Hybrid vehicle queue nonlinear robust data driving prediction control method and device

Abstract

The invention relates to a nonlinear robust data driving prediction control method and device for a hybrid vehicle queue, and the method comprises the steps: collecting a control input sequence, an attack input sequence and a head vehicle interference input sequence of an intelligent connected vehicle in the hybrid vehicle queue, and a system state sequence of the hybrid vehicle queue; training a deep neural network through the collected data sequence to establish a target lifting function of a Koopman operator, constructing an equivalent Koopman lifting system model according to the target lifting function, and further constructing an over-approximation system represented by a matrix holosymmetric polytope set; and based on an over-approximation system, determining a data-driven reachable set of a system state corresponding to the hybrid vehicle queue so as to construct and solve a nonlinear data-driven predictive control problem and obtain a target control input sequence. Therefore, the problem that the algorithm robustness is poor due to the fact that the existing data-driven predictive control research depends on linear model hypothesis and lacks key consideration on data noise, external disturbance and attack input is solved.

Description

Technical Field

[0001] The present application relates to the technical field of data-driven predictive control, and in particular to a method and device for nonlinear robust data-driven predictive control of a mixed vehicle platoon. Background Art

[0002] Of particular note is that cooperative adaptive cruise control, as an extension of adaptive cruise control, demonstrates significant potential in reducing vehicle distances and alleviating traffic disturbances by organizing multiple adjacent autonomous vehicles into a convoy. This convoy technology has received widespread attention worldwide.

[0003] However, existing fleet cooperative control technologies are primarily designed for fully intelligent connected vehicle environments. With the gradual rollout of intelligent connected vehicles (ICVs), the future will usher in a mixed traffic phase where intelligent and connected vehicles (ICVs) and human-driven cars will coexist for a long time. To achieve the economic benefits of ICVs in mixed traffic environments, breakthroughs in ICV cooperative control technologies are urgently needed.

[0004] Research on mixed traffic control technologies has attracted widespread attention and has been repeatedly validated in experimental and simulation platforms. Leveraging communication mechanisms such as vehicle-to-vehicle and vehicle-to-infrastructure communications, ICVs can access information from multiple human-driven vehicles, integrate multiple vehicles into a mixed platoon, and implement safe and optimal control. The current state of research suggests that all relevant research can be categorized as Lagrangian control approaches, which treat ICVs as controllable agents in a platoon and aim to optimize the overall performance of mixed traffic by directly regulating their behavior. Within this framework, most existing research on mixed platoon control employs model-based approaches. These strategies typically utilize established vehicle-following models, such as optimal speed models or intelligent driving models, to describe human driver behavior. This allows for the development of state-space models of the mixed platoon, which serve as the basis for controller design. Control methods based on these models include robust control, linear quadratic regulators, model predictive control, and control barrier functions. While model-based approaches can provide optimal or near-optimal control with rigorous theoretical guarantees, their effectiveness depends heavily on the accuracy of the underlying models. However, accurately identifying the parameters in the human driver behavior model is a challenging task, which can limit the performance of these model-based strategies.

[0005] To address these limitations, techniques such as adaptive dynamic programming and reinforcement learning do not require prior knowledge of the dynamics of mixed-vehicle fleets, but instead rely on iterative training to achieve accurate system predictions and effective control. However, they often face challenges related to the computational complexity of training, as well as concerns about generalization capabilities and the optimality of control inputs in dynamically changing environments.

[0006] Data-driven model predictive control (MPC) combines the established MPC framework with data-driven methods, showing potential for achieving optimal control while satisfying system constraints and maintaining stability guarantees. For example, by applying data-driven predictive control techniques to the Leading Cruise Control (LCC) framework, strategies such as DeepP-LCC and its variants have been validated in simulation studies. These strategies have shown improvements in suppressing traffic waves, reducing energy consumption, and preserving privacy. However, in real-world traffic environments, inherent noise in vehicle perception systems and V2X (Vehicle-to-Everything) communications can affect the accuracy of collected data. Furthermore, the implementation of Internet of Vehicles (IoV) technologies can make ICV control systems more vulnerable to hostile attacks, such as maliciously altered control inputs or manipulated sensor data to execute attacks, which can compromise the safety of vehicle control. These studies generally ignore the impact of noise on data collection and online predictive control, while assuming the absence of external attacks. These assumptions can limit the ability to effectively track trajectories, lack robustness, and introduce potential safety issues.

[0007] Recent research has made significant progress in enhancing the robustness of mixed-race platoon systems. For example, reformulating the DeepP-LCC method using min-max robust optimization has been shown to reduce the impact of unknown disturbances. Distributed data-driven MPC methods with feedforward compensation have also been shown to be effective in combating external disturbances. Furthermore, fully symmetric polytope data-driven predictive control (DPC) using linear reachability analysis has successfully minimized the impact of observation noise on data collection. However, under noise-free conditions, the DeePC predictor has been shown to be equivalent to a linear MPC predictor for a linear time-invariant system. Furthermore, the generation of the subspace identification matrix used by distributed data-driven MPC methods with feedforward compensation relies on linear assumptions, and the computation of the reachability set used by fully symmetric polytope data-driven predictive control also relies on the properties of the linear system. In practice, mixed-race platoons exhibit strong nonlinear behavior, especially in driver responses. These inherent nonlinearities are not fully captured by the aforementioned methods, limiting their effectiveness in real-world applications.

[0008] In summary, existing data-driven predictive control research relies on linear model assumptions and lacks focus on data noise and external disturbances, resulting in poor robustness of the algorithm, which urgently needs to be addressed. Summary of the Invention

[0009] The present application provides a nonlinear robust data-driven predictive control method and device for a mixed vehicle platoon to address the problems in existing data-driven predictive control research, such as reliance on linear model assumptions, lack of consideration of data noise, external disturbances, and attack inputs, resulting in poor algorithm robustness.

[0010] In a first aspect, an embodiment of the present application provides a nonlinear robust data-driven predictive control method for a mixed vehicle queue, comprising the following steps: collecting a control input sequence, an attack input sequence, an interference input sequence of a leading vehicle in a target mixed vehicle queue, and a system state sequence of the target mixed vehicle queue; training a pre-constructed deep neural network based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence to establish a target lifting function of a Koopman operator, constructing an equivalent Koopman lifting system model based on the target lifting function, and using the equivalent Koopman lifting system model to construct an over-approximation system represented by a set of matrix fully symmetric polytopes; determining a data-driven reachable set of system states corresponding to the target mixed vehicle queue based on the over-approximation system, constructing a nonlinear data-driven predictive control problem using the data-driven reachable set, and solving the nonlinear data-driven predictive control problem to obtain a target control input sequence corresponding to the target mixed vehicle queue, so as to control the target mixed vehicle queue to perform corresponding operating operations through the target control input sequence.

[0011] Optionally, in one embodiment of the present application, the method of training a pre-constructed deep neural network based on the control input sequence, the attack input sequence, the interference input sequence and the system state sequence to establish a target lifting function of the Koopman operator, and constructing an equivalent Koopman lifting system model according to the target lifting function includes: constructing the deep neural network based on a preset encoder network, multiple linear networks, a decoder network and a target loss function, wherein the target loss function includes a total prediction loss function, a linear transformation loss function, a data reconstruction loss function and a regularization loss function; inputting the system state sequence into the encoder network of the deep neural network, To obtain the encoder output result, and generate a corresponding lifting function based on the encoder output result and the system state sequence; input the lifting function, the control input sequence, the attack input sequence and the interference input sequence into the corresponding linear network respectively to obtain the output result of each linear network; based on the output result of each linear network, the decoder network and the target loss function, generate the forward prediction state information corresponding to the target mixed vehicle queue, and train the deep neural network using the forward prediction state information; generate the target lifting function based on the trained deep neural network, and use the target lifting function to construct the equivalent Koopman lifting system model.

[0012] Optionally, in one embodiment of the present application, the use of the equivalent Koopman lifting system model to construct an over-approximated system represented by a matrix fully symmetric polytope set includes: obtaining a lifting state sequence corresponding to the equivalent Koopman lifting system model based on the system state sequence and the target lifting function; standardizing the system state sequence, the control input sequence, the attack input sequence, the interference input sequence and the lifting state sequence to obtain corresponding standardized data, and based on the standardized data, constructing an over-approximated system represented by a matrix fully symmetric polytope set.

[0013] Optionally, in one embodiment of the present application, the data-driven reachable set of system states corresponding to the target mixed vehicle queue is determined based on the over-approximation system, and the nonlinear data-driven predictive control problem is constructed using the data-driven reachable set, including: determining the data-driven reachable set of system states corresponding to the target mixed vehicle queue based on the over-approximation system and a preset recursive expression; converting the data-driven reachable set of system states into an interval-type reachability set, and constructing the nonlinear data-driven predictive control problem based on the interval-type reachability set.

[0014] Optionally, in one embodiment of the present application, the mathematical expression of the nonlinear data-driven predictive control problem is:

[0015]

[0016] subject to

[0017]

[0018] x(0|k)=x(k),

[0019] Wherein, u(k) represents the control input sequence of the kth time step; x(k) represents the predicted state sequence of the kth time step; and Represent the lower bound vector and upper bound vector of each state respectively; Represents the constraints on the control input; represents an over-approximated reachable set of the boosted state s(i|k) of the target mixed vehicle platoon; An over-approximated reachable set representing the system state x(i|k) of the target mixed vehicle queue; and They represent the upper and lower limits of an interval set of the over-approximation reachable set of the system state x(i|k); u(i|k) represents the i-th control input in the k-th time step; A set of fully symmetric polytopes representing the control input; A set of fully symmetric polytopes representing the interference input; A set of fully symmetric polytopes representing the attack input; and represents the set of fully symmetric polytopes of the matrix; and represents a fully symmetric polytope set of modeling errors; x(0|k) represents the first system state in the k-th time step; x(i|k) represents the i-th system state in the k-th time step; r(i|k) represents the expected state to be tracked in the k+1-th time step; Q represents the penalty weight matrix of the state quantity; R represents the penalty weight matrix of the control quantity; N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0020] In a second aspect, an embodiment of the present application provides a nonlinear robust data-driven predictive control device for a mixed vehicle queue, comprising: a data acquisition module for collecting control input sequences, attack input sequences, interference input sequences of leading vehicles in a target mixed vehicle queue, and a system state sequence of the target mixed vehicle queue; an offline learning module for training a pre-constructed deep neural network based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence to establish a target lifting function of a Koopman operator, construct an equivalent Koopman lifting system model based on the target lifting function, and use the equivalent Koopman lifting system model to construct an over-approximated system represented by a set of matrix fully symmetric polytopes; an online control module for determining a data-driven reachable set of system states corresponding to the target mixed vehicle queue based on the over-approximated system, constructing a nonlinear data-driven predictive control problem using the data-driven reachable set, and solving the nonlinear data-driven predictive control problem to obtain a target control input sequence corresponding to the target mixed vehicle queue, so as to control the target mixed vehicle queue to perform corresponding operating operations through the target control input sequence.

[0021] Optionally, in one embodiment of the present application, the offline learning module includes: a modeling unit for constructing the deep neural network based on a preset encoder network, multiple linear networks, a decoder network and a target loss function, wherein the target loss function includes a total prediction loss function, a linear transformation loss function, a data reconstruction loss function and a regularization loss function; an encoding unit for inputting the system state sequence into the encoder network of the deep neural network to obtain an encoder output result, and generating a corresponding lifting function based on the encoder output result and the system state sequence; a linear processing unit for inputting the lifting function, the control input sequence, the attack input sequence and the interference input sequence into the corresponding linear network respectively to obtain the output result of each linear network; a generation unit for generating forward prediction state information corresponding to the target mixed vehicle queue based on the output result of each linear network, the decoder network and the target loss function, so as to train the deep neural network using the forward prediction state information; a construction unit for generating the target lifting function based on the trained deep neural network, and constructing the equivalent Koopman lifting system model using the target lifting function.

[0022] Optionally, in one embodiment of the present application, the offline learning module further includes: an acquisition unit, used to obtain the boosted state sequence corresponding to the equivalent Koopman boosted system model based on the system state sequence and the target boost function; a standardization processing unit, used to perform standardization processing on the system state sequence, the control input sequence, the attack input sequence, the interference input sequence and the boosted state sequence to obtain corresponding standardized data, and based on the standardized data, construct an over-approximated system represented by a set of matrix-fully symmetric polytopes.

[0023] Optionally, in one embodiment of the present application, the online control module includes: a determination unit, used to determine the data-driven reachable set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system and a preset recursive expression; a conversion unit, used to convert the data-driven reachable set of the system state into an interval type reachability set, and construct the nonlinear data-driven predictive control problem based on the interval type reachability set.

[0024] Optionally, in one embodiment of the present application, the mathematical expression of the nonlinear data-driven predictive control problem is:

[0025]

[0026] subject to

[0027]

[0028]

[0029] x(0|k)=x(k),

[0030] Wherein, u(k) represents the control input sequence of the kth time step; x(k) represents the predicted state sequence of the kth time step; and Represent the lower bound vector and upper bound vector of each state respectively; Represents the constraints on the control input; represents an over-approximated reachable set of the boosted state s(i|k) of the target mixed vehicle platoon; An over-approximated reachable set representing the system state x(i|k) of the target mixed vehicle queue; and They represent the upper and lower limits of an interval set of the over-approximation reachable set of the system state x(i|k); u(i|k) represents the i-th control input in the k-th time step; A set of fully symmetric polytopes representing the control input; A set of fully symmetric polytopes representing the interference input; A set of fully symmetric polytopes representing the attack input; and represents the set of fully symmetric polytopes of the matrix; and represents a fully symmetric polytope set of modeling errors; x(0|k) represents the first system state in the k-th time step; x(i|k) represents the i-th system state in the k-th time step; r(i|k) represents the expected state to be tracked in the k+1-th time step; Q represents the penalty weight matrix of the state quantity; R represents the penalty weight matrix of the control quantity; N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0031] A third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the nonlinear robust data-driven predictive control method for a hybrid vehicle platoon as described in the above embodiment.

[0032] A fourth aspect of the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned nonlinear robust data-driven predictive control method for a hybrid vehicle platoon.

[0033] A fifth aspect of the present application provides a computer program product, including a computer program, which is executed to implement the above-mentioned nonlinear robust data-driven predictive control method for a mixed vehicle platoon.

[0034] Therefore, the embodiments of the present application have the following beneficial effects:

[0035] In an embodiment of the present application, control input sequences, attack input sequences, interference input sequences of the leading vehicle in the target mixed vehicle queue, and a system state sequence of the target mixed vehicle queue are collected; a pre-built deep neural network is trained based on the control input sequence, attack input sequence, interference input sequence, and system state sequence to establish a target lifting function of the Koopman operator, and an equivalent Koopman lifting system model is constructed based on the target lifting function. An over-approximation system represented by a set of fully symmetric polytopes of matrices is constructed using the equivalent Koopman lifting system model; a data-driven reachable set of system states corresponding to the target mixed vehicle queue is determined based on the over-approximation system, and a nonlinear data-driven predictive control problem is constructed using the data-driven reachable set. The nonlinear data-driven predictive control problem is solved to obtain a target control input sequence corresponding to the target mixed vehicle queue, so as to control the target mixed vehicle queue to perform corresponding operating operations using the target control input sequence, thereby achieving robust control even in the presence of interference, noise, and attacks, thereby ensuring system security and facilitating the deployment and development of intelligent connected vehicles. This solves the problems in existing data-driven predictive control research, such as reliance on linear model assumptions, lack of focus on data noise, external disturbances and attack inputs, and poor algorithm robustness.

[0036] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0038] Figure 1 This is a flowchart of a nonlinear robust data-driven predictive control method for a mixed vehicle platoon according to an embodiment of the present application;

[0039] Figure 2 A schematic diagram of a mixed vehicle platoon provided for one embodiment of the present application;

[0040] Figure 3 A schematic diagram of an execution logic of a nonlinear robust data-driven predictive control method for a mixed vehicle platoon provided in accordance with an embodiment of the present application;

[0041] Figure 4 A schematic diagram of the structure of a deep neural network provided for one embodiment of the present application;

[0042] Figure 5 1 is an exemplary diagram of a nonlinear robust data-driven predictive control device for a hybrid vehicle platoon according to an embodiment of the present application;

[0043] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application.

[0044] Among them, 10 is a nonlinear robust data-driven predictive control device for a mixed vehicle platoon; 100 is a data acquisition module, 200 is an offline learning module, 300 is an online control module; 601 is a memory, 602 is a processor, and 603 is a communication interface. DETAILED DESCRIPTION

[0045] The following describes in detail embodiments of the present application, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0046] The following describes a nonlinear robust data-driven predictive control method and apparatus for a hybrid vehicle platoon according to an embodiment of the present application with reference to the accompanying drawings. In response to the problems mentioned in the above background technology, the present application provides a nonlinear robust data-driven predictive control method for a mixed vehicle platoon. In this method, a control input sequence, an attack input sequence, an interference input sequence of the leading vehicle in the target mixed vehicle platoon, and a system state sequence of the target mixed vehicle platoon are collected; based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence, a pre-constructed deep neural network is trained to establish a target lifting function of the Koopman operator, and an equivalent Koopman lifting system model is constructed based on the target lifting function. The equivalent Koopman lifting system model is used to construct an over-approximation system represented by a set of fully symmetric polytopes of a matrix; based on the over-approximation system, a data-driven reachable set of the system state corresponding to the target mixed vehicle platoon is determined, and a nonlinear data-driven predictive control problem is constructed using the data-driven reachable set. The nonlinear data-driven predictive control problem is solved to obtain a target control input sequence corresponding to the target mixed vehicle platoon, so as to control the target mixed vehicle platoon to perform corresponding operating operations through the target control input sequence, thereby achieving robust control even in the presence of interference, noise, and attacks, thereby ensuring system safety and facilitating the deployment and development of intelligent connected vehicles. This solves the problems in existing data-driven predictive control research, such as reliance on linear model assumptions, lack of focus on data noise, external disturbances and attack inputs, and poor algorithm robustness.

[0047] Specifically, Figure 1 A flowchart of a nonlinear robust data-driven predictive control method for a mixed vehicle platoon provided in an embodiment of the present application.

[0048] like Figure 1 As shown, the nonlinear robust data-driven predictive control method for a mixed vehicle platoon includes the following steps:

[0049] In step S101 , control input sequences, attack input sequences, interference input sequences of the leading vehicle in the target mixed vehicle queue, and system state sequences of the target mixed vehicle queue are collected.

[0050] For example Figure 2 For the mixed vehicle platoon shown, the embodiment of the present application can provide a nonlinear system model of the general form of the system:

[0051] x(k+1)=f(x(k),u(k),∈(k),θ(k))+ω(k)

[0052] Where f(·) represents the nonlinear dynamics function; u(k)∈R represents the control input of the ICV; ∈(k)=v0(k)∈R represents the external disturbance (the speed of the leading vehicle); θ(k)∈R represents the adversarial attack; and represents unknown but bounded noise. These inputs satisfy the bounded condition correspond to the maximum allowed values of control input, external disturbance, adversarial attack, and noise, respectively.

[0053] By solving the least squares problem and defining the lifted state s(k) = Φ(x(k)), the linear Koopman predictor of the equation x(k+1) = f(x(k),u(k),∈(k),θ(k)) can be expressed as:

[0054] s(k+1)=As(k)+Bu(k)+H∈(k)+Jθ(k),

[0055] x(k)=Cs(k),

[0056] Among them, A, B, H, and J are linear transformation matrices in high-dimensional space, and C is the dimensionality reduction matrix from high-dimensional space to low-dimensional space.

[0057] It is understandable that the Koopman lifting system model derived using the Koopman operator provides a linear approximation of the original nonlinear dynamics. This linearization helps in formulating and solving the predictive control optimization problem. However, the presence of noise in the original system and the finite-dimensional lifting function used in the lifting function may lead to modeling errors, which may reduce the performance of the closed-loop control system. Existing methods have not yet fully solved the problem of these inaccurate modeling. In order to overcome this problem, an embodiment of the present application proposes a nonlinear robust data-driven predictive control strategy that utilizes the Koopman operator and reachability analysis.

[0058] First, the embodiments of this application require the collection and use of relevant data. For the original mixed vehicle platoon system x(k+1)=f(x(k),u(k),∈(k),θ(k))+ω(k), offline data is collected by applying control inputs to the ICVs, interference inputs to the external vehicle (lead vehicle), and attack inputs to the ICVs, thereby stimulating the mixed platoon system. It is clear from the mixed platoon system that the system state x(k) is affected by the control input u(k), interference input ∈(k), attack input θ(k), and noise ω(k).

[0059] Therefore, during the data collection phase, the embodiments of the present application need to collect the control input u(k) of the ICVs, the interference input ∈(k) of the lead vehicle, the attack input θ(k), and the system state x(k) of all vehicles in the mixed platoon system, all of which are affected by the noise ω(k).

[0060] During data collection, u(k), ∈(k), and θ(k) are manually specified, while x(k) is measurable, although ω(k) is unknown but bounded. To collect sufficient data, a series of continuous excitation inputs u(k), ∈(k), and θ(k) are applied to the hybrid fleet system with a length of T+1.

[0061] Specifically, the control input sequence U, interference input sequence E, attack input sequence F, and the corresponding state sequence X are defined as follows:

[0062] U=[u(1),u(2),…,u(T+1)]∈R 1×(T+1)

[0063] E=[∈(1),∈(2),…,∈(T+1)]∈R 1×(T+1)

[0064] F=[θ(1),θ(2),…,θ(T+1)]∈R 1×(T+1)

[0065] X=[x(1),x(2),…,x(T+1)]∈R 2n×(T+1)

[0066] In step S102, a pre-constructed deep neural network is trained based on the control input sequence, the attack input sequence, the interference input sequence and the system state sequence to establish a target lifting function of the Koopman operator, and an equivalent Koopman lifting system model is constructed according to the target lifting function, and the equivalent Koopman lifting system model is used to construct an over-approximated system represented by a set of matrix fully symmetric polytopes.

[0067] Furthermore, if Figure 3As shown, in the offline learning phase, the embodiment of the present application can use the above-mentioned pre-collected relevant data to train a pre-built deep neural network to learn the lifting function of the Koopman operator, thereby being able to approximate the nonlinear dynamics of the mixed fleet system in a higher-dimensional space. As a result, the embodiment of the present application constructs an over-approximation of the system matrix set, that is, a matrix fully symmetric polytope set. and To capture the uncertain dynamics of mixed fleets, the and It can be used to calculate the data-driven reachability set in the subsequent online control stage.

[0068] Optionally, in one embodiment of the present application, a pre-constructed deep neural network is trained based on a control input sequence, an attack input sequence, an interference input sequence, and a system state sequence to establish a target lifting function of the Koopman operator, and an equivalent Koopman lifting system model is constructed based on the target lifting function, including: constructing a deep neural network based on a preset encoder network, multiple linear networks, a decoder network, and a target loss function, wherein the target loss function includes a total prediction loss function, a linear transformation loss function, a data reconstruction loss function, and a regularization loss function; inputting the system state sequence into the encoder network of the deep neural network to obtain an encoder output result, and generating a corresponding lifting function based on the encoder output result and the system state sequence; inputting the lifting function, the control input sequence, the attack input sequence, and the interference input sequence into the corresponding linear network respectively to obtain the output result of each linear network; generating forward prediction state information corresponding to the target mixed vehicle queue based on the output result of each linear network, the decoder network, and the target loss function, so as to train the deep neural network using the forward prediction state information; generating a target lifting function based on the trained deep neural network, and constructing an equivalent Koopman lifting system model using the target lifting function.

[0069] To derive high-quality matrices A, B, H, J, and C in a linear Koopman lifting system, which characterize the nonlinear dynamics in the original system, a key challenge is to choose an appropriate lifting function Φ(x(k)); although common choices include radial basis functions, polynomial functions, and Gaussian functions, determining the optimal lifting function remains an open research problem.

[0070] To solve the above problems, the embodiment of the present application may use a deep extended dynamic pattern decomposition algorithm to model the mixed fleet system, wherein DNN (Deep Neural Network) is used to automatically construct the lifting function Φ(x(k)) of the Koopman operator.

[0071] In an embodiment of the present application, the lifting function Φ(x(k)) at time step k is defined as:

[0072]

[0073] Among them, x(k) corresponds to the first 2n basis functions of Φ(x(k)), denoted as Then, the remaining number n can be φ The basis function of -2n is expressed as And learned by DNN.

[0074] It should be noted that if Figure 4 As shown, the structure of the DNN in the embodiment of the present application mainly includes three parts: encoder network, linear network and decoder network, which are described in detail as follows:

[0075] 1. Encoder network:

[0076] The encoder network maps the system state x(k) to a high-dimensional space g(x(k)), including n φ -2n basis functions, the network is a multi-layer perceptron, including n e fully connected layers. For any hidden layer p∈1,2,…,n e , the output is defined as follows:

[0077] o e (p)=σ e (p)(W e (p)o e (p-1)+b e (p))

[0078] Among them, e (p) and o e (p-1) represents the output and input of layer p respectively, and the activation function of layer p is σ e (p); weight matrix W e (p) and the bias vector b e (p) is related to layer p, n p is the number of neurons in this layer; the encoder network is in o e (0) = x(k) as input, generating o e (n e )=g(x(k)) as output; for p∈1,2,…,n e -1 layer can apply the rectified linear unit (ReLU) activation function, while the last layer does not use an activation function; thus, the embodiment of the present application can obtain the improved state Φ(x(k)) by combining the state x(k) and the output g(x(k)) of the encoder network.

[0079] 2. Linear network:

[0080] The linear network consists of four sub-networks: linear network A, linear network B, linear network H and linear network J. Figure 4 As shown, these sub-networks are specifically designed to approximate the matrices A, B, H, and J in the Koopman lifting system; the output of the linear network is expressed as:

[0081] Φ(x(k+1))=W A Φ(x(k))+W B u(k)+W H ∈(k)+W J θ(k),

[0082] in, and Represent the weights of the linear networks A, B, H, and J respectively; in order to improve the efficiency of back propagation and accelerate convergence, the biases in all sub-networks of the linear network are set to zero.

[0083] 3. Decoder network:

[0084] The decoder network approximates the matrix C in the Koopman lifting system and reconstructs the original system state from the high-dimensional lifting space. Similar to the linear network, the output of the decoder network is the forward prediction state, which is mathematically expressed as:

[0085] x(k+1)=W C Φ(x(k+1)),

[0086] Among them, W C represents the weights of the decoder network.

[0087] To achieve excellent performance of DNN, the embodiments of the present application can train DNN by solving the following optimization problems:

[0088]

[0089] Among them, θ e ,θ A ,θ B ,θ H ,θ J and θ d Represent the learning parameters of the encoder network, linear network A, linear network B, linear network H, linear network J and decoder network respectively. The loss function Used to learn DNN parameters, which are defined as:

[0090]

[0091] Among them, α1, α2, α3 and α4 are weight coefficients; and They represent the total prediction loss, linear transformation loss, data reconstruction loss, and regularization loss respectively. The relevant loss functions are defined as follows:

[0092] 1. Total prediction loss: To ensure accurate prediction of the next state of the original system, the total prediction loss is defined as:

[0093]

[0094] 2. Linear transformation loss: The linear transformation loss aims to minimize the prediction error in the boost state space, which quantifies the difference between the predicted next boost state and the boost state obtained from the true value of the next state of the original system. The mathematical expression of the loss function is:

[0095]

[0096] 3. Data reconstruction loss: In order to minimize the data reconstruction error, the mathematical expression of the data reconstruction loss function is:

[0097]

[0098] 4. Regularization loss: To prevent overfitting, the embodiment of the present application adds a regularization term, as shown in the following formula:

[0099]

[0100] Based on the defined DNN structure and loss function, the embodiment of the present application can use pre-collected data to train the DNN. After the training is completed, the embodiment of the present application can obtain the matrices A, B, H, J and C in the Koopman boosting system, as well as the boosting function Φ(x(k)) of the neural network (i.e., the target boosting function).

[0101] It should be understood by those skilled in the art that using the Koopman operator to model the original nonlinear system with a high-dimensional linear representation will inevitably introduce model errors. Therefore, the embodiment of the present application first formulates an equivalent Koopman lifting system model that includes these model errors:

[0102] s(k+1)=As(k)+Bu(k)+H∈(k)+Jθ(k)+σ(k),

[0103]

[0104] Among them, σ(k) and represents the modeling error of the Koopman system, which is caused by inaccurate modeling and noise. Subject to the following restrictions:

[0105] |σ(k)|≤σ max ,

[0106]

[0107] in, and They represent σ(k) and The upper bound of .

[0108] During actual implementation, the estimation modeling error boundary strategy of the embodiment of the present application can draw on noise estimation methods such as the minimum statistics method, Kalman filtering method, frequency domain method and Monte Carlo method.

[0109] Optionally, in one embodiment of the present application, an equivalent Koopman lifting system model is used to construct an over-approximated system represented by a matrix fully symmetric polytope set, including: obtaining a lifting state sequence corresponding to the equivalent Koopman lifting system model based on the system state sequence and the target lifting function; standardizing the system state sequence, control input sequence, attack input sequence, interference input sequence and lifting state sequence to obtain corresponding standardized data, and based on the standardized data, constructing an over-approximated system represented by a matrix fully symmetric polytope set.

[0110] In the actual implementation process, the embodiment of the present application can use the lifting function Φ(x(k)) in Koopman and the system state sequence X to obtain the lifting state sequence S of the state s(k) in the Koopman lifting system model, as shown in the following formula:

[0111]

[0112] Afterwards, the embodiments of the present application can process all collected or calculated data into a standardized format and use it to construct a matrix of fully symmetric polytopes for reachable set calculations. and Specifically, the data series are reorganized as follows:

[0113] U _ =[u(1),u(2),…,u(T)]∈R 1×T ,

[0114] E _ =[∈(1),∈(2),…,∈(T)]∈R 1×T ,

[0115] F=[θ(1),θ(2),…,θ(T)]∈R 1×T ,

[0116] X -=[x(1),x(2),…,x(T)]∈R 2n×T .

[0117] X + =[x(2),x(3),…,x(T+1)]∈R 2n×T .

[0118]

[0119] It should be noted that for the equivalent Koopman lifting system model, modeling errors may result in multiple representations of [ABHJ] and C, which are consistent with the data sequence. In order to take this uncertainty into account, the embodiment of the present application constructs a matrix full symmetric polytope set and to over-approximate all possible system models [ABHJ] and C.

[0120] Given a data sequence U in a mixed fleet system _ 、E _ 、F _ 、X _ and X + , and the lifting function Φ(x(k)) obtained by deep neural network training is derived from the lifting system S _ and S + , the embodiment of the present application may define the modeling error sequence as follows:

[0121]

[0122] Among them, O _ and Γ - Cannot be measured directly.

[0123] In addition, the embodiment of the present application combines the modeling error σ(k) and The bounded form of is transformed into a set of fully symmetric polytopes to obtain the following formula:

[0124]

[0125] If the matrix and With complete row rank, the set of all possible [ABHJ] and C matrices can be expressed as:

[0126]

[0127] in, Represents the Moore-Penrose pseudoinverse of a matrix. and Represents the set of fully symmetric polytopes of a matrix.

[0128] Therefore, the embodiments of the present application introduce an extended dynamic modal decomposition method based on deep learning to model mixed vehicle fleets. Unlike previous work that relies on linear assumptions, the embodiments of the present application explicitly capture the nonlinear characteristics of the system. By utilizing actual measurement data and deep neural networks to approximate the Koopman operator, a high-dimensional Koopman-based linear model is generated to effectively represent the power system of the mixed vehicle fleet, eliminating the explicit model knowledge typically required by traditional methods.

[0129] In step S103, based on the over-approximated system, a data-driven reachable set of system states corresponding to the target mixed vehicle fleet is determined, and a nonlinear data-driven predictive control problem is constructed using the data-driven reachable set. The nonlinear data-driven predictive control problem is solved to obtain a target control input sequence corresponding to the target mixed vehicle fleet, so as to control the target mixed vehicle fleet to perform corresponding operating operations through the target control input sequence.

[0130] Furthermore, in the online control phase, the embodiment of the present application can calculate the optimal control input to ensure robustness. Specifically, the embodiment of the present application can first use the learned matrix fully symmetric polytope set and The set of over-approximated data-driven reachabilities of the system state within the prediction horizon is recursively computed while accounting for potential modeling errors.

[0131] Secondly, to improve computational efficiency, embodiments of the present application approximate the reachability set of the fully symmetric polytope set type as an interval-type reachability set, providing upper and lower bounds for each state. Subsequently, embodiments of the present application formulate a convex optimization problem for the nonlinear robust data-driven predictive control method by ensuring that these interval bounds remain within predefined safety constraints. This problem is solved using a decreasing horizon control strategy to determine the optimal control inputs for the ICVs, thereby ensuring safe operation even in the presence of process noise and hostile attacks.

[0132] Optionally, in one embodiment of the present application, based on the over-approximation system, a data-driven reachable set of system states corresponding to the target mixed vehicle queue is determined, and the data-driven reachable set is used to construct a nonlinear data-driven predictive control problem, including: based on the over-approximation system and a preset recursive expression, determining the data-driven reachable set of system states corresponding to the target mixed vehicle queue; converting the data-driven reachable set of system states into an interval-type reachability set, and constructing a nonlinear data-driven predictive control problem based on the interval-type reachability set.

[0133] It should be noted that during the online control phase, the goal of the embodiments of this application is to ensure that mixed fleet control is robust to unavoidable modeling errors. To achieve this, the embodiments of this application propose a nonlinear robust data-driven predictive control method that combines the Koopman operator and reachability analysis. First, the embodiments of this application calculate the reachable set of system states within the control range, while also accounting for the impact of modeling errors. Next, the embodiments of this application construct an optimization problem for the nonlinear robust data-driven predictive control method and determine the optimal control input for the ICVs by solving this problem.

[0134] In the actual implementation process, the embodiment of the present application uses the obtained model matrix cone sleeve set (i.e., the matrix fully symmetric polytope set) and The data-driven reachable set of the system state in the hybrid queue system can be determined by the following relationship. The recursive expression of the over-approximated data-driven reachable set is given by the following formula:

[0135]

[0136] in, represents the over-approximate reachable set of state x(i|k); represents the over-approximate reachable set of the lifted state s(i|k) of the system; A set of fully symmetric polytopes representing control input, interference input, and attack input respectively.

[0137] Furthermore, embodiments of the present application can design a control optimization problem based on reachable set analysis. Those skilled in the art should understand that for a mixed fleet system, offline data is often interfered with by unknown noise, making it difficult to accurately model using the Koopman boosting system model.

[0138] To solve this problem, the embodiment of the present application can reformulate the problem as a nonlinear robust data-driven predictive control problem. The core idea is to determine the control input u(k) at each time step k to ensure that the predicted state x(k) remains within the calculated reachable set, while keeping these sets within the safety constraints and minimizing the associated costs. The nonlinear robust data-driven predictive control problem can be formulated as follows:

[0139]

[0140] subject to

[0141]

[0142] x(0|k)=x(k),

[0143] Where, and Among them, ∈ max and θ max Represent the upper limits of interference and attack respectively; the optimization variables u(k)=u(0|k),u(1|k),…,u(N-1|k) and x(k)=x(0|k),x(1|k),…,x(N-1|k) in the objective function represent the control input sequence and the predicted state sequence respectively; is the expected state to be tracked at time step k+1; N is the length of the prediction horizon; the weight matrix and R∈R penalize the deviations from the state and control input, respectively.

[0144] Specifically, Q x =diag(ρ s ,ρ v ) represents the penalty weight for spacing and speed deviation; ρ s and ρ v are the corresponding weights; the decay factor 0<ξ≤1 ensures that the penalty for HDVs farther from the ICV is reduced; the constraints impose restrictions on the system state, where and and are the constraints on spacing and speed deviation respectively; in addition, 1 n is an n-dimensional column vector of all ones, represents the Kronecker product; for the control input constraint, the embodiment of the present application can define andu max The maximum control input allowed for ICVs is defined; finally, the optimization problem is initialized with the current state measurement x(k), which is classified as a convex optimization problem and is easy to solve.

[0145] In order to implement the constraint problem, the embodiment of the present application needs to confirm the predicted reachable set is a collection To achieve this, the embodiment of the present application first applies an over-approximation operation to approximate As a set of intervals:

[0146]

[0147] Afterwards, embodiments of the present application may reformulate the optimization problem to construct the final nonlinear data-driven predictive control problem.

[0148] Optionally, in one embodiment of the present application, the mathematical expression of the nonlinear data-driven predictive control problem is:

[0149]

[0150] subject to

[0151]

[0152] x(0|k)=x(k),

[0153] Where u(k) represents the control input sequence of the kth time step; x(k) represents the predicted state sequence of the kth time step; and Represent the lower bound vector and upper bound vector of each state respectively; Represents the constraints on the control input; represents the over-approximate reachable set of the promotion state s(i|k) of the target mixed vehicle platoon; The over-approximated reachable set representing the system state x(i|k) of the target mixed vehicle platoon; and They represent the upper and lower bounds of an interval set of the over-approximated reachable set of the system state x(i|k); u(i|k) represents the i-th control input in the k-th time step; A set of fully symmetric polytopes representing the control input; A set of fully symmetric polytopes representing the interference input; A set of fully symmetric polytopes representing the attack input; and represents the set of fully symmetric polytopes of a matrix; and represents the set of fully symmetric polytopes of modeling errors; x(0|k) represents the first system state in the k-th time step; x(i|k) represents the i-th system state in the k-th time step; r(i|k) represents the expected state to be tracked in the k+1-th time step; Q represents the penalty weight matrix of state quantities; R represents the penalty weight matrix of control quantities; N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0154] In an embodiment of the present application, the mathematical expression of the nonlinear data-driven predictive control problem is:

[0155]

[0156] subject to

[0157]

[0158]

[0159] x(0|k)=x(k),

[0160] Where u(k) represents the control input sequence of the kth time step; x(k) represents the predicted state sequence of the kth time step; and Represent the lower bound vector and upper bound vector of each state respectively; Represents the constraints on the control input; represents the over-approximate reachable set of the promotion state s(i|k) of the target mixed vehicle platoon; The over-approximated reachable set representing the system state x(i|k) of the target mixed vehicle platoon; and They represent the upper and lower bounds of an interval set of the over-approximated reachable set of the system state x(i|k); u(i|k) represents the i-th control input in the k-th time step; A set of fully symmetric polytopes representing the control input; A set of fully symmetric polytopes representing the interference input; A set of fully symmetric polytopes representing the attack input; and represents the set of fully symmetric polytopes of a matrix; and represents the set of fully symmetric polytopes of modeling errors; x(0|k) represents the first system state in the k-th time step; x(i|k) represents the i-th system state in the k-th time step; r(i|k) represents the expected state to be tracked in the k+1-th time step; Q represents the penalty weight matrix of state quantities; R represents the penalty weight matrix of control quantities; N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0161] It should be noted that at each time step k, the embodiment of the present application solves the final nonlinear robust data-driven predictive control optimization problem online in a rolling time domain manner, thereby generating the optimal control input sequence as shown in the following formula:

[0162] u(k)=u(0|k),u(1|k),…,u(N-1|k)

[0163] x(k)=x(0|k),x(1|k),…,x(N-1|k)

[0164] Then, embodiments of the present application may apply the first control input u(0|k) to the ICVs.

[0165] It is understood that the embodiments of the present application address modeling errors caused by noise and inaccuracy by applying nonlinear robust data-driven predictive control methods to mixed fleets. To enhance robustness, the embodiments of the present application use matrix fully symmetric polyhedron set technology for secondary learning to construct a robust system model set. In addition, the embodiments of the present application take potential interference and attacks into account by defining them as fully symmetric polyhedron sets rather than assuming them to be zero. For each control horizon, the embodiments of the present application use matrix polyhedron set technology to formulate a data-driven reachability set predictor and design an NRDDPC optimization problem to ensure that the predicted state always meets safety constraints, thereby achieving safe and optimal control of ICVs.

[0166] In summary, the embodiments of the present application can target the inherent nonlinear dynamics of mixed vehicle fleets to ensure robustness against noise, interference, and hostile attacks. In order to deal with the nonlinearity of the system, the embodiments of the present application can adopt deep Koopman operator learning technology to map the nonlinear behavior of the system into a linear representation in a high-dimensional space, providing a more tractable model for control design; in order to further enhance the robustness of the model, the embodiments of the present application introduce an over-approximated matrix fully symmetric polytope set method, which can perform secondary learning based on reachable sets, construct a global linear model, and effectively compensate for potential modeling inaccuracies; by combining Koopman operator theory with reachable set technology, the embodiments of the present application construct a nonlinear robust data-driven predictive control optimization problem to achieve robust control even in the presence of interference, noise, and attacks, thereby ensuring system safety and facilitating the deployment and development of intelligent connected vehicles.

[0167] According to the nonlinear robust data-driven predictive control method for a mixed vehicle platoon proposed in an embodiment of the present application, based on the nonlinear characteristics of a mixed platoon, the embodiment of the present application adopts the Koopman operator theory to represent the nonlinear mixed platoon system as a high-dimensional linear system, and utilizes the extended dynamic mode decomposition method to effectively use deep neural networks to learn and construct a Koopman-based linear predictor. This predictor approximates the dynamic system of the original nonlinear system and explicitly considers the uncertainty in the Koopman predictor modeling as well as the effects of noise, interference, and hostile attacks. To this end, the embodiment of the present application introduces data-driven reachability set analysis and uses a matrix-fully symmetric polytope set for secondary learning to generate a robust reachability set predictor. This predictor over-approximates the future state of the system, thereby enhancing robustness. Within the diminishing horizon framework, the embodiment of the present application formulates and solves a nonlinear robust data-driven predictive control optimization problem with safety constraints to calculate robust control inputs. A robust data-driven predictive control strategy can be designed for the nonlinear mixed platoon system, thereby ensuring system safety and performance, and solving the dual challenges of nonlinearity and robustness in mixed platoons.

[0168] Next, a nonlinear robust data-driven predictive control device for a hybrid vehicle platoon proposed according to an embodiment of the present application will be described with reference to the accompanying drawings.

[0169] Figure 5 4 is a block diagram of a nonlinear robust data-driven predictive control device for a hybrid vehicle platoon according to an embodiment of the present application.

[0170] like Figure 5 As shown, the hybrid vehicle platoon nonlinear robust data-driven predictive control device 10 includes: a data acquisition module 100 , an offline learning module 200 and an online control module 300 .

[0171] The data acquisition module 100 is used to collect the control input sequence, attack input sequence, interference input sequence of the leading vehicle in the target mixed vehicle queue, and system status sequence of the target mixed vehicle queue.

[0172] The offline learning module 200 is used to train a pre-built deep neural network based on a control input sequence, an attack input sequence, an interference input sequence, and a system state sequence to establish a target lifting function of the Koopman operator, and to construct an equivalent Koopman lifting system model based on the target lifting function, and to use the equivalent Koopman lifting system model to construct an over-approximated system represented by a set of matrix-fully symmetric polytopes.

[0173] The online control module 300 is used to determine a data-driven reachable set of system states corresponding to the target mixed vehicle fleet based on the over-approximated system, construct a nonlinear data-driven predictive control problem using the data-driven reachable set, and solve the nonlinear data-driven predictive control problem to obtain a target control input sequence corresponding to the target mixed vehicle fleet, so as to control the target mixed vehicle fleet to perform corresponding operating operations using the target control input sequence.

[0174] Optionally, in one embodiment of the present application, the offline learning module 200 includes: a modeling unit, an encoding unit, a linear processing unit, a generation unit and a construction unit.

[0175] Among them, the modeling unit is used to construct a deep neural network based on a preset encoder network, multiple linear networks, a decoder network and a target loss function, wherein the target loss function includes a total prediction loss function, a linear transformation loss function, a data reconstruction loss function and a regularization loss function.

[0176] The encoding unit is used to input the system state sequence into the encoder network of the deep neural network to obtain the encoder output result, and generate a corresponding lifting function based on the encoder output result and the system state sequence.

[0177] The linear processing unit is used to input the lifting function, the control input sequence, the attack input sequence and the interference input sequence into the corresponding linear network respectively to obtain the output result of each linear network.

[0178] The generation unit is used to generate forward prediction state information corresponding to the target mixed vehicle queue based on the output results of each linear network, the decoder network and the target loss function, so as to train the deep neural network using the forward prediction state information.

[0179] A construction unit is used to generate a target improvement function according to the trained deep neural network, and to construct an equivalent Koopman improvement system model using the target improvement function.

[0180] Optionally, in one embodiment of the present application, the offline learning module 200 further includes: an acquisition unit and a standardization processing unit.

[0181] The acquisition unit is used to obtain the boosted state sequence corresponding to the equivalent Koopman boosted system model according to the system state sequence and the target boost function.

[0182] The standardization processing unit is used to standardize the system state sequence, control input sequence, attack input sequence, interference input sequence and improved state sequence to obtain corresponding standardized data, and based on the standardized data, construct an over-approximation system represented by a set of matrix fully symmetric polytopes.

[0183] Optionally, in one embodiment of the present application, the online control module 300 includes: a determination unit and a conversion unit.

[0184] The determination unit is used to determine the data-driven reachable set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system and a preset recursive expression.

[0185] The conversion unit is used to convert the data-driven reachability set of the system state into an interval-type reachability set, and construct a nonlinear data-driven predictive control problem based on the interval-type reachability set.

[0186] Optionally, in one embodiment of the present application, the mathematical expression of the nonlinear data-driven predictive control problem is:

[0187]

[0188] subject to

[0189]

[0190]

[0191] x(0|k)=x(k),

[0192] Where u(k) represents the control input sequence of the kth time step; x(k) represents the predicted state sequence of the kth time step; and Represent the lower bound vector and upper bound vector of each state respectively; Represents the constraints on the control input; represents the over-approximate reachable set of the promotion state s(i|k) of the target mixed vehicle platoon; The over-approximated reachable set representing the system state x(i|k) of the target mixed vehicle platoon; and They represent the upper and lower bounds of an interval set of the over-approximated reachable set of the system state x(i|k); u(i|k) represents the i-th control input in the k-th time step; A set of fully symmetric polytopes representing the control input; A set of fully symmetric polytopes representing the interference input; A set of fully symmetric polytopes representing the attack input; and represents the set of fully symmetric polytopes of a matrix; and represents the set of fully symmetric polytopes of modeling errors; x(0|k) represents the first system state in the k-th time step; x(i|k) represents the i-th system state in the k-th time step; r(i|k) represents the expected state to be tracked in the k+1-th time step; Q represents the penalty weight matrix of state quantities; R represents the penalty weight matrix of control quantities; N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0193] It should be noted that the aforementioned explanation of the embodiment of the nonlinear robust data-driven predictive control method for a mixed vehicle platoon is also applicable to the nonlinear robust data-driven predictive control device for a mixed vehicle platoon of this embodiment, and will not be repeated here.

[0194] The nonlinear robust data-driven predictive control device for a mixed vehicle queue proposed in an embodiment of the present application includes a data acquisition module 100 for collecting a control input sequence, an attack input sequence, an interference input sequence of a leading vehicle in a target mixed vehicle queue, and a system state sequence of the target mixed vehicle queue; an offline learning module 200 for training a pre-built deep neural network based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence to establish a target boost function of a Koopman operator, and construct an equivalent Koopman boost system model based on the target boost function, and utilize the equivalent Koopman boost function to improve the prediction control system. The man enhancement system model constructs an over-approximated system represented by a set of fully symmetric polytopes of matrices; the online control module 300 is used to determine the data-driven reachable set of system states corresponding to the target mixed vehicle queue based on the over-approximated system, and use the data-driven reachable set to construct a nonlinear data-driven predictive control problem, and solve the nonlinear data-driven predictive control problem to obtain the target control input sequence corresponding to the target mixed vehicle queue, so as to control the target mixed vehicle queue to perform corresponding operating operations through the target control input sequence, thereby achieving robust control even in the presence of interference, noise and attacks, so as to ensure system safety and facilitate the deployment and development of intelligent connected vehicles.

[0195] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0196] A memory 601 , a processor 602 , and a computer program stored in the memory 601 and executable on the processor 602 .

[0197] When the processor 602 executes the program, the nonlinear robust data-driven predictive control method for a hybrid vehicle platoon provided in the above embodiment is implemented.

[0198] Furthermore, the electronic device further includes:

[0199] The communication interface 603 is used for communication between the memory 601 and the processor 602 .

[0200] The memory 601 is used to store computer programs that can be run on the processor 602 .

[0201] The memory 601 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0202] If the memory 601, processor 602, and communication interface 603 are implemented independently, the communication interface 603, memory 601, and processor 602 can be connected to each other via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 6 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0203] Optionally, in a specific implementation, if the memory 601, the processor 602 and the communication interface 603 are integrated on a chip, the memory 601, the processor 602 and the communication interface 603 can communicate with each other through an internal interface.

[0204] The processor 602 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0205] An embodiment of the present application further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned nonlinear robust data-driven predictive control method for a hybrid vehicle platoon.

[0206] An embodiment of the present application further provides a computer program product, including a computer program, which, when executed, is used to implement the above-mentioned nonlinear robust data-driven predictive control method for a hybrid vehicle platoon.

[0207] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0208] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this application, "N" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0209] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing a custom logical function or process step, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed in a different order than shown or discussed, including performing functions in a substantially simultaneous manner or in a reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application pertain.

[0210] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or N wires (electronic devices), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program can be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or processing it in other suitable ways as necessary, and then storing it in a computer memory.

[0211] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0212] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0213] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0214] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A nonlinear robust data-driven predictive control method for a mixed vehicle platoon, characterized in that: The following steps are involved: Collecting a control input sequence, an attack input sequence, an interference input sequence of a leading vehicle in a target mixed vehicle queue, and a system state sequence of the target mixed vehicle queue; Based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence, a pre-constructed deep neural network is trained to establish a target lifting function of a Koopman operator, and an equivalent Koopman lifting system model is constructed according to the target lifting function, and an over-approximated system represented by a set of matrix fully symmetric polytopes is constructed using the equivalent Koopman lifting system model; Based on the over-approximated system, a data-driven reachable set of system states corresponding to the target mixed vehicle fleet is determined, and a nonlinear data-driven predictive control problem is constructed using the data-driven reachable set. The nonlinear data-driven predictive control problem is solved to obtain a target control input sequence corresponding to the target mixed vehicle fleet, so as to control the target mixed vehicle fleet to perform corresponding operating operations through the target control input sequence.

2. The method according to claim 1, characterized in that The method of training a pre-built deep neural network based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence to establish a target lifting function of a Koopman operator, and constructing an equivalent Koopman lifting system model according to the target lifting function, includes: Constructing the deep neural network based on a preset encoder network, multiple linear networks, a decoder network, and a target loss function, wherein the target loss function includes a total prediction loss function, a linear transformation loss function, a data reconstruction loss function, and a regularization loss function; Inputting the system state sequence into an encoder network of the deep neural network to obtain an encoder output result, and generating a corresponding lifting function according to the encoder output result and the system state sequence; Inputting the lifting function, the control input sequence, the attack input sequence, and the interference input sequence into corresponding linear networks respectively to obtain an output result of each linear network; generating forward prediction state information corresponding to the target mixed vehicle platoon based on the output results of each linear network, the decoder network, and the target loss function, so as to train the deep neural network using the forward prediction state information; The target boosting function is generated according to the trained deep neural network, and the equivalent Koopman boosting system model is constructed using the target boosting function.

3. The method according to claim 2, characterized in that The method of using the equivalent Koopman lifting system model to construct an over-approximation system represented by a matrix fully symmetric polytope set includes: Obtaining a boosted state sequence corresponding to the equivalent Koopman boosted system model according to the system state sequence and the target boost function; The system state sequence, the control input sequence, the attack input sequence, the interference input sequence and the boost state sequence are standardized to obtain corresponding standardized data, and based on the standardized data, an over-approximated system represented by a set of matrix fully symmetric polytopes is constructed.

4. The method according to claim 3, characterized in that The method of determining a data-driven reachable set of system states corresponding to the target mixed vehicle platoon based on the over-approximated system, and constructing a nonlinear data-driven predictive control problem using the data-driven reachable set, includes: Determining a data-driven reachable set of system states corresponding to the target mixed vehicle queue based on the over-approximated system and a preset recursive expression; The data-driven reachability set of the system state is converted into an interval-type reachability set, and the nonlinear data-driven predictive control problem is constructed according to the interval-type reachability set.

5. The method according to claim 1, wherein The mathematical expression of the nonlinear data-driven predictive control problem is: subject to x(0|k)=x(k), Wherein, u(k) represents the control input sequence of the kth time step; x(k) represents the predicted state sequence of the kth time step; and Represent the lower bound vector and upper bound vector of each state respectively; Represents the constraints on the control input; represents an over-approximated reachable set of the boosted state s(i|k) of the target mixed vehicle platoon; An over-approximated reachable set representing the system state x(i|k) of the target mixed vehicle queue; and They represent the upper and lower limits of an interval set of the over-approximation reachable set of the system state x(i|k); u(i|k) represents the i-th control input in the k-th time step; A set of fully symmetric polytopes representing the control input; A set of fully symmetric polytopes representing the interference input; A set of fully symmetric polytopes representing the attack input; and represents the set of fully symmetric polytopes of the matrix; and represents a fully symmetric polytope set of modeling errors; x(0|k) represents the first system state in the k-th time step; x(i|k) represents the i-th system state in the k-th time step; r(i|k) represents the expected state to be tracked in the k+1-th time step; Q represents the penalty weight matrix of the state quantity; R represents the penalty weight matrix of the control quantity; N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

6. A nonlinear robust data-driven predictive control device for a mixed vehicle platoon, characterized in that: include: a data acquisition module, configured to acquire a control input sequence, an attack input sequence, an interference input sequence of the leading vehicle in the target mixed vehicle queue, and a system state sequence of the target mixed vehicle queue; an offline learning module for training a pre-built deep neural network based on the control input sequence, the attack input sequence, the interference input sequence, and the system state sequence to establish a target lifting function of a Koopman operator, constructing an equivalent Koopman lifting system model based on the target lifting function, and using the equivalent Koopman lifting system model to construct an over-approximated system represented by a set of matrix fully symmetric polytopes; An online control module is configured to determine, based on the over-approximated system, a data-driven reachable set of system states corresponding to the target hybrid vehicle fleet, construct a nonlinear data-driven predictive control problem using the data-driven reachable set, and solve the nonlinear data-driven predictive control problem to obtain a target control input sequence corresponding to the target hybrid vehicle fleet, so as to control the target hybrid vehicle fleet to perform corresponding operating operations using the target control input sequence.

7. The device according to claim 6, characterized in that The offline learning module includes: A modeling unit, configured to construct the deep neural network based on a preset encoder network, a plurality of linear networks, a decoder network, and a target loss function, wherein the target loss function includes a total prediction loss function, a linear transformation loss function, a data reconstruction loss function, and a regularization loss function; an encoding unit, configured to input the system state sequence into an encoder network of the deep neural network to obtain an encoder output result, and generate a corresponding lifting function according to the encoder output result and the system state sequence; a linear processing unit, configured to input the lifting function, the control input sequence, the attack input sequence, and the interference input sequence into corresponding linear networks, respectively, to obtain an output result of each linear network; a generating unit, configured to generate forward prediction state information corresponding to the target mixed vehicle platoon based on an output result of each linear network, the decoder network, and the target loss function, so as to train the deep neural network using the forward prediction state information; A construction unit is used to generate the target improvement function according to the trained deep neural network, and to construct the equivalent Koopman improvement system model using the target improvement function.

8. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the nonlinear robust data-driven predictive control method for a mixed vehicle platoon as claimed in any one of claims 1 to 5.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the nonlinear robust data-driven predictive control method for a mixed vehicle platoon as claimed in any one of claims 1 to 5.

10. A computer program product comprising a computer program, characterized in that The computer program is executed to implement the nonlinear robust data-driven predictive control method for a mixed vehicle platoon as claimed in any one of claims 1 to 5.

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