Multi-vehicle system event-triggered preset time two-division platoon control method

Abstract

The application relates to a multi-vehicle system event-triggered preset time two-division platoon control method. A preset time controller is constructed by introducing a time-varying function, so that two-division time-varying platoon tracking can be realized at a preset time. Meanwhile, an event-triggered controller is established based on a designed continuous event controller and an event-triggered function, communication resources are effectively saved, and the stability of a vehicle platoon system is ensured.

Description

Technical Field

[0001] This invention pertains to multi-vehicle time-varying formation control technology, specifically relating to a binary formation control method for multi-vehicle systems with event-triggered preset times. Background Technology

[0002] The multi-vehicle binary formation problem typically refers to constructing cooperative relationships between vehicles while considering their competitive relationships, given a single lead vehicle and multiple follower vehicles. In practical applications, considering the impact of competition is essential, such as in area search and rescue and multi-target encirclement. In recent years, binary formation / consistency control has become a research focus. Furthermore, the controller design involves several key factors, including the error convergence time of formation construction, when vehicles exchange information, and when actuators perform operations. In addition, the design of vehicle event trigger functions is crucial, requiring minimizing communication resource waste while ensuring system stability and preventing the Zeno phenomenon in the event-triggered controller. In summary, multi-vehicle formation systems are a typical system optimization problem. The goal is to design a suitable controller to maximize system performance and overall efficiency, while ensuring stable convergence to a specified formation, addressing the convergence time and communication constraints.

[0003] The convergence time of a system is a crucial performance criterion. Traditional asymptotic stability is no longer sufficient for the demands of rapid system response. This led to the development of finite-time (FT) and fixed-time (FXT) control concepts, but these have limitations, as the convergence time depends on the system's design parameters and initial conditions. The concept of preset-time (PT) control effectively inherits the advantages of both FT and FXT control, precisely setting the system convergence time. Furthermore, the control input is smooth during dynamic processes and exhibits strong robustness against external disturbances.

[0004] The basic idea of ​​Event Triggered Control (ETC) is to abandon traditional periodic (or continuous) sampling / control and instead transform it into intentional, opportunistic non-periodic sampling / control. This effectively solves the problem of when to sample / control the system and has the advantage of saving communication resources. In Event Triggered Control, the Zeno phenomenon must be avoided; the Zeno phenomenon refers to the system's inability to avoid an unlimited number of triggers within a finite time period.

[0005] Currently, existing technologies primarily focus on multi-agent system control under fixed-time event-triggered control and preset-time time-varying formation control for high-order nonlinear systems. In fixed-time system control, the system's settling time is highly dependent on the initial conditions and system parameter design, resulting in the drawback of the settling time not converging to zero at a specified moment and typically involving large control inputs. In preset-time time-varying formation control for high-order nonlinear systems, communication resources are wasted; when the system is stable, inter-vehicle information transmission and actuator operation are meaningless when the error is too small or zero. Therefore, in practical applications, it is necessary to design a preset-time time-varying formation controller for high-order nonlinear systems based on event-triggered control algorithms. Summary of the Invention

[0006] The purpose of this invention is to provide a binary formation control method for multi-vehicle system event triggering preset time, which considers the vehicle steering angle and internal system factors as dynamic variables of the event triggering interval for high-order nonlinear vehicle systems, thereby reducing the number of triggers and saving communication resources.

[0007] The present invention adopts the following technical solution: A multi-vehicle system event-triggered preset-time binary formation control method, employing the following controller: in, Indicates the vehicle's controller input; Indicates the input from the neighbor's vehicle controller; Indicates the weight of information exchange between following vehicles; This indicates the weight of information exchange between the lead vehicle and the following vehicles. This is the quality matrix; Represented as a rotation matrix; It is a time-varying function; Represents the linearization parameters of the vehicle system; the system's position error. ; The initial position error; the velocity error of the system. ; This refers to the initial velocity error. , and These are the expected output formation vectors for the vehicles; It is a positive constant; This indicates whether the leader's vehicle and the following vehicles follow the same trajectory. Indicates the leader's acceleration; Auxiliary functions representing system design; For followers The latest event trigger time; , , , , , , , , , , These represent the parameters at the trigger time. The value below.

[0008] Furthermore, the position error of the system is expressed as: ; The speed error of the system is expressed as: .

[0009] in, This indicates the system's position error; This indicates the system's speed error; Indicates the vehicle's location; This represents the linearization parameters of the vehicle model's speed; , , This represents the desired output formation vector for the vehicles.

[0010] Furthermore, auxiliary functions for system design The form of expression is as follows: ; in, ; Auxiliary functions representing system design; and Auxiliary functions for design; This indicates the system's position error; This indicates the system's speed error.

[0011] Furthermore, the event triggering condition is expressed as follows: Where E represents the event triggering error. It is a constant that satisfies . For followers The latest event trigger time; This is the quality matrix; Represented as a rotation matrix; Auxiliary functions representing system design.

[0012] Furthermore, the event triggering error is: in, Indicates the event triggering error. This is the quality matrix; Represented as a rotation matrix; Indicates the weight of information exchange; This indicates the information exchange between the following vehicle and the lead vehicle; and These are the expected output formation vectors for the vehicles; express At the moment of triggering the vehicle Control input; It is a time-varying function; This represents the system linearization parameters at the moment the vehicle is triggered; Represents the linearization parameters of the system over continuous time; system position error. System speed error ; Auxiliary functions representing system design; This indicates the auxiliary function that constructs the set at the triggering time.

[0013] An application of the above-mentioned control method in time-varying formation control of multiple vehicles.

[0014] The beneficial effects of this invention are as follows: the control algorithm of this invention is no longer the traditional mass model and linear system model, but adopts a high-order nonlinear vehicle model that includes factors such as mass and steering angle, which is more realistic.

[0015] This invention introduces a class of time-varying functions across the entire time domain to construct a bipartite formation controller for a high-order nonlinear multi-vehicle system under a preset time. Through two types of auxiliary functions, it is proven that the tracking error of the formation system can converge to zero within the preset time. Based on the designed preset-time controller, this invention proposes a novel dynamic event triggering function for high-order vehicle systems that incorporates two dynamic factors. This effectively improves the resource waste problem in the formation control system while ensuring system stability and error convergence to zero within the preset time.

[0016] The preset time controller of the present invention controls the position and velocity changes of the system by using acceleration as the control input. While maintaining the preset time characteristics of the system, it greatly simplifies the controller design of the system and can realize the time-varying characteristics of the system, thereby enhancing the robustness of the system.

[0017] The event triggering function proposed in this invention is designed for high-order nonlinear vehicle systems. It takes the vehicle steering angle and internal system factors as dynamic variables for the event triggering interval, which reduces the number of triggers in the entire time domain and effectively saves communication resources. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention.

[0019] Figure 2 The time-varying function of the whole time domain of the present invention Simulation example diagram.

[0020] Figure 3 The time-varying function of the whole time domain of the present invention Simulation example diagram.

[0021] Figure 4 This is a topology diagram of information interaction in a multi-vehicle system.

[0022] Figure 5 This is a simulation diagram of the X position error under the preset time event trigger controller of the present invention.

[0023] Figure 6 This is a simulation diagram of the Y position error under the preset time event trigger controller of the present invention.

[0024] Figure 7 This is a simulation diagram of the angle error under the preset time event trigger controller of the present invention.

[0025] Figure 8 This is a simulation diagram of the X-speed error under the preset time event trigger controller of the present invention.

[0026] Figure 9 This is a simulation diagram of the Y-velocity error under the preset time event trigger controller of the present invention.

[0027] Figure 10 This is a simulation diagram of the angular velocity error under the preset time event trigger controller of the present invention.

[0028] Figure 11 The preset time event trigger controller outputs a formation control trajectory diagram for the present invention.

[0029] Figure 12 For each vehicle, the event trigger time point is set according to the preset time event trigger controller input. Figure 1 .

[0030] Figure 13 For each vehicle, the event trigger time point is set according to the preset time event trigger controller input. Figure 2 . Detailed Implementation

[0031] To make this invention clearer and easier to understand, the design process of the preset time controller for a multi-vehicle system based on an event-triggered control algorithm will be described below with reference to flowchart illustrations. It is understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0032] The purpose of this embodiment is to demonstrate how to implement the technical solution of the present invention in practical applications, and its flowchart is as follows. Figure 1 As shown.

[0033] I. Formation System The information exchange network of the formation system is described by a directed graph G, where Indicates the weight of information interaction. Let represent the adjacency matrix of a directed graph G. The Laplace moment of a directed graph. Depend on Definition. Divide the vertices of a directed graph into... ,in For example, for Represented as ,for Represented as At this point, the directed graph G is called structurally balanced.

[0034] II. Definitions and Lemmas (a) Suppose that the directed graph G is strongly connected and structurally balanced, and that at least one following vehicle utilizes information directly obtained from the leader.

[0035] (b) There exists a diagonal matrix For all like There are no non-negative terms. 0 is an eigenvalue of the Laplace matrix L, and .

[0036] (c) makes It is a diagonally dominant matrix and for There exists a sequence Z of non-zero elements, for example, for , where Z is nonsingular.

[0037] (d) Based on assumption (a), It is strange and unusual.

[0038] III. Establish a dynamic model of the multi-vehicle system and give the system control objective. The multi-vehicle platooning system considers N following vehicles and M leader vehicles. The developed dynamics model is used to simulate the motion of the vehicles. The dynamics model for the ith vehicle is described in the following form.

[0039] (1) in, , Represented as a position vector, This is expressed as the vehicle's steering angle. Defined as the velocity vector under a fixed frame. Indicates angular velocity, Indicates the system's control input, For the Coriolis matrix and the centripetal matrix, Damping matrix, For the quality matrix, It is represented as a rotation matrix.

[0040] (2) in, The rotation matrix satisfies , , and .

[0041] (3) Make ,for Differentiation yields: (4) make ,Will Combined with system (1), the system can be reconstructed as follows: (5) The dynamics of a leader can be described as follows: (6) in, , , This is represented by the leader's position vector, velocity vector, and acceleration vector.

[0042] To understand preset-time bipartite time-varying formation control under a dynamic event-triggered algorithm, the main objective of this invention is to design a suitable controller for multi-vehicle formation systems in directed graphs. Preset-time bipartite time-varying formation control can be demonstrated when the following conditions are met.

[0043] (7) (8) in, This indicates the time set for the formation to reach the preset time. Let be the time-varying function of the design, representing the change in positional distance between the followers. The main objective of the controller design is to ensure that the tracking error satisfies the relationships described in (7) and (8) and converges to zero at a preset time.

[0044] IV. Results and Proof of the Invention This invention designs a time-varying formation controller for a multi-vehicle system based on a dynamic event-triggered algorithm and a pre-defined time. Building upon the proposed continuous event controller, an event-triggered controller incorporating a dynamic event-triggered function is designed, which effectively saves communication resources and achieves time-varying formation of multiple vehicles at a preset time. Furthermore, the Zeno phenomenon has been proven to not occur.

[0045] (I) Time-varying function Before creating the control input for a multi-vehicle formation, the definition of a time-varying function is first given.

[0046] (1) At least exist In terms of scope.

[0047] (2) It is a continuous function and satisfies the initial conditions. ,and ,in It is a preset time.

[0048] (3) It is a continuous function and satisfies the initial value. , .

[0049] (4) ,in, and .

[0050] (5) ,in, and .

[0051] The proposed The examples given are as follows: (9) (10) The preset time set in this invention is ,like Figure 2 and Figure 3 As shown, it can be observed at time... The time-varying function then converges to zero.

[0052] (II) Design of a Preset Time Event Triggered Binary Time-Varying Formation Controller First, let's consider the system's position error. and speed error When defined, it can be described in the following two forms: (11) (12) The expected output formation vector of the vehicle is , ,in Both are twice differentiable, which is easy to obtain. .

[0053] The controller design process begins by defining two auxiliary functions. , The auxiliary function is expressed as follows: (13) It is worth pointing out At the same time, auxiliary functions are further constructed. The form of expression is (14) in, It is a positive number, and at the same time... (15) At this point, for the auxiliary function Differentiation yields (16) in, It can be represented as (17) Combining (16) and (17), we can obtain (18) At this time, for the multi-vehicle system (1), the bipartite time-varying formation control can be achieved at a preset time by means of the proposed controller (19).

[0054] (19) At this time, it can be obtained (20) From the initial conditions (13) and (14) and the designed time function, it can be seen that Further, we can obtain Equation (14) can then be rewritten in the following form. (twenty one) because , exist The upper part is maintained. Similarly, it can be concluded that... exist The above is preserved. Further, through equation (13), we can obtain... In time Within the range.

[0055] Next, we will prove... Equivalent to as well as .

[0056] At this time, .Will and Substituting (13) yields... (twenty two) therefore In time The upper part is kept. In time The upper part is maintained. At this time... Equivalent to , At this point, the pre-set time for splitting into two groups was reached.

[0057] Based on the preset-time time-varying formation controller, this invention designs an event-triggered preset-time binary time-varying formation controller. The designed controller only exchanges information between vehicles when the event triggering conditions are met.

[0058] For following vehicles The event-triggered controller is designed in the following form (twenty three) in Defined as a follower The latest event triggering time. The proposed dynamic event triggering function, which incorporates two dynamic factors, takes the following form. (twenty four) Where E is defined as the event triggering error. It is a constant that satisfies The error E can be defined in the following form: (25) To prove the stability of the system, we choose to construct a Lyapunov function: (26) Differentiating the Lyapunov function yields: (27) By scaling and simplifying the Lyapunov function, we can obtain: (28) Based on the designed event trigger function, we can obtain: (29) when hour .so It decays over time. Because to further obtain At this time, according to We can conclude that .at this time ,because achievable At this point, further progress can be made. At this time, you can obtain At this point, according to the designed time function... You can get In time It is possible to obtain Maintained in terms of time range .therefore In time The above is maintained. Further acquisition is possible. and Because it satisfies At this point, the stability of the pre-set time binary sorting under the event trigger was proven.

[0059] In the invention, it was proven that the Zeno phenomenon does not occur, and the existence of a lower bound on the event triggering interval was also proven. Therefore, we first consider... The derivative yields: (30) definition The above equation can be rewritten as follows after substituting the control inputs into the design and scaling it: (31) because (32) Solving the above equation yields: (33) At this point, the lower bound of the event trigger interval can be obtained as: (34)

[0060] V. Simulation Results Verification of the Invention First, the information interaction topology diagram of the multi-vehicle system in this invention is given, such as... Figure 4 As shown.

[0061] The initial value of the leader designed in this invention is The leader's acceleration in the XY direction is designed to be , The initial values ​​for the twelve following vehicles were designed as follows: The desired formation output vector in the X direction is: The expected formation output vector in the Y direction is The expected formation output vector is... The time-varying function of the leader in the X direction is: The time-varying function in the Y direction is The angle time-varying function is angular acceleration is Preset time . The value is defined as 100. Defined as 0.25.

[0062] The controller (23) designed for the vehicle system model (1) of this invention, and the simulation diagrams of position, speed and angle errors are as follows. Figures 5-10 As shown. In the design of the time-varying vector function... The output formation control trajectory diagram obtained according to the designed controller (23) under the action is as follows: Figure 11 As shown. Based on the designed event trigger function (24), the event trigger timing diagram is represented by a dot plot as follows. Figures 12-13 As shown. Figure 12 This indicates the number of times the controller's events are triggered in the X-axis direction of the vehicle. Figure 13 This indicates the number of times the controller triggers an event for the vehicle along the Y-axis. Each point represents one event trigger for the corresponding vehicle at the current moment.

[0063] This invention constructs a binary preset-time formation controller for vehicle systems, incorporating a competition-aware, event-triggered algorithm. Figure 1 The flowchart shown illustrates the invention process. This invention first constructs as follows: Figure 2 Figure 3 The piecewise time-varying function shown is used to implement the preset timing characteristics of the formation controller. The information interaction method between vehicles in this invention is as follows: Figure 3 As shown, the communication method is a leader-follower approach incorporating a competitive mindset. Simulation diagrams for position, speed, and angle errors are shown below. Figures 5-10 As shown, Figures 5-7 This represents the position error and angle error in the XY directions. Figures 8-10 The figure shows the velocity and angular velocity errors in the X and Y directions. As can be seen from the figure, the controller constructed by this invention can realize that the position, velocity, and angular errors are within a preset time. It converges to zero. Figure 11 A two-dimensional planar trajectory diagram representing a single leader vehicle and twelve following vehicles, with the leader vehicle represented by a star and the remaining vehicles by points, provides snapshots of the vehicle system at different times. Figure 11 It can be seen that the multi-vehicle system can converge to the specified formation at t=5. Due to the characteristics of time-varying formation, the relative positions of the formation at time t=11.28 are the same as those at time t=5, that is, the system can form the same formation after a 2π period, thus realizing time-varying formation. Figures 12-13 The diagram shows the changes in the trigger time for vehicle platooning control, including a magnified view that reveals a minimum time interval. This analysis verifies the effectiveness of the designed controller and demonstrates that it avoids the Zeno phenomenon in event-triggered control. It effectively reduces communication resource waste while ensuring the periodic changes of the event trigger function and the event trigger interval.

Claims

1. A binary formation control method for multi-vehicle system event triggering at preset times, characterized in that, The following controller is used: in, Indicates the vehicle's controller input; Indicates the input from the neighbor's vehicle controller; Indicates the weight of information exchange between following vehicles; This indicates the weight of information exchange between the lead vehicle and the following vehicles. This is the quality matrix; Represented as a rotation matrix; It is a time-varying function; Represents the linearization parameters of the vehicle system; the system's position error. ; The initial position error; the velocity error of the system. ; This refers to the initial velocity error. , and These are the expected output formation vectors for the vehicles; It is a positive constant; This indicates whether the leader's vehicle and the following vehicles follow the same trajectory. Indicates the leader's acceleration; Auxiliary functions representing system design; For followers The latest event trigger time; , , , , , , , , , , These represent the parameters at the trigger time. The value below.

2. The multi-vehicle system event-triggered preset-time binary formation control method according to claim 1, characterized in that, The position error of the system is expressed as: ； The speed error of the system is expressed as: ； in, This indicates the system's position error; This indicates the system's speed error; Indicates the vehicle's location; This represents the linearization parameters of the vehicle model's speed; , , This represents the desired output formation vector for the vehicles.

3. The multi-vehicle system event triggering preset time binary formation control method according to claim 2, characterized in that, Auxiliary functions for system design The form of expression is as follows: ； in, ; Auxiliary functions representing system design; and Auxiliary functions for design; This indicates the system's position error; This indicates the system's speed error.

4. The multi-vehicle system event-triggered preset-time binary formation control method according to claim 3, characterized in that, The event triggering condition is expressed as follows: Where E represents the event triggering error. It is a constant that satisfies , For followers The latest event trigger time; This is the quality matrix; Represented as a rotation matrix; Auxiliary functions representing system design.

5. The multi-vehicle system event-triggered preset-time binary formation control method according to claim 4, characterized in that, The event triggering error is: in, Indicates the event triggering error. This is the quality matrix; Represented as a rotation matrix; Indicates the weight of information exchange; This indicates the information exchange between the following vehicle and the lead vehicle; and These are the expected output formation vectors for the vehicles; express At the moment of triggering the vehicle Control input; It is a time-varying function; This represents the system linearization parameters at the moment the vehicle is triggered; Represents the linearization parameters of the system over continuous time; system position error. System speed error ; Auxiliary functions representing system design; This indicates the auxiliary function that constructs the set at the triggering time.

6. The application of the control method as described in any one of claims 1 to 5 in multi-vehicle time-varying formation control.

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