Distributed multi-trolley optimal hunting control method based on switching observer

Abstract

The invention discloses a distributed multi-trolley optimal hunting control method based on a switching observer, and belongs to the technical field of multi-agent cooperative control. The method comprises the following steps: constructing a trolley dynamic system model; according to the denial of service attack state variable, whether the denial of service attack is eliminated is judged; constructing a surrounding object estimator to obtain a surrounding object estimation position of the neighbor trolley; constructing a distributed adaptive optimal estimator to obtain an optimal position local estimation value of the surrounding object; and constructing a trolley controller. According to the invention, through the switching type neighbor information state observer, the advantage of information compensation is provided in a denial of service attack environment; a distributed self-adaptive optimal estimator of a cost function is introduced, so that each trolley can cooperatively track a global optimal solution changing along with time; when the communication fails, each trolley performs open-loop prediction by depending on the historical state and the own model, and continuously estimates the information state of the neighbor trolley, thereby improving the robustness and stability of the multi-trolley hunting system.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control technology, specifically relating to a distributed multi-vehicle optimal encirclement control method based on a switching observer. Background Technology

[0002] Multi-robot encirclement control is a type of multi-agent cooperative control that achieves rapid encirclement and capture of a target area through local observation and distributed decision-making. As a typical swarm of ground mobile robots, multi-robot systems are characterized by flexible deployment, controllable cost, and strong scalability, and have gained widespread attention in scenarios such as park inspection, security duty, hazard isolation, and material interception. Due to the iteration of technologies such as microprocessors, sensors, wireless communication, and distributed optimization, cooperative control methods have placed higher demands on mobility, safety, and real-time performance. Therefore, research on multi-robot encirclement control methods provides a convenient and effective platform for the development of these technological fields, which is of great significance.

[0003] As the demand for collaborative operations in complex environments during multi-vehicle encirclement continues to grow, the requirements for the robustness and security of encirclement control are constantly increasing. In actual target encirclement tasks, complex environments are often encountered: targets or adversaries may launch denial-of-service attacks, causing intermittent communication disruptions between vehicles. The resulting information loss poses a greater challenge to the stability of multi-vehicle systems during encirclement operations. Therefore, establishing distributed observers to compensate for information loss under denial-of-service attacks and maintaining effective encirclement control under conditions of communication unavailability and data loss has significant practical implications and engineering value.

[0004] For increasingly complex and diverse task scenarios, the multi-vehicle encirclement process needs to consider factors such as energy consumption, path length, and task time. Traditional encirclement control methods struggle to balance efficiency, safety, and robustness. Therefore, achieving optimal encirclement path planning and reducing energy costs has significant engineering implications and application value, enabling multiple vehicles to efficiently encircle and capture target objects.

[0005] Therefore, the technical problem that this invention aims to solve is how to effectively observe a dynamically captured target under denial-of-service attack conditions and ultimately achieve the target capture task using the optimal path. Summary of the Invention

[0006] The purpose of this invention is to provide a distributed multi-vehicle optimal encirclement control method based on a switching observer, so as to solve the problems mentioned in the background art.

[0007] The objective of this invention is achieved as follows: a distributed multi-vehicle optimal encirclement control method based on a switching observer, characterized by the following steps:

[0008] Step S1: Construct a dynamic system model of the vehicle to determine its position and real-time status;

[0009] Step S2: Define a denial-of-service attack status variable, and determine whether a denial-of-service attack has occurred based on the denial-of-service attack status variable;

[0010] Define the first observer state switching variable based on the denial-of-service attack state variable;

[0011] Define a second observer state switching variable based on the denial-of-service attack state variable;

[0012] Step S3: Construct a target estimator to obtain the estimated location of the target of the neighboring car, and use the first switching neighbor information state observer to perform online estimation and compensation of the target location of the neighboring car.

[0013] Step S4: Construct a distributed adaptive optimal estimator to obtain the optimal local location estimate of the target, and use the second switching neighbor information state observer to perform online estimation and compensation of the optimal local location estimate;

[0014] Step S5: Construct a vehicle controller to enable multiple vehicles to surround and capture the target object using the optimal path in a denial-of-service attack environment.

[0015] Preferably, the construction of the vehicle dynamic system model in step S1 specifically includes:

[0016] Step S1-1: Determine the position state space equation of the vehicle. The position state space equation of the vehicle is:

[0017] ;

[0018] in, It is the position vector of the car. For the car in the two-dimensional plane, the first... Dimensional motion trajectory , It is the velocity vector of the car. It is the first time the car moves in a two-dimensional plane. Dimensional motion speed, , It is a car controller. It is an unknown nonlinear function. It is a group of small cars, among which, It is the number of cars;

[0019] Step S1-2: Define the movement trajectory of the target to be captured;

[0020] The location of the target to be surrounded is defined as: ;

[0021] in, For the target to be captured in a two-dimensional plane, the first Dimensional motion trajectory For the target in the two-dimensional plane, the first Dimensional motion trajectory;

[0022] Step S1-3: Define the communication network between the vehicle and the workshop, and between the vehicle and the target to be captured.

[0023] Preferably, the communication network defined in steps S1-3 between the vehicle and the workshop, and between the vehicle and the target to be captured, specifically includes:

[0024] Group of cars The communication network, consisting of an undirected topological graph connecting each individual and a target, ensures that at least one vehicle can communicate with the target to obtain its location. ;

[0025] Communication in a communication network is based on undirected graphs It means that among them express A set of nodes, This indicates the distance from the first car to the second car. A small car, Representing a topology graph edge set in Representing a topology graph The edge, , They represent the first The car and the first A small car;

[0026] definition ,in, for The adjacent nodes, For the first A group of neighbors of a small car;

[0027] Define adjacency matrix , Let the neighbor adjacency coefficient be the factor that satisfies the condition. Under the conditions ,otherwise ;

[0028] Define degree matrix ,in, For the first The weighted in-degree coefficient of each car;

[0029] Define the adjacency matrix between the vehicle and the target being captured. ,in, For the first The weighted coefficients of the target objects of each car, when the first... When a small vehicle can communicate with the target being apprehended, ,otherwise .

[0030] Preferably, in step S2, a denial-of-service attack state variable is defined, specifically as follows:

[0031] Define the first observer state switching variable Specifically:

[0032] ;

[0033] when At that time, the first switchable neighbor information state observer operates in the state it would have been in if it had not suffered a denial-of-service attack; when At that time, the first switchable neighbor information state observer operates in the state under a denial-of-service attack;

[0034] Define the second observer state switching variable Specifically:

[0035] ;

[0036] when At that time, the second switchable neighbor information state observer operates in the state it would be in if it were not under a denial-of-service attack; when At that time, the second switchable neighbor information state observer operates in the state under a denial-of-service attack.

[0037] Preferably, in step S3, the object estimator is constructed to obtain the estimated location of the object to be captured by the neighboring vehicles, and the first switching neighbor information state observer is used to perform online estimation and compensation of the location of the object to be captured by the neighboring vehicles, specifically as follows:

[0038] Step S3-1: Construct the target estimator;

[0039] The target estimator:

[0040] ;

[0041] in, Indicates the current moment. Indicates the previous moment, , It is the time step, which satisfies ; For the first The estimated location of the target in the encirclement of the small car. for The estimated location of the target to be captured corresponds to the dimension. for The estimated location of the target to be captured corresponds to the dimension. It is the transpose matrix; For the first Intermediate state of the target estimator for a small vehicle; Define the observation status of the neighboring target. In the formula Indicates the initial moment of the encirclement and capture process; The location of the target to be apprehended; For the first The weighted in-degree coefficient of each car. For the first Weighting coefficients for the target objects of each small car; The neighbor adjacency coefficient is; the first estimated gain is... The second estimated gain is And satisfy , , ; It is a collection of small cars; For the first A group of neighbors of a small car;

[0042] The target estimator calculates the difference between its own estimated target position at the previous moment and the observed state of its neighboring targets. The estimated location of the target is adjusted to its actual location using the difference.

[0043] Step S3-2: Construct the first switchable neighbor information state observer.

[0044] Preferably, in step S3-2, constructing the first switching neighbor information state observer specifically involves:

[0045] Based on the target estimator constructed by the neighbors, construct the first switching neighbor information state observer:

[0046] ;

[0047] in, The observed state of the neighboring target is used to estimate the estimated location of the target established by the neighbor in its local area. ;in For the first The estimated location of the target to be captured corresponds to the dimension. ; The correction gain for the first observer satisfies ; The relative error of the neighboring targets is estimated to compensate for the estimation. The estimation error satisfies ; Observe the status of the target being surrounded by neighbors; ,and For the first A group of neighbors of a small car;

[0048] The first switchable neighbor information state observer obtains the estimate through the first radial basis neural network. , used to estimate The rate of change;

[0049] The first radial basis function neural network includes a first input layer, a first hidden layer, a first weight estimation unit, and a first output layer. The input of the first input layer is a co-input vector. , For a local cooperative input vector, satisfying:

[0050] ;

[0051] in, ;

[0052] The first hidden layer utilizes the Gaussian function. The collaborative input vector is nonlinearly mapped to a high-dimensional feature space, and the center parameter of the activation function is dynamically switched by monitoring the network attack status. and To adapt to changes in the input signal structure, an adaptive basis function response matrix is ​​provided for the changing trends of the approximating neighbor states;

[0053] The update rule for the first hidden layer is:

[0054] ;

[0055] in, For activation function, As the first center of the activation function, As the second center of the activation function, It is the width of the activation function. It is the number of nodes; The response matrix is ​​the basis function. A vector of value functions; , ;

[0056] The first weight estimation unit is used to update the value function vector of the first radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as:

[0057] ;

[0058] in, Update the gain for the weights and satisfy the following conditions: ; The leakage coefficient is and satisfies The output of the first radial basis function neural network output layer is the estimator. , is represented as:

[0059] ;

[0060] The first weight estimation unit switches variables according to the state of the first observer. The state determines the update strategy for the weights of the first radial basis function neural network: under normal network communication conditions, this unit uses neighboring objects to estimate the relative error. With basis function response matrix The product and combination Leakage coefficient weighted by historical estimates from the previous moment For estimated weights Adaptive adjustments are made; however, when communication is disrupted due to a denial-of-service attack, only the historical estimated weights from the previous time step are used. The resulting damping effect updates the weights to prevent weight divergence and parameter drift caused by a lack of effective error signals or unreliable signals.

[0061] Preferably, in step S4, a distributed adaptive optimal estimator is constructed to obtain the optimal local position estimate of the target object, and the optimal local position estimate is estimated and compensated online using a second switched neighbor information state observer, specifically as follows:

[0062] Step S4-1: Construct a distributed adaptive optimal estimator, specifically as follows:

[0063] The distributed adaptive optimal estimator comprises an adaptive optimization unit, a relative difference weight unit, and a robust correction weight unit, as expressed below:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] in, This represents a distributed adaptive optimal estimation state. For relative difference weights, To robustly adjust the weights, For adaptive compensation parameters; Let cost function be ;

[0069] in, For the first The estimated location of the targets in the encirclement of the vehicles, among which... For the first The estimated location of the target to be captured corresponds to the dimension. ; It is a relative wrapping vector; The neighbor adaptive optimal estimated state;

[0070] For smoothing functions, ,Depend on composition;

[0071] in, satisfy ; For performance weight parameters, satisfying ; To smooth the canonical gain, satisfying ; For exponential decay rate, satisfying ; For coupling gain, satisfying ; express Norm; It is a collection of small cars; For the first A group of neighbors of a small car; and The initial value satisfies , ;

[0072] The distributed adaptive optimal estimator calculates the gradient direction that minimizes the encirclement formation cost function and adaptively compensates for the parameters. Using gradient terms The driving force generated by the feedforward and feedback terms propels the estimated value toward a locally optimal position that satisfies the preset orbital formation requirements; combined with its own and its neighbors' estimated states, i.e. and The relative deviation between them is determined by adaptively and dynamically adjusting the relative difference weights. With robust weight correction Co-correction is applied to the evolutionary process to eliminate estimation biases between individuals;

[0073] Step S4-2: Construct the second switchable neighbor information state observer.

[0074] Preferably, in step S4-2, constructing the second switchable neighbor information state observer specifically involves:

[0075] Based on the distributed adaptive optimal estimator constructed by the neighbors, a second switching neighbor information state observer is constructed.

[0076] The second switchable neighbor information state observer is:

[0077] ;

[0078] in, Indicates the current moment. Indicates the previous moment, , It is the time step, which satisfies ; The neighbor adaptive optimal estimated state; The correction gain for the second observer satisfies ; The relative error of the best neighbor estimate is used to compensate for the estimator. The estimation error satisfies ; The distributed adaptive optimal estimation state is designed locally for the neighbors, where... For the first The distributed adaptive optimal estimation state corresponding to dimension. ;

[0079] The second switched neighbor information state observer obtains the estimate through a second radial basis neural network. Used to estimate The rate of change of the second radial basis neural network includes a second input layer, a second hidden layer, a second weight estimation unit, and a second output layer;

[0080] The input to the second input layer is the adaptive collaborative estimation vector. , For a locally adaptive collaborative estimation vector, satisfying:

[0081] ;

[0082] The update rule for the second hidden layer is:

[0083] ;

[0084] in, For activation function, As the first center of the activation function, As the second center of the activation function, It is the width of the activation function. It is the number of nodes; For value function vectors, The response matrix is ​​the basis function. , ;

[0085] The second hidden layer of the second radial basis function neural network utilizes the Gaussian function. The collaborative input vector is nonlinearly mapped to a high-dimensional feature space, and the center parameter of the activation function is dynamically switched by monitoring the network attack status. and To adapt to changes in the input signal structure, thereby providing an adaptive basis function response matrix for accurately approximating the changing trends of neighboring states;

[0086] The second weight estimation unit is used to update the value function vector of the second radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as:

[0087] ;

[0088] in, Update the gain for the weights, satisfying ; Let be the leakage coefficient, satisfying... ,

[0089] The output of the second output layer is the estimate. , represented as:

[0090] ;

[0091] The second weight estimation unit switches variables based on the state of the second observer. The state determines the update strategy for the weights of the second radial basis function neural network: under normal network communication conditions, this unit utilizes the relative error estimated by the best neighbor estimate. With basis function response matrix The product of the two factors and the historical estimated weights from the previous time step. For estimated weights Adaptive adjustments are made; however, when communication is disrupted due to a denial-of-service attack, only the historical estimated weights from the previous time step are used. The resulting damping effect updates the weights to prevent weight divergence and parameter drift caused by a lack of effective error signals or unreliable signals.

[0092] Preferably, the construction of the vehicle controller in step S5 specifically involves:

[0093] Step S5-1: Construct a virtual control law and a first-order filter to eliminate the computational complexity explosion caused by repeated differentiation of the virtual control law in the car controller. The virtual control law and the first-order filter are as follows:

[0094] ;

[0095] in, This represents a distributed adaptive optimal estimation state. The first-order error suppression coefficient satisfies the following conditions: ; It is a virtual control law. Let be the filter coefficients, satisfying , It is a filtering state that satisfies The first estimation error is ,satisfy ,in It is the position vector of the car; It is a collection of small cars;

[0096] Step S5-2: Construct the car controller.

[0097] Preferably, the vehicle controller is:

[0098] ;

[0099] in, It is the first A small car controller; It is the second-order error suppression coefficient, and satisfies... Define the second estimation error. ,in, It is a velocity vector. It is in the filtering state; It is a collection of small cars; The output value of the 3rd output layer of the radial basis function neural network is expressed as:

[0100] ;

[0101] in, This is the feature vector of the motion state. , , and The first The car in the first The corresponding motion trajectory and speed in each dimension ;

[0102] The basis function response matrix is ​​the output of the hidden layer of the third radial basis neural network. , For the value function vector of the third radial basis neural network,

[0103] For the third radial basis function neural network, , ; It is the width of the activation function of the third radial basis neural network; It is the center of the activation function of the third radial basis function neural network. It is the number of hidden layer nodes in the third radial basis function neural network; The update law for estimating the weights of the third radial basis function neural network is expressed as:

[0104] ;

[0105] in, Update the gain for the weights of the third radial basis function neural network. ; Let be the leakage coefficient of the third radial basis neural network, satisfying .

[0106] Compared with the prior art, the present invention has the following improvements and advantages:

[0107] 1. By designing two switching neighbor information state observers, the system provides the advantage of information compensation in the denial-of-service attack environment. By introducing the observer mechanism and combining it with the approximation performance of the radial basis neural network, when communication fails, each vehicle can make open-loop predictions based on its historical state and its own model, and continuously estimate the information state of neighboring vehicles, thereby improving the robustness and stability of the multi-vehicle capture system.

[0108] 2. By introducing a distributed adaptive optimal estimator designed with a cost function, each vehicle in the system can collaboratively track a global optimal solution that changes over time, improving the vehicle's efficient capture and accurate tracking of the target object; and assisting the vehicle in achieving adaptive path optimization during the capture process. Attached Figure Description

[0109] Figure 1 This is an overall flowchart of the method of the present invention.

[0110] Figure 2 This is a communication topology diagram between the capture vehicle and the target.

[0111] Figure 3 This is a schematic diagram of the two-dimensional planar motion trajectory of the vehicle at time t=0.0s during the encirclement process.

[0112] Figure 4This is a schematic diagram of the two-dimensional planar motion trajectory of the vehicle at time t=2.0s during the encirclement process.

[0113] Figure 5 This is a schematic diagram of the two-dimensional planar motion trajectory of the vehicle at time t=4.0s during the encirclement process.

[0114] Figure 6 This is a schematic diagram of the two-dimensional planar motion trajectory of the vehicle at time t=6.0s during the encirclement process.

[0115] Figure 7 This is a schematic diagram showing the curves of the position of the capture vehicle and the position of the target on the X-axis of a two-dimensional plane as a function of time.

[0116] Figure 8 This is a schematic diagram showing the curves of the position of the capture vehicle and the position of the target on the Y-axis in a two-dimensional plane as a function of time.

[0117] Figure 9 This is a schematic diagram showing the curve of the X-axis changing over time in a two-dimensional plane, representing the estimation of the target's location by the capture vehicle.

[0118] Figure 10 This is a schematic diagram showing the curve of the Y-axis changing over time in a two-dimensional plane, representing the estimation of the target's location by the capture vehicle.

[0119] Figure 11 This is a schematic diagram showing the curves of the distributed adaptive optimal estimation state and the position of the target being captured on the X-axis of a two-dimensional plane as a function of time.

[0120] Figure 12 This is a schematic diagram showing the curves of the distributed adaptive optimal estimation state and the position of the target being captured, corresponding to the Y-axis in a two-dimensional plane, as a function of time. Detailed Implementation

[0121] The invention will be further summarized below with reference to the accompanying drawings.

[0122] like Figure 1 As shown, a distributed multi-vehicle optimal encirclement control method based on a switching observer is proposed, which includes the following steps:

[0123] Step S1: Construct a dynamic system model of the vehicle to determine its position and real-time status;

[0124] Step S1-1: Determine the position state space equation of the vehicle. The position state space equation of the vehicle is:

[0125] ;

[0126] in, It is the position vector of the car. For the car in the two-dimensional plane, the first... Dimensional motion trajectory , It is the velocity vector of the car. It is the first time the car moves in a two-dimensional plane. Dimensional motion speed, , It is a car controller. It is an unknown nonlinear function. It is a group of small cars, among which, It is the number of cars;

[0127] Step S1-2: Define the movement trajectory of the target to be captured;

[0128] The location of the target to be surrounded is defined as: ;

[0129] in, For the target to be captured in a two-dimensional plane, the first Dimensional motion trajectory For the target in the two-dimensional plane, the first Dimensional motion trajectory;

[0130] Step S1-3: Define the communication network between the vehicle and the workshop, and between the vehicle and the target being captured. Step S1-1: Determine the position-state space equation of the vehicle. The position-state space equation of the vehicle is:

[0131] ;

[0132] in, It is the position vector of the car. For the car in the two-dimensional plane, the first... Dimensional motion trajectory , It is the velocity vector of the car. It is the first time the car moves in a two-dimensional plane. Dimensional motion speed, , It is a car controller. It is an unknown nonlinear function. It is a group of small cars, among which, It is the number of cars;

[0133] Step S1-2: Define the movement trajectory of the target to be captured;

[0134] The location of the target to be surrounded is defined as: ;

[0135] in, For the target to be captured in a two-dimensional plane, the first Dimensional motion trajectory For the target in the two-dimensional plane, the first Dimensional motion trajectory;

[0136] Step S1-3: Define the communication network between the vehicle and the workshop, and between the vehicle and the target to be captured.

[0137] Step S2: Define a denial-of-service attack status variable, and determine whether a denial-of-service attack has occurred based on the denial-of-service attack status variable. Specifically:

[0138] Define the first observer state switching variable and the second observer state switching variable based on the denial-of-service attack state variable;

[0139] Define denial-of-service attack state variables Denial-of-service attack state variables represent the first... Did the car suffer a denial-of-service attack? ;when When, it indicates the first The car was not subjected to a denial-of-service attack and was able to communicate normally with its neighbors; when When, it indicates the first A car is under denial-of-service attack, causing its communication with its neighbors to be interrupted or fail.

[0140] Define the first observer state switching variable Specifically:

[0141] ;

[0142] when At that time, the first switchable neighbor information state observer operates in the state it would have been in if it had not suffered a denial-of-service attack; when At that time, the first switchable neighbor information state observer operates in the state under a denial-of-service attack;

[0143] Define the second observer state switching variable Specifically:

[0144] ;

[0145] when At that time, the second switchable neighbor information state observer operates in the state it would be in if it were not under a denial-of-service attack; when At that time, the second switchable neighbor information state observer operates in the state under a denial-of-service attack.

[0146] Step S3: Construct a target estimator to obtain the estimated location of the target from neighboring vehicles, and use the first switching neighbor information state observer to perform online estimation and compensation of the target location from neighboring vehicles, specifically:

[0147] Encirclement target estimator:

[0148] ;

[0149] in, Indicates the current moment. Indicates the previous moment, , It is the time step, which satisfies ; For the first The estimated location of the target being apprehended in the small car; For the first Intermediate state of the target estimator for a small vehicle; Define the observation status of the neighboring target. In the formula Indicates the initial moment of the encirclement and capture process; The location of the target to be apprehended; For the first The weighted in-degree coefficient of each car. For the first Weighting coefficients for the target objects of each small car; The neighbor adjacency coefficient is; the first estimated gain is... The second estimated gain is And satisfy , , ; It is a collection of small cars; For the first A group of neighbors of a small car;

[0150] The target estimator calculates the difference between its own estimated position at the previous time step and the observed state of its neighboring targets. The estimated location of the target is adjusted to its actual location using the difference; simultaneously, a buffer term is introduced. This suppresses the shaking caused by excessively rapid adjustments, thereby ensuring that all vehicles can observe the status of neighboring targets even when the target cannot be directly seen. It can smoothly and accurately update the estimated location of the target.

[0151] Construct the first switchable neighbor information state observer, specifically as follows:

[0152] Based on the target estimator constructed by the neighbors, construct the first switching neighbor information state observer:

[0153] ;

[0154] in, The observed state of the neighboring target is used to estimate the estimated location of the target established by the neighbor in its local area. ;in For the first The estimated location of the target to be captured corresponds to the dimension. ; The correction gain for the first observer satisfies ; The relative error of the neighboring targets is estimated to compensate for the estimation. The estimation error satisfies ; Observe the status of the target being surrounded by neighbors; ,and For the first A group of neighbors of a small car;

[0155] The first switchable neighbor information state observer obtains the estimate through the first radial basis neural network. , used to estimate The rate of change;

[0156] The first radial basis function neural network includes a first input layer, a first hidden layer, a first weight estimation unit, and a first output layer. The input of the first input layer is a co-input vector. , For a local cooperative input vector, satisfying:

[0157] ;

[0158] in, ;

[0159] The first hidden layer utilizes the Gaussian function. The collaborative input vector is nonlinearly mapped to a high-dimensional feature space, and the center parameter of the activation function is dynamically switched by monitoring the network attack status. and To adapt to changes in the input signal structure, an adaptive basis function response matrix is ​​provided for the changing trends of the approximating neighbor states;

[0160] The update rule for the first hidden layer is:

[0161] ;

[0162] in, For activation function, As the first center of the activation function, As the second center of the activation function, It is the width of the activation function. It is the number of nodes; The response matrix is ​​the basis function. A vector of value functions; , ;

[0163] The first weight estimation unit is used to update the value function vector of the first radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as:

[0164] ;

[0165] in, Update the gain for the weights and satisfy the following conditions: ; The leakage coefficient is and satisfies The output of the first radial basis function neural network output layer is the estimator. , represented as:

[0166] ;

[0167] The first weight estimation unit switches variables according to the state of the first observer. The state determines the update strategy for the weights of the first radial basis function neural network: under normal network communication conditions, this unit uses neighboring objects to estimate the relative error. With basis function response matrix The product and combination Leakage coefficient weighted by historical estimates from the previous moment For estimated weights Adaptive adjustments are made; however, when communication is disrupted due to a denial-of-service attack, only the historical estimated weights from the previous time step are used. The resulting damping effect updates the weights to prevent weight divergence and parameter drift caused by a lack of effective error signals or unreliable signals, thereby ensuring the boundedness of neural network parameters and the robust stability of the system during attacks.

[0168] The constructed first switchable neighbor information state observer uses the first observer state switching variable. The value of the value determines whether the vehicle is under network attack, and it flexibly switches between two estimation modes: when communication is normal, the observer uses the trend predicted by the first radial basis function neural network and outputs its output layer. The difference between the estimated location of the neighboring target and its own observed state of the neighboring target is calculated by combining the received information. It performs real-time corrections; and when an attack causes communication interruption, it breaks free from dependence on external signals and instead utilizes the output of the first radial basis function neural network at this time. It extrapolates and compensates for the observed state at the previous moment, thereby ensuring that even when the latest data of the neighbors cannot be obtained, it can maintain an effective estimate of the neighbor's state continuously and stably by relying on its own calculation ability.

[0169] Step S4: Construct a distributed adaptive optimal estimator to obtain the optimal local position estimate of the target, and use the second switching neighbor information state observer to perform online estimation and compensation of the optimal local position estimate, specifically:

[0170] Constructing a distributed adaptive optimal estimator, specifically:

[0171] The distributed adaptive optimal estimator comprises an adaptive optimization unit, a relative difference weight unit, and a robust correction weight unit, as expressed below:

[0172] ;

[0173] ;

[0174] ;

[0175] ;

[0176] in, This represents a distributed adaptive optimal estimation state. For relative difference weights, To robustly adjust the weights, For adaptive compensation parameters; Let cost function be ;

[0177] in, For the first The estimated location of the targets in the encirclement of the vehicles, among which... For the first The estimated location of the target to be captured corresponds to the dimension. ; It is a relative wrapping vector; The neighbor adaptive optimal estimated state;

[0178] For smoothing functions, ,Depend on composition;

[0179] in, satisfy ; For performance weight parameters, satisfying ; To smooth the canonical gain, satisfying ; For exponential decay rate, satisfying ; For coupling gain, satisfying ; express Norm; It is a collection of small cars; For the first A group of neighbors of a small car; and The initial value satisfies , ;

[0180] The distributed adaptive optimal estimator calculates the gradient direction that minimizes the cost function of the encirclement formation and adaptively compensates for the parameters. Using gradient terms The driving force generated by the feedforward and feedback terms propels the estimated value toward a locally optimal position that satisfies the preset orbital formation requirements; combined with its own and its neighbors' estimated states, i.e. and The relative deviation between them is determined by adaptively and dynamically adjusting the relative difference weights. With robust weight correction The evolution process is collaboratively corrected to eliminate estimation biases between individuals, thereby ensuring that in a distributed network environment, each vehicle can collaboratively obtain a local estimate of the optimal location of the target that satisfies both the optimal capture path constraint and maintains global consistency.

[0181] Construct a second switchable neighbor information state observer, specifically as follows:

[0182] Based on the distributed adaptive optimal estimator constructed by the neighbors, a second switching neighbor information state observer is constructed.

[0183] The second switchable neighbor information state observer is:

[0184] ;

[0185] in, The neighbor adaptive optimal estimated state; The correction gain for the second observer satisfies ; The relative error of the best neighbor estimate is used to compensate for the estimator. The estimation error satisfies ; The distributed adaptive optimal estimation state is designed locally for the neighbors, where... For the first The distributed adaptive optimal estimation state corresponding to dimension. ;

[0186] The second switched neighbor information state observer obtains the estimate through the second radial basis neural network. , used to estimate The rate of change, the second radial basis neural network includes a second input layer, a second hidden layer, a second weight estimation unit and a second output layer;

[0187] The input to the second input layer is the adaptive co-estimation vector. , For a locally adaptive collaborative estimation vector, satisfying:

[0188] ;

[0189] The update rule for the second hidden layer is:

[0190] ;

[0191] in, For activation function, As the first center of the activation function, As the second center of the activation function, It is the width of the activation function. It is the number of nodes; For value function vectors, The response matrix is ​​the basis function. , ;

[0192] The second hidden layer of the second radial basis function neural network utilizes the Gaussian function. The collaborative input vector is nonlinearly mapped to a high-dimensional feature space, and the center parameter of the activation function is dynamically switched by monitoring the network attack status. and To adapt to changes in the input signal structure, thereby providing an adaptive basis function response matrix for accurately approximating the changing trends of neighboring states;

[0193] The second weight estimation unit is used to update the value function vector of the second radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as:

[0194] ;

[0195] in, Update the gain for the weights, satisfying ; Let be the leakage coefficient, satisfying... ,

[0196] The output of the second output layer is the estimate. , represented as:

[0197] ;

[0198] The second weight estimation unit switches variables based on the state of the second observer. The state determines the update strategy for the weights of the second radial basis function neural network: under normal network communication conditions, this unit utilizes the relative error estimated by the best neighbor estimate. With basis function response matrix The product of the two factors and the historical estimated weights from the previous time step. For estimated weights Adaptive adjustments are made; however, when communication is disrupted due to a denial-of-service attack, only the historical estimated weights from the previous time step are used. The resulting damping effect updates the weights to prevent weight divergence and parameter drift due to a lack of effective error signals or unreliable signals; thereby ensuring the boundedness of neural network parameters and the robust stability of the system during attacks.

[0199] The constructed second-switchable neighbor information state observer uses the second observer state switching variable. The value of the value determines whether the car is under network attack, and it flexibly switches between two estimation modes: when communication is normal, the observer uses the trend predicted by the second radial basis neural network and outputs its output layer. Combining the difference between the received adaptive optimal estimated state of the neighbor and the observed state of itself It performs real-time corrections; and when an attack causes communication interruption, it breaks free from dependence on external signals and instead utilizes the output of the second radial basis function neural network at this time. It extrapolates and compensates for the estimated state from the previous moment, thereby ensuring that even when the latest data of the neighbors cannot be obtained, it can continuously and smoothly maintain an effective estimate of the optimal estimated state of the neighbors by virtue of its own calculation ability.

[0200] Step S5: Construct a vehicle controller to enable multiple vehicles to optimally surround and capture the target object under a denial-of-service attack environment. Specifically:

[0201] The virtual control law and the first-order filter are:

[0202] ;

[0203] in, This represents a distributed adaptive optimal estimation state. The first-order error suppression coefficient satisfies the following conditions: ; It is a virtual control law. Let be the filter coefficients, satisfying , It is a filtering state that satisfies The first estimation error is ,satisfy ,in It is the position vector of the car; It is a collection of small cars;

[0204] The virtual control law and first-order filter first calculate the tracking error between the actual position and the optimal estimated position of the vehicle. The system generates virtual control commands based on the changing trends of the optimal estimated state to drive the vehicle to quickly approach the optimal path; subsequently, this virtual control law is applied... Input first-order filter The system performs dynamic smoothing to obtain a continuously differentiable filtered state. By introducing a filtering stage, this mechanism effectively avoids the "computational complexity explosion" problem caused by repeatedly differentiating the virtual control law in the traditional backstepping method design, thus providing a smooth, stable and easy-to-implement reference signal for the subsequent vehicle speed controller.

[0205] The car controller is:

[0206] ;

[0207] in, It is the first A small car controller; It is the second-order error suppression coefficient, and satisfies... Define the second estimation error. ,in, It is a velocity vector. It is in the filtering state; It is a collection of small cars;

[0208] The vehicle controller obtains the state estimate of the nonlinear function through a third radial basis neural network. Used to estimate unknown nonlinear functions ;

[0209] The third radial basis function neural network includes a third input layer, a third hidden layer, a third weight estimation unit, and a third output layer. The input of the third input layer is the state input vector. , Let the local state input vector satisfy:

[0210] ;

[0211] in, ;

[0212] The update rule for the third hidden layer is as follows:

[0213] ;

[0214] The third hidden layer utilizes the Gaussian function. Mapping the state input vector to a high-dimensional feature space allows for accurate approximation of unknown nonlinear functions. The changing trend provides an adaptive basis function response matrix;

[0215] in, For activation function, As the center of the activation function, It is the width of the activation function. It is the number of nodes; The response matrix is ​​the basis function. A vector of value functions; , ;

[0216] The third weight estimation unit is used to update the value function vector of the third radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as:

[0217] ;

[0218] in, Update the gain for the weights of the third radial basis function neural network. ; Let be the leakage coefficient of the third radial basis neural network, satisfying The output of the first radial basis function neural network output layer is the state estimate of the nonlinear function. , represented as:

[0219] ;

[0220] The third weight estimation unit determines the update strategy for the weights of the third radial basis function neural network; this unit utilizes the second estimation error. With basis function response matrix The product of these factors and the weights estimated at the previous time step. Weights of the third radial basis function neural network Adjustments are made to accurately approximate the unknown nonlinear function. The changing trend provides continuously updated radial basis neural network weights.

[0221] Intermediate state of the target estimator rate of change The input is the estimated location of the target at the previous time step. The observation status of the neighboring targets in the previous moment. The location of the target at the previous moment. (If the first (When the small vehicle can communicate with the target being hunted) and the intermediate state of the target estimator at the previous moment. Estimated location of the target to be apprehended The input is the intermediate state of the target estimator. rate of change Intermediate state of the target estimator at the previous moment Estimated location of the target from the previous moment. ;

[0222] Relative error in the estimation of targets in neighboring areas The input is the estimated location of the target established by the neighbors in their local area. Observation status of the neighboring target at the previous moment When not under denial-of-service attack, the observation status of the neighboring target. The input is the estimator Relative error in estimating neighboring targets Observation status of the neighboring target at the previous moment ; estimate The input is the basis function response matrix. and estimated weights Estimating weights The input is the basis function response matrix. Relative error in estimating neighboring targets Weights estimated at the previous time step When subjected to a denial-of-service attack, the neighboring target's observation status. The input is the estimator Observation status of the neighboring target at the previous moment ; estimate The input is the basis function response matrix. and estimated weights Estimating weights The input is the weights estimated at the previous time step. ;

[0223] Distributed adaptive optimal estimation state The input is the relative difference weight. Robust weight adjustment The distributed adaptive optimal estimation state at the previous time step Neighbor adaptive optimal estimation state Adaptive compensation parameters The distributed adaptive optimal estimation state at the previous time step Relative difference weights The input is the adaptive optimal estimated state from the previous time step. Neighbor adaptive optimal estimation state relative difference weights compared to the previous time step Robust weight adjustment The input is the adaptive optimal estimated state from the previous time step. Neighbor adaptive optimal estimation state Robust adjustment weights from the previous time step ;

[0224] Neighbor's best estimation relative error The input is the distributed adaptive optimal estimation state designed locally by the neighbors. Adaptive optimal estimation state of neighbors at the previous time step When not under a denial-of-service attack, the neighbor adaptive optimal estimation state The input is the estimator Relative error of the best neighbor estimate Adaptive optimal estimation state of neighbors at the previous time step ; estimate The input is the basis function response matrix. and estimated weights Estimating weights The input is the basis function response matrix. Relative error of the best neighbor estimate Weights estimated at the previous time step When subjected to a denial-of-service attack, the neighbor adaptive optimal estimation state The input is the estimator Adaptive optimal estimation state of neighbors at the previous time step ; estimate The input is the basis function response matrix. and estimated weights Estimating weights The input is the weights estimated at the previous time step. ;

[0225] First estimation error The input is the car's position vector. and distributed adaptive optimal estimation state Virtual control law The input is the first estimation error. and distributed adaptive optimal estimation state rate of change ; Filtering status The input is a virtual control law ;

[0226] Second estimation error The input is the vehicle's velocity vector. and filter state ;No. A small car controller The input is the second estimation error. Nonlinear function state estimate and filter state rate of change Nonlinear function state estimate The input is the basis function response matrix. and estimated weights Estimating weights The input is the basis function response matrix. Second estimation error Estimated weights from the previous time step .

[0227] The vehicle controller calculates the speed tracking error between the vehicle's actual speed and the filtered desired speed, and uses an error suppression coefficient to apply negative feedback to adjust this error and eliminate the deviation; simultaneously, it utilizes the estimated output value of a third radial basis function neural network. Online cancellation and active compensation are performed on the unknown nonlinear functions in the vehicle dynamics model, and the derivative term of the filtered state is introduced. As a feedforward control component, it is used to synthesize the final control input, ensuring that the vehicle can accurately, quickly, and stably track the planned optimal capture speed in an environment with model uncertainty.

[0228] To verify the effectiveness and feasibility of the method of the present invention, simulation was conducted under a simulation model of a multi-vehicle encirclement system; the simulation model includes 4 encirclement vehicles and 1 moving object to be encircled, the first... The nonlinear term of each capture vehicle is set as follows: . No. The encirclement vectors of the encirclement vehicles are set as follows: ,in For the first The encirclement phase and encirclement radius of the encirclement vehicle. (m).

[0229] Set the communication topology of the initial encirclement system as follows: Figure 2As shown, the denial-of-service attack occurred on the capture vehicle, affecting communication between the vehicle and its neighbors, preventing normal communication. The denial-of-service attack was set up as follows: the first vehicle was in... The internal system suffered a denial-of-service attack; the second car was in the... The third car suffered a denial-of-service attack. The first car suffered a denial-of-service attack; the fourth car was not affected. The aforementioned denial-of-service attack only affected the communication link of the car being pursued when it was communicating with its neighbors; at other times, the communication link remained normal.

[0230] The planar trajectory of the target is modeled using a multi-harmonic sinusoidal superposition model, and its time-varying characteristic is defined as follows:

[0231] ;

[0232] Take the harmonic number The fundamental harmonic amplitude is ,

[0233] , , , , The harmonic amplitude attenuation factor is , , The harmonic angular frequency is , , , , , The initial phase of the harmonic is , , , , , ;

[0234] In the vehicle encirclement control method model, the parameters are selected as follows: Parameter selection for the neighbor information state observer module:

[0235] , , , , , ,

[0236] , Parameter selection for the target estimator: Parameter selection for distributed adaptive optimal estimator Parameter selection for the car controller: Additionally, the initial positions of the four capture vehicles are set as follows: .

[0237] like Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown, under the aforementioned vehicle encirclement control method, the encirclement vehicle is in its initial position, chasing the target, circling the target, and achieving and maintaining encirclement at 0.0, 2.0, 4.0, and 6.0 seconds, respectively. The bright blue line represents the trajectory of the encirclement vehicle's center of gravity, while the position of the target changes under a set sinusoidal harmonic function. The magenta line represents the trajectory of the target. During the chase, the vehicle can approach the target using an optimized trajectory via a local distributed adaptive optimal estimator. During the approach, the vehicle successfully surrounds the target based on the pre-set encirclement phase and radius.

[0238] like Figure 7 , Figure 8 As shown, the trapping vehicle rapidly and smoothly approaches the target from a distance, demonstrating the balance between efficiency and safety in the trapping control method during task execution. During a denial-of-service attack, the vehicle can still rely on the constructed switching neighbor information state observer to compensate for missing information, reconstruct the trackable target information, and continue the trapping process. After the denial-of-service attack ends, the positional error between the vehicle and the target converges rapidly, and then returns to the small error following state before the denial-of-service attack. This shows that the trapping control method has good robustness and recoverability in the face of denial-of-service attacks.

[0239] like Figure 9 , Figure 10 As shown, the vehicle's target estimator can accurately estimate the location of the target in real time on the vehicle itself when it is not under a denial-of-service attack; even when under a denial-of-service attack, the target estimator can still make a bounded estimate of the target's location based on the information from the neighbor information state observer.

[0240] like Figure 11 , Figure 12 As shown, it demonstrates how the vehicle's distributed adaptive optimal estimator calculates the optimal location information of the target locally, enabling the vehicle's position to quickly converge to the optimal solution that constitutes the capture of the target, and achieving more flexible autonomous optimization in dynamic environments.

[0241] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A distributed multi-vehicle optimal encirclement control method based on a switching observer, characterized in that: The method includes the following steps: Step S1: Construct a dynamic system model of the vehicle to determine its position and real-time status; Step S2: Define a denial-of-service attack status variable, and determine whether a denial-of-service attack has occurred based on the denial-of-service attack status variable; Define the first observer state switching variable and the second observer state switching variable based on the denial-of-service attack state variable; Step S3: Construct a target estimator to obtain the estimated location of the target of the neighboring car, and use the first switching neighbor information state observer to perform online estimation and compensation of the target location of the neighboring car. Step S4: Construct a distributed adaptive optimal estimator to obtain the optimal local location estimate of the target, and use the second switching neighbor information state observer to perform online estimation and compensation of the optimal local location estimate; Step S5: Construct a vehicle controller to enable multiple vehicles to surround and capture the target object using the optimal path in a denial-of-service attack environment.

2. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 1, characterized in that: The construction of the vehicle dynamic system model in step S1 is specifically as follows: Step S1-1: Determine the position state space equation of the vehicle. The position state space equation of the vehicle is: ； in, It is the position vector of the car. For the car in the two-dimensional plane, the first... Dimensional motion trajectory , It is the velocity vector of the car. It is the first time the car moves in a two-dimensional plane. Dimensional motion speed, , It is a car controller. It is an unknown nonlinear function. It is a group of small cars, among which, It is the number of cars; Step S1-2: Define the movement trajectory of the target to be captured; The location of the target to be surrounded is defined as follows: ; in, For the target to be captured in a two-dimensional plane, the first Dimensional motion trajectory For the target in the two-dimensional plane, the first Dimensional motion trajectory; Step S1-3: Define the communication network between the vehicle and the workshop, and between the vehicle and the target to be captured.

3. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 2, characterized in that: The communication network defined in steps S1-3 between the vehicle and the workshop, and between the vehicle and the target being captured, is as follows: Group of cars The communication network between the individuals and the target is formed by an undirected topological graph. At least one vehicle can communicate with the target to obtain the target's location. ; Communication in a communication network is based on undirected graphs It means that, among them express A set of nodes, This indicates the distance from the first car to the second car. A small car, Representing a topology graph edge set in Representing a topology graph The edge, , They represent the first The car and the first A small car; definition ,in, for The adjacent nodes, For the first A group of neighbors of a small car; Define adjacency matrix , Let the neighbor adjacency coefficient be the factor that satisfies the condition. Under the conditions ,otherwise ; Define degree matrix ,in, For the first The weighted in-degree coefficient of each car; Define the adjacency matrix between the vehicle and the target being captured. ,in, For the first The weighted coefficients of the target objects of each car, when the first... When a small vehicle can communicate with the target being apprehended, ,otherwise .

4. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 1, characterized in that: In step S2, the denial-of-service attack state variable is defined as follows: Define denial-of-service attack state variables ; Among them, the denial-of-service attack state variable represents the first Did the car suffer a denial-of-service attack? ,when When, it indicates the first The car was not subjected to a denial-of-service attack and was able to communicate normally with its neighbors; when When, it indicates the first A car is under denial-of-service attack, causing its communication with its neighbors to be interrupted or fail. Define the first observer state switching variable Specifically: ； when At that time, the first switchable neighbor information state observer operates in the state it would have been in if it had not suffered a denial-of-service attack; when At that time, the first switchable neighbor information state observer operates in the state under a denial-of-service attack; Define the second observer state switching variable Specifically: ； when At that time, the second switchable neighbor information state observer operates in the state it would be in if it were not under a denial-of-service attack; when At that time, the second switchable neighbor information state observer operates in the state under a denial-of-service attack.

5. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 4, characterized in that: In step S3, a target estimator is constructed to obtain the estimated location of the target from neighboring vehicles, and a first switching neighbor information state observer is used to perform online estimation and compensation of the target location from neighboring vehicles. Specifically: Step S3-1: Construct the target estimator; The target estimator: ； in, Indicates the current moment. Indicates the previous moment, , It is the time step, which satisfies ; For the first The estimated location of the target in the encirclement of the small car. for The estimated location of the target to be captured corresponds to the dimension. for The estimated location of the target to be captured corresponds to the dimension. It is the transpose matrix; For the first Intermediate state of the target estimator for a small vehicle; Define the observation status of the neighboring target. In the formula Indicates the initial moment of the encirclement and capture process; The location of the target to be apprehended; For the first The weighted in-degree coefficient of each car. For the first Weighting coefficients for the target objects of each small car; The neighbor adjacency coefficient is; the first estimated gain is... The second estimated gain is And satisfy , , ; It is a collection of small cars; For the first A group of neighbors of a small car; The target estimator calculates the difference between its own estimated target position at the previous moment and the observed state of its neighboring targets. The estimated location of the target is adjusted to its actual location using the difference. Step S3-2: Construct the first switchable neighbor information state observer.

6. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 5, characterized in that: The construction of the first switchable neighbor information state observer in step S3-2 is specifically as follows: Based on the target estimator constructed by the neighbors, construct the first switching neighbor information state observer: ； in, The observed state of the neighboring target is used to estimate the estimated location of the target established by the neighbor in its local area. ;in For the first The estimated location of the target to be captured corresponds to the dimension. ; The correction gain for the first observer satisfies ; The relative error of the neighboring targets is estimated to compensate for the estimation. The estimation error satisfies ; Observe the status of the target being surrounded by neighbors; ,and For the first A group of neighbors of a small car; The first switchable neighbor information state observer obtains the estimate through the first radial basis neural network. Used to estimate The rate of change; The first radial basis function neural network includes a first input layer, a first hidden layer, a first weight estimation unit, and a first output layer. The input of the first input layer is a co-input vector. , For a local cooperative input vector, satisfying: ； in, ; The first hidden layer utilizes the Gaussian function. The collaborative input vector is nonlinearly mapped to a high-dimensional feature space, and the center parameter of the activation function is dynamically switched by monitoring the network attack status. and To adapt to changes in the input signal structure, an adaptive basis function response matrix is ​​provided for the changing trends of the approximating neighbor states; The update rule for the first hidden layer is: ； in, For activation function, As the first center of the activation function, As the second center of the activation function, It is the width of the activation function. It is the number of nodes; The response matrix is ​​the basis function. A vector of value functions; , ; The first weight estimation unit is used to update the value function vector of the first radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as: ； in, Update the gain for the weights and satisfy the following conditions: ; The leakage coefficient is and satisfies The output of the first radial basis function neural network output layer is the estimator. , is represented as: ； The first weight estimation unit switches variables according to the state of the first observer. The state determines the update strategy for the weights of the first radial basis function neural network: under normal network communication conditions, this unit estimates the relative error by using neighboring objects. With basis function response matrix The product and combination Leakage coefficient weighted by historical estimates from the previous moment For estimated weights Adaptive adjustments are made; however, when communication is disrupted due to a denial-of-service attack, only the historical estimated weights from the previous time step are used. The resulting damping effect updates the weights to prevent weight divergence and parameter drift caused by a lack of effective error signals or unreliable signals.

7. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 4, characterized in that: In step S4, a distributed adaptive optimal estimator is constructed to obtain the optimal local position estimate of the target object, and the optimal local position estimate is estimated and compensated online using the second switched neighbor information state observer. Specifically: Step S4-1: Construct a distributed adaptive optimal estimator, specifically as follows: The distributed adaptive optimal estimator comprises an adaptive optimization unit, a relative difference weight unit, and a robust correction weight unit, as expressed below: ； ； ； ； in, This represents a distributed adaptive optimal estimation state. For relative difference weights, To robustly adjust the weights, For adaptive compensation parameters; Let cost function be ; in, For the first The estimated location of the targets in the encirclement of the vehicles, among which... For the first The estimated location of the target to be captured corresponds to the dimension. ; It is a relative wrapping vector; The neighbor adaptive optimal estimated state; For smoothing functions, ,Depend on composition; in, satisfy ; For performance weight parameters, satisfying ; To smooth the regularized gain, satisfying ; For exponential decay rate, satisfying ; For coupling gain, satisfying ; express Norm; It is a collection of small cars; For the first A group of neighbors of a small car; and The initial value satisfies , ; The distributed adaptive optimal estimator calculates the gradient direction that minimizes the encirclement formation cost function and adaptively compensates for the parameters. Using gradient terms The driving force generated by the feedforward and feedback terms propels the estimated value toward a locally optimal position that satisfies the preset orbital formation requirements; combined with its own and its neighbors' estimated states, i.e. and The relative deviation between them is determined by adaptively and dynamically adjusting the relative difference weights. With robust weight correction Co-correction is applied to the evolutionary process to eliminate estimation biases between individuals; Step S4-2: Construct the second switchable neighbor information state observer.

8. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 7, characterized in that: The construction of the second switchable neighbor information state observer in step S4-2 is specifically as follows: Based on the distributed adaptive optimal estimator constructed by the neighbors, a second switching neighbor information state observer is constructed. The second switchable neighbor information state observer is: ； in, Indicates the current moment. Indicates the previous moment, , It is the time step, which satisfies ; The neighbor adaptive optimal estimated state; The correction gain for the second observer satisfies ; The relative error of the best neighbor estimate is used to compensate for the estimator. The estimation error satisfies ; The distributed adaptive optimal estimation state is designed locally for the neighbors, where... For the first The distributed adaptive optimal estimation state corresponding to dimension. ; The second switched neighbor information state observer obtains the estimate through a second radial basis neural network. Used to estimate The rate of change of the second radial basis neural network includes a second input layer, a second hidden layer, a second weight estimation unit, and a second output layer; The input to the second input layer is the adaptive collaborative estimation vector. , For the local adaptive collaborative estimation vector, satisfying: ； The update rule for the second hidden layer is: ； in, For activation function, As the first center of the activation function, As the second center of the activation function, It is the width of the activation function. It is the number of nodes; For value function vectors, The response matrix is ​​the basis function. , ; The second hidden layer of the second radial basis function neural network utilizes the Gaussian function. The collaborative input vector is nonlinearly mapped to a high-dimensional feature space, and the center parameter of the activation function is dynamically switched by monitoring the network attack status. and To adapt to changes in the input signal structure, thereby providing an adaptive basis function response matrix for accurately approximating the changing trends of neighboring states; The second weight estimation unit is used to update the value function vector of the second radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as: ； in, Update the gain for the weights, satisfying ; Let be the leakage coefficient, satisfying... , The output of the second output layer is the estimate. , is represented as: ； The second weight estimation unit switches variables based on the state of the second observer. The state determines the update strategy for the weights of the second radial basis function neural network: under normal network communication conditions, this unit utilizes the relative error estimated by the best neighbor estimate. With basis function response matrix The product of the two factors and the historical estimated weights from the previous time step. For estimated weights Adaptive adjustments are made; however, when communication is disrupted due to a denial-of-service attack, only the historical estimated weights from the previous time step are used. The resulting damping effect updates the weights to prevent weight divergence and parameter drift caused by a lack of effective error signals or unreliable signals.

9. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 1, characterized in that: The construction of the vehicle controller in step S5 is specifically as follows: Step S5-1: Construct a virtual control law and a first-order filter to eliminate the computational complexity explosion caused by repeated differentiation of the virtual control law in the car controller. The virtual control law and the first-order filter are as follows: ； in, This represents a distributed adaptive optimal estimation state. The first-order error suppression coefficient satisfies the following conditions: ; It is a virtual control law. Let be the filter coefficients, satisfying , It is a filtering state that satisfies The first estimation error is ,satisfy ,in It is the position vector of the car; It is a collection of small cars; Step S5-2: Construct the car controller.

10. The distributed multi-vehicle optimal encirclement control method based on a switching observer according to claim 9, characterized in that: The vehicle controller is: ； in, It is the first A small car controller; It is the second-order error suppression coefficient, and satisfies... Define the second estimation error. ,in, It is a velocity vector. It is in the filtering state; It is a collection of small cars; The vehicle controller obtains the state estimate of the nonlinear function through a third radial basis neural network. Used to estimate unknown nonlinear functions ; The third radial basis function neural network includes a third input layer, a third hidden layer, a third weight estimation unit, and a third output layer. The input of the third input layer is the state input vector. , Let the local state input vector satisfy: ； in, ; The update rule for the third hidden layer is as follows: ； The third hidden layer utilizes the Gaussian function. Mapping the state input vector to a high-dimensional feature space allows for accurate approximation of unknown nonlinear functions. The changing trend provides an adaptive basis function response matrix; in, For activation function, As the center of the activation function, It is the width of the activation function. It is the number of nodes; The response matrix is ​​the basis function. A vector of value functions; , ; The third weight estimation unit is used to update the value function vector of the third radial basis function neural network. Corresponding estimated weights ,and The update law is expressed as: ； in, Update the gain for the weights of the third radial basis function neural network. ; Let be the leakage coefficient of the third radial basis neural network, satisfying The output of the first radial basis function neural network output layer is the state estimate of the nonlinear function. , is represented as: ； The third weight estimation unit determines the update strategy for the weights of the third radial basis function neural network; this unit utilizes the second estimation error. With basis function response matrix The product of these factors and the weights estimated at the previous time step. Weights of the third radial basis function neural network Adjustments are made to accurately approximate the unknown nonlinear function. The changing trend provides continuously updated radial basis neural network weights.

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