Formation controller for multiple underwater vehicles under limited state

Abstract

The invention discloses a formation controller for multiple underwater vehicles under limited states, and belongs to the technical field of industrial process control. The formation controller comprises a neural network weight updating unit, a neural network activation function unit, a nonlinear operation unit, a comparator unit, a state limited unit, a predictor unit, a disturbance observer unit, a first differential tracker unit and a first filtering unit. According to the method, an intermediate variable of a limited state is constructed through the neural network disturbance observer, interference is compensated through a difference value between the intermediate variable and an estimated state, and the dynamic approximation precision and anti-interference performance of the system are greatly improved; through the predictor of the obstacle Lyapunov function, under the condition that the neural network has a limited state, initial value oscillation generated under large adaptive gain can be avoided, the approximation performance of the neural network is improved, and the selection range of controller parameters is expanded.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial process control, and in particular relates to a formation controller for multiple underwater vehicles under state constraints. Background Art

[0002] In recent years, underwater vehicles have attracted much attention due to their wide applications in ocean exploration, environmental monitoring, scientific research and other fields. However, quadcopters have a history of nearly a hundred years. During World War I and World War II, military needs promoted the development of diving technology and gave rise to the concept of early underwater unmanned vehicles. In the 1970s, the first generation of autonomous underwater vehicles (AUVs) appeared. In 1985, the deep-sea unmanned submersible "Alvin" successfully explored the wreckage of the Titanic, marking a major breakthrough in deep-sea exploration technology. Modern underwater vehicles integrate advanced sensors and control systems, with higher navigation accuracy and autonomous decision-making capabilities. Today, researchers have begun to focus on the formation control of multiple underwater vehicles, using their collaborative operation capabilities to improve the efficiency and success rate of missions.

[0003] The research and application of underwater vehicles are facing multiple challenges, especially in terms of anti-interference, state constraints and unknown dynamics. Unstable factors in the underwater environment, such as water flow, turbulence and temperature gradient, often cause interference to the control system of the vehicle, reducing the accuracy and stability of its position control. In addition, the motion state of underwater vehicles is limited by water depth, pressure and environmental conditions, making their operation more complicated and difficult to achieve accurate navigation and positioning. In the collaborative operation of multiple underwater vehicles, the complexity of the system is further increased due to the unknown dynamics of the system itself and external unknown disturbances such as water flow and temperature. When multiple vehicles work together, they must be able to effectively deal with mutual interference and changes in the external environment to ensure the stability and safety of the formation.

[0004] In summary, how to solve the problem of underwater vehicles obtaining navigation and positioning when they are restricted and the mutual interference of underwater navigation devices is the technical problem that the present invention aims to solve. Summary of the invention

[0005] The object of the present invention is to provide a formation controller for multiple underwater vehicles under state constraints to solve the problems raised in the above background technology.

[0006] The object of the present invention is achieved as follows: a formation controller for multiple underwater vehicles under state constraints, characterized in that: the formation controller regards N state-constrained underwater vehicles with unknown dynamics as followers, and a multi-agent network formed by connecting the followers and a leader through a unidirectional topological graph as a controlled object, the leader provides a leadership expectation signal, and the formation controller is designed using the follower position information so that the output of the followers and the leader form a desired formation formation;

[0007] The input end of the formation controller is connected to the output end of the directed graph G, and the output end of the formation controller is connected to the input end of the i-th follower;

[0008] The formation controller includes a neural network identification module, an estimator module, a disturbance observer module, a state-limited module, a comparator module and an anti-disturbance controller module. The neural network identification module calculates the activation function through the state of the i-th underwater vehicle, and updates the neural network weight norm through the estimated error of the estimator module, and then identifies the state of the vehicle through the output of the state-limited module; at the same time, the state estimated by the estimator module is fed back to the neural network identification module and the disturbance observer module;

[0009] The anti-disturbance controller module realizes the normal operation of multiple underwater vehicles under state constraints and external disturbances according to the characteristics of the neural network identification module, the estimator module, the disturbance observer module and the state constraint module.

[0010] Preferably, there is communication between at least one follower and the leader in the multi-agent network, and the unidirectional topology graph is represented by a directed graph G=(V,E);

[0011] Where V = {ν1,…,ν N} represents a set of N nodes, ν1,…,ν N represents underwater vehicle follower 1 to underwater vehicle follower N; represents the edge set, (ν i ,ν j ) represents the edge of the topological graph G, ν i ,ν j denote the i-th aircraft and the j-th aircraft respectively;

[0012] If (ν i ,ν j )∈E then ν j ν i The adjacent nodes of i = { j ∈ν(ν j ,ν i )∈E}, where Ω i Indicates ν i The set of adjacent nodes of ;

[0013] Define the adjacency matrix A = [a ij ]∈R N×N , if (ν i ,ν j )∈E and the i agent and the j agent are in a cooperative relationship, then a ij =1, for competitive relationship a ij =-1; if Then a ij =0;

[0014] Define the degree matrix D = diag[d1,...,d N ],in

[0015] Define the Laplace matrix L = DA;

[0016] Define the adjacency matrix B associated with the leader = diag[b1,…,b N ], if the i-th vehicle can access the leader's information, then b i =1, otherwise b i =0.

[0017] Preferably, the mathematical model of the position of the i-th underwater vehicle among the followers is:

[0018]

[0019] Among them, η i represents the position coordinates of the i-th underwater vehicle [x i ,y i ,z i ] T ;v i,1r =[u i,r ,v i,r ,w i,r ] T Respectively represent the acceleration in the x-axis, y-axis, and z-axis directions; u i =[u i,x ,u i,y ,u i,z ] T Respectively represent the forces acting on the x-axis, y-axis, and z-axis directions, M i is the inertia matrix of the ith underwater vehicle, D i is the damping matrix of the ith underwater vehicle, U i,f It is an unknown disturbance.

[0020] Preferably, the neural network identification module includes a first neural network weight update unit, a first neural network activation function unit, a first nonlinear operation unit, a second state-restricted operation unit, and a second neural network weight update unit, a second neural network activation function unit, a second nonlinear operation unit, and a fourth state-restricted operation unit;

[0021] The inputs of the first neural network weight update unit are the first neural network function activation function unit input and the second comparator unit output, which are calculated by the following formula:

[0022]

[0023] Among them, Φ i,x , Φ i,y and Φ i,z They are the activation functions of the x-axis, y-axis, and z-axis of the first neural network activation function unit, and are the estimated errors of the x-axis, y-axis and z-axis of the second comparator unit respectively; Γ i,η is the neural network adaptive gain, Γ i,η >0;ζ i,η is the neural network weight proportional coefficient, ζ i,η >0;k i,p,1 is the bound of the position estimation error, k i,p,1 >0; finally get the output

[0024] The input end of the first neural network activation function unit is the system position state η i ; Calculated by the following formula:

[0025]

[0026] Among them, γ i,χ is the proportional coefficient of the activation function, γ i,χ >0; are the activation functions of the x-axis, y-axis, and z-axis respectively; i ,y i and z i are the states of the x-axis, y-axis, and z-axis, all of which are η i The elements in , μ is the center value of the activation function, ξ is the width of the activation function; finally, the output Φ i,1 =diag[Φ i,x ,Φ i,y ,Φ i,z ];

[0027] The input ends of the first nonlinear operation unit are the output Φ of the first neural network activation function uniti,1 , the output of the first neural weight update unit and the output of the second comparator unit All inputs are multiplied to obtain the output of the second nonlinear operation unit.

[0028] The input of the second state restricted operation unit is the output of the second nonlinear operation unit, which is processed by the derivative of the barrier Lyapunov function as follows: Among them, k i,p,1 is the limit of the position state estimation error, k i,p,1 >0; is the neural network weight norm, is the estimation error, Φ i,1 is the neural network activation function;

[0029] The inputs of the second neural network weight update unit are respectively the input of the second neural network function activation function unit Φ i,2 and the third comparator unit output It is calculated by the following formula:

[0030]

[0031] Among them, Φ i,u , Φ i,v and Φ i,w They are respectively the activation functions of the x-axis acceleration, y-axis acceleration, and z-axis acceleration of the second neural network activation function unit. and The output of the third comparator unit is The estimated errors of x-axis acceleration, y-axis acceleration, and z-axis acceleration; Γ i,r is the neural network adaptive gain, Γ i,r >0;ζ i,r is the neural network weight proportional coefficient, ζ i,r >0;k i,p,2 is the limit of the acceleration state estimation error, k i,p,2 >0; finally get the output

[0032] The input of the second neural network activation function unit is the acceleration state v in all directions of the system i.1r ; Calculated by the following formula:

[0033]

[0034] Among them, γ i,r For, γ i,r >0; The activation functions of x-axis acceleration, y-axis acceleration, and z-axis acceleration, u i,r 、v i,r , and w i,r are the system acceleration states v i.1r The x-axis acceleration, y-axis acceleration, and z-axis acceleration in are: μ is the center value of the activation function, and ξ is the width of the activation function; finally, the output Φ is obtained. i,2 =diag[Φ i,u ,Φ i,v ,Φ i,w ];

[0035] The input ends of the third nonlinear operation unit are the output Φ of the second neural network activation function unit. i,2 , the output of the second neural network weight update unit and the output of the third comparator unit All inputs are multiplied to obtain the output of the third nonlinear operation unit.

[0036] The input end of the fourth state-restricted operation unit is the output end of the third nonlinear operation unit. By taking the derivative of the barrier Lyapunov function, we can treat it as

[0037] Among them, k i,p,2 is the limit of the acceleration state estimation error, k i,p,2 >0; is the neural network weight norm, is the acceleration state estimation error, Φ i,2 is the activation function of the second neural network.

[0038] Preferably, the estimator module comprises a first estimator unit and a second estimator unit, the first estimator unit is used to estimate the position state of the aircraft, and the second estimator unit is used to estimate the acceleration state of the aircraft;

[0039] The input terminals of the first estimator operation unit are the output terminals of the second comparator unit. The output of the second state-restricted arithmetic unit The output of the first disturbance observer unit is and the agent's acceleration state v i,1r ; Calculated by the following formula:

[0040]

[0041] Among them, c i,1 is the virtual controller proportional coefficient, c i,1 >0; is the position state predictor proportional coefficient, v i,1r is the acceleration state of the ith agent;

[0042] The input terminals of the second estimator operation unit are respectively the output terminals of the fourth comparator unit Output of the fourth state restricted operation unit The output of the second disturbance observer unit and the output u of the fourth nonlinear operation unit i ; Calculated by the following formula:

[0043]

[0044] Among them, c i,2 is the controller proportional coefficient, c i,2 >0; is the acceleration state predictor proportional coefficient, u i is the output of the fourth nonlinear operation unit.

[0045] Preferably, the disturbance observer module comprises a first disturbance observer unit and a second disturbance observer unit, and the disturbance observer module designs an intermediate variable according to the output of the neural network identification module block, and compares it with the output of the estimator module to achieve the effect of observing external disturbances and compensating neural network errors;

[0046] The input of the first disturbance observer unit is the output of the second comparator unit. Position state η i , the output of the second state restricted operation unit and the agent's acceleration state v i,1r ; Calculated by the following formula:

[0047]

[0048] in, The intermediate variable constructed for the disturbance observer, c d,i,1 is the state-constrained proportionality coefficient, c d,i,1 >0;c D,i,1 is the disturbance observer proportional coefficient, c D,i,1 >0;

[0049] The input of the second disturbance observer unit is the output of the fourth comparator unit.

[0050] Output of the fourth state restricted operation unit and the output u of the fourth nonlinear operation unit i ; Calculated by the following formula:

[0051]

[0052] Among them, c d,i,2 is the state-constrained proportionality coefficient, c d,i,2 >0;c D,i,2 is the disturbance observer proportional coefficient, c D,i,2 >0.

[0053] Preferably, the state-limited module comprises a first state-limited operation unit, a second state-limited operation unit, a third state-limited operation unit and a fourth state-limited operation unit. The first state-limited operation unit and the second state-limited operation unit respectively limit the estimated error of the position state of the aircraft and the surface error based on the predictor through the derivative of the obstacle Lyapunov; the third state-limited operation unit and the fourth state-limited operation unit respectively limit the estimated error of the acceleration state of the aircraft and the surface error based on the predictor through the derivative of the obstacle Lyapunov;

[0054] The input terminal of the first state limiting unit is the output of the first comparator The output of the first state restricted unit is obtained by calculating the derivative of the barrier Lyapunov function Among them, k i,l,1 is the bound on the position surface error based on the estimator, k i,l,1 >0;

[0055] The input terminal of the third state limiting unit is the output of the third comparator The output of the third state restricted unit is obtained by calculating the derivative of the barrier Lyapunov function Among them, k i,l,2 is the bound on the acceleration surface error based on the estimator, k i,l,2 >0.

[0056] Preferably, the comparator module includes a first comparator unit, a second comparator unit, a third comparator unit and a fourth comparator unit, the first comparator unit is an error surface Its input is the first estimator unit and the desired signal y provided by the directed graph d ; Calculated by the following formula:

[0057]

[0058] Among them, a ij and b i are the communication relationships between neighbors and leaders, y r is the leader signal, σ i Represents the cooperative and confrontational relationship between the intelligent agent and the leader;

[0059] The input of the second comparator unit is the output of the first estimator unit. and the agent's position state η i , obtained through the following formula:

[0060]

[0061] The third comparator unit is the error surface Its input is the second estimator unit and the output v of the first filter unit i,1r,d ; Calculated by the following formula:

[0062]

[0063] The input terminal of the fourth comparator unit is the output terminal of the second estimator unit. and the agent's acceleration state v i,1r , obtained through the following formula:

[0064]

[0065] Preferably, the anti-disturbance controller module includes a second nonlinear operation unit, a first filtering unit and a fourth nonlinear operation unit, and the input end of the second nonlinear operation unit is the position state η of the jth follower in the directed graph. j , Adjacent communication ij and b i , Leader derivative information Formation Information Derivative The output of the first differential tracker is r j,2 , the output of the first state restricted operation unit The output of the first state restricted unit First disturbance observer output unit The output of the second nonlinear operation unit is α i :

[0066]

[0067] Among them, m i,1 is the state-limited proportionality coefficient, m i,1 >0;

[0068] The input of the first tracking differentiator unit is the neighbor information η provided by the directed graph j ; Calculated by the following formula:

[0069]

[0070] Among them, r j,2 Neighbor information η provided for the directed graph jEstimate of the derivative, k TD is the tracking differentiator speed factor; k TD >0;α TD,j ∈(0,1) is the tracking differentiator filter factor;

[0071] The input end of the first filtering unit is the output α of the second nonlinear operation unit. i ; Calculated by the following formula:

[0072]

[0073] Among them, χ i is the filter time constant;

[0074] The input end of the fourth nonlinear operation unit is the output end of the third state-limited operation unit. Output of the fourth state restricted unit Second disturbance observer output unit The output of the third comparator unit

[0075] Among them, m i,2 is the state-limited proportionality coefficient, m i,2 >0.

[0076] Compared with the prior art, the present invention has the following improvements and advantages:

[0077] 1. The obstacle Lyapunov function is used to constrain the estimation error and the surface error based on the estimator; the state of the underwater vehicle is guaranteed to be within a predetermined interval. When the vehicle approaches the edge of the interval, the obstacle Lyapunov function will increase smoothly to prevent the underwater vehicle from entering the area outside the interval, thereby increasing the safety and reliability of the vehicle.

[0078] 2. Through the predictor of the barrier Lyapunov function, the neural network can avoid the initial value oscillation caused by large adaptive gain when the state is restricted, which improves the approximation performance of the neural network and expands the selection range of controller parameters.

[0079] 3. The neural network disturbance observer based on the obstacle Lyapunov function is used to observe generalized disturbances including external unknown disturbances, system transformation errors, and neural network approximation errors. The neural network disturbance observer constructs an intermediate variable of a restricted state and compensates for the disturbance through the difference between the intermediate variable and the estimated state, which greatly improves the approximation accuracy and anti-disturbance performance of the system dynamics. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a structural schematic diagram of the formation controller of the present invention.

[0081] Figure 2 Figure 2 is the motion trajectory diagram of the obstacle avoidance formation of two underwater vehicles and the leader.

[0082] Figure 3 Schematic diagram of performance effects for two underwater vehicles and the leader and communications maintenance.

[0083] Figure 4 Schematic diagram of the control input curves of two underwater vehicles.

[0084] Figure 5 This is a schematic diagram of the dynamic approach effect of the first quadrotor. DETAILED DESCRIPTION

[0085] The present invention is further summarized below with reference to the accompanying drawings.

[0086] like Figure 1 As shown, a formation controller for multiple underwater vehicles under state constraints is provided. The formation controller regards N state-constrained underwater vehicles with unknown dynamics as followers, and a multi-agent network formed by connecting the followers and a leader through a unidirectional topological graph as a controlled object. The leader provides a leadership expectation signal, and the formation controller is designed using the follower position information so that the output of the followers and the leader form an expected formation formation; the input ends of the formation controller are all connected to the output end of the directed graph G, and the output end of the formation controller is connected to the input end of the i-th follower.

[0087] In a multi-agent network, there is communication between at least one follower and the leader, and the unidirectional topology graph is represented by a directed graph G = (V, E);

[0088] Where V = {ν1,…,ν N} represents a set of N nodes, ν1,…,ν N represents underwater vehicle follower 1 to underwater vehicle follower N; represents the edge set, (ν i ,ν j ) represents the edge of the topological graph G, ν i ,ν j denote the i-th aircraft and the j-th aircraft respectively;

[0089] If (ν i ,ν j )∈E then ν j ν i The adjacent nodes of i = { j ∈ν|(ν j ,ν i )∈E}, where Ω i Indicates ν i The set of adjacent nodes of ;

[0090] Define the adjacency matrix A = [a ij ]∈R N×N , if (ν i ,ν j )∈E and the i agent and the j agent are in a cooperative relationship, then a ij =1, for competitive relationship a ij =-1; if Then a ij =0;

[0091] Define the degree matrix D = diag[d1,...,d N ],in

[0092] Define the Laplace matrix L = DA;

[0093] Define the adjacency matrix B associated with the leader = diag[b1,…,b N ], if the i-th vehicle can access the leader's information, then b i =1, otherwise b i =0.

[0094] The mathematical model of the position of the i-th underwater vehicle is as follows:

[0095]

[0096] Among them, η i represents the position coordinates of the i-th underwater vehicle [x i ,y i ,z i ] T ;v i,1r =[u i,r ,v i,r ,w i,r ] T Respectively represent the acceleration in the x-axis, y-axis, and z-axis directions; u i =[u i,x ,u i,y ,u i,z ] T Respectively represent the forces acting on the x-axis, y-axis, and z-axis directions, M i is the inertia matrix of the ith underwater vehicle, D i is the damping matrix of the ith underwater vehicle, U i,f It is an unknown disturbance.

[0097] The formation controller includes a neural network identification module, an estimator module, a disturbance observer module, a state-constrained module, a comparator module and an anti-disturbance controller module. The neural network identification module calculates the activation function through the state of the i-th underwater vehicle, and estimates the error through the estimator module to update the neural network weight norm, and then the state of the vehicle is identified through the output of the state-constrained module; at the same time, the state estimated by the estimator module is fed back to the neural network identification module and the disturbance observer module;

[0098] The anti-disturbance controller module realizes the normal operation of multiple underwater vehicles under state constraints and external disturbances based on the characteristics of the neural network identification module, the estimator module, the disturbance observer module and the state constraint module.

[0099] The neural network identification module includes a first neural network weight update unit, a first neural network activation function unit, a first nonlinear operation unit, a second state-restricted operation unit and a second neural network weight update unit, a second neural network activation function unit, a second nonlinear operation unit and a fourth state-restricted operation unit;

[0100] The inputs of the first neural network weight update unit are the first neural network function activation function unit input and the second comparator unit output, which are calculated by the following formula:

[0101]

[0102] Among them, Φ i,x , Φ i,y and Φ i,z They are the activation functions of the x-axis, y-axis, and z-axis of the first neural network activation function unit, and are the estimated errors of the x-axis, y-axis and z-axis of the second comparator unit respectively; Γ i,η is the neural network adaptive gain, Γ i,η >0;ζ i,η is the neural network weight proportional coefficient, ζ i,η >0;k i,p,1 is the bound of the position estimation error, k i,p,1 >0; finally get the output

[0103] The input end of the first neural network activation function unit is the system position state η i ; Calculated by the following formula:

[0104]

[0105] Among them, γ i,χ is the proportional coefficient of the activation function, γ i,χ >0; are the activation functions of the x-axis, y-axis, and z-axis respectively; i ,y i and z i are the states of the x-axis, y-axis, and z-axis, all of which are η i The elements in , μ is the center value of the activation function, ξ is the width of the activation function; finally, the output Φ i,1 =diag[Φ i,x ,Φ i,y ,Φ i,z ];

[0106] The input ends of the first nonlinear operation unit are the output Φ of the first neural network activation function unit i,1 , the output of the first neural weight update unit and the output of the second comparator unit All inputs are multiplied to obtain the output of the second nonlinear operation unit.

[0107] The input of the second state restricted operation unit is the output of the second nonlinear operation unit, which is processed by the derivative of the barrier Lyapunov function as follows: Among them, k i,p,1 is the limit of the position state estimation error, k i,p,1 >0; is the neural network weight norm, is the estimation error, Φ i,1 is the neural network activation function;

[0108] The above is the identification of the first-order unknown dynamics of the i-th underwater vehicle by the neural network identification module. It is based on the traditional neural network and applies the weight norm technology to reduce the number of neural network update parameters, and through the estimation error To update the weights of the neural network, the initial value oscillation caused by the neural network identification is avoided, and then the derivative of the barrier Lyapunov function is processed as It can be used in state-constrained aircraft.

[0109] The inputs of the second neural network weight update unit are respectively the input of the second neural network function activation function unit Φ i,2 and the third comparator unit output It is calculated by the following formula:

[0110]

[0111] Among them, Φ i,u , Φ i,v and Φ i,wThey are respectively the activation functions of the x-axis acceleration, y-axis acceleration, and z-axis acceleration of the second neural network activation function unit. and The output of the third comparator unit is The estimated errors of x-axis acceleration, y-axis acceleration, and z-axis acceleration; Γ i,r is the neural network adaptive gain, Γ i,r >0;ζ i,r is the neural network weight proportional coefficient, ζ i,r >0;k i,p,2 is the limit of the acceleration state estimation error, k i,p,2 >0; finally get the output

[0112] The input of the second neural network activation function unit is the acceleration state v in all directions of the system i.1r ; Calculated by the following formula:

[0113]

[0114] Among them, γ i,r For, γ i,r >0; The activation functions of x-axis acceleration, y-axis acceleration, and z-axis acceleration, u i,r 、v i,r , and w i,r are the system acceleration states v i.1r The x-axis acceleration, y-axis acceleration, and z-axis acceleration in are: μ is the center value of the activation function, and ξ is the width of the activation function; finally, the output Φ is obtained. i,2 =diag[Φ i,u ,Φ i,v ,Φ i,w ];

[0115] The input ends of the third nonlinear operation unit are the output Φ of the second neural network activation function unit. i,2 , the output of the second neural network weight update unit and the output of the third comparator unit All inputs are multiplied to obtain the output of the third nonlinear operation unit.

[0116] The input end of the fourth state-restricted operation unit is the output end of the third nonlinear operation unit. By taking the derivative of the barrier Lyapunov function, we can treat it as

[0117] Among them, k i,p,2 is the limit of the acceleration state estimation error, ki,p,2 >0; is the neural network weight norm, is the acceleration state estimation error, Φ i,2 is the activation function of the second neural network.

[0118] The above is the identification of the second-order unknown dynamics of the i-th underwater vehicle by the neural network identification module. It is based on the traditional neural network and applies the weight norm technology to reduce the number of neural network update parameters, and through the estimation error To update the weights of the neural network, the initial value oscillation caused by the neural network identification is avoided, and then the derivative of the barrier Lyapunov function is processed as It can be used in state-constrained aircraft.

[0119] The estimator module includes a first estimator unit and a second estimator unit. The estimator module estimates the state of the i-th agent through the output of the neural network module and the disturbance observer module, and then feeds back the estimated state to the neural network module and the disturbance observer module; the first estimator unit is used to estimate the position state of the aircraft, and the second estimator unit is used to estimate the acceleration state of the aircraft;

[0120] The input terminals of the first estimator operation unit are the output terminals of the second comparator unit. The output of the second state-restricted arithmetic unit The output of the first disturbance observer unit is and the agent's acceleration state v i,1r ; Calculated by the following formula:

[0121]

[0122] Among them, c i,1 is the virtual controller proportional coefficient, c i,1 >0; is the position state predictor proportional coefficient, v i,1r is the acceleration state of the ith agent;

[0123] The input terminals of the second estimator operation unit are respectively the output terminals of the fourth comparator unit Output of the fourth state restricted operation unit The output of the second disturbance observer unit and the output u of the fourth nonlinear operation unit i ; Calculated by the following formula:

[0124]

[0125] Among them, c i,2is the controller proportional coefficient, c i,2 >0; is the acceleration state predictor proportional coefficient, u i is the output of the fourth nonlinear operation unit.

[0126] The disturbance observer module includes a first disturbance observer unit and a second disturbance observer unit. The disturbance observer module designs an intermediate variable according to the output of the neural network identification module block and compares it with the output of the predictor module to achieve the effect of observing external disturbances and compensating neural network errors.

[0127] The input of the first disturbance observer unit is the output of the second comparator unit. Position state η i , the output of the second state restricted operation unit and the agent's acceleration state v i,1r ; Calculated by the following formula:

[0128]

[0129] in, The intermediate variable constructed for the disturbance observer, c d,i,1 is the state-constrained proportionality coefficient, c d,i,1 >0;c D,i,1 is the disturbance observer proportional coefficient, c D,i,1 >0;

[0130] The input of the second disturbance observer unit is the output of the fourth comparator unit. Output of the fourth state restricted operation unit and the output u of the fourth nonlinear operation unit i ; Calculated by the following formula:

[0131]

[0132] Among them, c d,i,2 is the state-constrained proportionality coefficient, c d,i,2 >0;c D,i,2 is the disturbance observer proportional coefficient, c D,i,2 >0.

[0133] The state-limited module includes a first state-limited computing unit, a second state-limited computing unit, a third state-limited computing unit, and a fourth state-limited computing unit. The first state-limited computing unit and the second state-limited computing unit respectively limit the estimated error of the aircraft position state and the surface error based on the predictor through the derivative of the obstacle Lyapunov; the third state-limited computing unit and the fourth state-limited computing unit respectively limit the estimated error of the aircraft acceleration state and the surface error based on the predictor through the derivative of the obstacle Lyapunov;

[0134] The input terminal of the first state limiting unit is the output of the first comparator The output of the first state restricted unit is obtained by calculating the derivative of the barrier Lyapunov function Among them, k i,l,1 is the bound on the position surface error based on the estimator, k i,l,1 >0;

[0135] The input terminal of the third state limiting unit is the output of the third comparator The output of the third state restricted unit is obtained by calculating the derivative of the barrier Lyapunov function Among them, k i,l,2 is the bound on the acceleration surface error based on the estimator, k i,l,2 >0.

[0136] The comparator module includes a first comparator unit, a second comparator unit, a third comparator unit and a fourth comparator unit;

[0137] The first comparator unit is the error surface Its input is the first estimator unit and the desired signal y provided by the directed graph d ; Calculated by the following formula:

[0138]

[0139] Among them, a ij and b i are the communication relationships between neighbors and leaders, y r is the leader signal, σ i Represents the cooperative and confrontational relationship between the intelligent agent and the leader;

[0140] The input of the second comparator unit is the output of the first estimator unit. and the agent's position state η i , obtained through the following formula:

[0141]

[0142] The third comparator unit is the error surface Its input is the second estimator unit and the output v of the first filter unit i,1r,d ; Calculated by the following formula:

[0143]

[0144] The input terminal of the fourth comparator unit is the output terminal of the second estimator unit. and the agent's acceleration state v i,1r , obtained through the following formula:

[0145]

[0146] The anti-disturbance controller module includes a second nonlinear operation unit, a first filtering unit and a fourth nonlinear operation unit;

[0147] The input end of the second nonlinear operation unit is the position state η of the jth follower in the directed graph j , Adjacent communication ij and b i , Leader derivative information Formation Information Derivative The output of the first differential tracker is r j,2 , the output of the first state restricted operation unit The output of the first state restricted unit First disturbance observer output unit The output of the second nonlinear operation unit is α i :

[0148]

[0149] Among them, m i,1 is the state-limited proportionality coefficient, m i,1 >0;

[0150] The input of the first tracking differentiator unit is the neighbor information η provided by the directed graph j ; Calculated by the following formula:

[0151]

[0152] Among them, r j,2 Neighbor information η provided for the directed graph j Estimate of the derivative, k TD is the tracking differentiator speed factor; k TD >0;α TD,j ∈(0,1) is the tracking differentiator filter factor;

[0153] The input end of the first filtering unit is the output α of the second nonlinear operation unit. i; Calculated by the following formula:

[0154]

[0155] Among them, χ i is the filter time constant;

[0156] The input end of the fourth nonlinear operation unit is the output end of the third state-limited operation unit. Output of the fourth state restricted unit Second disturbance observer output unit The output of the third comparator unit

[0157] Among them, m i,2 is the state-limited proportionality coefficient, m i,2 >0.

[0158] An input end of the first neural network weight update unit is connected to the output of the second comparator unit and the output of the first neural network activation function unit, and an input end of the first neural network activation function unit is connected to the position information of the underwater vehicle;

[0159] The input end of the first nonlinear operation unit is connected to the output of the first neural network weight update unit and the output of the first neural network activation function unit; the input end of the second state restricted unit is connected to the output of the first neural network weight update unit and the output of the first neural network activation function unit; the input end of the first comparator unit is connected to the first predictor unit and the expected signal provided by the directed graph; the input end of the second comparator unit is connected to the output of the first predictor unit and the position state of the agent; the input end of the first predictor unit is respectively connected to the output of the second comparator unit, the output of the second state restricted operation unit, the output of the first disturbance observer unit and the agent added state. speed state; the input end of the first disturbance observer unit is connected to the output of the second comparator unit, the position state, the output of the second state constrained operation unit and the acceleration state of the agent; the input end of the first state constrained unit is connected to the output of the first estimator unit and the error of the expected signal; the input end of the second nonlinear operation unit is connected to the position state of the follower in the directed graph, the adjacent communication, the leader derivative information, the formation information derivative, the output of the first differential tracker, the output of the first state constrained operation unit, the output of the first state constrained unit, and the first disturbance observer output unit; the input end of the first tracking differentiator unit is connected to the neighbor information provided by the directed graph; The input end of the first filtering unit is connected to the output of the second nonlinear operation unit; the input of the second neural network weight updating unit is respectively connected to the input of the second neural network function activation function unit and the output of the third comparator unit; the input end of the second neural network activation function unit is connected to the acceleration state of the system in all directions; the input end of the third nonlinear operation unit is respectively connected to the output of the second neural network activation function unit, the output of the second neural network weight updating unit and the output of the third comparator unit; the input end of the fourth state restricted operation unit is connected to the output of the third nonlinear operation unit; the third comparator unit is connected to the error surface, and its input end is connected to the output of the second estimator unit and the first filtering unit; the input end of the fourth comparator unit is connected to the output of the second estimator unit and the acceleration state of the agent; the input end of the second estimator unit is respectively connected to the output of the fourth comparator unit, the output of the fourth state restricted operation unit, the output of the second disturbance observer unit and the output of the fourth nonlinear operation unit; the input end of the second disturbance observer unit is connected to the output of the fourth comparator unit, the output of the fourth state restricted operation unit and the output of the fourth nonlinear operation unit; the input end of the third state restricted unit is connected to the output of the third comparator; the input end of the fourth state restricted operation unit is connected to the output of the third nonlinear operation unit.

[0160] In order to verify the effect of the present invention, experimental verification is carried out:

[0161] Model parameter selection for four underwater vehicles: inertia matrix M i =diag{175.4,140.8,140.8} and the damping matrix D i(v i,1r )=diag(120+90|u i,r |,90+90|v i,r |,150+120|w i,r |), the state constraint condition of the i-th underwater vehicle |x i |<15m,|y i |<20m,|z i |<3m, the acceleration limit is 0.62m / s 2 , U i,f is an unknown disturbance. Control parameter selection: Γ i,η =1000,Γ i,r =1000,ζ i,η =0.02, ζ i,r =0.02, k i,p,1 =0.02, k i,p,2 =0.02, c i,1 =10, c i,2 =10, c d,i,1 =5, c d,i,2 =5, k i,l,1 =0.02, k i,l,2 =0.02, m i,1 =0.1, m i,2 =0.1, k TD =10, α TD,j =0.8, χ i =0.02 for all parameters i=1,2,3,4;

[0162] Leader signal r (t) = [x d ,y d ,z d ] T ,x d =3-2cos(0.25t),y d =3+2sin(0.25t), z d =-e -0.2t .

[0163] like Figure 2 As shown, the four underwater vehicles and the leader remain balanced, meeting the control objectives.

[0164] like Figure 3 It can be seen that the estimation error of the underwater vehicle and the surface error based on the predictor are guaranteed to be within a predetermined range.

[0165] like Figure 4 The position signal and acceleration signal of the underwater vehicle shown can be guaranteed to work within a limited range.

[0166] like Figure 5 As shown, it can be found that the first underwater vehicle can still maintain a good approximation effect when the system dynamics changes under the joint action of the neural network based on the estimator and the disturbance observer.

[0167] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A formation controller for multiple underwater vehicles under state constraints, characterized by: The formation controller regards N state-constrained underwater vehicles with unknown dynamics as followers, and a multi-agent network formed by connecting the followers and a leader through a unidirectional topological graph as a controlled object. The leader provides a leadership expectation signal, and uses the follower position information to design the formation controller so that the output of the followers and the leader form a desired formation. The input end of the formation controller is connected to the output end of the directed graph G, and the output end of the formation controller is connected to the input end of the i-th follower; The formation controller includes a neural network identification module, an estimator module, a disturbance observer module, a state-limited module, a comparator module and an anti-disturbance controller module. The neural network identification module calculates the activation function through the state of the i-th underwater vehicle, and updates the neural network weight norm through the estimated error of the estimator module, and then identifies the state of the vehicle through the output of the state-limited module; at the same time, the state estimated by the estimator module is fed back to the neural network identification module and the disturbance observer module; The anti-disturbance controller module realizes the normal operation of multiple underwater vehicles under state constraints and external disturbances according to the characteristics of the neural network identification module, the estimator module, the disturbance observer module and the state constraint module.

2. A formation controller for multiple underwater vehicles under state constraints according to claim 1, characterized in that: There is communication between at least one follower and the leader in the multi-agent network, and the unidirectional topology graph is represented by a directed graph G=(V,E); Where V = {ν1,…,ν N } represents a set of N nodes, ν1,…,ν N represents underwater vehicle follower 1 to underwater vehicle follower N; represents the edge set, (ν i ,ν j ) represents the edge of the topological graph G, ν i ,ν j denote the i-th aircraft and the j-th aircraft respectively; If (ν i ,ν j )∈E then ν j ν i The adjacent nodes of i = {ν j ∈ν(ν j ,ν i )∈E}, where Ω i Indicates ν i The set of adjacent nodes of ; Define the adjacency matrix A = [a ij ]∈R N×N , if (ν i ,ν j )∈E and the i agent and the j agent are in a cooperative relationship, then a ij =1, for competitive relationship a ij =-1; if Then a ij =0; Define the degree matrix D = diag[d1,...,d N ],in Define the Laplace matrix L = DA; Define the adjacency matrix B associated with the leader = diag[b1,…,b N ], if the i-th vehicle can access the leader's information, then b i =1, otherwise b i =0.

3. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The mathematical model of the position of the i-th underwater vehicle in the follower is: Among them, η i represents the position coordinates of the i-th underwater vehicle [x i ,y i ,z i ] T ;v i,1r =[u i,r ,v i,r ,w i,r ] T Respectively represent the acceleration in the x-axis, y-axis, and z-axis directions; u i =[u i,x ,u i,y ,u i,z ] T Respectively represent the forces acting on the x-axis, y-axis, and z-axis directions, M i is the inertia matrix of the ith underwater vehicle, D i is the damping matrix of the ith underwater vehicle, U i,f It is an unknown disturbance.

4. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The neural network identification module includes a first neural network weight update unit, a first neural network activation function unit, a first nonlinear operation unit, a second state-restricted operation unit, and a second neural network weight update unit, a second neural network activation function unit, a second nonlinear operation unit, and a fourth state-restricted operation unit; The inputs of the first neural network weight update unit are the first neural network function activation function unit input and the second comparator unit output, which are calculated by the following formula: Among them, Φ i,x , Φ i,y and Φ i,z They are the activation functions of the x-axis, y-axis, and z-axis of the first neural network activation function unit, and are the estimated errors of the x-axis, y-axis and z-axis of the second comparator unit respectively; Γ i,η is the neural network adaptive gain, Γ i,η >0;ζ i,η is the neural network weight proportional coefficient, ζ i,η >0;k i,p,1 is the bound of the position estimation error, k i,p,1 >0; finally get the output The input end of the first neural network activation function unit is the system position state η i ; Calculated by the following formula: Among them, γ i,χ is the proportional coefficient of the activation function, γ i,χ >0; are the activation functions of the x-axis, y-axis, and z-axis respectively; i ,y i and z i are the states of the x-axis, y-axis, and z-axis, all of which are η i The elements in , μ is the center value of the activation function, ξ is the width of the activation function; finally, the output Φ i,1 =diag[Φ i,x ,Φ i,y ,Φ i,z ]; The input ends of the first nonlinear operation unit are the output Φ of the first neural network activation function unit i,1 , the output of the first neural weight update unit and the output of the second comparator unit All inputs are multiplied to obtain the output of the second nonlinear operation unit. The input of the second state restricted operation unit is the output of the second nonlinear operation unit, which is processed by the derivative of the barrier Lyapunov function as follows: Among them, k i,p,1 is the limit of the position state estimation error, k i,p,1 >0; is the neural network weight norm, is the estimation error, Φ i,1 is the neural network activation function; The inputs of the second neural network weight update unit are respectively the input of the second neural network function activation function unit Φ i,2 and the third comparator unit output It is calculated by the following formula: Among them, Φ i,u , Φ i,v and Φ i,w They are respectively the activation functions of the x-axis acceleration, y-axis acceleration, and z-axis acceleration of the second neural network activation function unit. and The output of the third comparator unit is The estimated errors of x-axis acceleration, y-axis acceleration, and z-axis acceleration; Γ i,r is the neural network adaptive gain, Γ i,r >0;ζ i,r is the neural network weight proportional coefficient, ζ i,r >0;k i,p,2 is the limit of the acceleration state estimation error, k i,p,2 >0; finally get the output The input of the second neural network activation function unit is the acceleration state v in all directions of the system i.1r ; Calculated by the following formula: Among them, γ i,r For, γ i,r >0; The activation functions of x-axis acceleration, y-axis acceleration, and z-axis acceleration, u i,r 、v i,r , and w i,r are the system acceleration states v i.1r The x-axis acceleration, y-axis acceleration, and z-axis acceleration in are: μ is the center value of the activation function, and ξ is the width of the activation function; finally, the output Φ is obtained. i,2 =diag[Φ i,u ,Φ i,v ,Φ i,w ]; The input ends of the third nonlinear operation unit are the output Φ of the second neural network activation function unit. i,2 , the output of the second neural network weight update unit and the output of the third comparator unit All inputs are multiplied to obtain the output of the third nonlinear operation unit. The input end of the fourth state-restricted operation unit is the output end of the third nonlinear operation unit. By taking the derivative of the barrier Lyapunov function, we can treat it as Among them, k i,p,2 is the limit of the acceleration state estimation error, k i,p,2 >0; is the neural network weight norm, is the acceleration state estimation error, Φ i,2 is the activation function of the second neural network.

5. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The estimator module includes a first estimator unit and a second estimator unit, the first estimator unit is used to estimate the position state of the aircraft, and the second estimator unit is used to estimate the acceleration state of the aircraft; The input terminals of the first estimator operation unit are the output terminals of the second comparator unit. The output of the second state-restricted arithmetic unit The output of the first disturbance observer unit is and the agent's acceleration state v i,1r ; It is calculated by the following formula: Among them, c i,1 is the virtual controller proportional coefficient, is the position state predictor proportional coefficient, is the acceleration state of the ith agent; The input terminals of the second estimator operation unit are respectively the output terminals of the fourth comparator unit Output of the fourth state restricted operation unit The output of the second disturbance observer unit and the output u of the fourth nonlinear operation unit i ; Calculated by the following formula: Among them, c i,2 is the controller proportional coefficient, is the acceleration state predictor proportional coefficient, is the output of the fourth nonlinear operation unit.

6. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The disturbance observer module includes a first disturbance observer unit and a second disturbance observer unit. The disturbance observer module designs an intermediate variable according to the output of the neural network identification module block and compares it with the output of the estimator module to achieve the effect of observing external disturbances and compensating neural network errors. The input of the first disturbance observer unit is the output of the second comparator unit. Position state η i , the output of the second state restricted operation unit and the agent's acceleration state v i,1r ; It is calculated by the following formula: in, The intermediate variable constructed for the disturbance observer, c d,i,1 is the state-constrained proportionality coefficient, c d,i,1 >0;c D,i,1 is the disturbance observer proportional coefficient, c D,i,1 >0; The input of the second disturbance observer unit is the output of the fourth comparator unit. Output of the fourth state restricted operation unit and the output u of the fourth nonlinear operation unit i ; Calculated by the following formula: Among them, c d,i,2 is the state-constrained proportionality coefficient, c d,i,2 >0;c D,i,2 is the disturbance observer proportional coefficient, c D,i,2 >0.

7. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The state-limited module has a first state-limited computing unit, a second state-limited computing unit, a third state-limited computing unit, and a fourth state-limited computing unit. The first state-limited computing unit and the second state-limited computing unit respectively limit the estimated error of the position state of the aircraft and the surface error based on the predictor through the derivative of the obstacle Lyapunov; The third state-limited operation unit and the fourth state-limited operation unit respectively limit the estimated error of the acceleration state of the spacecraft and the surface error based on the predictor through the derivative of the obstacle Lyapunov; The input terminal of the first state limiting unit is the output of the first comparator The output of the first state restricted unit is obtained by calculating the derivative of the barrier Lyapunov function Among them, k i,l,1 is the bound on the position surface error based on the estimator, k i,l,1 >0; The input terminal of the third state limiting unit is the output of the third comparator The output of the third state restricted unit is obtained by calculating the derivative of the barrier Lyapunov function Among them, k i,l,2 is the bound on the acceleration surface error based on the estimator, k i,l,2 >0.

8. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The comparator module includes a first comparator unit, a second comparator unit, a third comparator unit and a fourth comparator unit. The first comparator unit is an error surface Its input is the first estimator unit and the desired signal y provided by the directed graph d ; It is calculated by the following formula: Among them, a ij and b i are the communication relationships between neighbors and leaders, y r is the leader signal, σ i Represents the cooperative and confrontational relationship between the intelligent agent and the leader; The input of the second comparator unit is the output of the first estimator unit. and the agent's position state η i , obtained through the following formula: The third comparator unit is the error surface Its input is the second estimator unit and the output v of the first filter unit i,1r,d ; Calculated by the following formula: The input terminal of the fourth comparator unit is the output terminal of the second estimator unit. and the agent's acceleration state v i,1r , obtained through the following formula:

9. The formation controller of multiple underwater vehicles under state constraints according to claim 1, characterized in that: The anti-disturbance controller module includes a second nonlinear operation unit, a first filtering unit and a fourth nonlinear operation unit, wherein the input end of the second nonlinear operation unit is the position state η of the jth follower in the directed graph. j , Adjacent Communicationa ij and b i , Leader derivative information Formation Information Derivative The output of the first differential tracker r j,2 , the output of the first state restricted operation unit The output of the first state restricted unit First disturbance observer output unit The output of the second nonlinear operation unit is α i : Among them, m i,1 is the state-limited proportionality coefficient, m i,1 >0; The input of the first tracking differentiator unit is the neighbor information η provided by the directed graph j ; Calculated by the following formula: Among them, r j,2 Neighbor information η provided for the directed graph j Estimate of the derivative, k TD is the tracking differentiator speed factor; k TD >0;α TD,j ∈(0,1) is the tracking differentiator filter factor; The input end of the first filtering unit is the output α of the second nonlinear operation unit. i ; Calculated by the following formula: Among them, χ i is the filter time constant; The input end of the fourth nonlinear operation unit is the output end of the third state-limited operation unit. Output of the fourth state restricted unit Second disturbance observer output unit The output of the third comparator unit Among them, m i,2 is the state-limited proportionality coefficient, m i,2 >0.

Images