a =K a y a (k) = K a C a x a (k).

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