Fixed-time consensus control method for unmanned watercraft with actuator failure

Abstract

The present invention discloses a fixed-time consensus control method for an unmanned boat with actuator failure. According to the fixed-time consensus control method for an unmanned boat with actuator failure, even if the unmanned boat system is affected by actuator failure, unknown time-varying control gain and external interference, the tracking error of the system can converge to the vicinity of the origin within a fixed time, and the convergence time is independent of the initial state of the system. By targeting the influence of factors such as actuator failure, external interference and time-varying control gain on the unmanned boat system, the system has higher control accuracy. In addition, an event trigger mechanism is designed in the controller to alleviate communication pressure, and a fixed-time consensus controller is designed based on backstepping technology, neural network adaptive control technology and fixed-time stable control theory. Finally, the proposed method is simulated. The simulation results show that it has good tracking accuracy and effectively saves communication resources.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned boats, and in particular to a fixed-time consensus control method for an unmanned boat with actuator failure. Background Art

[0002] As ocean technology garners increasing attention, oceanographic vehicles such as autonomous submersibles, drones, and unmanned boats (UAVs) have become a research hotspot in ocean exploration. The control of UAVs uses navigation outputs as desired signals and forms a stable control system with navigation laws to address dynamic positioning, trajectory tracking, and path tracking during navigation. However, UAV control faces challenges such as highly nonlinear models, actuator failures, external interference, and unknown time-varying control gains. Furthermore, UAVs, in their basic configuration, carry different payload modules, requiring extensive communication resources between these modules to maintain system stability.

[0003] Most of the existing technical solutions are control methods for a single unmanned boat system. The present invention proposes a consensus control method for multiple unmanned boat systems connected by a communication topology graph, which can achieve consensus and consistent tracking of the unmanned boats.

[0004] Most existing technical solutions ignore the problem that communication resources are limited. The present invention designs an event trigger mechanism in the controller to reduce the update frequency of the control signal, thereby alleviating the communication pressure of the system to a certain extent.

[0005] The current finite-time control method makes the system convergence time related to the initial state of the system. However, in practical applications, the state variables cannot be measured in advance. Moreover, when the system is far from the equilibrium point, the convergence time will be longer. The controller designed by this invention uses fixed-time control theory to achieve fast finite-time stabilization of the system, and the convergence time is independent of the initial state of the system. Summary of the Invention

[0006] (1) Technical problems solved

[0007] In response to the shortcomings of the existing technology, the present invention provides a fixed-time consensus control method for an unmanned boat with actuator failure, which has the advantages of good tracking accuracy and solves the problem that state variables cannot be measured in advance.

[0008] (2) Technical solution

[0009] To achieve the above-mentioned purpose of having good tracking accuracy, the present invention provides the following technical solution: a fixed-time consensus control method for an unmanned boat with actuator failure, comprising the following steps:

[0010] S1. Model the unmanned boat and obtain the state equation.

[0011] S2. Define the error system and design the first virtual control law α k,i1 .

[0012] S3. Design event triggering mechanism.

[0013] S4. Design the second virtual law α k,i2 .

[0014] S5. Design Adaptive Law

[0015] S6. Conduct simulation experiments on the algorithm.

[0016] Preferably, in step S1.1, the mathematical model of the unmanned boat is given as follows:

[0017]

[0018] Where k = 1, 2, ..., N, x k,1 =[x k,11 ,x k,21 ,x k,31 ] T and x k,2 =[x k,12 ,x k,22 ,x k,32 ] T Represents position and velocity respectively Represents x k,1 The derivative of Represents x k,2 The derivative of y k Indicates system output; f k (x k,1 ,x k,2 ) is the inertial damping matrix; g k (t) = diag{g k,1 (t),g k,2 (t),g k,3 (t)} represents the time-varying mass matrix; is the nonlinear model of system actuator failure, ρ k (t) is the health factor of the actuator, r k (t) is the uncontrollable characteristic of the actuator, ρ k (t) and r k (t) are all time-varying.

[0019] Preferably, in step S2.1, the error system is defined as follows:

[0020]

[0021] Among them, e k,i1 is the synchronization error, ek,i2 is the virtual control error, α k.i1 is the first virtual control law, y 0,i Output signal for the leader. h k (k=1,2,...,N) represents the information transmission coefficient from the leader to the kth follower. If the follower k can obtain information from the leader 0, then h k >0, otherwise h k =0. a kj Represents the weight parameter.

[0022] The first virtual control law α k,i1 The design is as follows:

[0023]

[0024] Among them, b k,i1 、c k,i1 is a positive design parameter; y 0,i The derivative of ; q is a constant, and

[0025] Preferably, in the step S3.1, in the traditional time trigger mechanism, the unmanned boat actuator input It is updated regularly, which requires a lot of communication resources. Therefore, a switching threshold event trigger mechanism is designed to further reduce The update frequency can be increased to alleviate the communication pressure of the system. The event trigger mechanism is designed as follows:

[0026]

[0027]

[0028]

[0029] Among them, Δ k,i 、s k,i1 、s k,i2 and δ k,i All are positive numbers; 0<ι k,i <1; is the measurement error; t k,i,z+1 Indicates the controller signal update time, t k,i,1 represents the initial time t0, z is a positive integer; inf{·} represents the lower bound; α k,i2 is the second virtual control law.

[0030] Whenever an event is triggered, the control The control signal update mechanism can reduce the update frequency and thus reduce the communication pressure.

[0031] Preferably, in step S4.1, since the system model has an uncertain part, the uncertain part of the system model is processed by using a neural network approximation, and the virtual control error e is used. k,i2 Design virtual control law α k,i2 and adaptive law Furthermore, S4.11 specifically includes: There is a continuous nonlinear function in the system where X represents the input vector, and if but Represents α k,i1 The derivative of ; introduce an unknown positive parameter where ||·|| represents the binorm; the parameter θ can be obtained by Estimation, that is is the estimated value of parameter θ, then the final estimation error can be defined as Therefore, neural networks are used to approximate nonlinear continuous functions. The expression is as follows:

[0032]

[0033] in, is an ideal unknown weight vector, and express The transpose of S k,j (X k,j ) is the basis function vector, and S k,j (X k,j )=[S k,j1 (X k,j ),S k,j2 (X k,j ),...,S k,jn (X k,j )] T ; n is the number of nodes in the neural network, and n>1; υ k,i (X k,i ) is the approximation error, satisfying and And S4.12, according to the backstepping design method, the above neural network and the virtual control error e k,i2 Construct the second virtual control law α k,i2 :

[0034]

[0035]

[0036] Among them, μ k,i 、b k,i2 、c k,i2 , ε k,i , τ k,i are all positive numbers, is θ k,i The estimated value of ||·|| represents the two-norm.

[0037] Preferably, in step S5.1, the adaptive law is designed

[0038]

[0039]

[0040]

[0041] Among them, γ k,i , κ k,i , σ k,i ,λ k,i 、μ k,i ,ξ k,i 、l k,i are all positive numbers. and and define its boundaries and And k,i =inf t≥0 {ζ k,i}>0, sup{·} represents the supremum, inf{·} represents the infimum. Define the adaptive parameters and To estimate and The estimated error can be obtained and

[0042] Preferably, in step S6.1, in order to verify the effectiveness of the algorithm, the algorithm is deployed to an unmanned boat. Figure 1 The communication topology between unmanned boats is shown in Figure 1 (0 represents the leader, 1, 2, and 3 represent followers). The model of the unmanned boat is as follows:

[0043]

[0044] Where k = 1, 2, ..., N, x k,1 =[x k,11 ,x k,21,x k,31 ] T and x k,2 =[x k,12 ,x k,22 ,x k,32 ] T Represent position and velocity respectively; Represents x k,1 The derivative of Represents x k,2 The derivative of g k (t) = diag{g k,1 (t),g k,2 (t),g k,3 (t)} is the time-varying mass matrix; d k =[d k,1 ,d k,2 ,d k,3 ] T It is unknown external interference; and y k =[y k,1 ,y k,2 ,y k,3 ] T represent the control input and system output respectively; is the nonlinear model of system actuator failure, ρ k (t) = diag{ρ k,1 (t),ρ k,2 (t),ρ k,3 (t)} is the health factor of the actuator, r k (t)=[r k,1 (t),r k,2 (t),r k,3 (t)] T is the uncontrollable characteristic of the actuator, ρ k (t) and r k (t) are all time-varying; f k (x k,1 ,x k,2 ) are centripetal, Coriolis and hydrodynamic damping and torque, where f k (x k,1 ,x k,2 )=Ξ·x k,2 ,

[0045]

[0046]

[0047]

[0048] The relevant system parameters of the unmanned boat are as follows: A=-1+0.1(-1) k , A=-25+2.5(-1) k , B=-10+(-1) k , B=-200+20(-1) k , C=-0.5+0.05(-1) k , C=-1500+150(-1) k ,

[0049] The initial state of the system is as follows: 1,1 (0) = [0.3, 0.3, 0.3] T , x 2,1 (0) = [0.2, 0.2, 0.2] T , x 3,1 (0) = [0.1, 0.1, 0.1] T , x 1,2 (0) = [0,0,0] T , x 2,2 (0) = [0,0,0] T , x 3,2 (0) = [0,0,0] T Assume that the leader’s output is y0 = [sin(2t), sin(2t), 0] T . Initial values ​​of adaptive parameters: and Among them, k=1,2,3, i=1,2,3,

[0050] (3) Beneficial effects

[0051] Compared with the prior art, the present invention provides a fixed-time consensus control method for an unmanned boat with actuator failure, which has the following beneficial effects:

[0052] 1. This fixed-time consensus control method for unmanned boats with actuator failure can converge the tracking error to the vicinity of the origin within a fixed time even if the unmanned boat system is affected by actuator failure, unknown time-varying control gain and external disturbances, and the convergence time is independent of the initial state of the system.

[0053] 2. This fixed-time consensus control method for an unmanned vehicle with actuator failure addresses the impact of actuator failure, external interference, and time-varying control gains on the unmanned vehicle system. A boundary estimation method is proposed to compensate for these effects, resulting in higher control accuracy. Furthermore, an event triggering mechanism is designed into the controller to alleviate communication pressure. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a schematic diagram of the system output of the present invention;

[0055] Figure 2 This is a schematic diagram of the system output of the present invention;

[0056] Figure 3 This is a schematic diagram of the system output of the present invention;

[0057] Figure 4 This is a schematic diagram of the control signal of the present invention;

[0058] Figure 5 This is a schematic diagram of the control signal of the present invention;

[0059] Figure 6 This is a schematic diagram of the control signal of the present invention;

[0060] Figure 7 This is a schematic diagram of the control signal of the present invention;

[0061] Figure 8 This is a schematic diagram of the control signal of the present invention;

[0062] Figure 9 This is a schematic diagram of the control signal of the present invention;

[0063] Figure 10 This is a schematic diagram of the control signal of the present invention;

[0064] Figure 11 This is a schematic diagram of the control signal of the present invention;

[0065] Figure 12 This is a schematic diagram of the control signal of the present invention;

[0066] Figure 13 Schematic diagram of synchronization error in different initial system states of the present invention. DETAILED DESCRIPTION

[0067] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0068] See also Figure 1-3 The present invention provides a technical solution: a fixed-time consensus control method for an unmanned boat with actuator failure, comprising the following steps:

[0069] S1. Model the unmanned boat and obtain the state equation.

[0070] S2. Define the error system and design the first virtual control law αk,i1 .

[0071] S3. Design event triggering mechanism.

[0072] S4. Design the second virtual law α k,i2 .

[0073] S5. Design Adaptive Law

[0074] S6. Conduct simulation experiments on the algorithm.

[0075] In step S1.1, the mathematical model of the unmanned boat is given as follows:

[0076]

[0077] Where k = 1, 2, ..., N, x k,1 =[x k,11 ,x k,21 ,x k,31 ] T and x k,2 =[x k,12 ,x k,22 ,x k,32 ] T Represents position and velocity respectively Represents x k,1 The derivative of Represents x k,2 The derivative of y k Indicates system output; f k (x k,1 ,x k,2 ) is the inertial damping matrix; g k (t) = diag{g k,1 (t),g k,2 (t),g k,3 (t)} represents the time-varying mass matrix; is the nonlinear model of system actuator failure, ρ k (t) is the health factor of the actuator, r k (t) is the uncontrollable characteristic of the actuator, ρ k (t) and r k (t) is time-varying. In step S2.1, the error system is defined as follows:

[0078]

[0079] Among them, e k,i1 is the synchronization error, e k,i2 is the virtual control error, α k.i1 is the first virtual control law, y 0,i For leadership The output signal. k (k=1,2,...,N) represents the information transmission coefficient from the leader to the kth follower. k can obtain information from leader 0, then h k >0, otherwise h k =0. a kj Represents the weight parameter.

[0080] The first virtual control law α k,i 1The design is as follows:

[0081]

[0082] Among them, b k,i1 、c k,i1 is a positive design parameter; y 0,i The derivative of ; q is a constant, and In step S3.1, in the traditional time trigger mechanism, the UAV actuator input It is updated regularly, which requires a lot of communication resources. Therefore, a switching threshold event trigger mechanism is designed to further reduce The update frequency can be increased to alleviate the communication pressure of the system. The event trigger mechanism is designed as follows:

[0083]

[0084]

[0085]

[0086] Among them, Δ k,i 、s k,i1 、s k,i2 and δ k,i All are positive numbers; 0<ι k,i <1; is the measurement error; t k,i,z+1 Indicates the controller signal update time, t k,i,1 represents the initial time t0, z is a positive integer; inf{·} represents the lower bound; α k,i2 is the second virtual control law.

[0087] Whenever an event is triggered, the control It will act on the actuator, and the control amount will remain until the next event is triggered. Obviously, the control signal update mechanism can reduce the update frequency, thereby reducing the communication pressure. In step S4.1, due to the uncertainty of the system model, the neural network is used to approximate the uncertainty of the system model, and the virtual control error e is used to calculate the control error. k,i2 Design virtual control law α k,i2 and adaptive law Furthermore, S4.11 specifically includes: There is a continuous nonlinear function in the system where X represents the input vector, and if but Represents α k,i1 The derivative of ; introduce an unknown positive parameter where ||·|| represents the binorm; the parameter θ can be obtained by Estimation, that is is the estimated value of parameter θ, then the final estimation error can be defined as Therefore, neural networks are used to approximate nonlinear continuous functions. The expression is as follows:

[0088]

[0089] in, is an ideal unknown weight vector, and express The transpose of S k,j (X k,j ) is the basis function vector, and S k,j (X k,j )=[S k,j1 (X k,j ),S k,j2 (X k,j ),...,S k,jn (X k,j )] T ; n is the number of nodes in the neural network, and n>1; υ k,i (X k,i ) is the approximation error, satisfying and And S4.12, according to the backstepping design method, the above neural network and the virtual control error e k,i2 Construct the second virtual control law α k,i2 :

[0090]

[0091]

[0092] Among them, μ k,i 、b k,i2 、c k,i2 , ε k,i , τ k,i are all positive numbers, is θ k,i The estimated value of ||·|| represents the two-norm. In step S5.1, the adaptive law is designed.

[0093]

[0094]

[0095]

[0096] Among them, γ k,i , κ k,i , σ k,i ,λ k,i 、μ k,i ,ξ k,i 、l k,i are all positive numbers. and and define its boundaries and And k,i =inf t≥0 {ζ k,i}>0, sup{·} represents the supremum, inf{·} represents the infimum. Define the adaptive parameters and To estimate and The estimated error can be obtained and In step S6.1, in order to verify the effectiveness of the algorithm, the algorithm is deployed to the unmanned boat. Figure 1 The communication topology between unmanned boats is shown in Figure 1 (0 represents the leader, 1, 2, and 3 represent followers). The model of the unmanned boat is as follows:

[0097]

[0098] Where k = 1, 2, ..., N, x k,1 =[x k,11 ,x k,21 ,x k,31 ] T and x k,2 =[x k,12 ,x k,22 ,x k,32 ] T Represent position and velocity respectively; Represents x k,1 The derivative of Represents x k,2 The derivative of g k (t) = diag{g k,1 (t),g k,2 (t),g k,3 (t)} is the time-varying mass matrix; d k =[d k,1 ,d k,2 ,d k,3 ] T It is unknown external interference; and y k =[y k,1 ,yk,2 ,y k,3 ] T represent the control input and system output respectively; is the nonlinear model of system actuator failure, ρ k (t) = diag{ρ k,1 (t),ρ k,2 (t),ρ k,3 (t)} is the health factor of the actuator, r k (t)=[r k,1 (t),r k,2 (t),r k,3 (t)] T is the uncontrollable characteristic of the actuator, ρ k (t) and r k (t) are all time-varying; f k (x k,1 ,x k,2 ) are centripetal, Coriolis and hydrodynamic damping and torque, where f k (x k,1 ,x k,2 )=Ξ·x k,2 ,

[0099]

[0100]

[0101]

[0102] The relevant system parameters of the unmanned boat are as follows: A=-1+0.1(-1) k , A=-25+2.5(-1) k , B=-10+(-1) k , B=-200+20(-1) k , C=-0.5+0.05(-1) k , C=-1500+150(-1) k ,

[0103]

[0104] The initial state of the system is as follows: 1,1 (0) = [0.3, 0.3, 0.3] T , x 2,1 (0) = [0.2, 0.2, 0.2] T , x 3,1 (0) = [0.1, 0.1, 0.1] T , x 1,2(0) = [0,0,0] T , x 2,2 (0) = [0,0,0] T , x 3,2 (0) = [0,0,0] T Assume that the leader’s output is y0 = [sin(2t), sin(2t), 0] T . Initial values ​​of adaptive parameters: and Among them, k=1,2,3, i=1,2,3, Relevant design parameters are shown in Tables 1 and 2.

[0105] Table 1 Controller parameter design

[0106]

[0107] Table 2 Controller parameter design

[0108]

[0109] Table 3 Detailed trigger data

[0110]

[0111]

[0112] The simulation results are as follows Figure 1-13 As shown in Table 3, it can be seen that all signals are bounded. Figure 1-3 The output trajectory of each follower is depicted, and even if the system is affected by the failure of the actuator, the system output of the follower can effectively track the output of the leader. Figure 4-12 As shown in Figure 3, the actuator begins to fail after running for 5 seconds. In order to prove that the proposed method can save communication resources, the detailed trigger data is recorded in Table 3. In the simulation experiment, the sampling period is 0.01s, which means that within the 15s running time, the system needs to update the control signal Obviously, it can be concluded from Table 3 that the proposed method saves a lot of communication resources. Figure 13 Given e 1,11 Convergence curves under different initial states. Simulation results show that the convergence time under different initial states is about 0.25s, proving that the upper bound of convergence is independent of the initial state of the system.

[0113] In order to facilitate the description of directed communication, the relevant knowledge of algebraic graph theory is introduced. The leader and followers are connected through a known directed communication topology graph. The directed communication topology graph can be used To describe, is the weighted adjacency matrix between followers; is the weighted adjacency vector between the follower and the leader 0; It is a collection of leaders and followers; represents a set of edges. If And j≠k (follower k can get information from follower j), then a kj >0, otherwise a kj = 0. Therefore, the adjacency set of follower k is If follower k can get information from leader 0, then h k >0, otherwise h k = 0. Then, we can get the matrix And the Laplace matrix L = DA, where

[0114] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A fixed-time consensus control method for an unmanned boat with actuator failure, characterized in that: The following steps are involved: S1. Model the unmanned boat and obtain the state equation; S2. Define the error system and design the first virtual control law ; The first virtual control law The design is as follows: (3) in, 、 is a positive design parameter; for The derivative of is a constant, and ; ; S3. Design event triggering mechanism; S4. Design the second virtual law ; Constructing the second virtual control law : (8) (9) in, 、 、 、 、 are all positive numbers, ; yes The estimated value of , , represents the two-norm; S5. Design Adaptive Law 、 、 ; S6. Conduct simulation experiments on the algorithm.

2. The fixed-time consensus control method for an unmanned boat with actuator failure according to claim 1 is characterized in that: In S1, the mathematical model of the unmanned boat is given as follows: (1) in, , and Represent position and velocity respectively; express The derivative of express The derivative of Indicates system output; is the inertial damping matrix; represents the time-varying mass matrix; is the nonlinear model of system actuator failure, is the health factor of the actuator, is the uncontrollable characteristic of the actuator, and All are time-varying.

3. The fixed-time consensus control method for an unmanned boat with actuator failure according to claim 2 is characterized in that: In S2, the error system is defined as follows: (2) in, is the synchronization error, is the virtual control error, is the first virtual control law, Output signals for leaders; From leader to The information transmission coefficient of followers; if followed Can learn from leaders Get information, then ,on the contrary ; represents the weight parameter; The first virtual control law The design is as follows: （3） in, 、 is a positive design parameter; for The derivative of is a constant, and ; .

4. The fixed-time consensus control method for an unmanned boat with actuator failure according to claim 3 is characterized in that: In S3, In the traditional time trigger mechanism, the UAV actuator input It is updated regularly, which requires a lot of communication resources; therefore, a switching threshold event trigger mechanism is designed to further reduce The update frequency can be increased to alleviate the communication pressure of the system. The event triggering mechanism is designed as follows: in, 、 、 and are all positive numbers; ; is the measurement error; Indicates the controller's signal update time, Indicates the initial time , is a positive integer; represents the infimum; is the second virtual control law; Whenever an event is triggered, the control It will act on the actuator and the control quantity will be maintained until the next event is triggered; obviously, the control signal update mechanism can reduce the update frequency, thereby reducing the communication pressure.

5. The fixed-time consensus control method for an unmanned boat with actuator failure according to claim 4 is characterized in that: In S4, due to the uncertainty of the system model, the neural network is used to approximate the uncertainty of the system model, and the virtual control error is used to calculate the uncertainty of the system model. Design of virtual control laws and adaptive law 、 、 ; S4 specifically includes: there is a continuous nonlinear function in the system ,in represents the input vector, and ,if but ; express The derivative of ; introduce an unknown positive parameter ,in represents the two norm; parameter Can be achieved through Estimation, that is For parameters The estimated value of , then the final estimation error can be defined as Therefore, using neural networks to approximate nonlinear continuous functions The expression is as follows: (7) in, is an ideal unknown weight vector, and ; express The transpose of is the basis function vector, and ; is the number of nodes in the neural network, and ; is the approximation error, satisfying ,and ; And S4.12, according to the backstepping design method, the above neural network and virtual control error Constructing the second virtual control law : in, 、 、 、 、 are all positive numbers, ; yes The estimated value of , , represents the two-norm.

6. The fixed-time consensus control method for an unmanned vehicle with actuator failure according to claim 5 is characterized in that: In S5, the adaptive law is designed 、 、 : (10) in, 、 、 、 、 、 、 are all positive numbers; let and , and define its boundaries and ,and , represents the supremum, Denotes the lower bound; defines the adaptive parameters and To estimate and , we can get the estimated error and ; , , .

7. The fixed-time consensus control method for an unmanned boat with actuator failure according to claim 6 is characterized in that: In S6, in order to verify the effectiveness of the algorithm, the algorithm is deployed to the unmanned boat; , The relevant system parameters of the unmanned boat are as follows: , , , , , , , , , , , ; The initial state of the system is as follows: , , , , , ; Assume the leader's output is ; Initial values ​​of adaptive parameters: , and ;in, , , .

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