Vehicle formation system adaptive control method based on neural network

Abstract

The invention relates to a neural network-based adaptive control method for a vehicle formation system. Compared with the prior art, the method solves the defects that a complete target trajectory cannot be known in advance due to the influence of an actual environment and the control direction is unknown due to the unstable state of a vehicle engine. The method comprises the following steps: acquiring tracking data of a vehicle formation system; establishing a dynamic model of the vehicle formation system; establishing an error equation; designing a nusturb type function; designing a radial basis function neural network architecture; designing a GRNN training set and an evaluation index for trajectory reconstruction; designing an event trigger function of an actual controller of the system; carrying out self-adaptive control on the vehicle formation; and controlling the vehicle formation with an unknown target trajectory and an unknown control direction. According to the method, a neural network (NN)-based adaptive control architecture is adopted for a vehicle formation system (VPSs), a real-time trajectory can be predicted online by using a GRNN based on historical data of a target trajectory, and an unknown nonlinear term in the system is compensated, so that the position of a vehicle tracks the predicted target trajectory.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle platoon system control, and particularly relates to a vehicle platoon system adaptive control method based on a neural network. BACKGROUND

[0002] Vehicle platoon system (VPSs) as an important research object in intelligent transportation systems, not only can effectively alleviate traffic congestion and improve traffic safety, but also can provide more reliable solutions for traffic flow optimization under complex urban traffic environment. The related research of vehicle platoon system has been widely applied in automatic driving cooperative control, intelligent transportation system optimization and other key fields. The mathematical essence of these problems can be attributed to the cooperative control problem of multi-agent system. However, in actual traffic operation, sensor faults and vehicle power system uncertainties lead to significant errors in the system model; in addition, random traffic disturbances make it difficult to accurately obtain the target trajectory. Therefore, the research on robust control method of vehicle platoon system for model uncertainty and unknown control direction has important academic value and application prospect for improving the cooperative performance and anti-interference ability of vehicle platoon.

[0003] The key to solving the formation keeping and uncertain target tracking in vehicle platoon is to compensate for the model uncertainty in the system and predict the uncertain target trajectory. Due to the complex factors such as vehicle power system uncertainty, sensor failure and random traffic disturbance in the actual traffic environment, the traditional control method based on deterministic model and known target trajectory is difficult to realize accurate control of vehicle platoon. In the prior art, for the unknown target trajectory of vehicle platoon system, GRNN is often used for prediction, and an exponential function is used for continuous processing. Compared with the existing exponential function continuous method, the sine-cosine smoothing function can more accurately approximate the predicted value at the sampling time, thereby significantly improving the accuracy of trajectory prediction.

[0004] Therefore, it is necessary to use a target trajectory real-time prediction algorithm based on GRNN, and combine a dynamic memory event triggering mechanism (DMETM) and a Nussbaum type function method to design an adaptive control strategy based on a neural network. This strategy aims to realize the tracking of the target trajectory of vehicle platoon and ensure that the vehicle spacing error finally converges to a safe range, thereby guaranteeing the cooperative performance of vehicle platoon. SUMMARY

[0005] The purpose of the present application is to solve the defects that the complete target trajectory cannot be known in advance due to the influence of the actual environment, and the control direction is unknown due to the unstable state of the vehicle engine in the prior art, and to provide a vehicle platoon system adaptive control method based on a neural network to solve the above problems.

[0006] In order to achieve the above object, the technical scheme of the present application is as follows:

[0007] A neural network-based vehicle platoon system adaptive control method, comprising the following steps:

[0008] Obtaining tracking data of the vehicle platoon system;

[0009] Establishing a dynamic model of the vehicle platoon system: constructing a dynamic model of the vehicle platoon system and converting it into a state model;

[0010] Establishing an error equation: introducing graph theory knowledge to describe the communication relationship between vehicles, and establishing an error equation based on the communication relationship;

[0011] Designing a Nussbaum function: compensating for the unknown control direction caused by the uncertain engine state in the system;

[0012] Designing a radial basis neural network architecture: estimating the uncertain nonlinear function existing in the system and designing a GRNN architecture to predict the unknown target trajectory;

[0013] Designing a GRNN training set and evaluation index for trajectory reconstruction;

[0014] Designing an event-triggered function for the actual controller of the system;

[0015] Adaptive control of vehicle platoon: Lyapunov analysis of tracking error, synchronization error and weight norm estimation error, verifying that the designed controller and adaptive law keep all signals bounded;

[0016] Control of vehicle platoon with unknown target trajectory and unknown control direction.

[0017] The establishment of the dynamic model of the vehicle platoon system includes the following steps:

[0018] Using the formula Establishing a dynamic model of the vehicle platoon system:

[0019] ,

[0020] Wherein, , and represent the position, velocity and acceleration of the vehicle respectively; , and represent the derivatives of the position, velocity and acceleration of the vehicle respectively; is the engine input; is an unknown disturbance caused by external factors; , and represents an unknown nonlinear function; and is a function describing the vehicle dynamics;

[0021] drag and inertia compensation terms and control efficiency coefficient are defined as follows:

[0022] ;

[0023] where, is the vehicle's velocity, is the vehicle's acceleration, is the vehicle's weight, is the mechanical drag, is the air drag coefficient, is the cross-sectional volume, is the air density, is an unknown engine constant;

[0024] ;

[0025] where, is the vehicle's weight, is an unknown engine constant;

[0026] engine's input is defined as follows:

[0027] ;

[0028] where, is the control input;

[0029] reconstruct the dynamics model into a state model;

[0030] let , , reconstruct the dynamics model into a state model as shown in equation :

[0031] ,

[0032] where, , and all represent the system state of the vehicle platoon system; , and Both represent the derivatives of the system state of the vehicle platooning system; , and Represents an unknown nonlinear function; Indicates control input; unknown disturbance satisfy , For positive integers; control direction sign Unknown but remains unchanged and satisfies ,in, and It is an unknown positive constant.

[0033] The establishment of the error equation includes the following steps:

[0034] Using a simple directed graph To describe the communication relationships between vehicles.

[0035] in, For the image The vertex set, Representing the vehicle;

[0036] For the image The edge set, where each edge corresponds to the communication relationship between vehicles;

[0037] For the image An adjacency matrix is ​​used to record the communication relationships between vehicles. Representing the vertex and vertex Is there communication between them?

[0038] when When, it indicates the vertex Receive from vertex Information at this time ;

[0039] Conversely, if ,but ;

[0040] Vertices in a directed graph The in-degree is denoted as ,

[0041] definition Indicates the first One vehicle can receive information from the lead vehicle, and vice versa. ;

[0042] Based on graph theory, the following error equation is established:

[0043] ;

[0044] ;

[0045] where, is the tracking error, is the synchronization error, , is the predicted target reference trajectory, is the safety distance between any two vehicles, is the length of the i-th vehicle, and are defined constants in graph theory;

[0046] In addition, the velocity error and the acceleration error are defined as follows:

[0047] ;

[0048] ;

[0049] where, and are the virtual control laws to be designed.

[0050] The design of the Nussbaum-type function includes the following steps:

[0051] Introducing the Nussbaum-type function satisfying and ;

[0052] where, denotes the upper limit, denotes the lower limit, denotes the Nussbaum-type function, denotes a variable tending to infinity, denotes a smooth function;

[0053] For a strict feedback nonlinear system, the following inequality is defined:

[0054] ;

[0055] where, , , is the designed global Lyapunov function, is the derivative of the global Lyapunov function, for the Nussbaum-type function, unknown engine constants, is a smooth function, and is a finite constant, if the inequality holds, then and are bounded.

[0056] The design of the RBFNN architecture includes the following steps:

[0057] The design of the RBFNN architecture is ;

[0058] where the unknown function is approximated on a compact set , , is a weight vector, denotes the number of nodes; is the approximation error, satisfying , and is a pre-set constant;

[0059] The basis function vector is composed of Gaussian functions, specifically represented as:

[0060] ,

[0061] where is the center of the receptive field, denotes the width of the Gaussian function; is a weight vector;

[0062] The GRNN is set up by the following four layers:

[0063] The input layer receives the input vector composed of the input quantity and the output quantity of the observation data set, where is used to construct hidden nodes, is the weight of the hidden node;

[0064] The pattern layer calculates the similarity between the input feature vector and the training samples;

[0065] The summation layer performs weighted summation on the output of the pattern layer, and the summation operation is divided into arithmetic and weighted sum ;

[0066] The output layer outputs the result of the network, i.e. .

[0067] The design of the GRNN training set and evaluation index for trajectory reconstruction includes the following steps:

[0068] The reference trajectory of the positioning sensor capable of measuring the tracking signal is defined as follows:

[0069] ;

[0070] wherein, is the total number of data sets at the current time, is the sampling value at the sampling time , , is the sampling period;

[0071] In order to meet the demand of prediction, the following training set and test set are introduced:

[0072] ,

[0073] ,

[0074] wherein, and are the number of training sets and test sets and satisfy and ;

[0075] The process of prediction using GRNN is as follows:

[0076] When the sampling time satisfies , wherein, is a specific small positive number and satisfies , the prediction is defined as follows:

[0077] All existing data are taken as the training samples of GRNN, and is randomly selected for prediction, and the predicted value is recorded as , wherein, is the standard deviation in GRNN;

[0078] When the sampling time satisfies , the prediction is defined as follows:

[0079] Define and , wherein, is the start time of the training set, is the start time of the test set; in order to obtain the optimal , the performance function of GRNN is selected as follows:

[0080] ;

[0081] wherein, is the output of GRNN;

[0082] The optimal is obtained by using GRNN prediction.

[0083] Firstly, the upper and lower bounds of the standard deviation are defined, wherein, is the upper bound of , and is the lower bound of ; secondly, the golden section method is used to train the GRNN model with as the training sample, and the optimal standard deviation is obtained when the formula is minimized; finally, the optimal standard deviation is used to train the GRNN to obtain the optimal value of ;

[0084] On the basis of determining the optimal value of , the points are selected before the starting time of the test set, and the selected points are taken as the fitting data set, denoted as , wherein, is derived online by the golden section method; The polynomial

[0085] and the performance function are introduced and defined as follows:

[0086] ;

[0087] ;

[0088] wherein,

[0089] ,

[0090] ,

[0091] ,

[0092] satisfy ; ​It is a positive integer;

[0093] In time To obtain the optimal result It consists of the following steps:

[0094] First, choose the appropriate , and The upper and lower bounds, of which, for The upper realm, for The lower bound is determined; secondly, the optimal number of data sets for the fit is obtained through online training using the golden section method. Make the formula Minimize; finally, based on the obtained and formula To obtain the optimal ;

[0095] The reference trajectory predicted at the current moment is calculated as follows:

[0096] Smooth functions for continuity The definition is as follows:

[0097] ;

[0098] in, ;

[0099] The function for predicting the reference trajectory is defined as follows:

[0100] ;

[0101] in, .

[0102] The event triggering function of the actual controller of the designed system includes the following steps:

[0103] Design the event triggering conditions for the actual controller. The event triggering conditions are as follows:

[0104] ;

[0105] ;

[0106] in, Represents the infimum function, controlling the signal error. , and Belongs to set , belongs to the set of positive real numbers , is a triggering sensitivity factor satisfying , denotes the actual control signal, denotes the DMETM output, a dynamic compensation term and satisfies the following condition:

[0107] ;

[0108] wherein is a derivative of , is a positive real number and there exists a positive scalar such that , is a positive memory span, then for , and the following holds:

[0109] ;

[0110] wherein and are two unknown time-varying parameters and satisfy and .

[0111] The adaptive control of the vehicle platoon comprises the following steps:

[0112] constructing a first candidate Lyapunov function, performing derivative calculation on the first candidate Lyapunov function, and designing a first fractional-order adaptive law;

[0113] constructing a first candidate Lyapunov function as shown in the formula :

[0114] ;

[0115] wherein denotes a first-order Lyapunov function; denotes a tracking error; denotes a synchronization error; denotes a norm of a weight vector ideal value approximating an unknown but bounded function, denotes an estimation of , denotes a difference between and estimation, ; denotes the learning rate of the RBFNN, and are positive numbers;

[0116] When , the first candidate Lyapunov function is considered to track the reference target trajectory by the leader, and the derivative of the first candidate Lyapunov function with respect to time is:

[0117] ,

[0118] where , denotes the tracking error, denotes the second-order error, denotes the virtual controller, denotes the unknown function, denotes the derivative of the target reference trajectory, and are positive numbers;

[0119] The virtual controller and the adaptive law are designed as follows:

[0120] ;

[0121] where is the control gain, denotes the norm of the basis function vector, denotes the adjustment rate of the RBFNN;

[0122] According to the formula and , we have:

[0123] ;

[0124] where denotes the unknown bounded function approximated by the RBFNN, which is expressed as follows:

[0125] ;

[0126] Using the RBFNN to approximate , we have ;

[0127] According to the Young inequality, the formula is simplified as:

[0128] ;

[0129] where, ; is the formula simplify the sum of all constant terms; is a positive constant satisfying ;

[0130] When , considering the cooperative control of leaders and followers, the first candidate Lyapunov function The derivative of time is:

[0131] ;

[0132] where, , denotes the synchronization error, denotes the second-order error, denotes the virtual controller, and denote unknown functions, , denotes the derivative of the leader, and are positive numbers, denotes whether there is communication between the leader and the follower, denotes whether there is communication between the th vehicle and the th vehicle, denotes the total number of communications between the th vehicle and other vehicles, denoted as ; Design the virtual controller and adaptive law as shown in the formula :

[0133] ;

[0134] where, is the control gain, denotes the norm of the basis function vector, denotes the adjustment rate of the RBFNN;

[0135] According to the formula and :

[0136] ;

[0137] where, denotes an unknown bounded function approximated by the RBFNN, whose expression is as follows:

[0138] ;

[0139] Using RBFNN to approximate , the formula can be simplified to:

[0140] ;

[0141] wherein, is a normal number satisfying , ; is the sum of all constant terms after simplifying the formula ;

[0142] The second candidate Lyapunov function is constructed, the derivative of the second candidate Lyapunov function is taken, the second order virtual controller and the adaptive law are designed, and the specific steps include the following steps:

[0143] The second candidate Lyapunov function is constructed as shown in the formula :

[0144] ;

[0145] wherein, represents a first order Lyapunov function; represents a speed error; represents the norm of the ideal value of the weight vector approximating the unknown but bounded function, represents the estimation of , represents the difference between and the estimation, ; represents the learning rate of the RBFNN, and are positive numbers; The derivative of the second candidate Lyapunov function

[0146] with respect to time is:

[0147] ;

[0148] wherein, , represents a speed error, represents a third order error, represents a virtual controller, represents an unknown function, ​​denotes the derivative of the first-order virtual controller, and are positive numbers;

[0149] The virtual controller and adaptive law are designed as formula

[0150]

[0151] wherein, is a control gain, denotes the norm of the basis function vector, denotes the adjustment rate of the RBFNN;

[0152] According to formula and there are:

[0153]

[0154] wherein, denotes an unknown bounded function that needs to be approximated by the RBFNN, and its expression is as follows:

[0155]

[0156] Using the RBFNN to approximate , the formula can be simplified to:

[0157]

[0158] wherein,

[0159] is a positive number satisfying , is the sum of all constant terms after the formula is simplified;

[0160] A third candidate Lyapunov function is constructed, which combines the dynamic memory event triggering mechanism and the estimation error of the error term and weight norm under unknown control direction. The third candidate Lyapunov function is differentiated to design the third-order virtual controller and adaptive law.

[0161] Specifically, the method comprises the following steps:

[0162] A third candidate Lyapunov function is constructed as shown in formula

[0163] ​​​​​​​ ;

[0164] wherein, represents a first Lyapunov function; represents an acceleration error; represents a norm of a weight vector ideal value approximating an unknown but bounded function, represents an estimate of represents a difference between and an estimate of ; represents a learning rate of the RBFNN, and are positive numbers;

[0165] In combination with the formula the third candidate Lyapunov function has a derivative with respect to time as follows:

[0166] ;

[0167] wherein, , represents an acceleration error, represents an unknown constant, represents an actual control signal, represents a DMETM output, and are two unknown time-varying parameters, belong to the positive real number set , is a triggering sensitivity factor, a dynamic compensation term, represents an unknown function, represents an unknown disturbance, represents a derivative of a second-order virtual controller, and are positive numbers;

[0168] According to the Nussbaum-type function and the dynamic event-triggered mechanism, a virtual controller and an adaptive law as shown in the formula are designed:

[0169] ;

[0170] wherein, is a control gain, represents a norm of a basis function vector, represents an adjustment rate of the RBFNN,​ denotes a smooth function, denotes a Nussbaum-type function;

[0171] By the Young inequality and the properties of the event-triggered function, we have

[0172] ;

[0173] Combining the formulas , and we have

[0174] ;

[0175] where denotes a constant satisfying , denotes an unknown bounded function to be approximated by the RBFNN, which is expressed as

[0176] ;

[0177] Using the RBFNN to approximate we obtain ;

[0178] By the Young inequality, the formula is simplified as

[0179] ;

[0180] where is a positive constant satisfying , is a positive constant satisfying , ; is the sum of all constant terms after simplifying the formula ;

[0181] Based on the first candidate Lyapunov function to the third candidate Lyapunov function, a global Lyapunov function is constructed, and the upper bound of its derivative is derived to verify that the system satisfies semi-global uniform boundedness, which includes the following steps:

[0182] Based on the first candidate Lyapunov function to the third candidate Lyapunov function, a global Lyapunov function is constructed:

[0183] ;

[0184] Taking the derivative of the global Lyapunov function and determining the upper bound of its derivative:

[0185] ;

[0186] wherein , the exponential coefficient of the system convergence speed, is the derivative of the global Lyapunov function ;

[0187] According to the above analysis of the Lyapunov equation, the formula is obtained. It is seen that the Lyapunov stability theorem is satisfied, and thus the global Lyapunov function , the smooth function and its derivative are all bounded;

[0188] According to the three Lyapunov functions , and constructed, it is proved in the formula that the three are stable, and it is concluded that the variables designed in the formulas , and are all bounded, i.e. , , , , and are all bounded;

[0189] By analyzing the triggering condition, it is determined that the event triggering interval has a lower bound,

[0190] According to the formula , the event triggering interval duration is defined as , and obviously, for , there is:

[0191] ;

[0192] wherein is the upper right derivative, is the derivative of the actual control signal ; according to the above conclusion, is bounded; therefore, there is a positive constant such that ;

[0193] In view of and ,

[0194] get wherein Therefore, it is concluded that the Zeno behavior is effectively avoided.

[0195] The control for the vehicle platoon with unknown target trajectory and unknown control direction comprises the following steps:

[0196] An online prediction technology of GRNN is adopted to predict the trajectory of the unknown target, and the predicted trajectory and the current position information of the vehicle are input into the vehicle platoon system to calculate the tracking error and the synchronization error of the vehicle;

[0197] The tracking error and the synchronization error are used to design a first-order virtual controller; based on the speed information of the vehicle and the output of the first-order virtual controller, a second-order error is established, and a second-order virtual controller is designed accordingly; based on the acceleration information of the vehicle and the output of the second-order virtual controller, a third-order error is established, and a corresponding third-order virtual controller is designed;

[0198] A dynamic memory event triggering mechanism and a Nussbaum type function are introduced, and a real controller is designed in combination with the third-order error;

[0199] The obtained information is fed back to the system for real-time adjustment, so as to realize the adaptive backstepping control of the vehicle platoon system.

[0200] Advantages

[0201] Compared with the prior art, the adaptive control method of the vehicle platoon system based on the neural network can use the GRNN online prediction to predict the real-time trajectory based on the historical data of the target trajectory, and compensate for the unknown nonlinear term in the system, so that the position tracking of the vehicle can predict the target trajectory.

[0202] Compared with the prior art, considering that the target trajectory is unknown, the prediction algorithm based on GRNN is adopted to process the uncertain trajectory, and the real-time trajectory prediction based on the historical monitoring data is realized; and in combination with the dynamic memory event triggering mechanism (DMETM) and the Nussbaum type function method, an adaptive control strategy based on the neural network is designed.

[0203] This invention addresses the problem of inaccurate vehicle target trajectory acquisition due to random traffic interference. To solve this problem, a Generalized Regressive Neural Network (GRNN) is employed to predict unknown target trajectories, combined with a sine-cosine smoothing function for continuous processing. By optimizing the characteristics of these functions, the predicted value can be more accurately approximated at the sampling time, significantly improving the accuracy of trajectory prediction. When engine failure leads to unknown control direction, a control strategy based on a Nussbaum function is proposed to solve the uncertainty in control direction caused by engine failure. Furthermore, to make the design more practical, the constraints of the control algorithm on the leader vehicle are considered, while retaining the advantages of multi-vehicle coordinated control of followers in existing technologies. In addition, this invention employs a dynamic event triggering mechanism and proposes an adaptive event triggering condition based on Lyapunov stability. This method effectively reduces the communication resource waste caused by traditional time-triggered control strategies, reduces the number of triggers, and thus reduces system resource consumption. Attached Figure Description

[0204] Figure 1 This is a schematic diagram of the vehicle platooning system.

[0205] Figure 2 The control flowchart for the vehicle platooning system;

[0206] Figure 3 For the vehicle's actual desired trajectory Predicting trajectory and leadership position A curve graph;

[0207] Figure 4 A graph showing the position of each car in a platoon;

[0208] Figure 5 For system tracking error and synchronization error A curve graph;

[0209] Figure 6 For system control input A curve graph;

[0210] Figure 7 This is a diagram illustrating the event trigger interval. Detailed Implementation

[0211] To provide a better understanding of the structural features and effects achieved by the present invention, a detailed description is provided with reference to preferred embodiments and accompanying drawings. The present invention addresses the following: Figure 1 The vehicle platooning system shown is implemented to track and control vehicle platoons with uncertain target trajectories and unknown control directions. For example...Figure 2 The adaptive control method of the vehicle platoon system based on the NN architecture according to the present application is shown in the following steps:

[0212] S1, a dynamic model of a single-machine infinite power system is established, and the dynamic model of the system is converted into a state model.

[0213] The step S1 specifically includes the following steps:

[0214] S11, the formula The dynamic model of the vehicle platoon system is established:

[0215] ;

[0216] wherein, , and represent the position, speed and acceleration of the vehicle respectively; , and represent the derivatives of the position, speed and acceleration of the vehicle respectively; is the engine input; is an unknown disturbance caused by external factors; , and represent unknown nonlinear functions; and are functions for describing the dynamics of the vehicle;

[0217] The definition of the resistance and inertia compensation term and the control efficiency coefficient is as follows:

[0218] ;

[0219] wherein, is the speed of the vehicle, is the acceleration of the vehicle, is the weight of the vehicle, is the mechanical resistance, is the air resistance coefficient, is the cross-sectional volume, is the air density, is an unknown engine constant;

[0220] ;

[0221] wherein, is the weight of the vehicle, is an unknown engine constant;

[0222] Input of engine The definitions are as follows:

[0223] ;

[0224] wherein, is the control input;

[0225] S12, reconstructing the dynamic model, converting the dynamic model into a state model;

[0226] The step S12 specifically comprises the following steps:

[0227] Let , , Reconstruct the dynamic model of the vehicle platoon system to obtain a state model as shown in the formula :

[0228] ;

[0229] wherein, , and all represent the system state of the vehicle platoon system; , and all represent the derivative of the system state of the vehicle platoon system; , and represent unknown nonlinear functions; represents the control input; unknown disturbance satisfies , is a normal number; control direction symbol is unknown but remains unchanged and satisfies wherein, and are unknown normal numbers.

[0230] S2, introduce graph theory knowledge, describe the communication relationship between vehicles, and establish an error equation based on the communication relationship, which is specifically defined as follows:

[0231] The step S2 specifically comprises the following steps:

[0232] S21, the communication relationship between vehicles is described by using graph theory knowledge, which is introduced in detail as follows:

[0233] A simple directed graph is used to describe the communication relationship between vehicles, wherein, is a vertex set of the graph, represents the i-th vehicle; is an edge set of the graph, each edge corresponds to a communication relationship between vehicles; is an adjacency matrix of the graph, used to record the communication relationship between vehicles, represents whether there is a communication between vertex and vertex ; when , it indicates that vertex receives information from vertex , at this time ; otherwise, if , then ; the in-degree of vertex in the directed graph is denoted as , and is defined as represents that the i-th vehicle can receive information from the leading vehicle, and vice versa ; ;

[0234] S22, according to the knowledge of graph theory, the following error equation is established:

[0235] ;

[0236] ;

[0237] wherein, is a tracking error, is a synchronization error, , is a predicted target reference trajectory, is a safety distance between any two vehicles, is the length of the i-th vehicle, and are defined constants in graph theory;

[0238] In addition, the velocity error and the acceleration error are defined as follows:

[0239] ;

[0240] ;

[0241] wherein, and ​​​​for the virtual control law to be designed.

[0242] S3, design a Nussbaum-type function for handling control direction unknown problem, which is used to solve the control direction uncertainty problem caused by the unknown engine state in the system.

[0243] The step S3 specifically comprises the following steps:

[0244] S31, introduce a Nussbaum-type function , which satisfies and ;

[0245] wherein, represents the upper limit, represents the lower limit, represents the Nussbaum-type function, represents a variable tending to infinity, represents a smooth function;

[0246] S32, for a strict feedback nonlinear system, define the following inequality:

[0247] ;

[0248] wherein, , , is a designed global Lyapunov function, is the derivative of the global Lyapunov function, is a Nussbaum-type function, is an unknown engine constant, is a smooth function, and are finite constants, if the inequality holds, then and are bounded.

[0249] S4, design a radial basis function neural network (RBFNN) architecture for function approximation and a GRNN architecture for target trajectory prediction, estimate the uncertain nonlinear function in the system, and predict the unknown target trajectory, the specific process is as follows:

[0250] The step S4 specifically comprises the following steps:

[0251] S41, design the RBFNN architecture as ;

[0252] wherein, the unknown function is approximated on a compact set , , is a weight vector, represents the number of nodes; is an approximation error, satisfying , and is a preset constant;

[0253] a basis function vector is composed of Gaussian functions, and is specifically represented as:

[0254] ,

[0255] wherein, is a center of a receptive field, represents a width of a Gaussian function; is a weight vector;

[0256] S42, regarding the principle of GRNN, the following is introduced:

[0257] GRNN is a neural network model using radial basis functions, which is composed of the following four layers: the input layer receives the input vector composed of the input quantity and the output quantity of the observation data set, wherein is used to construct a hidden node, is a weight of the hidden node; the mode layer calculates the similarity between the input feature vector and the training sample; the summation layer performs weighted summation on the output of the mode layer, and the summation operation is divided into arithmetic and and weighted sum ; the output layer outputs the result of the network, that is, .

[0258] S5, design the GRNN training set and evaluation index for trajectory reconstruction, and use GRNN to predict uncertain reference trajectories, the process is as follows:

[0259] The step S5 specifically includes the following steps:

[0260] S51, define the reference trajectory of the positioning sensor capable of measuring the tracking signal as follows:

[0261] ;

[0262] wherein, is the total number of data sets at the current time, is the sampling value at the th sampling time , and is a sampling period.

[0263] S52, in order to meet the predicted demand, introduce the following training set and test set :

[0264]

[0265]

[0266] wherein, and is the number of training sets and the number of test sets and satisfies and .

[0267] S53, the process of prediction using GRNN is as follows:

[0268] The step S53, specifically includes the following steps:

[0269] S531, when the sampling time satisfies wherein, is a specific very small positive number and satisfies , the prediction is defined as follows:

[0270] All existing data as GRNN training samples, and randomly select to predict, and the predicted value is recorded as wherein, is the standard deviation in GRNN.

[0271] S532, when the sampling time satisfies , the prediction is defined as follows:

[0272] In order to facilitate expression, define and wherein, is the start time of the training set, is the start time of the test set; in order to select the optimal effect, the performance function of GRNN is selected as follows.

[0273] ;

[0274] wherein, is the output of GRNN.

[0275] The optimal obtained by using GRNN is composed of the following steps. First, define the upper and lower bounds of the standard deviation wherein, is the upper bound, is the lower bound; secondly, For training samples, the golden section method is used to train the GRNN model online, and the optimal standard deviation is obtained when the formula is minimized. Finally, the optimal standard deviation obtained is used to train the GRNN to obtain the optimal value of .

[0276] On the basis of obtaining the optimal value of , before the starting time of the test set sampling , the fitting sampling period is taken points, and the taken points are taken as the fitting data set, denoted as . Among them, is derived online by the golden section method. The polynomial and performance function are defined as follows:

[0277] ;

[0278] ;

[0279] Among them, , , , satisfy ; wherein is a positive constant.

[0280] The optimal is obtained within time . It consists of the following steps. First, select the upper and lower bounds of , and , wherein is the upper bound, and is the lower bound; second, the optimal fitting data set number is obtained by online training by the golden section method, so that the formula is minimized; finally, the optimal is obtained according to the obtained and the formula .

[0281] S54, calculate the predicted reference trajectory at the current time as follows:

[0282] The step S54 specifically includes the following steps:

[0283] S541, the smoothing function for continuous is defined as follows:

[0284] ​ ;

[0285] wherein, .

[0286] S542, the function definition of the predicted reference trajectory is as follows:

[0287] ;

[0288] wherein, .

[0289] S6, in order to reduce the consumption of system communication resources, it is necessary to use an event-triggered function in the actual controller design process.

[0290] The step S6 specifically includes the following steps:

[0291] The event-triggered condition of the actual controller is designed, and the event-triggered condition is as follows:

[0292] ;

[0293] ;

[0294] wherein, denotes the lower bound function, the control signal error , and belongs to the set , belongs to the positive real number set , is a trigger sensitivity factor, and satisfies , denotes the actual control signal, denotes the DMETM output, a dynamic compensation term and satisfies the following conditions:

[0295] ;

[0296] wherein, is a positive real number, and there is a positive scalar , such that , is a positive memory span. Then for , the following formula can be obtained from and :

[0297] ;

[0298] where, and are two unknown time-varying parameters, and satisfy and .

[0299] S7, Lyapunov analysis is performed on the tracking error and weight estimation error to ensure that each signal of the system is bounded.

[0300] The step S7 specifically includes the following steps:

[0301] S71, a first candidate Lyapunov function is constructed, derivative calculation is performed on the first candidate Lyapunov function, and a first fractional order adaptive law is designed.

[0302] The step S71 specifically includes the following steps:

[0303] S711, a first candidate Lyapunov function as shown in the formula is constructed:

[0304] ;

[0305] where, represents a first-order Lyapunov function; represents a tracking error; represents a synchronization error; represents a norm of an ideal value of a weight vector approximating an unknown but bounded function, represents an estimation of , represents a difference between and an estimation, ; represents a learning rate of the RBFNN, and are both positive numbers;

[0306] S712, when , the leader tracks the reference target trajectory, and a derivative of the first candidate Lyapunov function with respect to time is:

[0307] ,

[0308] where, , represents a tracking error, represents a second-order error, represents a virtual controller, represents an unknown function, derivative of the target reference trajectory, and are positive numbers;

[0309] The virtual controller and adaptive law are designed as follows:

[0310] ;

[0311] where, is the control gain, denotes the norm of the basis function vector, denotes the adjustment rate of the RBFNN;

[0312] According to the formula and we have:

[0313] ;

[0314] where, denotes the unknown bounded function approximated by the RBFNN, whose expression is as follows:

[0315] ;

[0316] Using the RBFNN to approximate we obtain ;

[0317] According to the Young inequality, the formula is simplified as:

[0318] ;

[0319] where, ; is the sum of all constant terms after simplifying the formula ; is a positive number satisfying ;

[0320] S713, when , the leader-follower cooperative control is considered, and the derivative of the first candidate Lyapunov function with respect to time is:

[0321] ;

[0322] where, , denotes the synchronization error,​ represents the second order error, represents the virtual controller, and represents the unknown function, , represents the derivative of the leader, and are positive numbers, represents whether there is communication with the leader, represents whether there is communication between the th vehicle and the th vehicle, represents the total number of communications between the th vehicle and other vehicles, denoted as ; the virtual controller and adaptive law are designed as formula

[0323] ;

[0324] wherein, is the control gain, represents the norm of the basis function vector, represents the adjustment rate of the RBFNN;

[0325] According to formula and , we have:

[0326] ;

[0327] wherein, represents the unknown bounded function approximated by the RBFNN, and its expression is as follows:

[0328] ;

[0329] Using the RBFNN to approximate , we obtain , and by using the Young inequality, formula can be simplified as:

[0330] ;

[0331] wherein, is a normal number satisfying , ; is the sum of all constant terms after formula is simplified;

[0332] ​Step S71 establishes a theoretical framework for the stability analysis of the vehicle platoon system by constructing a Lyapunov function containing the estimation error of the tracking error, the synchronization error and the RBFNN weight norm. Specifically, in steps S712 (leader tracking) and S713 (follower coordination), the Lyapunov derivative is expanded into an expression containing the ideal RBFNN output and its estimation value by substituting the variables and using the estimation error definition of the weight norm; further application of Young's inequality to the nonlinear cross term converts it into a combination of positive, negative definite error terms and a bounded constant term. This constant term integrates the norm of the neural network weight vector and the upper bound information of the function approximation error. Step S71 provides a simplified mathematical basis for system stability analysis and supports the progressive proof of semi-global stability.

[0333] S72, constructing a second candidate Lyapunov function, deriving the second candidate Lyapunov function, designing a second-order virtual controller and adaptive law.

[0334] The step S72 specifically includes the following steps:

[0335] S721, constructing a second candidate Lyapunov function as shown in the formula

[0336] ;

[0337] Wherein, represents the first Lyapunov function; represents the speed error; represents the norm of the ideal value of the weight vector approximating the unknown but bounded function, represents the estimation of , represents the difference between and estimation, ; represents the learning rate of RBFNN, and are both positive numbers;

[0338] S722, the derivative of the second candidate Lyapunov function with respect to time is:

[0339] ;

[0340] Wherein, , represents the speed error, represents the third-order error, ​represents a virtual controller, represents an unknown function, represents a derivative of the first-order virtual controller, and are positive numbers;

[0341] The virtual controller and adaptive law are designed as formulas

[0342] ;

[0343] wherein, is a control gain, represents a norm of a basis function vector, represents an adjustment rate of the RBFNN;

[0344] According to formulas and , we have:

[0345] ;

[0346] wherein, represents an unknown bounded function that needs to be approximated by the RBFNN, and its expression is as follows:

[0347] ;

[0348] The RBFNN is used to approximate to obtain , and by using the Young inequality, the formula can be simplified as:

[0349] ;

[0350] wherein,

[0351] is a positive constant satisfying , ; is the sum of all constant terms after the formula is simplified;

[0352] S73, a third candidate Lyapunov function is constructed, the dynamic memory event triggering mechanism and the estimation error of the error term and weight norm under unknown control direction are fused, the third candidate Lyapunov function is derived, and a third-order virtual controller and adaptive law are designed. The step S73 specifically includes the following steps:

[0353] S731, a third candidate Lyapunov function is constructed as shown in the formula​

[0354] ;

[0355] wherein, represents a first order Lyapunov function; represents an acceleration error; represents a norm of the weight vector ideal value approximating an unknown but bounded function, represents an estimate of , a difference between and ; represents a learning rate of the RBFNN, and are positive numbers;

[0356] S732, combining equation , the third candidate Lyapunov function has a derivative with respect to time as follows:

[0357] ;

[0358] wherein, , represents an acceleration error, represents an unknown constant, represents an actual control signal, represents a DMETM output, and are two unknown time-varying parameters, belong to the positive real number set , is a triggering sensitivity factor, a dynamic compensation term, represents an unknown function, represents an unknown disturbance, represents a derivative of the second order virtual controller, and are positive numbers;

[0359] According to the Nussbaum type function and the dynamic event-triggered mechanism, a virtual controller and an adaptive law as shown in equation are designed:

[0360] ;

[0361] wherein, is a control gain, represents a norm of a basis function vector, denotes the adjustment rate of the RBFNN, denotes a smooth function, denotes a Nussbaum-type function;

[0362] By the Young inequality and the properties of the event-triggered function, we have

[0363] ;

[0364] Combining the formulas , and we have

[0365] ;

[0366] where denotes a constant satisfying , denotes an unknown bounded function that needs to be approximated by the RBFNN, and its expression is as follows:

[0367] ;

[0368] Using the RBFNN to approximate we obtain ;

[0369] By the Young inequality, the formula is simplified as

[0370] ;

[0371] where is a positive constant satisfying , is a positive constant satisfying , ; is the sum of all constant terms after simplifying the formula ;

[0372] S74, according to the first candidate Lyapunov function to the third candidate Lyapunov function, constructing a global Lyapunov function, and deriving the upper bound of its derivative, verifying that the system satisfies the semi-global uniform boundedness.

[0373] The step S74 specifically includes the following steps:

[0374] S741, based on the first candidate Lyapunov function to the third candidate Lyapunov function, constructing a global Lyapunov function :

[0375] ;

[0376] S742, the derivative of the global Lyapunov function is derived, and the upper bound of its derivative is determined:

[0377] ;

[0378] wherein, , the exponential coefficient of the system convergence speed, is the derivative of the global Lyapunov function ;

[0379] According to the above analysis of the Lyapunov equation, the formula is obtained. It is seen that the Lyapunov stability theorem is satisfied, and thus the global Lyapunov function , the smooth function and its derivative are all bounded;

[0380] According to the constructed , and three Lyapunov functions, it is proved in the formula that the three are stable, and it is concluded that the variables designed in the formulas , and are all bounded, i.e. , , , , and are all bounded;

[0381] S75, by analyzing the triggering condition, it is determined that the event triggering interval has a lower bound,

[0382] According to the formula , the event triggering interval length is defined as , and obviously, for , there is:

[0383] ;

[0384] wherein, is the upper right derivative, is the derivative of the actual control signal ; it is known from the above conclusion that is bounded; therefore, there exists a positive constant , such that ;

[0385] In view of and ,

[0386] It is derived that wherein Therefore, it is concluded that the Zeno behavior is effectively avoided.

[0387] Step S1, a dynamic model of the vehicle platoon system is established, and the system dynamic model is converted into a state model; Step S2, graph theory knowledge is introduced, and the communication between vehicles is described, and an error equation is established based thereon; Step S3, a Nussbaum function is introduced, and the problem of unknown control direction in the system is processed; Step S4, a function approximation RBFNN architecture is designed to approximate unknown functions in the system, and a GRNN prediction architecture is designed to predict an unknown target trajectory; Step S5, a GRNN training set for trajectory reconstruction and an evaluation index are designed, and an uncertain reference trajectory is predicted by using the GRNN; Step S6, a dynamic memory event trigger function is designed, and consumption of communication resources of the system is reduced; and finally, Step S7, backstepping control is used, a virtual controller and an actual controller are constructed by using backstepping technology, adaptive control of the vehicle platoon system is realized, Lyapunov analysis is performed, and it is ensured that each signal of the system is bounded.

[0388] A specific dynamic model of a vehicle used in this embodiment is as follows:

[0389] .

[0390] Parameters of the RBFNN architecture used for approximating unknown terms in this embodiment are as follows:

[0391] The learning rate is , , , , , , , , , , and ; the initial value of the weight vector is subject to a random uniform distribution of .

[0392] Parameters of the GRNN prediction in this embodiment are as follows:

[0393] When , is set to 0.001, ,

[0394] The controller parameters in this embodiment are selected as follows:

[0395]

[0396] The event trigger parameters in this embodiment are selected as follows:

[0397]

[0398] The desired unknown target trajectory in this embodiment is ; the initial values of the system state variables and the adaptive signal are

[0399] Numerical simulation is performed based on the above controller parameters, and the simulation results are shown in Figures 3-7 .The horizontal coordinate in Figure 3 represents time, in seconds, and the vertical coordinate represents position, in meters. The curves in the figure are the actual desired target trajectory , the predicted target trajectory , and the leader position ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​The curve; Figure 4 The horizontal axis in the graph represents time in seconds, and the vertical axis represents position in meters. The curve in the graph represents the positions of all vehicles. The curve; Figure 5 The horizontal axis represents time in seconds, and the vertical axis represents the magnitude of the error. The curve in the graph represents the system's tracking error. and synchronization error The closer the curve is to zero, the better the tracking performance. Figure 6 The horizontal axis represents time in seconds, and the vertical axis represents the actual size of the controller, which is the system's control input. The curve; Figure 7 The horizontal axis in the graph represents time, in seconds, and the graph shows the event trigger interval. According to the simulation results, from... Figure 3 It can be seen that the designed algorithm can accurately predict and track trajectories; for example... Figure 4 As shown, all following vehicles are able to synchronously track the lead vehicle and maintain a safe distance; Figure 5 The curve approaches zero, indicating that the tracking error and synchronization error are approaching zero; Figure 6 The curve oscillates around zero, indicating that the control input is gradually stabilizing. Figure 7 Compared to a trigger frequency of once every 0.001 seconds, the trigger points are more sparse, indicating fewer event triggers and effectively reducing control resource consumption. Therefore, in vehicle platooning systems with unknown target trajectories and unknown control directions, the control method designed in this invention can enable vehicles to track unknown target trajectories while maintaining platooning. Furthermore, the boundedness of the designed signals ensures system stability, which is beneficial for practical engineering applications.

[0400] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A neural network-based adaptive control method for a vehicle platoon system, characterized in that, The method comprises the following steps: 11) obtaining tracking data of the vehicle platoon system; 12) establishing a dynamic model of the vehicle platoon system: constructing a dynamic model of the vehicle platoon system and converting it into a state model; 13) establishing an error equation: introducing graph theory knowledge to describe the communication relationship between vehicles, and establishing an error equation based on the communication relationship; 14) designing a Nussbaum function: compensating for the unknown control direction caused by the uncertain engine state in the system; 15) designing a radial basis neural network architecture: estimating the uncertain nonlinear function existing in the system and designing a GRNN architecture, and predicting the unknown target trajectory; 16) designing a GRNN training set and evaluation index for trajectory reconstruction; 17) designing an event-triggered function of the actual controller of the system; 18) adaptive control of the vehicle platoon: performing Lyapunov analysis on the tracking error, synchronization error, and weight norm estimation error, and verifying that the designed controller and adaptive law keep all signals bounded; 19) controlling the vehicle platoon with unknown target trajectory and unknown control direction. 2.The neural network-based adaptive control method for vehicle platoon system according to claim 1, wherein, The step of establishing a dynamic model of the vehicle platoon system comprises the following steps: 21) using the formula Establish the dynamics model of vehicle platoon system: ， where, , and denote the position, velocity and acceleration of the vehicle, respectively; , and denote the derivative of the position, velocity and acceleration of the vehicle, respectively; is the engine input; is an unknown disturbance caused by external factors; , and denote unknown nonlinear functions; and are functions describing the dynamics of the vehicle; Resistance and inertia compensation terms And control efficiency factor Are defined as follows: ； wherein, is the speed of the vehicle, is the acceleration of the vehicle, is the weight of the vehicle, is the mechanical resistance, is the air resistance coefficient, is the cross-sectional volume, is the air density, is an unknown engine constant; ； ； wherein, is the weight of the vehicle, is an unknown engine constant; Input to the engine The following definitions apply: ； wherein u is a control input; 22) reconstructing the dynamic model and converting it into a state model; Let , , The dynamics model is reconstructed to obtain a state model as shown in equation . ， wherein, , and all represent the system state of the vehicle platooning system; , and all represent the derivative of the system state of the vehicle platooning system; , and represent unknown nonlinear functions; represents the control input; unknown disturbance satisfies , is a positive constant; control direction sign is unknown but remains constant and satisfies wherein, and are unknown positive constants.

3. The neural network-based adaptive control method for vehicle platoon system according to claim 2, wherein, The step of establishing an error equation comprises the following steps: 31) using simple directed graphs to describe inter-vehicle communication relationships, wherein is a vertex set of the graph is a vertex set of the graph represents the first vehicle represents the first vehicle is a set of edges, each edge corresponding to a communication relationship between vehicles; is a set of edges, each edge corresponding to a communication relationship between vehicles; is a graph whose adjacency matrix is used to record the communication relationship between vehicles, represents whether there is communication between vertices and vertices ; When the vertex sends information to the vertex , at which point Conversely, if then ; Let the indegree of a vertex in a directed graph be denoted by , Definitions representing the vehicle can receive information from the lead vehicle, and vice versa, ; 32) according to the knowledge of graph theory, the following error equation is established: ； ； wherein, is a tracking error, is a synchronization error, , is a predicted target reference trajectory, is a safety distance between any two vehicles, is a vehicle length of the i-th vehicle, and is a defined constant in graph theory; Further, the velocity error and the acceleration error are defined as follows: ； ； wherein and is a virtual control law to be designed.

4. The neural network-based adaptive control method for vehicle platoon system according to claim 3, wherein, The step of designing a Nussbaum function comprises the following steps: 41) Introducing the Nussbaum-type function satisfying and ; wherein, denotes an upper limit, denotes a lower limit, denotes a Nussbaum-type function, denotes a variable that tends to infinity, denotes a smooth function; 42) for a strict feedback nonlinear system, the following inequality is defined: ； where , , is a designed global Lyapunov function, is the derivative of the global Lyapunov function, is a Nussbaum-type function, is an unknown engine constant, is a smooth function, and are finite constants, if the inequality holds, then and are bounded.

5. The neural network-based adaptive control method for vehicle platooning system according to claim 4, wherein, The step of designing a radial basis neural network architecture comprises the following steps: 51) Design the RBFNN architecture as ; where the unknown function is approximated on a compact set , , is the weight vector, denotes the number of nodes; is the approximation error, satisfying , and is a preset constant; basis function vector is composed of Gaussian functions, and is specifically expressed as: ， wherein, is the center of the receptive field, denotes the width of the Gaussian function; is the weight vector; 52) set the GRNN to consist of the following four layers: The input layer receives an input vector consisting of input quantities of an observation data set and output quantities wherein weights for the hidden nodes are constructed, weights for the hidden nodes; The mode layer calculates the similarity between the input feature vector and the training sample; The summation layer performs a weighted sum of the outputs of the pattern layer, the summation operation being divided into arithmetic and and the weighted sum ; output the result of the network, i.e. .

6. The neural network-based adaptive control method for vehicle platooning system according to claim 5, wherein, The step of designing a GRNN training set and evaluation index for trajectory reconstruction comprises the following steps: 61) define the reference trajectory that the positioning sensor can measure the tracking signal as follows: ； wherein, is the total number of data sets at the current time instant, is the sampling value at the sampling time instant , , is the sampling period; 62) To meet the predicted demand, introduce a training set as follows and a test set : ， ， wherein, and is the number of training sets and the number of test sets and satisfies and ; 63) the process of prediction using GRNN is as follows: 631) when the sampling time meets where, is a small positive number specific to the proximity and satisfies The prediction is defined as follows: All the existing data are taken as the training samples of the GRNN, and are arbitrarily selected to predict, and the predicted value is denoted as wherein, is the standard deviation in the GRNN; 632) when the sampling time meets The prediction is defined as follows: Definition and wherein, is the start time chosen for the training set, is the start time chosen for the test set; to get the optimal performance function of the GRNN is chosen as follows: ； wherein, is the output of the GRNN; The optimal prediction is obtained by using GRNN It consists of the following steps: First, the upper and lower bounds of the standard deviation are defined, where is the upper bound of , and is the lower bound of ; second, using as the training sample, the golden section method is used to train the GRNN model online, and the optimal standard deviation is obtained when the formula is minimized; finally, the optimal standard deviation is used to train the GRNN, and the optimal value of is obtained; On the basis of determining the optimal value of , the fitting sampling period is taken as the reference, and points are selected before the starting time of the test set . The selected points are taken as the fitting data set, denoted as , where is derived online by the golden section method; Introducing polynomials and performance functions are defined as follows: ； ； wherein, ， ， ， satisfies ; is a positive constant; The optimal time is obtained within comprises the following steps: First, the upper and lower bounds of , and are selected, where is the upper bound of , is the lower bound of ; second, the optimal number of fitting data sets is obtained by online training with the golden section method, so that the formula is minimized; finally, the optimal is obtained according to the obtained and the formula ; 64) the predicted reference trajectory at the current time is calculated as follows: 641) Smoothing function for continuous is defined as follows: ； wherein ; 642) the function definition of the predicted reference trajectory is as follows: ； wherein .

7. The neural network-based adaptive control method for vehicle platooning system according to claim 6, wherein, The step of designing an event-triggered function of the actual controller of the system comprises the following steps: The event-triggered condition of the actual controller is designed as follows: ； ； wherein denotes the lower bound function, the control signal error , and belongs to the set , belongs to the set of positive real numbers , is a trigger sensitivity factor satisfying , denotes the actual control signal, denotes the DMETM output, a dynamic compensation term and satisfies the following conditions: ； wherein is derivative of is a positive real number and there exists a positive scalar such that , is a positive memory span, then for , and the formula is ； wherein, and are two unknown time-varying parameters, and satisfy and . 8.The neural network based adaptive control method for vehicle platoon system according to claim 1, wherein, The adaptive control of the vehicle platoon comprises the following steps: 81) constructing a first candidate Lyapunov function, performing derivative calculation on the first candidate Lyapunov function, and designing a first fractional order adaptive law; 811) Construct the first candidate Lyapunov function as shown in the equation V1(x) = xTQx ； wherein, represents a first order Lyapunov function; represents a tracking error; represents a synchronization error; represents a norm of a weight vector ideal value approximating an unknown but bounded function, represents an estimate of represents a difference between an estimate and ; represents a learning rate of the RBFNN, and are positive numbers; 812) When When considering the leader tracking the reference target trajectory, the first candidate Lyapunov function is... Regarding time The derivative is: ， wherein, , denotes a tracking error, denotes a second order error, denotes a virtual controller, denotes an unknown function, denotes a derivative of a target reference trajectory, and are positive numbers; Virtual controller and adaptive law designed as formula ​ ； wherein, is a control gain, denotes a norm of the basis function vector, denotes an adjustment rate of the RBFNN; According to the formula and there are: ； where, denotes the unknown bounded function approximated by the RBFNN, whose expression is as follows: ； Using RBFNN for Approximation results ; According to the Young inequality, the formula is simplified as: ； wherein ; is a normal number satisfying simplifying the sum of all constant terms; is a normal number satisfying ; 813)When the leader and the follower are considered, the first candidate Lyapunov function has a derivative with respect to time of: ； where , denotes the synchronization error, denotes the second order error, denotes the virtual controller, and denotes the unknown function, , denotes the derivative of the leader, and are positive numbers, denotes whether there is communication with the leader, denotes whether there is communication between the th vehicle and the th vehicle, denotes the total number of vehicles with which the th vehicle is in communication, denoted by ; a virtual controller and an adaptive law are designed as in the equation . ； wherein, is a control gain, denotes a norm of the basis function vector, denotes an adjustment rate of the RBFNN; According to the formula and there are: ； where, denotes the unknown bounded function approximated by the RBFNN, whose expression is as follows: ； Using RBFNN to approximate , the formula can be simplified to: ​ ； wherein is a constant satisfying , ; is the sum of all constant terms after simplifying the formula ​ 82) constructing a second candidate Lyapunov function, performing derivative calculation on the second candidate Lyapunov function, and designing a second order virtual controller and adaptive law, which specifically comprises the following steps: 821) Construct the second candidate Lyapunov function as shown in equation V2(x) = xTQx ； wherein, represents a first order Lyapunov function; represents a velocity error; represents a norm of the weight vector ideal value approximating an unknown but bounded function, represents an estimate of represents a difference between an estimate and ; represents a learning rate of the RBFNN, and are positive numbers; 822) second candidate lyapunov function derivative with respect to time is: ； wherein, , denotes a velocity error, denotes a third order error, denotes a virtual controller, denotes an unknown function, denotes a derivative of the first order virtual controller, and are positive numbers; Virtual controller and adaptive law designed as formula ​ ； wherein, is a control gain, denotes a norm of the basis function vector, denotes an adjustment rate of the RBFNN; According to the formula and there are: ； where, denotes an unknown bounded function that needs to be approximated by the RBFNN, whose expression is as follows: ； Using RBFNN to approximate , the formula can be simplified to: ​ ； wherein, Let c be a constant satisfying , ; the sum of all constant terms after simplifying the formula ; 83) constructing a third candidate Lyapunov function, fusing a dynamic memory event-triggering mechanism and an error term and an estimation error of the weight norm under unknown control direction, performing derivative calculation on the third candidate Lyapunov function, and designing a third order virtual controller and adaptive law; which specifically comprises the following steps: 831) constructing a third candidate Lyapunov function as shown in the formula: ； wherein, represents a first order Lyapunov function; represents an acceleration error; represents a norm of the weight vector ideal value approximating an unknown but bounded function, represents an estimate of represents a difference between an estimate and ; represents a learning rate of the RBFNN, and are positive numbers; 832) Combining the equations , the third candidate Lyapunov function derivative with respect to time is: ； wherein , denotes the acceleration error, denotes an unknown constant, denotes the actual control signal, denotes the DMETM output, and are two unknown time-varying parameters, belongs to the set of positive real numbers , is a triggering sensitivity factor, a dynamic compensation term, denotes an unknown function, denotes an unknown disturbance, denotes the derivative of the second order virtual controller, and are positive numbers; According to the Nussbaum-type function and dynamic event-triggered mechanism, a virtual controller and adaptive law are designed as follows: ​ ； wherein, for controlling the gain, denotes a norm of the basis function vector, denotes an adjustment rate of the RBFNN, denotes a smoothing function, denotes a Nussbaum-type function; from Young's inequality and the properties of the event-triggered function, it has: ； Combining equations , and have: ； where represents a constant satisfying , represents an unknown bounded function that needs to be approximated by the RBFNN, whose expression is as follows: ； Using RBFNN for Approximation results ; Using the inequality of Young, the formula is simplified to: (47)； wherein is a constant satisfying , is a constant satisfying , ; is the sum of all constant terms after simplifying the formula ; 84) According to the first candidate Lyapunov function to the third candidate Lyapunov function, a global Lyapunov function is constructed, and the upper bound of its derivative is derived to verify that the system satisfies the semi-global uniform boundedness, which specifically includes the following steps: 841) constructing a global Lyapunov function based on the first candidate Lyapunov function to the third candidate Lyapunov function : ； 842) Derive the global Lyapunov function and determine an upper bound on its derivative: ； wherein , an exponential coefficient of the system convergence speed, is the derivative of the global Lyapunov function . According to the above analysis of Lyapunov equation, the formula is obtained. It is seen that the Lyapunov stability theorem is satisfied, so the global Lyapunov function is obtained. The smooth function and its derivative are bounded. According to the construction of , and three Lyapunov functions, and prove that the three are stable in formula, draw the conclusion that the variable designed in the formula , and are bounded, that is, , , , , and are bounded; 85) By analyzing the triggering condition, it is determined that the event-triggered interval has a lower bound, According to the formula Know, The event trigger interval duration is defined as Obviously, for There is: ； wherein, is the upper right derivative, is the derivative of the actual control signal From the above conclusion, is bounded; therefore, there exists a positive constant such that ; In view of and , Get wherein Thus, it is concluded that Zeno behavior is effectively avoided. 9.The neural network based adaptive control method for vehicle platoon system according to claim 1, wherein, The control for the vehicle formation with unknown target trajectory and unknown control direction includes the following steps: 91) The GRNN online prediction technology is used to predict the trajectory of the unknown target, and the predicted trajectory and the current position information of the vehicle are input into the vehicle formation system to calculate the tracking error and synchronization error of the vehicle; 92) The tracking error and synchronization error are used to design a first-order virtual controller; based on the speed information of the vehicle and the output of the first-order virtual controller, a second-order error is established, and a second-order virtual controller is designed accordingly; according to the acceleration information of the vehicle and the output of the second-order virtual controller, a third-order error is established, and a corresponding third-order virtual controller is designed; 93) A dynamic memory event-triggered mechanism and a Nussbaum-type function are introduced, and a real controller is designed in combination with the third-order error; 94) The obtained information is fed back to the system for real-time adjustment to realize adaptive backstepping control of the vehicle formation system.

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