Automatic driving fleet transverse dynamics inclusion control method based on output feedback

Abstract

The invention relates to an automatic driving fleet transverse dynamics inclusion control method based on output feedback, and the method comprises the steps: constructing a transverse dynamics model of an automatic driving vehicle, abstracting the transverse dynamics model as a leader following multi-agent system, and constructing a communication topological graph; designing an open-loop reference model and a closed-loop reference model for the follower agent; an open-loop reference model is constructed, the open-loop reference model comprises a controller, reference control input of a follower agent is solved, and the open-loop reference model is converged into a convex hull formed by the system state of the leader vehicle; and constructing a decentralized model reference adaptive output controller, updating the gain matrix and resolving the control input of the follower vehicle, so that the follower vehicle tracks the open-loop reference model, and the inclusion control of the automatic driving vehicle is realized. According to the method, when uncertain system parameters, unknown input gains and directed communication topology exist, the stability of a closed-loop system can still be ensured, a multi-agent inclusion control target is realized, and the engineering realizability and robustness of the method are improved.

Description

Technical Field

[0001] This invention relates to the field of unmanned swarm control technology, and more particularly to a lateral dynamics control method for an autonomous driving fleet based on output feedback. Background Technology

[0002] In applications such as autonomous driving fleet cooperative control, unmanned system platooning, and swarm robotics, the dynamics of multiple vehicles / machines are often abstracted as a multi-agent system, achieving cooperative behavior through information exchange via communication networks. "Inclusion control," as a crucial branch of leader-follower cooperative control, typically requires the follower's state or output to eventually converge and enter the convex hull spanned by multiple leader trajectories, thereby achieving objectives such as fleet formation maintenance, queue safety constraints, and cooperative maneuvering. Taking the lateral dynamics of autonomous vehicles as an example, the vehicle's lateral offset and heading angle error constitute the follower system's state vector. The leader corresponds to the lead vehicle (or multiple key vehicles) in the fleet, and its state forms the reference boundary for fleet cooperative control. Under communication topology constraints, each follower vehicle does not need to precisely track a specific lead vehicle. Instead, through local information exchange, it gradually enters and maintains its lateral offset and heading angle states within the convex hull safety region spanned by multiple leader trajectories, thus achieving formation maintenance and safety constraints that are "keeping up without crossing boundaries." It should be noted that under the influence of factors such as changes in road surface adhesion coefficient, speed measurement error, and load variation, the model often suffers from problems such as parameter uncertainty or even unknown input gain, which brings certain challenges to the lateral dynamics and control problems of the vehicle fleet.

[0003] Existing research has proposed various distributed protocols and output feedback methods for inclusion control and consensus control. However, many schemes rely on known system dynamics and measurable full states. When the communication topology is a directed graph and information is limited, these methods often require additional global topology information, conservative prior estimates, or more complex hierarchical structures, significantly increasing engineering implementation costs and parameter tuning difficulties. Furthermore, in leaderless or multi-leader scenarios, system uncertainties propagate through network coupling, amplifying the complexity of closed-loop analysis and stability proofs. This results in insufficient applicability and robustness of existing methods under the combined conditions of "directed communication + available output + parameter uncertainty." Therefore, it is necessary to further investigate an inclusion control method that is easier to implement in a decentralized manner and more robust to uncertainty. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a lateral dynamics-inclusive control method for autonomous driving fleets based on output feedback. This method solves the problems of traditional approaches relying on known system dynamics and measurable full-state conditions, as well as insufficient applicability and robustness caused by the accumulation of system uncertainties. This invention designs a decentralized control and parameter adaptive update mechanism, ensuring closed-loop system stability and achieving multi-agent inclusive control objectives even with uncertain system parameters, unknown input gains, and directed communication topologies. Simultaneously, it avoids strong dependence on full-state measurability, thereby improving the method's engineering feasibility and robustness.

[0005] To achieve the above technical objectives, the present invention provides the following technical solution: a control method for the lateral dynamics of an autonomous driving fleet based on output feedback, comprising the following steps: Construct a lateral dynamics model for autonomous vehicles; Using the leader vehicle and follower vehicles as intelligent agents, the lateral dynamics model of the autonomous vehicle is abstracted into a leader-follower multi-agent system; the leader-follower multi-agent system includes a follower vehicle dynamics model and a leader vehicle dynamics model; the intelligent agents include follower intelligent agents and leader intelligent agents; A communication topology graph is constructed based on the leader-follower multi-agent system, with agents as nodes and communication relationships between agents as edges. Design an open-loop reference model for the follower agent, update the system state and control output of the open-loop reference model for each follower agent, and calculate the control output error of the open-loop reference model. An observer gain matrix is ​​introduced to design a closed-loop reference model for the follower agent. The estimated control output and estimated system state of the follower agent are solved, and the control output error of the closed-loop reference model is calculated. Construct a follower state estimator and update the estimated state of each follower agent by combining the control output of the open-loop reference model; Construct a leader state estimator and update the estimated state of each leader agent; The open-loop reference model is constructed by including the controller, combining the communication topology graph, the estimated states of the leader agent and the follower agent, and solving the reference control input of the follower agent so that the open-loop reference model converges to the convex hull spanned by the system state of the leader vehicle. A decentralized model reference adaptive output controller is constructed. Based on the control output error of the closed-loop reference model and the control output error of the open-loop reference model, and combined with the reference control input of the follower agent, the control input of the follower vehicle is calculated, so that the follower vehicle tracks the open-loop reference model, thereby realizing the inclusion control of the autonomous vehicle.

[0006] Optionally, the lateral dynamics model of the autonomous vehicle is described by the following equations: ; in, This represents the lateral offset of the vehicle relative to the lane centerline. This represents the vehicle's heading angle error. , They are respectively , The first-order time derivatives describe respectively , Dynamic changes over time; , , These are the vehicle's front wheel lateral stiffness, mass, and longitudinal velocity, respectively. Representing the unknown input gain, it is a diagonal matrix with positive elements. This is the control input to be designed.

[0007] Optionally, the follower vehicle dynamics model is described by the following equations: ; in, Indicates the number is The system status of the following vehicles, including their lateral offset and heading angle error. for The first-order time derivative describes Dynamic changes over time; This is a transpose operation; The system matrix for following vehicles; Let be the unknown input gain, and be a diagonal matrix with positive elements; , These are the input matrix and the output matrix, respectively. , They represent the numbers respectively. The control inputs and outputs of the follower vehicles; The leader vehicle dynamics model is described by the following equations: ; in, The number is indicated. The system status of the leader vehicle, including the leader vehicle's lateral offset and heading angle error. for The first-order time derivative describes Dynamic changes over time; The system matrix for leader vehicles; , They represent the numbers respectively. The leader's vehicle's control inputs and control outputs, and Bounded.

[0008] Optionally, the leader-following multi-agent system, triplet It is controllable and observable, and the transfer function... For strict and truthful purposes, among which Represents the identity matrix. express The inverse matrix, Represents the complex frequency domain variables of the Laplace transform; This is a transpose operation; The leader-following multi-agent system has an ideal matching gain. , making ,and , It is a set of known uncertainties.

[0009] Optionally, the communication topology is undirected between follower agents, and for each follower agent, there exists at least one leader agent that can reach that follower agent via a directed path.

[0010] Optionally, the step of designing an open-loop reference model for the follower agent includes: designing an open-loop reference model for each follower agent, described by the following equations: ; in, Represents follower intelligent agents The system state of the open-loop reference model, Represents follower intelligent agents The control output of the open-loop reference model, Represents follower intelligent agents Reference control input, The system matrix for leader vehicles, For the input matrix, This is the output matrix; for The first-order time derivative describes Dynamic changes over time; The introduction of the observer gain matrix to design a closed-loop reference model for the follower agent includes: designing a closed-loop reference model for each follower agent that corresponds to the open-loop reference model, described by the following equations: ; in, Represents follower intelligent agents Estimate the system state, Represents follower intelligent agents The estimated control output, for The first-order time derivative describes Dynamic changes over time; Represents the observer gain matrix; Indicates the number is The control output of the follower vehicle, i.e., the follower intelligent agent. Control output; The open-loop reference model control output error is calculated as follows: ; in Represents follower intelligent agents Open-loop reference model controls output error; The closed-loop reference model control output error is calculated as follows: ; in Represents follower intelligent agents The closed-loop reference model controls the output error.

[0011] Optionally, the follower state estimator is described by the following equation: ; in, Represents follower intelligent agents The estimated state, for The first-order time derivative describes Dynamic changes over time; The system matrix for leader vehicles, For the input matrix, This is the output matrix; Represents follower intelligent agents Reference control input; This is a transpose operation; Represents follower intelligent agents The control output of the open-loop reference model; The leader state estimator is described by the following equation: ; in, Represents the leader intelligent agent The estimated state, for The first-order time derivative describes Dynamic changes over time Represents the leader intelligent agent The control output, Represents the leader intelligent agent Input, This represents the output error feedback gain matrix; The open-loop reference model includes a controller described by the following equations: ; in, This represents the feedback gain matrix, which performs a linear weighted mapping on the neighbor difference information. The coupling gain coefficient represents the coefficient that adjusts the strength of the linear differential feedback term. Represents the follower agents in the adjacency matrix of the communication topology graph. With the leader intelligent agent Connection weights; Represents the follower agents in the adjacency matrix of the communication topology graph. With follower intelligent agents Connection weights; Indicates the adjustment of nonlinear functions The coupling gain coefficient corresponding to the strength of the feedback term, and , ; This represents the total number of following vehicles, which is equivalent to the total number of following agents. For nonlinear functions, with nonlinear function of independent variable The definition is as follows: ; in, It is a constant used to characterize the width of the boundary layer; This indicates the calculation of the Euclidean norm.

[0012] Optionally, the construction of a decentralized model reference adaptive output controller, based on the closed-loop reference model control output error and the open-loop reference model control output error, combined with the reference control input of the follower agent, updates the gain matrix and solves for the control input of the follower vehicle, including: A decentralized model reference adaptive output controller is designed for the follower vehicle dynamics model, described by the following equations: ; in, Indicates the number is The control input of the follower vehicle, This represents the feedback gain under ideal conditions. This represents the ideal coupling gain. Indicates pre-selected adjustment The adaptive adjustment matrix for updating speed. Indicates pre-selected adjustment The adaptive adjustment matrix for updating speed. and They are intelligent agents For ideal matched gain and The estimate, Indicates unknown input gain The inverse matrix, Indicates time, for The first-order time derivative describes Dynamic changes over time for The first-order time derivative describes Dynamic changes over time This is a transpose operation; Represents follower intelligent agents Open-loop reference model controls output error; Represents follower intelligent agents The closed-loop reference model controls the output error.

[0013] Optionally, the observer gain matrix Designed for ;in, The positive scalar adjustment coefficient representing the observer gain, and .

[0014] The present invention also provides an output feedback-based lateral dynamics-inclusive control system for autonomous driving fleets, for applying the aforementioned output feedback-based lateral dynamics-inclusive control method for autonomous driving fleets, comprising: The dynamics model building module is used to construct the lateral dynamics model of autonomous vehicles and abstract it as a leader-follower multi-agent system; The reference model building module is used to design an open-loop reference model for the follower agent and to design a closed-loop reference model by introducing the observer gain matrix. The reference model controller module is used to construct an open-loop reference model containing a controller, and, in conjunction with the communication topology diagram and the estimated states of the leader and follower agents, calculates the reference control input of the follower agent and sends it to the vehicle output controller module. The vehicle output controller module is used to construct a decentralized model reference adaptive output controller. Based on the closed-loop reference model control output error and the open-loop reference model control output error, it combines the reference control input from the follower agent from the reference model controller module to update the gain matrix and solve the control input of the follower vehicle, which is then sent to the vehicle-included control module. The vehicle includes a control module for receiving control inputs from the follower vehicle from the vehicle output controller module, thereby enabling the autonomous vehicle to be controlled.

[0015] By employing the above technical solution, the present invention provides a control method for the lateral dynamics of an autonomous driving fleet based on output feedback, which has at least the following beneficial effects: (1) The method proposed in this invention can complete the construction and online update of the control law by relying only on the local output information and neighbor output information of each agent, reducing the dependence on full state measurement and centralized information, and thus making it easier to deploy and scale up in engineering. (2) In view of the common problems of model uncertainty and input channel uncertainty in multi-agent systems, this invention introduces corresponding adaptive gain and compensation mechanism so that the inclusion error of the closed-loop system satisfies the stability index such as consistent eventual boundedness, and theoretically ensures that the system state of the follower vehicle can converge into the convex hull formed by the leader vehicle, thereby achieving the inclusion control objective. (3) This invention provides a parameter selection method based on stability analysis and linear matrix inequality conditions, making the controller design process more operable and repeatable; (4) The simulation results further show that the adaptive gain can converge to a finite value and the system state convergence effect is significant, which verifies the effectiveness and robustness of the method of the present invention in typical lateral dynamics scenarios of autonomous vehicles. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This invention provides a control flowchart for a control method for the lateral dynamics of an autonomous driving fleet based on output feedback. Figure 2 This is a schematic diagram of the communication topology constructed based on the leader-follower multi-agent system of the present invention; Figure 3 This is a two-dimensional schematic diagram showing the change of the lateral offset of the follower vehicle and the leader vehicle over time in the simulation verification of an embodiment of the present invention. Figure 4 This is a two-dimensional schematic diagram showing the change of heading angle error of the follower vehicle and the leader vehicle over time in the simulation verification of an embodiment of the present invention; Figure 5 This is a three-dimensional schematic diagram showing the changes in lateral offset and heading angle error of the follower vehicle and the leader vehicle over time during simulation verification of an embodiment of the present invention. Figure 6 The adaptive gain is used for simulation verification in the embodiments of the present invention. and A schematic diagram illustrating the process of change over time. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0018] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0019] Please refer to Figures 1-6 This illustration demonstrates a specific implementation of this embodiment. This embodiment constructs a lateral dynamics model of the autonomous vehicle and abstracts it as a leader-follower multi-agent system, constructing a communication topology graph. Open-loop and closed-loop reference models are designed for the follower agents. An open-loop reference model containing a controller is constructed, and the reference control input of the follower agents is calculated, causing the open-loop reference model to converge to the convex hull spanned by the system state of the leader vehicle. A decentralized model reference adaptive output controller is constructed, updating the gain matrix and calculating the control input of the follower vehicles, enabling the follower vehicles to track the open-loop reference model and achieve inclusion control of the autonomous vehicle. This ensures the stability of the closed-loop system and achieves the inclusion control objective of the multi-agent system even with uncertain system parameters, unknown input gains, and directed communication topology. Simultaneously, it avoids strong dependence on fully measurable states, thereby improving the engineering feasibility and robustness of the method.

[0020] This embodiment proposes a lateral dynamics-based control method for autonomous driving fleets, which includes the following steps: S1. Construct a lateral dynamics model for autonomous vehicles.

[0021] As a preferred embodiment of step S1, it specifically includes: Consider the following class of lateral dynamics models for autonomous vehicles: ;(Formula 1) in, This represents the lateral offset of the vehicle relative to the lane centerline. This refers to the vehicle's heading angle error, which is the angle between the vehicle's current heading angle and the road tangent direction. , They are respectively , The first-order time derivatives describe respectively , Dynamic changes over time; , , These are the vehicle's front wheel lateral stiffness, mass, and longitudinal velocity, respectively. Representing the unknown input gain, it is a diagonal matrix with positive elements, describing uncertainties in the vehicle control process, such as changes in road friction coefficient and longitudinal velocity. Measurement errors or disturbances, etc. This is the control input to be designed.

[0022] S2. Taking the leader vehicle and follower vehicles as intelligent agents, the lateral dynamics model of the autonomous vehicle is abstracted into a leader-follower multi-agent system.

[0023] This invention is considered to contain The cluster system of autonomous vehicles involves control problems, and the lateral dynamics model of the above-mentioned autonomous vehicles is abstracted into a class of leader-follower multi-agent systems.

[0024] As a preferred embodiment of step S2, it specifically includes: For the following vehicle, consider the following dynamic model with parameter uncertainties: ;(Formula 2) Formula 2 is the dynamics model of the following vehicle, where Indicates the number is The system status of the following vehicles, including their lateral offset and heading angle error. for The first-order time derivative describes Dynamic changes over time; This is a transpose operation; The system matrix for following vehicles; Let be the unknown input gain, and be a diagonal matrix with positive elements; , These are the input matrix and the output matrix, respectively. , They represent the numbers respectively. The control inputs and outputs of the follower vehicles; Represents the space of real numbers. Indicates system state Dimensions Indicates control input With control output The dimension. In the control process of this invention, the input matrix... Output matrix It is known, while the system matrix and unknown input gain It is unknown. and These are used to characterize cases where the dynamics are unknown and the input gain is unknown, respectively.

[0025] For the leader vehicle, consider the following dynamics model: ;(Formula 3) Formula 3 is the leader vehicle dynamics model, where, The number is indicated. The system status of the leader vehicle, including the leader vehicle's lateral offset and heading angle error. for The first-order time derivative describes Dynamic changes over time; The system matrix for the leader vehicle, and Known; , They represent the numbers respectively. The leader's vehicle control inputs and control outputs.

[0026] Assume there is One follower vehicle, If there are leader vehicles, then the index sets of follower vehicles and leader vehicles are represented as follows: and ,in For the set of indexes of follower vehicles, For the leader vehicle index set.

[0027] Consider the following assumptions 1-4: Assumption 1 (Matching Condition): There exists an ideal matching gain. , making ,in Given a matrix, and , It is a set of known uncertainties.

[0028] Assumption 2 (KYP Lemma Conditions): Triples It is controllable and observable, and the transfer function... For strict and truthful purposes, among which Represents the identity matrix. express The inverse matrix, The complex frequency domain variable (complex number) represents the Laplace transform and is used to express the state-space form of the reference model as a transfer function. This is a transpose operation.

[0029] Assumption 3 (Input Uncertainty): It is a diagonal matrix with positive elements.

[0030] Assumption 4: The control inputs to the leader's vehicle are bounded, i.e. ,in A positive number indicates The upper boundary.

[0031] S3. Construct a communication topology graph based on the leader-follower multi-agent system, with agents as nodes and communication relationships between agents as edges.

[0032] As a preferred embodiment of step S3, it specifically includes: Consider the following assumption 5: Assumption 5: There are no direct connections between the follower agents, and for each follower agent, there exists at least one leader agent that can reach it via a directed path.

[0033] Let the constructed communication topology be denoted as . , For communication topology diagram The associated Laplace matrix, the communication topology diagram Used to represent the logical relationships that allow communication connections to be established between agents. Since the leader agent has no neighboring nodes, the Laplace matrix... The block representation is as follows: ; in Representing the communication topology diagram The Laplacian submatrix corresponding to the follower subgraph is used to characterize the communication relationships between follower agents. This represents the coupling submatrix between the follower agent and the leader agent, used to characterize the reachability of each follower agent to the leader agent's information and its weights.

[0034] Based on assumptions 1-5, we can obtain the following lemmas 1 and 2: Lemma 1: Under the condition that Assumption 2 holds, there exists a matrix ,as well as ,in For a certain matrix, For positive integers, such that .

[0035] Lemma 2: Under the condition that Assumption 5 holds, the matrix All eigenvalues ​​of the matrix are positive; Each element is nonnegative; and The sum of the elements in each row is equal to 1.

[0036] in Represents a symmetric positive definite matrix (Lyapunov matrix); Represents a symmetric positive definite matrix, used in equations The dissipation term in the equation characterizes the rate of error energy decay and ensures that the Lyapunov equation has a positive definite solution. This represents the design matrix / weight matrix associated with the strictly positive real (SPR) condition of the transfer function, used for construction. Make it stable. The dimension of the matrix matches the output dimension and can be any given constant matrix, preferably an identity matrix or a diagonal positive definite matrix, used to weight different output channels; Represents positive scalar design parameters, used to enhance... Its positive definiteness and numerical stability, and Let be any positive integer.

[0037] The communication topology diagram constructed in this step, using the leader vehicle (leader agent) and follower vehicles (follower agents) as nodes, can be found in the following reference. Figure 2 . Figure 2 The middle arrow indicates the direction of communication / information interaction, that is, information is sent from the node indicated by the tail of the arrow and received by the node pointed to by the arrow (directed edge).

[0038] S4. Design an open-loop reference model for the follower agent and introduce an observer gain matrix to design a closed-loop reference model. Update the system state and control output of the open-loop reference model of each follower agent, solve the estimated control output and estimated system state of the follower agent, and then calculate the control output error of the open-loop reference model and the control output error of the closed-loop reference model.

[0039] As a preferred embodiment of step S4, the design of an open-loop reference model for the follower agent specifically includes: For each follower agent Design an open-loop reference model (ORM) described by the following equations: ;(Formula 4) in, Represents follower intelligent agents The system state of the open-loop reference model, Represents follower intelligent agents The control output of the open-loop reference model, Represents follower intelligent agents The reference control input needs to be calculated later; for The first-order time derivative describes Dynamic changes over time.

[0040] As a preferred embodiment of step S4, the introduction of the observer gain matrix to design the closed-loop reference model specifically includes: For each follower agent Design a closed-loop reference model (CRM) corresponding to the open-loop reference model, described by the following equations: ;(Formula 5) in, Represents follower intelligent agents Estimate the system state, Represents follower intelligent agents The estimated control output, for The first-order time derivative describes Dynamic changes over time; This represents the observer gain matrix, which needs to be designed later. Indicates the number is The control output of the follower vehicle, i.e., the follower intelligent agent. The control output.

[0041] As a preferred embodiment of step S4, the open-loop reference model control output error is calculated as follows: ; in Represents follower intelligent agents The open-loop reference model controls the output error.

[0042] As a preferred embodiment of step S4, the closed-loop reference model control output error is calculated as follows: ; in Represents follower intelligent agents The closed-loop reference model controls the output error.

[0043] S5. Construct an open-loop reference model including the controller, and combine the communication topology diagram, the estimated states of the leader agent and the follower agent to solve the reference control input of the follower agent, so that the open-loop reference model converges to the convex hull spanned by the system state of the leader vehicle.

[0044] As a preferred embodiment of step S5, the specific process includes: S51. Construct a follower state estimator to estimate the state of the follower agent. The follower state estimator is described by the following equation: ;(Formula 8a) in, Represents follower intelligent agents The estimated state, for The first-order time derivative describes Dynamic changes over time; express, This represents the dimension of the system output vector.

[0045] S52. Construct a leader state estimator to estimate the state of the leader agent. The leader state estimator is described by the following equation: ;(Formula 9) in, Represents the leader intelligent agent The estimated state, for The first-order time derivative describes Dynamic changes over time Represents the leader intelligent agent The output, Represents the leader intelligent agent Input.

[0046] S53. Based on the state estimation results of the follower agent and the leader agent, an open-loop reference model including a controller is constructed, and the reference control input of the follower agent is calculated. The open-loop reference model including the controller is described by the following equation: ;(Formula 8b) in This represents the feedback gain matrix, which performs a linear weighted mapping on the neighbor difference information. Indicates reference control input dimensionality The coupling gain coefficient represents the coefficient that adjusts the strength of the linear differential feedback term. Represents the follower agents in the adjacency matrix of the communication topology graph. With the leader intelligent agent Connection weights; Represents the follower agents in the adjacency matrix of the communication topology graph. With follower intelligent agents Connection weights; Indicates the adjustment of nonlinear functions The coupling gain coefficient corresponding to the strength of the feedback term, and , ; This represents the total number of following vehicles, which is equivalent to the total number of following agents. For nonlinear functions, with nonlinear function of independent variable The definition is as follows: ;(Formula 10) in, The value is a constant used to characterize the width of the boundary layer, which refers to a continuous buffer area artificially set near the sliding mode switching surface to smooth out discontinuous switching control and reduce chattering during actual execution. This indicates the calculation of the Euclidean norm.

[0047] make and define ; in, Indicates the first The extended state vector of each follower agent This represents the expanded state vector formed by all follower agents. The overall vector obtained by stacking This represents the overall vector obtained by stacking the leader's extended state vectors. Let represent the overall network extended state vector obtained by concatenating the extended state vectors of the follower agents and the leader agents; Representing the Kronecker product (an extended operation of system structure), the closed-loop network dynamics can be obtained from Equation 4, Equations 8a and 8b, and can be written in the following form: ;(Formula 11) in , They are respectively , The first-order time derivatives describe respectively , Dynamic changes over time express An identity matrix of order 1. express An identity matrix of order 1. This represents the control input vector of the leader agent. Represents the system matrix of the leader vehicle in the open-loop reference model. With observer injection gain The extended state system matrix is ​​defined as follows: ; This indicates that the extended state system is controlled by reference control input. (Reference control input) The input channel matrix (for distributed coupled signals) entering the system is defined as follows: ; The input matrix corresponding to the extended state system is defined as follows: ; The stacking vector representing the nonlinear coupling terms of each follower agent is defined as follows: ; Represents the extended state vector The mapping matrix is ​​defined as follows: ; In this case, an inclusion error of the following form is introduced. : ;(Formula 12) in express An identity matrix of order 1, including error You can then obtain: ;(Formula 13) and ;in To include error The first-order time derivative describes Dynamic changes over time.

[0048] Therefore, we can construct the following Theorem 1: Theorem 1: Under the condition that Assumptions 1-4 hold, design the parameters in Formulas 8a and 8b such that... It is the Hurwitz matrix. , ,and ,in Linear matrix inequalities The solution, Representation matrix The smallest eigenvalue, Indicates all Take the maximum value. To indicate The upper bound of the equation; then the error described by Equation 12 is included. It is uniformly bounded, and thus the open-loop reference model (Equation 4) can converge to the convex hull spanned by the system state of the leader vehicle.

[0049] The following proof demonstrates that the open-loop reference model converges to the convex hull spanned by the system state of the leader vehicle in this step.

[0050] First, consider the Lyapunov function. as follows: ; in, This represents the Lyapunov weight matrix (symmetric positive definite), used to construct... And perform stability proofs, based on the given block matrix form. , , The construction is defined as: ,in Denotes a Lyapunov matrix (symmetric positive definite), and satisfy ; Let be a positive constant to be determined. This can be easily verified using Schur's supplementary lemma. And because It can be seen that the Lyapunov function It is a positive definite function.

[0051] Following the trajectory of Formula 12, The time derivative can be obtained as: ;(Formula 14) in Indicates by The auxiliary vector obtained after the equivalent transformation is used to define the nonlinear terms in the subsequent Lyapunov analysis; make ; in Indicates the inclusion error The transformation error vector obtained after performing linear coordinate transformation The invertible transformation matrix is ​​defined as: , Represents the identity matrix.

[0052] Formula 14 can then be rewritten as: ;(Formula 15) Formula 15 utilizes ,and ; In the above formula This represents the block weight matrix introduced in Lyapunov analysis. This represents the state matrix of the extended state system. This represents the input channel matrix representing the reference control input in the extended state system. The input matrices of the extended state system are defined as follows: ; ; ; .

[0053] Consider the following scenario: ,have ; in This represents the calculation of the Euclidean norm. Representation matrix The Line number Column elements; then it is not difficult to obtain: ;(Formula 16) in Represents the transformation error vector Middle and the first Subvectors corresponding to each follower Indicated by It serves as an auxiliary vector for the overall nonlinear coupling of the independent variable; Given the set of indices for the leader agent, according to hypothesis 4, Represents the leader intelligent agent The upper bound of the input; further, we can obtain: ;(Formula 17) Substituting formulas 16 and 17 into formula 15, we get: ; For satisfying The following situation can be obtained from formulas 17, 10, and 16: ; ; Clearly, in this case: ;(Formula 18) For satisfying , For interval A random integer value within the range, and In the mixed case, following similar derivation steps to the two cases above, it is not difficult to obtain: ; Therefore, as can be seen from the above, for all , All satisfy the inequality in Formula 18, where Represents the extended state vector of the entire network The dimension of. Further note We can obtain: ;(Formula 19) also: ;(Formula 20) in This represents the construction of a diagonal matrix, which involves arranging multiple scalars or matrices sequentially in diagonal positions. Because From Formula 10, we can know Furthermore, by selecting a sufficiently large... And by using Schur's supplementary lemma, we can obtain Combining formulas 19 and 20, we can obtain... Therefore, as shown in Formula 18, it includes error. It is uniformly bounded. That is, the open-loop reference model (Equation 4) can converge to the convex hull spanned by the system state of the leader vehicle.

[0054] This invention addresses the common problems of model uncertainty and input channel uncertainty in multi-agent systems by introducing corresponding adaptive gain and compensation mechanisms. This ensures that the inclusion error of the closed-loop system meets stability indices such as consistent eventual boundedness, and theoretically guarantees that the system state of the follower vehicle can converge into the convex hull formed by the leader vehicle, thereby achieving the inclusion control objective.

[0055] S6. Construct a decentralized MRACO controller (MRACO: Model Reference Adaptive Output Control). Based on the control output error of the closed-loop reference model and the control output error of the open-loop reference model, and combined with the reference control input of the follower agent, update the gain matrix and solve the control input of the follower vehicle, so that the follower vehicle tracks the open-loop reference model, thereby achieving inclusive control of the autonomous vehicle.

[0056] As a preferred embodiment of step S6, the construction of a decentralized model reference adaptive output controller, based on the closed-loop reference model control output error and the open-loop reference model control output error, combined with the reference control input of the follower agent, updates the gain matrix and solves for the control input of the follower vehicle, specifically includes:

[0057] A decentralized model reference adaptive output controller is designed for the follower vehicle dynamics model, described by the following equations: ;(Formula 6) in, Indicates the number is The control input of the follower vehicle, This represents the ideal state feedback gain, used to generate the ideal feedback control term for a single agent relative to the reference model. This represents the ideal coupling gain, used to generate ideal distributed control terms that reflect the coupling effect of neighbor information. Indicates pre-selected adjustment The adaptive adjustment matrix for updating speed. Indicates pre-selected adjustment The adaptive adjustment matrix for updating speed. and It can maintain the stability of the adaptive law while adjusting the update speed. and They are intelligent agents For ideal matched gain and The estimate, Indicates time, for The first-order time derivative describes Dynamic changes over time for The first-order time derivative describes Dynamic changes over time; Represents follower intelligent agents Open-loop reference model controls output error; Represents follower intelligent agents The closed-loop reference model controls the output error.

[0058] Based on assumptions 1-4, the following proposition 1 can be constructed: Proposition 1: Under the condition that Assumptions 1-4 hold, consider any following agent in Formula 2. The corresponding open-loop reference model (ORM) is shown in Equation 4, and the closed-loop reference model (CRM) is shown in Equation 5. The observer gain matrix in Equation 5... Designed for , making

[0059] in , Represents a symmetric matrix block. The positive scalar adjustment coefficient (design parameter) representing the observer gain is used to adjust the observer error convergence speed, and ; Represents a symmetric matrix block (the decision matrix for the Linear Matrix Inequality (LMI)). Defined in Lemma 1. Then, under the action of the decentralized model reference adaptive output controller (Equation 6), when the reference control input... When bounded, decentralized tracking can be achieved, that is... Furthermore, the ideal matching gain estimate and It will converge to a matrix with certain elements having finite values.

[0060] In step S5, the open-loop reference model (Equation 4) converges to the convex hull spanned by the system state of the leader vehicle, and the reference control input can be further obtained. Bounded, as can be seen from Proposition 1, the following vehicle The corresponding open-loop reference model can be traced (Equation 4), that is... In summary, the system status of the following vehicle. The convergence to the convex hull formed by the system state of the leader vehicle, i.e., the follower vehicle dynamics model (Equation 2), achieves containment control.

[0061] The method proposed in this invention can complete the construction and online update of control laws by relying only on the local output information and neighbor output information of each agent, reducing the dependence on full-state measurement and centralized information, thus making it easier for engineering deployment and scale expansion. At the same time, this invention provides a parameter selection method based on stability analysis and linear matrix inequality conditions, making the controller design process more operable and repeatable.

[0062] The above control process can be referred to Figure 1 The entire control process can be viewed as a two-layer structure. The first layer consists of each follower vehicle (..., follower...). Followers Followers ...) traces the corresponding open-loop reference model (..., ORM) through a decentralized model reference adaptive output controller. ORM ORM The decentralized model reference adaptive output controller is shared by the first and second layers. The second layer centralized model reference adaptive output controller and the open-loop reference model contain controller (..., contain controller) Includes controller Includes controller The leader vehicles (leader1, ..., leaderNM) communicate through a communication network, causing the open-loop reference model to converge to the convex hull spanned by the leader states (i.e., the system states of the leader vehicles).

[0063] This application also provides an output feedback-based lateral dynamics-inclusive control system for autonomous driving fleets, used to apply the aforementioned output feedback-based lateral dynamics-inclusive control method for autonomous driving fleets, including: The dynamics model building module is used to construct the lateral dynamics model of autonomous vehicles and abstract it as a leader-follower multi-agent system; The reference model building module is used to design an open-loop reference model for the follower agent and to design a closed-loop reference model by introducing the observer gain matrix. The reference model controller module is used to construct an open-loop reference model containing a controller, and, in conjunction with the communication topology diagram and the estimated states of the leader and follower agents, calculates the reference control input of the follower agent and sends it to the vehicle output controller module. The vehicle output controller module is used to construct a decentralized model reference adaptive output controller. Based on the closed-loop reference model control output error and the open-loop reference model control output error, it combines the reference control input from the follower agent from the reference model controller module to update the gain matrix and solve the control input of the follower vehicle, which is then sent to the vehicle-included control module. The vehicle includes a control module for receiving control inputs from the follower vehicle from the vehicle output controller module, thereby enabling the autonomous vehicle to be controlled.

[0064] To enable researchers in this field to better understand the implementation of this invention, Matlab software is used for simulation verification.

[0065] The specific information about the simulation software is as follows: Software Name: MATLAB; Version information: 24.2.0.2712019 (R2024b); License number: 968398; Operating System: Microsoft Windows 11 Home Chinese Edition Version 10.0 (Build 26200); Java version: Java 1.8.0_202-b08 with Oracle Corporation Java HotSpot(TM) 64-Bit Server VM mixed mode; Special toolboxes: Statistics and Machine Learning Toolbox-11.7 (R2020a), Aircraft Control Toolbox-1.0.

[0066] This invention is based on a class of multi-agent autonomous vehicle systems, considering the lateral dynamics model of the autonomous vehicle (Equation 1) and Figure 2 The communication topology diagram will As the lateral offset of the vehicle, As the heading angle error of the vehicles, the system contains a total of eight vehicles ( Among them, vehicles numbered 1-6 are follower vehicles, and vehicles numbered 7-8 are leader vehicles. Each vehicle follows the dynamic equation of the form 21 below: ;(Formula 21) Define the system matrix of the following vehicles. Input matrix Unknown input gain Output matrix The system matrix of leader vehicles .choose Adaptive gain , The initial value is 0, with a fixed gain. , . , , , , .

[0067] In this simulation verification, the lateral offset of the follower vehicle and the leader vehicle over time can be referenced. Figure 3 In this embodiment, the changes in the heading angle error of the follower vehicle and the leader vehicle over time can be referenced. Figure 4 In this embodiment, the changes in lateral offset and heading angle error of the follower and leader vehicles over time can be referenced. Figure 5 . Figure 3 , Figure 4 , Figure 5 The proposed control method demonstrates that the system state of the following vehicles can converge to the convex hull formed by the system state of the leader vehicle. This shows that the lateral position and heading angle of the following vehicles gradually enter the safe and feasible region spanned by the trajectory of the leader vehicle in the road coordinate system, thereby achieving the cooperative following and lane keeping control objectives of the convoy in actual road scenarios.

[0068] In this embodiment, adaptive gain is verified through simulation. and The process of change over time can be seen by reference. Figure 6 . Figure 6 The proposed control method demonstrates that the adaptive gain can eventually converge to a finite value.

[0069] Simulation results further demonstrate that the adaptive gain can converge to a finite value, and the system state convergence effect is significant, verifying the effectiveness and robustness of the method of the present invention in typical lateral dynamics scenarios of autonomous vehicles.

[0070] 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. 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 those different embodiments or examples.

[0071] 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).

[0072] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A control method for lateral dynamics of an autonomous driving fleet based on output feedback, characterized in that, include: Construct a lateral dynamics model for autonomous vehicles; Using the leader vehicle and follower vehicles as intelligent agents, the lateral dynamics model of the autonomous vehicle is abstracted into a leader-follower multi-agent system; the leader-follower multi-agent system includes a follower vehicle dynamics model and a leader vehicle dynamics model; the intelligent agents include follower intelligent agents and leader intelligent agents; A communication topology graph is constructed based on the leader-follower multi-agent system, with agents as nodes and communication relationships between agents as edges. Design an open-loop reference model for the follower agent, update the system state and control output of the open-loop reference model for each follower agent, and calculate the control output error of the open-loop reference model. An observer gain matrix is ​​introduced to design a closed-loop reference model for the follower agent. The estimated control output and estimated system state of the follower agent are solved, and the control output error of the closed-loop reference model is calculated. Construct a follower state estimator and update the estimated state of each follower agent by combining the control output of the open-loop reference model; Construct a leader state estimator and update the estimated state of each leader agent; The open-loop reference model is constructed by including the controller, combining the communication topology graph, the estimated states of the leader agent and the follower agent, and solving the reference control input of the follower agent so that the open-loop reference model converges to the convex hull spanned by the system state of the leader vehicle. A decentralized model reference adaptive output controller is constructed. Based on the control output error of the closed-loop reference model and the control output error of the open-loop reference model, and combined with the reference control input of the follower agent, the control input of the follower vehicle is calculated, so that the follower vehicle tracks the open-loop reference model, thereby realizing the inclusion control of the autonomous vehicle.

2. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 1, characterized in that: The lateral dynamics model of the autonomous vehicle is described by the following equations: ； in, This represents the lateral offset of the vehicle relative to the lane centerline. This represents the vehicle's heading angle error. , They are respectively , The first-order time derivatives describe respectively , Dynamic changes over time; , , These are the vehicle's front wheel lateral stiffness, mass, and longitudinal velocity, respectively. Representing the unknown input gain, it is a diagonal matrix with positive elements. This is the control input to be designed.

3. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 1, characterized in that: The dynamics model of the follower vehicle is described by the following equations: ； in, Indicates the number is The system status of the following vehicles, including their lateral offset and heading angle error. for The first-order time derivative describes Dynamic changes over time; This is a transpose operation; The system matrix for following vehicles; Let be the unknown input gain, and be a diagonal matrix with positive elements; , These are the input matrix and the output matrix, respectively. , They represent the numbers respectively. The control inputs and outputs of the follower vehicles; The leader vehicle dynamics model is described by the following equations: ； in, The number is indicated. The system status of the leader vehicle, including the leader vehicle's lateral offset and heading angle error. for The first-order time derivative describes Dynamic changes over time; The system matrix for leader vehicles; , They represent the numbers respectively. The leader's vehicle's control inputs and control outputs, and Bounded.

4. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 3, characterized in that: The leader-following multi-agent system, triplet It is controllable and observable, and the transfer function... For strict and truthful purposes, among which Represents the identity matrix. express The inverse matrix, Represents the complex frequency domain variables of the Laplace transform; This is a transpose operation; The leader-following multi-agent system has an ideal matching gain. , making ,and , It is a set of known uncertainties.

5. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 1, characterized in that: The communication topology is such that there are undirected connections between follower agents, and for each follower agent, there exists at least one leader agent that can reach that follower agent through a directed path.

6. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 1, characterized in that: The design of open-loop reference models for follower agents includes: designing an open-loop reference model for each follower agent, described by the following equations: ； in, Represents follower intelligent agents The system state of the open-loop reference model, Represents follower intelligent agents The control output of the open-loop reference model, Represents follower intelligent agents Reference control input, The system matrix for leader vehicles, For the input matrix, This is the output matrix; for The first-order time derivative describes The dynamic changes over time; the introduction of the observer gain matrix to design a closed-loop reference model for the follower agent includes: designing a closed-loop reference model for each follower agent that corresponds to the open-loop reference model, described by the following equations: ； in, Represents follower intelligent agents Estimate the system state, Represents follower intelligent agents The estimated control output, for The first-order time derivative describes Dynamic changes over time; Represents the observer gain matrix; Indicates the number is The control output of the follower vehicle, i.e., the follower intelligent agent. Control output; The open-loop reference model control output error is calculated as follows: ;in Represents follower intelligent agents The open-loop reference model controls the output error; The closed-loop reference model control output error is calculated as follows: ;in Represents follower intelligent agents The closed-loop reference model controls the output error.

7. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 1, characterized in that: The follower state estimator is described by the following equation: ； in, Represents follower intelligent agents The estimated state, for The first-order time derivative describes Dynamic changes over time; The system matrix for leader vehicles, For the input matrix, This is the output matrix; Represents follower intelligent agents Reference control input; This is a transpose operation; Represents follower intelligent agents The control output of the open-loop reference model; The leader state estimator is described by the following equation: ； in, Represents the leader intelligent agent The estimated state, for The first-order time derivative describes Dynamic changes over time Represents the leader intelligent agent The control output, Represents the leader intelligent agent Input, This represents the output error feedback gain matrix; The open-loop reference model includes a controller described by the following equations: ； in, This represents the feedback gain matrix, which performs a linear weighted mapping on the neighbor difference information. The coupling gain coefficient represents the coefficient that adjusts the strength of the linear differential feedback term. Represents the follower agents in the adjacency matrix of the communication topology graph. With the leader intelligent agent Connection weights; Represents the follower agents in the adjacency matrix of the communication topology graph. With follower intelligent agents Connection weights; Indicates the adjustment of nonlinear functions The coupling gain coefficient corresponding to the strength of the feedback term, and , ; This represents the total number of following vehicles, which is equivalent to the total number of following agents. For nonlinear functions, with nonlinear function of independent variable The definition is as follows: ； in, It is a constant used to characterize the width of the boundary layer; This indicates the calculation of the Euclidean norm.

8. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 6, characterized in that: The construction of a decentralized model reference adaptive output controller, based on the closed-loop reference model control output error and the open-loop reference model control output error, combined with the reference control input of the follower agent, updates the gain matrix and solves for the control input of the follower vehicle, including: A decentralized model reference adaptive output controller is designed for the follower vehicle dynamics model, described by the following equations: ； in, Indicates the number is The control input of the follower vehicle, This represents the feedback gain under ideal conditions. This represents the ideal coupling gain. Indicates pre-selected adjustment The adaptive adjustment matrix for updating speed. Indicates pre-selected adjustment The adaptive adjustment matrix for updating speed. and They are intelligent agents For ideal matched gain and The estimate, Indicates unknown input gain The inverse matrix, Indicates time, for The first-order time derivative describes Dynamic changes over time for The first-order time derivative describes Dynamic changes over time This is a transpose operation; Represents follower intelligent agents The open-loop reference model controls the output error; Represents follower intelligent agents The closed-loop reference model controls the output error.

9. The control method for lateral dynamics of an autonomous driving fleet based on output feedback according to claim 7, characterized in that: The observer gain matrix Designed for ;in, The positive scalar adjustment coefficient representing the observer gain, and .

10. A lateral dynamics control system for an autonomous driving fleet based on output feedback, used to apply the lateral dynamics control method for an autonomous driving fleet based on output feedback as described in any one of claims 1-9, characterized in that, include: The dynamics model building module is used to construct the lateral dynamics model of autonomous vehicles and abstract it as a leader-follower multi-agent system; The reference model building module is used to design an open-loop reference model for the follower agent and to design a closed-loop reference model by introducing the observer gain matrix. The reference model controller module is used to construct an open-loop reference model containing a controller, and, in conjunction with the communication topology diagram and the estimated states of the leader and follower agents, calculates the reference control input of the follower agent and sends it to the vehicle output controller module. The vehicle output controller module is used to construct a decentralized model reference adaptive output controller. Based on the closed-loop reference model control output error and the open-loop reference model control output error, it combines the reference control input from the follower agent from the reference model controller module to update the gain matrix and solve the control input of the follower vehicle, which is then sent to the vehicle-included control module. The vehicle includes a control module for receiving control inputs from the follower vehicle from the vehicle output controller module, thereby enabling the autonomous vehicle to be controlled.

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