Hybrid vehicle platoon nonlinear robust data-driven predictive control method and device

Abstract

The application relates to a hybrid vehicle queue nonlinear robust data-driven predictive control method and device, wherein the method comprises the following steps: collecting control input sequences, attack input sequences, head vehicle disturbance input sequences of intelligent networked vehicles in a hybrid vehicle queue and system state sequences of the hybrid vehicle queue; training a deep neural network through the collected data sequences to establish a target lifting function of a Koopman operator, and constructing an equivalent Koopman lifting system model according to the target lifting function, and then constructing an over-approximation system represented by a matrix totally symmetric simplicial complex set; based on the over-approximation system, determining a data-driven reachable set of the system state corresponding to the hybrid vehicle queue to construct and solve a nonlinear data-driven predictive control problem and obtain a target control input sequence. Thus, the problems that the existing data-driven predictive control research relies on linear model assumptions, lacks key consideration of data noise, external disturbance and attack input and has poor algorithm robustness are solved.

Description

Technical Field

[0001] This application relates to the field of data-driven predictive control technology, and in particular to a nonlinear robust data-driven predictive control method and apparatus for hybrid vehicle platooning. Background Technology

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

[0003] However, existing fleet cooperative control technologies are primarily designed for fully intelligent connected vehicle environments. With the gradual rollout of intelligent connected vehicles, the future will see a hybrid transportation development phase where intelligent connected vehicles (ICVs) and driver-driven vehicles coexist for a long time. To realize the economic benefits of ICVs in hybrid transportation environments, breakthroughs in ICV cooperative control technologies for these environments are urgently needed.

[0004] Research on hybrid traffic control technology has attracted widespread attention and has been validated multiple times in experimental and simulation platforms. Utilizing communication methods such as vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication, ICVs can acquire information from multiple human-driven vehicles ahead and behind, incorporating them into a hybrid platoon and implementing safe and optimal control. Current research indicates that all relevant studies can be categorized as Lagrangian control methods, which treat ICVs as controllable agents within the platoon, aiming to optimize the overall performance of hybrid traffic by directly regulating the behavior of ICVs. Under this concept, most existing research on hybrid platoon control employs model-based approaches. These strategies typically use established following models, such as optimal speed models or intelligent driving models, to describe human driver behavior, enabling the development of state-space models of the hybrid platoon, which serve as the basis for controller design. Model-based control methods include robust control, linear quadratic regulators, model predictive control, and control obstacle functions. While model-based methods can provide optimal or near-optimal control with rigorous theoretical guarantees, their effectiveness largely depends on the accuracy of the underlying model. However, accurately identifying parameters in human driving behavior models is a challenging task, which may 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 hybrid vehicle fleets, but instead rely on iterative training to achieve accurate system predictions and effective control. However, they typically face challenges related to the computational complexity of training, as well as concerns about generalization ability 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, demonstrating the potential to achieve 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, showing improvements in suppressing traffic waves, reducing energy consumption, and protecting privacy and security. 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 may make ICV control systems more vulnerable to hostile attacks, such as maliciously altered control inputs or manipulated sensor data to execute attacks, potentially impacting vehicle control security. These studies often neglect the impact of noise on data collection and online predictive control, while assuming no external attacks. These assumptions may limit the ability to effectively track trajectories, lack robustness, and potentially introduce security issues.

[0007] Recent research has made significant progress in enhancing the robustness of hybrid vehicle fleet systems. For example, reformulating the DeepP-LCC method using mini-maximum robust optimization has proven effective in reducing the impact of unknown disturbances; distributed data-driven MPC methods with feedforward compensation have also proven effective against external disturbances; furthermore, fully symmetric multicellular data-driven predictive control utilizing linear reachability analysis has successfully minimized the impact of observation noise on data collection. However, under noise-free conditions, the DeepPC predictor has been shown to be equivalent to a linear MPC predictor for a linear time-invariant system; moreover, the generation of the subspace identification matrix used in the distributed data-driven MPC method with feedforward compensation depends on the linear assumption, and the computation of the reachability set used in the fully symmetric multicellular data-driven predictive control also depends on the properties of linear systems. In practice, hybrid vehicle fleets exhibit strong nonlinear behavior, especially in driver responses, and 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 a focus on data noise and external disturbances, resulting in poor robustness of the algorithms, which urgently needs to be addressed. Summary of the Invention

[0009] This application provides a nonlinear robust data-driven predictive control method and apparatus for hybrid vehicle platoons, which addresses the problems in existing data-driven predictive control research, such as reliance on linear model assumptions and lack of focus on data noise, external disturbances, and attack inputs, resulting in poor algorithm robustness.

[0010] The first aspect of this application provides a nonlinear robust data-driven predictive control method for a hybrid vehicle platoon, comprising the following steps: collecting control input sequences, attack input sequences, interference input sequences of the lead vehicle in the target hybrid vehicle platoon, and system state sequences of the target hybrid vehicle platoon; training a pre-constructed deep neural network based on the control input sequences, attack input sequences, interference input sequences, and system state sequences to establish a target boosting function of the Koopman operator, constructing an equivalent Koopman boosting system model based on the target boosting function, and constructing an over-approximation system represented by a matrix-symmetric polytope set using the equivalent Koopman boosting system model; determining the data-driven reachable set of the system state corresponding to the target hybrid vehicle platoon 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 hybrid vehicle platoon, thereby controlling the target hybrid vehicle platoon to perform corresponding operating operations through the target control input sequence.

[0011] Optionally, in one embodiment of this application, the step 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 boosting function for the Koopman operator, and constructing an equivalent Koopman boosting system model based on the target boosting 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; and inputting the system state sequence into the encoder network of the deep neural network. The encoder output is obtained, and a corresponding boosting function is generated based on the encoder output and the system state sequence. The boosting function, the control input sequence, the attack input sequence, and the interference input sequence are respectively input into the corresponding linear networks to obtain the output of each linear network. Based on the output of each linear network, the decoder network, and the target loss function, forward prediction state information corresponding to the target mixed vehicle queue is generated, and the deep neural network is trained using the forward prediction state information. The target boosting function is generated based on the trained deep neural network, and the equivalent Koopman boosting system model is constructed using the target boosting function.

[0012] Optionally, in one embodiment of this application, the step of constructing an over-approximation system represented by a set of matrix-symmetric polytopes using the equivalent Koopman boosting system model includes: obtaining a boosting state sequence corresponding to the equivalent Koopman boosting system model based on the system state sequence and the target boosting function; standardizing the system state sequence, the control input sequence, the attack input sequence, the interference input sequence, and the boosting state sequence to obtain corresponding standardized data; and constructing an over-approximation system represented by a set of matrix-symmetric polytopes based on the standardized data.

[0013] Optionally, in one embodiment of this application, the step of determining the data-driven reachability set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system, and constructing a nonlinear data-driven predictive control problem using the data-driven reachability set, includes: determining the data-driven reachability set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system and a preset recursive expression; converting the data-driven reachability set of the system state 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 this 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] Where u(k) represents the control input sequence at the k-th time step; x(k) represents the predicted state sequence at the k-th time step; and These represent the lower bound vector and upper bound vector for each state, respectively. This indicates constraints on the control inputs; This represents the over-approximate reachability set of the lifting state s(i|k) of the target mixed vehicle queue; The over-approximation reachable set of the system state x(i|k) of the target mixed vehicle queue; and Let x(i|k) represent the upper and lower bounds of an interval set of the over-approximation reachable set of the system state x(i|k), respectively; u(i|k) represents the i-th control input in the k-th time step. Represents a fully symmetric multicellular set of the control inputs; Represents a set of fully symmetric multicellular structures representing the interfering inputs; Represents a set of fully symmetric polytopes representing the attack input; and Represents the set of fully symmetric multicellular structures of the matrix; and Let x(0|k) represent the fully symmetric multicell set of modeling errors; x(0|k) represent the first system state in the k-th time step; x(i|k) represent the i-th system state in the k-th time step; r(i|k) represent the desired state to be tracked in the (k+1)-th time step; Q represents the penalty weight matrix of the state variables; R represents the penalty weight matrix of the control variables; and N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0020] A second aspect of this application provides a nonlinear robust data-driven predictive control device for a hybrid vehicle platoon, comprising: a data acquisition module for acquiring control input sequences, attack input sequences, interference input sequences of the lead vehicle in the target hybrid vehicle platoon, and system state sequences of the target hybrid vehicle platoon; an offline learning module for training a pre-constructed deep neural network based on the control input sequences, attack input sequences, interference input sequences, and system state sequences to establish a target boosting function of the Koopman operator, construct an equivalent Koopman boosting system model based on the target boosting function, and construct an over-approximation system represented by a matrix-symmetric polytope set using the equivalent Koopman boosting system model; and an online control module for determining the data-driven reachable set of the system state corresponding to the target hybrid vehicle platoon 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 hybrid vehicle platoon, so as to control the target hybrid vehicle platoon to perform corresponding operating operations through the target control input sequence.

[0021] Optionally, in one embodiment of this application, the offline learning module includes: a modeling unit, configured to construct 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, configured 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 boosting function based on the encoder output result and the system state sequence; a linear processing unit, configured to input the boosting function, the control input sequence, the attack input sequence, and the interference input sequence into the corresponding linear networks respectively to obtain the output result of each linear network; a generation unit, configured to generate 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; and a construction unit, configured to generate the target boosting function based on the trained deep neural network, and construct the equivalent Koopman boosting system model using the target boosting function.

[0022] Optionally, in one embodiment of this application, the offline learning module further includes: an acquisition unit, configured to obtain the boosted state sequence corresponding to the equivalent Koopman boosted system model based on the system state sequence and the target boosting function; and a standardization processing unit, configured to standardize 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 to construct an over-approximation system represented by a matrix-symmetric polytope set based on the standardized data.

[0023] Optionally, in one embodiment of this application, the online control module includes: a determination unit, configured to determine the data-driven reachability set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system and a preset recursive expression; and a conversion unit, configured to convert the data-driven reachability 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 this 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] Where u(k) represents the control input sequence at the k-th time step; x(k) represents the predicted state sequence at the k-th time step; and These represent the lower bound vector and upper bound vector for each state, respectively. This indicates constraints on the control inputs; This represents the over-approximate reachability set of the lifting state s(i|k) of the target mixed vehicle queue; The over-approximation reachable set of the system state x(i|k) of the target mixed vehicle queue; and Let x(i|k) represent the upper and lower bounds of an interval set of the over-approximation reachable set of the system state x(i|k), respectively; u(i|k) represents the i-th control input in the k-th time step. Represents a fully symmetric multicellular set of the control inputs; Represents a set of fully symmetric multicellular structures representing the interfering inputs; Represents a set of fully symmetric polytopes representing the attack input; and Represents the set of fully symmetric multicellular structures of the matrix; and Let x(0|k) represent the fully symmetric multicell set of modeling errors; x(0|k) represent the first system state in the k-th time step; x(i|k) represent the i-th system state in the k-th time step; r(i|k) represent the desired state to be tracked in the (k+1)-th time step; Q represents the penalty weight matrix of the state variables; R represents the penalty weight matrix of the control variables; and N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0031] A third aspect of this application provides an electronic device, including: 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 hybrid vehicle platoon nonlinear robust data-driven predictive control method as described in the above embodiments.

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

[0033] A fifth aspect of this application provides a computer program product, including a computer program that is executed to implement the above-described nonlinear robust data-driven predictive control method for hybrid vehicle platooning.

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

[0035] The embodiments of this application can collect the control input sequence, attack input sequence, interference input sequence of the lead vehicle in the target mixed vehicle queue, and system state sequence of the target mixed vehicle queue; based on the control input sequence, attack input sequence, interference input sequence, and system state sequence, a pre-constructed deep neural network is trained to establish the target lifting function of the Koopman operator, and an equivalent Koopman lifting system model is constructed according to the target lifting function. Furthermore, an over-approximation system represented by a matrix-symmetric polytope set is constructed using the equivalent Koopman lifting system model; based on the over-approximation system, the data-driven reachable set of the system state corresponding to the target mixed vehicle queue 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 the target control input sequence corresponding to the target mixed vehicle queue. This allows the target mixed vehicle queue to perform corresponding operational operations through the target control input sequence, thereby achieving robust control even in the presence of interference, noise, and attacks to ensure system safety and facilitate 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 and lack of focus on data noise, external disturbances, and attack inputs, resulting in poor algorithm robustness.

[0036] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

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

[0038] Figure 1 This is a flowchart of a nonlinear robust data-driven predictive control method for hybrid vehicle platoons provided according to an embodiment of this application;

[0039] Figure 2 A schematic diagram of a mixed vehicle queue is provided for one embodiment of this application;

[0040] Figure 3 A schematic diagram of the execution logic of a hybrid vehicle platoon nonlinear robust data-driven predictive control method provided in one embodiment of this application;

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

[0042] Figure 5 This is an example diagram of a hybrid vehicle platoon nonlinear robust data-driven predictive control device according to an embodiment of this application;

[0043] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

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

[0045] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0046] The following description, with reference to the accompanying drawings, illustrates a hybrid vehicle platoon nonlinear robust data-driven predictive control method and apparatus according to embodiments of this application. To address the problems mentioned in the background, this application provides a nonlinear robust data-driven predictive control method for hybrid vehicle platoons. This method involves collecting the control input sequence, attack input sequence, interference input sequence of the lead vehicle in the target hybrid vehicle platoon, and the system state sequence of the target hybrid vehicle platoon. Based on these sequences, a pre-constructed deep neural network is trained to establish a target lifting function for the Koopman operator. An equivalent Koopman lifting system model is then constructed based on this model, and an over-approximated system represented by a matrix-symmetric polytope set is built. Based on this over-approximated system, a data-driven reachable set of the system state corresponding to the target hybrid vehicle platoon is determined. A nonlinear data-driven predictive control problem is then constructed using this data-driven reachable set and solved to obtain the target control input sequence for the target hybrid vehicle platoon. This target control input sequence is then used to control the target hybrid vehicle platoon to perform corresponding operational operations, thereby achieving robust control even in the presence of interference, noise, and attacks, 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 and lack of focus on data noise, external disturbances, and attack inputs, resulting in poor algorithm robustness.

[0047] Specifically, Figure 1 The flowchart illustrates a nonlinear robust data-driven predictive control method for hybrid vehicle platooning provided in this application embodiment.

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

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

[0050] For example Figure 2 The mixed vehicle queue shown in this application provides a general nonlinear system model:

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

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

[0053] By solving the least squares problem and defining the lifting 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] Where A, B, H, and J are linear transformation matrices in high-dimensional space, and C is the dimension reduction matrix from high-dimensional space to low-dimensional space.

[0057] Understandably, the Koopman lift system model derived using the Koopman operator provides a linear approximation of the original nonlinear dynamics. This linearization facilitates the formulation and solution of predictive control optimization problems. However, the presence of noise in the original system and the use of a finite-dimensional lift function in the lift function can lead to modeling errors, which may degrade the performance of the closed-loop control system. Existing methods have not fully addressed these modeling inaccuracies. To overcome this problem, embodiments of this application propose 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 hybrid 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 ICVs, interference inputs to external vehicles (lead vehicles), and attack inputs to ICVs, thereby stimulating the hybrid platoon system. It can be clearly seen from the hybrid platoon system that the system state x(k) is affected by the control input u(k), the interference input ∈(k), the attack input θ(k), and the noise ω(k).

[0059] Therefore, during the data collection phase, embodiments of this 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 fleet system. All data are affected by 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 continuously excitation inputs u(k), ∈(k), and θ(k) of length T+1 are applied to the hybrid vehicle system.

[0061] Specifically, the control input sequence U, the interference input sequence E, the 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, attack input sequence, interference input sequence, and system state sequence to establish the target boosting function of the Koopman operator. An equivalent Koopman boosting system model is then constructed based on the target boosting function, and an over-approximation system represented by a matrix-symmetric polytope set is constructed using the equivalent Koopman boosting system model.

[0067] Furthermore, such as Figure 3As shown, during the offline learning phase, embodiments of this application can utilize the aforementioned pre-collected relevant data to train a pre-constructed deep neural network to learn the lifting function of the Koopman operator. This enables the approximation of the nonlinear dynamics of the hybrid vehicle system in a higher-dimensional space. Consequently, embodiments of this application construct an over-approximation of the system matrix set, namely, a matrix-fully symmetric polytopic set. and To capture the unpredictable dynamics of mixed vehicle fleets, the and In the subsequent online control phase, it can be used to compute the data-driven set of reachability.

[0068] Optionally, in one embodiment of this application, a pre-constructed deep neural network is trained based on a control input sequence, an attack input sequence, a interference input sequence, and a system state sequence to establish a target boosting function for the Koopman operator, and an equivalent Koopman boosting system model is constructed based on the target boosting function. This includes: constructing a deep neural network based on a pre-defined 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, and generating a corresponding boosting function based on the encoder output and the system state sequence; inputting the boosting function, the control input sequence, the attack input sequence, and the interference input sequence into the corresponding linear networks to obtain the output of each linear network; generating forward prediction state information corresponding to the target mixed vehicle queue based on the output of each linear network, the decoder network, and the target loss function, and using the forward prediction state information to train the deep neural network; generating a target boosting function based on the trained deep neural network, and constructing an equivalent Koopman boosting system model using the target boosting function.

[0069] To derive the high-quality matrices A, B, H, J, and C in a linear Koopman lifting system that characterize the nonlinear dynamics of the original system, a key challenge is choosing a suitable 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 address the aforementioned issues, embodiments of this application may employ a deep extended dynamic pattern decomposition algorithm to model the hybrid vehicle fleet system, wherein a DNN (Deep Neural Network) is used to automatically construct the lifting function Φ(x(k)) of the Koopman operator.

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

[0072]

[0073] Where x(k) corresponds to the first 2n basis functions of Φ(x(k)), denoted as Subsequently, in the embodiments of this application, the remaining number can be n. φ The basis functions of -2n are expressed as And it is learned by DNN.

[0074] It should be noted that, as Figure 4 As shown, the structure of the DNN in this embodiment mainly includes three parts: an encoder network, a linear network, and a decoder network, as described below:

[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 The network has -2n basis functions and is a multilayer perceptron containing n... e There are n 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, o e (p) and o e (p-1) represent 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 bias vector b e (p) is related to layer p, n p It is the number of neurons in that layer; the encoder network uses o e (0) = x(k) is used as input to generate o e (n e = g(x(k)) as the output; for p∈1,2,…,n e The layer with a value of -1 can be activated by the Modified Linear Unit (ReLU) activation function, while the last layer does not use an activation function; thus, the embodiments of this application can obtain the boosted state Φ(x(k)) by combining the state x(k) and the output g(x(k)) of the encoder network.

[0079] 2. Linear networks:

[0080] A linear network consists of four subnetworks: linear network A, linear network B, linear network H, and linear network J, such as... Figure 4 As shown, these subnetworks are specifically designed to approximate matrices A, B, H, and J in the Koopman boosting 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 These represent the weights of linear networks A, B, H, and J, respectively. To improve the efficiency of backpropagation and accelerate convergence, the biases in all subnetworks of the linear network are set to zero.

[0083] 3. Decoder Network:

[0084] The decoder network approximates matrix C in the Koopman boosting system and reconstructs the original system state from the high-dimensional boosting space. Similar to linear networks, the output of the decoder network is the forward predicted state, whose mathematical expression is:

[0085] x(k+1)=W C Φ(x(k+1)),

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

[0087] To achieve superior performance of DNNs, embodiments of this application can train DNNs by solving the following optimization problems:

[0088]

[0089] Where, θ e θ A θ B θ H θ J and θ d Let represent the learning parameters of the encoder network, linear network A, linear network B, linear network H, linear network J, and decoder network, respectively. This loss function... Used to learn DNN parameters, which are defined as follows:

[0090]

[0091] Among them, α1, α2, α3 and α4 are weighting coefficients; and These 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 Transform Loss: The linear transform loss aims to minimize the prediction error in the boosted state space. It quantifies the difference between the predicted next boosted state and the boosted state obtained from the true value of the next boosted state of the original system. The mathematical expression of this loss function is:

[0095]

[0096] 3. Data Reconstruction Loss: To minimize the data reconstruction error, the mathematical expression for the data reconstruction loss function is:

[0097]

[0098] 4. Regularization Loss: To prevent overfitting, a regularization term is added to the embodiments of this application, as shown in the following formula:

[0099]

[0100] Based on the defined DNN structure and loss function, embodiments of this application can use pre-collected data to train the DNN. After training, embodiments of this application can obtain 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] Those skilled in the art will understand that using the Koopman operator to model the original nonlinear system with a high-dimensional linear representation inevitably introduces model errors. Therefore, this application first presents an equivalent Koopman lifting system model that incorporates these model errors:

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

[0103]

[0104] Where, σ(k) and This represents the modeling error of the Koopman system, caused by inaccurate modeling and noise. The embodiments of this application assume σ(k) and... Subject to the following restrictions:

[0105] |σ(k)|≤σ max ,

[0106]

[0107] in, and Let σ(k) and σ(k) represent respectively. The upper boundary.

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

[0109] Optionally, in one embodiment of this application, constructing an over-approximation system represented by a set of matrix-fully symmetric polytopes using an equivalent Koopman boosting system model includes: obtaining the boosted state sequence corresponding to the equivalent Koopman boosting system model based on the system state sequence and the target boosting function; standardizing the system state sequence, control input sequence, attack input sequence, interference input sequence, and boosted state sequence to obtain corresponding standardized data; and constructing an over-approximation system represented by a set of matrix-fully symmetric polytopes based on the standardized data.

[0110] In actual implementation, embodiments of this application can utilize the lifting function Φ(x(k)) in Koopman and the system state sequence X to obtain the lifted state sequence S of state s(k) in the Koopman lifted system model, as shown in the following equation:

[0111]

[0112] Subsequently, embodiments of this application can process all collected or computed data into a standardized format and use it to construct a matrix-symmetric multi-cell set for reachability set computation. and Specifically, the data sequence is 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 boosting system model, modeling errors may lead to multiple representations of [ABHJ] and C, which are consistent with the data sequence. To account for this uncertainty, embodiments of this application construct a matrix-symmetric polytope set. and The system model is over-approximated by all possible system models [ABHJ] and C.

[0120] Given a data sequence U in a hybrid fleet system _ E _ F _ X _ and X + And the boosting function Φ(x(k)) obtained by training a deep neural network, derived from the S in the boosting system. _ and S + The modeling error sequence can be defined as follows in this embodiment:

[0121]

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

[0123] Furthermore, embodiments of this application utilize the modeling error σ(k) and The bounded form is transformed into a fully symmetric polytopic set to obtain the following equation:

[0124]

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

[0126]

[0127] in, This represents the Moore-Penrose pseudoinverse of the matrix. and It represents a set of fully symmetric multicellular matrix units.

[0128] Therefore, the embodiments of this application model hybrid vehicle fleets by introducing an extended dynamic mode decomposition method based on deep learning. Unlike previous work that relied on linear assumptions, the embodiments of this application explicitly capture the nonlinear characteristics of the system. By utilizing actual measurement data and deep neural network approximation of the Koopman operator, a high-dimensional Koopman-based linear model is generated, which effectively represents the dynamic system of the hybrid vehicle fleet and eliminates the explicit model knowledge usually required by traditional methods.

[0129] In step S103, based on the over-approximation system, the data-driven reachable set of the system state corresponding to the target mixed vehicle queue 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 then solved 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 the corresponding operation through the target control input sequence.

[0130] Furthermore, during the online control phase, embodiments of this application can compute the optimal control input to ensure robustness. Specifically, embodiments of this application can first utilize a learned set of matrix-symmetric polytopes. and The set of over-approximate data-driven reachability for the system state within the prediction range is calculated recursively, while taking into account potential modeling errors.

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

[0132] Optionally, in one embodiment of this application, the data-driven reachability set of the system state 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 reachability set, including: determining the data-driven reachability set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system and a preset recursive expression; converting the data-driven reachability set of the system state 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 objective of this application's embodiments is to ensure the robustness of the hybrid vehicle fleet control 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 can calculate the reachable set of the system state within the control range, while considering the impact of modeling errors. Then, 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 actual implementation, the embodiments of this application utilize the obtained model matrix cone set (i.e., the matrix fully symmetric multi-cell set). and The data-driven reachability set of the system state in a hybrid queue system can be determined through the following relationship, and the recursive expression for the over-approximation data-driven reachability set is given by the following equation:

[0135]

[0136] in, Denotes the over-approximation reachable set of state x(i|k); The set of over-approximations reachable from the improved state s(i|k) of the system; These represent fully symmetric polytopic sets representing control inputs, interference inputs, and attack inputs, respectively.

[0137] Furthermore, embodiments of this application can design control optimization problems based on reachability set analysis. Those skilled in the art should understand that for hybrid fleet systems, offline data is often subject to unknown noise, making accurate modeling using the Koopman algorithm to improve the system model more complex.

[0138] To address this problem, embodiments of this 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 safety constraints and minimizing associated costs. The nonlinear robust data-driven predictive control problem can be described as follows:

[0139]

[0140] Subject to

[0141]

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

[0143] In the formula, and Where, ∈ max and θ max These represent the upper limits of interference and attack, respectively; in the objective function, 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) represent the control input sequence and the predicted state sequence, respectively; The desired state to be tracked at time step k+1; N is the length of the prediction range; weight matrix. The deviations of the state and control inputs are penalized by R∈R, respectively.

[0144] Specifically, Q x =diag(ρ s ,ρ v ) represents the penalty weight for spacing and speed deviations; ρ s and ρ v The corresponding weights are used; the attenuation factor 0 < ξ ≤ 1 ensures reduced penalties for HDVs farther from the ICV; constraints impose restrictions on the system state, where, and and These are constraints on spacing and speed deviation, respectively; in addition, 1 n It is an n-dimensional column vector of all ones. Represents the Kronecker product; for control input constraints, embodiments of this application may define... andu max The maximum control input allowed by 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] To address this constraint, embodiments of this application require confirmation of the predicted reachability set. It is a set To achieve this, embodiments of this application first apply an over-approximation operation to approximate a subset of the subset. As an interval set:

[0146]

[0147] Subsequently, embodiments of this application can be used to reconstruct the optimization problem to construct the final nonlinear data-driven predictive control problem.

[0148] Optionally, in one embodiment of this application, the mathematical expression for 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 at the k-th time step; x(k) represents the predicted state sequence at the k-th time step; and These represent the lower bound vector and upper bound vector for each state, respectively. This indicates constraints on the control inputs; The set of over-approximate reachable states s(i|k) of the target mixed vehicle platoon is represented. The over-approximation reachability set of the system state x(i|k) of the target mixed vehicle platoon; and Let x(i|k) represent the upper and lower bounds of an interval set of the over-approximation reachable set of the system state x(i|k), respectively; u(i|k) represents the i-th control input in the k-th time step. Represents a fully symmetric multicellular set of control inputs; Represents a set of fully symmetric multicellular structures representing the interfering inputs; Represents a set of fully symmetric polytopes representing the attack input; and Represents a set of matrix-symmetric multicellular structures; and Let x(0|k) represent the fully symmetric multicell set of modeling errors; x(0|k) represent the first system state in the k-th time step; x(i|k) represent the ith system state in the k-th time step; r(i|k) represent the desired state to be tracked in the (k+1)-th time step; Q represents the penalty weight matrix of the state variables; R represents the penalty weight matrix of the control variables; and N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0154] In the embodiments of this application, the mathematical expression for 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 at the k-th time step; x(k) represents the predicted state sequence at the k-th time step; and These represent the lower bound vector and upper bound vector for each state, respectively. This indicates constraints on the control inputs; The set of over-approximate reachable states s(i|k) of the target mixed vehicle platoon is represented. The over-approximation reachability set of the system state x(i|k) of the target mixed vehicle platoon; and Let x(i|k) represent the upper and lower bounds of an interval set of the over-approximation reachable set of the system state x(i|k), respectively; u(i|k) represents the i-th control input in the k-th time step. Represents a fully symmetric multicellular set of control inputs; Represents a set of fully symmetric multicellular structures representing the interfering inputs; Represents a set of fully symmetric polytopes representing the attack input; and Represents a set of matrix-symmetric multicellular structures; and Let x(0|k) represent the fully symmetric multicell set of modeling errors; x(0|k) represent the first system state in the k-th time step; x(i|k) represent the ith system state in the k-th time step; r(i|k) represent the desired state to be tracked in the (k+1)-th time step; Q represents the penalty weight matrix of the state variables; R represents the penalty weight matrix of the control variables; and 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 embodiments of this application solve 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 equation:

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

[0165] It is understood that the embodiments of this application apply a nonlinear robust data-driven predictive control method to hybrid vehicle fleets. These embodiments address modeling errors caused by noise and inaccuracies. To enhance robustness, they employ matrix polyhedral set techniques for secondary learning to construct a robust system model set. Furthermore, these embodiments consider potential disturbances and attacks by defining them as fully symmetric polyhedral sets, rather than assuming them to be zero. For each control horizon, the embodiments use matrix polyhedral set techniques to formulate a data-driven reachability set predictor and design an NRDDPC optimization problem to ensure that the predicted state always meets safety constraints, achieving safe and optimal control of ICVs.

[0166] In summary, the embodiments of this application address the inherent nonlinear dynamics of hybrid vehicle fleets, ensuring robustness against noise, interference, and hostile attacks. To handle system nonlinearity, the embodiments of this application employ deep Koopman operator learning techniques to map the system's nonlinear behavior to a linear representation in a high-dimensional space, providing a more manageable model for control design. To further enhance the model's robustness, the embodiments of this application introduce an over-approximation matrix-symmetric polytope set method, which enables quadratic learning based on reachable sets to construct a global linear model, effectively compensating for potential modeling inaccuracies. By combining Koopman operator theory with reachable set techniques, the embodiments of this 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 hybrid vehicle platoons proposed in this application, based on the nonlinear characteristics of the hybrid vehicle platoon, this application adopts Koopman operator theory to represent the nonlinear hybrid vehicle 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 uncertainties in the Koopman predictor modeling as well as the effects of noise, interference, and hostile attacks. To this end, this application introduces data-driven reachability set analysis and uses matrix-symmetric polytope sets 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 decreasing horizon framework, this application formulates and solves the optimization problem of nonlinear robust data-driven predictive control with safety constraints to calculate robust control inputs. This allows for the design of robust data-driven predictive control strategies for nonlinear hybrid vehicle platoon systems, thereby ensuring system safety and performance and solving the dual challenges of nonlinearity and robustness in hybrid vehicle platoons.

[0168] Secondly, a hybrid vehicle platoon nonlinear robust data-driven predictive control device according to an embodiment of this application is described with reference to the accompanying drawings.

[0169] Figure 5 This is a block diagram of a hybrid vehicle queuing nonlinear robust data-driven predictive control device according to an embodiment of this 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 acquire the control input sequence, attack input sequence, interference input sequence of the lead vehicle in the target mixed vehicle queue, and system state 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 the control input sequence, attack input sequence, interference input sequence and system state sequence to establish the target boosting function of the Koopman operator, construct an equivalent Koopman boosting system model based on the target boosting function, and construct an over-approximation system represented by a matrix-fully symmetric polytope set using the equivalent Koopman boosting system model.

[0173] The online control module 300 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 to construct a nonlinear data-driven predictive control problem using the data-driven reachable set. The nonlinear data-driven predictive control problem is then solved 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 operation through the target control input sequence.

[0174] Optionally, in one embodiment of this 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] 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. 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, and to generate the corresponding boosting function based on the encoder output and the system state sequence.

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

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

[0179] The building unit is used to generate a target boosting function based on the trained deep neural network, and to construct an equivalent Koopman boosting system model using the target boosting function.

[0180] Optionally, in one embodiment of this 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 boosting state sequence corresponding to the equivalent Koopman boosting system model based on the system state sequence and the target boosting function.

[0182] The standardization processing unit is used to standardize the system state sequence, control input sequence, attack input sequence, interference input sequence, and boosting state sequence to obtain corresponding standardized data. Based on the standardized data, an over-approximation system represented by a matrix-symmetric polytope set is constructed.

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

[0184] The determining 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 the preset recursive expression.

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

[0186] Optionally, in one embodiment of this application, the mathematical expression for 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 at the k-th time step; x(k) represents the predicted state sequence at the k-th time step; and These represent the lower bound vector and upper bound vector for each state, respectively. This indicates constraints on the control inputs; The set of over-approximate reachable states s(i|k) of the target mixed vehicle platoon is represented. The over-approximation reachability set of the system state x(i|k) of the target mixed vehicle platoon; and Let x(i|k) represent the upper and lower bounds of an interval set of the over-approximation reachable set of the system state x(i|k), respectively; u(i|k) represents the i-th control input in the k-th time step. Represents a fully symmetric multicellular set of control inputs; Represents a set of fully symmetric multicellular structures representing the interfering inputs; Represents a set of fully symmetric polytopes representing the attack input; and Represents a set of matrix-symmetric multicellular structures; and Let x(0|k) represent the fully symmetric multicell set of modeling errors; x(0|k) represent the first system state in the k-th time step; x(i|k) represent the ith system state in the k-th time step; r(i|k) represent the desired state to be tracked in the (k+1)-th time step; Q represents the penalty weight matrix of the state variables; R represents the penalty weight matrix of the control variables; and N is the length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

[0193] It should be noted that the foregoing explanation of the embodiment of the nonlinear robust data-driven predictive control method for hybrid vehicle platoons also applies to the nonlinear robust data-driven predictive control device for hybrid vehicle platoons in this embodiment, and will not be repeated here.

[0194] The hybrid vehicle platoon nonlinear robust data-driven predictive control device proposed in this application includes a data acquisition module 100, used to acquire the control input sequence, attack input sequence, interference input sequence of the lead vehicle in the target hybrid vehicle platoon, and system state sequence of the target hybrid vehicle platoon; and an offline learning module 200, used to train a pre-constructed deep neural network based on the control input sequence, attack input sequence, interference input sequence, and system state sequence to establish the target boosting function of the Koopman operator, and to construct an equivalent Koopman boosting system model based on the target boosting function, and to utilize the equivalent Koopman boosting system model. The man-enhanced system model is constructed using an over-approximation system represented by a matrix-symmetric multi-cell set. The online control module 300 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 to construct a nonlinear data-driven predictive control problem using the data-driven reachable set. The nonlinear data-driven predictive control problem is solved to obtain the target control input sequence corresponding to the target mixed vehicle queue. The target control input sequence is used to control the target mixed vehicle queue to perform corresponding operation, thereby achieving robust control even in the presence of interference, noise, and attacks to ensure system safety and facilitate the deployment and development of intelligent connected vehicles.

[0195] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0196] The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0197] When the processor 602 executes the program, it implements the nonlinear robust data-driven predictive control method for hybrid vehicle queuing provided in the above embodiments.

[0198] Furthermore, electronic devices also include:

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

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

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

[0202] If the memory 601, processor 602, and communication interface 603 are implemented independently, then the communication interface 603, memory 601, and processor 602 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, 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, processor 602, and communication interface 603 are integrated on a single chip, then the memory 601, processor 602, and 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 this application.

[0205] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described nonlinear robust data-driven predictive control method for hybrid vehicle platooning.

[0206] This application also provides a computer program product, including a computer program, which, when executed, is used to implement the above-described nonlinear robust data-driven predictive control method for hybrid vehicle platoons.

[0207] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

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

[0209] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0210] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing 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 (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs 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: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0211] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0212] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

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

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

Claims

1. A hybrid vehicle platoon nonlinear robust data-driven predictive control method, characterized in that, Includes the following steps: Collect the control input sequence, attack input sequence, interference input sequence of the lead vehicle in the target mixed vehicle queue, and 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 the target boosting function of the Koopman operator, and an equivalent Koopman boosting system model is constructed according to the target boosting function. Furthermore, the equivalent Koopman boosting system model is used to construct an over-approximation system characterized by a matrix-fully symmetric polytope set. Based on the over-approximation system, a data-driven reachable set of the system state corresponding to the target mixed vehicle queue 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 then solved to obtain the target control input sequence corresponding to the target mixed vehicle queue, and the target mixed vehicle queue is controlled to perform corresponding operation through the target control input sequence. The step 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 the target boosting function of the Koopman operator, and constructing an equivalent Koopman boosting system model based on the target boosting function, includes: The deep neural network is constructed 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. The system state sequence is input into the encoder network of the deep neural network to obtain the encoder output, and a corresponding boosting function is generated based on the encoder output and the system state sequence. The boosting function, the control input sequence, the attack input sequence, and the interference input sequence are respectively input into the corresponding linear networks to obtain the output results of each linear network; Based on the output of each linear network, the decoder network, and the target loss function, forward prediction state information corresponding to the target mixed vehicle queue is generated, so as to train the deep neural network using the forward prediction state information; The target boosting function is generated based on the trained deep neural network, and the equivalent Koopman boosting system model is constructed using the target boosting function. The mathematical expression for the nonlinear data-driven predictive control problem is: Subject to in, Indicates the first A control input sequence for each time step; Indicates the first The predicted state sequence at each time step; and These represent the lower bound vector and upper bound vector for each state, respectively; Represents constraints on control inputs. Indicates the elevation status of the target mixed vehicle queue. The over-approximate reachable set; The system state representing the target mixed vehicle queue The over-approximate reachable set; and These respectively represent the system states. The lower and upper bounds of an interval set that can be reached by an over-approximation set; Indicates the first The first time step One control input; Represents a fully symmetric multicellular set of the control inputs; Represents a set of fully symmetric multicellular structures representing the interfering input; Represents a set of fully symmetric polytopes representing the attack input; and Represents the set of fully symmetric multicellular structures of the matrix; and Represents the set of fully symmetric multicells representing modeling errors. Indicates the first The first system state in each time step; Indicates the first The first time step Each system state; Indicates the first +1 more time steps to track the desired state; The penalty weight matrix represents the state variables; The penalty weight matrix represents the control quantity; The length of the prediction range corresponding to the nonlinear data-driven predictive control problem.

2. The method according to claim 1, characterized in that, The construction of an over-approximation system represented by a matrix-fully symmetric polytopic set using the equivalent Koopman lifting system model includes: Based on the system state sequence and the target lifting function, the lifting state sequence corresponding to the equivalent Koopman lifting system model is obtained; The system state sequence, the control input sequence, the attack input sequence, the interference input sequence, and the boosting state sequence are standardized to obtain corresponding standardized data. Based on the standardized data, an over-approximation system characterized by a matrix-symmetric polytope set is constructed.

3. The method according to claim 2, characterized in that, The process of determining the data-driven reachability set of the system state corresponding to the target mixed vehicle queue based on the over-approximation system, and constructing a nonlinear data-driven predictive control problem using the data-driven reachability set, includes: Based on the over-approximation system and the preset recursive expression, the data-driven reachable set of the system state corresponding to the target hybrid vehicle queue is determined; 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 based on the interval-type reachability set.

4. A hybrid vehicle platoon nonlinear robust data-driven predictive control device, used to implement the hybrid vehicle platoon nonlinear robust data-driven predictive control method as described in any one of claims 1-3, characterized in that, include: The data acquisition module is used to acquire the control input sequence, attack input sequence, interference input sequence of the lead vehicle in the target mixed vehicle queue, and system state sequence of the target mixed vehicle queue; The offline learning module is used to train 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 the target boosting function of the Koopman operator, construct an equivalent Koopman boosting system model based on the target boosting function, and construct an over-approximation system represented by a matrix-fully symmetric polytope set using the equivalent Koopman boosting system model. The online control module 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, 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 the target control input sequence corresponding to the target mixed vehicle queue, so as to control the target mixed vehicle queue to perform corresponding operation through the target control input sequence.

5. The apparatus according to claim 4, characterized in that, The offline learning module includes: The modeling unit is used to construct 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. 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 boosting function based on the encoder output result and the system state sequence; A linear processing unit is used to input the boosting function, the control input sequence, the attack input sequence, and the interference input sequence into the corresponding linear networks respectively, so as to obtain the output result of each linear network; 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; The building unit is used to generate the target boosting function based on the trained deep neural network, and to construct the equivalent Koopman boosting system model using the target boosting function.

6. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the hybrid vehicle platoon nonlinear robust data-driven predictive control method as described in any one of claims 1-3.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the hybrid vehicle platoon nonlinear robust data-driven predictive control method as described in any one of claims 1-3.

8. A computer program product, comprising a computer program, characterized in that, The computer program is executed to implement the hybrid vehicle platoon nonlinear robust data-driven predictive control method as described in any one of claims 1-3.

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