A design method for a multi-UAV leader-follower controller with input time delay

Abstract

This invention provides a design method for a multi-UAV leader-follower controller with input time delay, constructing a multi-UAV system. The multi-UAV system includes one leader and N followers. An observer for the multi-UAV system is designed. Based on the observer's observations of the leader's and follower's states, a controller for the multi-UAV system is designed. The controller controls the multi-UAV system so that its output promptly follows changes in a given signal. The beneficial effects of this invention are: it enables the output of the multi-UAV system to follow changes in a given signal well and promptly, and the designed controller effectively solves the leader-follower consistency problem in systems with input time delay.

Description

Technical Field

[0001] This invention relates to the field of multi-agent systems, and more particularly to a design method for a leader-follower controller for a multi-UAV system with input time delay. Background Technology

[0002] A drone is an unmanned platform capable of carrying various monitoring devices and autonomous operation. This platform can achieve flight control through remote control devices, onboard programs, or an onboard computer. Compared to manned aircraft, drones are relatively smaller, more adaptable to the battlefield, and eliminate the risk of personnel casualties, making them widely applicable in harsh battlefield environments. Currently, drones have evolved into miniaturized intelligent aircraft integrating functions such as target search, target identification, power line inspection, and express delivery.

[0003] With the rapid development of technologies in fields such as communication, computers, and networks, the related topics of UAVs and multi-UAV systems have become a new research direction in the field of automatic control. Since intelligent agents are a manifestation of human social intelligence and have strong adaptability and autonomy, more and more researchers are joining the theoretical research of multi-UAVs. In multi-UAV systems, how UAVs cooperate with each other in complex environments is an important prerequisite for achieving their goals, which is to complete the task together. Compared with a single UAV, multi-UAV swarms have the following main characteristics: (1) Information sharing: UAVs within the swarm use data links to transmit information, enabling real-time data transmission and sharing of various information such as location and terrain. (2) High fault tolerance: Multiple UAVs in the swarm can achieve distributed parallel perception through the mutual matching of sensors, improving the computing power of the UAV swarm. (3) Wide spatial range: UAV swarms can perform tasks collaboratively in different areas, which can effectively expand the activity coverage of the UAV swarm and improve the execution efficiency of the task to a certain extent. Drone swarm technology is widely used in both civilian and military fields. In the civilian field, it is mainly used for tasks such as power line inspection, express delivery, agricultural and forestry plant protection, aerial photography and surveying. In the military field, it is mainly used for tasks such as coordinated strikes, swarm warfare, coordinated reconnaissance and tactical jamming.

[0004] With the increasing networking capabilities of control technology, more and more intelligent agents are using networks for information interaction, leading to the emergence of networked multi-Agent systems (MAS). Networked MAS can solve problems through efficient collaboration, offering advantages such as high flexibility, reliability, and parallelism, thus enabling applications in more uncertain environments. A crucial factor for achieving coordinated control of multi-agent systems in a networked environment is the agents' ability to exchange information via communication network modules. In practical applications, communication delays are often unavoidable due to the limited transmission capacity of communication or sensing devices, the physical characteristics of transmission media, and the diversity of sensor signals. Multi-Agent systems frequently experience time lag problems, and prolonged delays can affect system stability. Latency issues are an active research area in control engineering.

[0005] As research on multi-UAV systems deepens, many researchers encounter numerous practical problems. For example, how to design controllers for input feedback models that differ from state feedback models? In output feedback models, the only usable information is the output signal; the internal state variables of the system are unavailable. Therefore, researchers have designed an observer model to observe unknown state variables and use the observed quantities to design the controller. Simultaneously, designing controllers in leaderless systems (where the input is unknown) requires considering how to address the uncertainties and leaderless nature inherent in fractional-order multi-UAV systems.

[0006] Therefore, based on the above analysis, research on the consistency of multi-UAV systems still faces numerous challenges and problems. In multi-agent systems, especially for UAV systems with input time delays, designing a suitable adaptive distributed controller becomes a new challenge. Furthermore, how to design an adaptive distributed controller for multi-agent systems with switching topologies is also a difficult problem that needs to be solved. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides a design method for a multi-UAV leader-follower controller with input time delay. It innovates in the research of input time delay, analyzes the basic ideas and methods of adaptive controller design for multi-UAV systems, and uses Lyapunov functions to design an adaptive controller that enables each follower's position to track the leader's changes, thus stabilizing the entire system. The design method of this multi-UAV system leader-follower consistency controller mainly includes:

[0008] S1: Construct a multi-drone system; the multi-drone system includes 1 leader and N followers;

[0009] S2: Design an observer for followers to observe leaders in a multi-UAV system;

[0010] S3: Design the controller in the followers based on the observer's observations of the leader's state and the state matrix;

[0011] S4: Control the followers in multiple drones through the designed controller, so that N followers can follow the leader's output in a timely manner.

[0012] Furthermore, the dynamic equations of the follower in the multi-UAV system are as follows:

[0013]

[0014] in, For a single follower, i = 1, 2, ..., N, where N represents the number of followers, s and r both represent the order, and x... si Represents vector x i The expression for each of the first r-1 orders; x 1i It is the position of the follower, x 2i It represents the speed of the follower, and 'a' represents the vector x. i The r-th order is the sum of the negatives of the previous orders plus the control U. i (td), It is the follower input with time delay d, i.e., the controller of the follower.

[0015] Furthermore, the leader's dynamic equation is:

[0016]

[0017] in, For the leader's state, is the leader's state matrix, c is the leader's output matrix, and y is the leader's output.

[0018] Furthermore, the observer is an adaptive distributed observer, and its formula is:

[0019]

[0020]

[0021] in, Let μ1 and μ2 represent the observations of the leader's state by the i-th follower and the j-th follower, respectively, where μ1 and μ2 are two positive constants. This indicates the communication relationships between the various followers. Let i and j represent the estimates of the leader's state matrix by the i-th follower and the j-th follower, respectively, i = 1, 2, ..., N, j = 1, 2, ..., N, j ≠ i, and N represent the number of followers.

[0022] Furthermore, the controller is:

[0023]

[0024] Where r represents the order, d represents the time delay, and u i (d,t) and These are the forms of the partial differential equations used to handle input time delays, and c is the output matrix of the leader state equation. Let represent the observation of the i-th follower on the leader's state matrix. Let and represent the j-th and r-1-th powers of the observations of the i-th follower regarding the leader's state matrix, respectively, where j = 0, 1, ..., r. Let i represent the observation of the i-th follower on the leader's state, where i = 1, 2, ..., N.

[0025] Furthermore, the designed controller needs to meet the following requirements:

[0026]

[0027] Where, x 1i y represents the position of the follower, and y represents the output of the leader.

[0028] The beneficial effects of the technical solution provided by this invention are: it enables the output of a multi-UAV system to follow the changes of a given signal well and in a timely manner, and the designed controller effectively solves the problem of leader-follower consistency in the presence of input time delay. Attached Figure Description

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0030] Figure 1 This is a flowchart of a design method for a multi-UAV leader-follower controller with input time delay in an embodiment of the present invention.

[0031] Figure 2 This is a schematic diagram of a distributed observer observing the leader state in an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram of system tracking in an embodiment of the present invention. Detailed Implementation

[0033] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0034] Embodiments of the present invention provide a design method for a leader-follower controller for a multi-UAV system with input time delay.

[0035] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a design method for a multi-UAV leader-follower controller with input time delay, as described in an embodiment of the present invention. The method specifically includes:

[0036] S1: Construct a multi-agent system; the multi-drone system includes N+1 drones, of which 1 is a leader and N are followers;

[0037] Consider a simple multi-agent system, whose follower's state dynamics equations are described as follows:

[0038]

[0039] in, For a single follower, i = 1, 2, ..., N, where N represents the number of followers, s and r both represent the order, and x... si Represents vector x i The expression for each of the first r-1 orders; x 1i It is the position of the follower, x 2i It is the speed of the followers, from which we can see x i Each order in the first r-1 orders is obtained by differentiating the previous order, where a represents the vector x. i The r-th order is the sum of the negatives of the previous orders plus the control U. i (td), The input consists of followers with a time delay of d. N followers and a single leader constitute a complete multi-UAV system. The dynamic equation of the leader state is described as follows:

[0040]

[0041] in, For the leader's state, is the leader's state matrix, c is the leader's output matrix, and y is the leader's output.

[0042] S2: Design an observer for a multi-agent system;

[0043] In a multi-agent system, a distributed observer is designed to obtain target information from each agent based on the system's communication topology. Simultaneously, based on the communication topology, the distributed observer can transmit information about the leader to each follower. The designed adaptive distributed observer is shown below:

[0044]

[0045] in, and It consists of the observations of the leader's state and state matrix by the observers in each follower. Let μ1 and μ2 represent the observations of the leader's state from the i-th follower and the j-th follower, respectively. μ1 and μ2 are two positive constants; in this embodiment, μ1 = 5 and μ2 = 2 can be taken. This represents the communication relationship between the followers. If the i-th follower and the j-th follower are connected, that is, they can communicate, then they have a communication relationship. otherwise These represent the estimates of the leader's state matrix by the i-th follower and the j-th follower, respectively, which are used in the design of the subsequent controller.

[0046] S3: Based on the observer's observations of the leader's state and the follower's state, design a controller for the multi-UAV system;

[0047] To make the follower's position x 1i To follow the leader's output y, a controller needs to be designed to...

[0048] First, consider the scenario where followers can directly obtain information such as the leader's state matrix and state.

[0049] Let e 1i =x 1i -y, That is, e ji =x ji -y (j-1) Where j = 1, 2, ..., r, and e is rearranged. ji =x ji -y (j-1) We can obtain:

[0050]

[0051] Let X i =col(e 1i ,e 2i ,...,e ri ), The aforementioned multi-UAV system can then be transformed into the following form:

[0052]

[0053] Among them, X i =col(e 1i ,e 2i ,...,e ri ),

[0054]

[0055] Transforming the leader-follower consistency problem into equation (5) above, if the designed controller will... but

[0056] Due to the long input delay, it is necessary to predict future states and use these states to design the controller. First, the following distributed input is introduced:

[0057] u i (x,t)=U i (t+xd) (6)

[0058] From the leader state dynamics equation shown in formula (2), we can obtain:

[0059]

[0060] make:

[0061]

[0062] When x = 0, equation (5) can be transformed into equation (7):

[0063]

[0064] The controller designed is as follows:

[0065]

[0066] in, Matrix A+BK can be made to form a Hurwitz. The controller can also be written in the following form:

[0067]

[0068] The controller can be transformed from equation (7) into The equation satisfies the Herwitz criterion, that is, it can be Therefore, it is also satisfied. Therefore, the controller in each follower takes the following form:

[0069]

[0070] The above assumes that followers can directly obtain various information from the leader and use this information to design the controller. However, in reality, followers may not be able to directly obtain information from the leader, so a distributed observer is needed (Formula (3)). Based on the above controller design idea, we consider using the values ​​of the observer to design the controller. First, let:

[0071]

[0072] The observed values ​​of the leader's output are make:

[0073]

[0074] definition:

[0075]

[0076] so,

[0077]

[0078] The simplified form of the above equation (13) is:

[0079]

[0080] in

[0081]

[0082] Based on the design principles of the reference controller, design the controller:

[0083]

[0084] From (11), the controller of the multi-UAV system is...

[0085]

[0086] The stability of the controller can be demonstrated through the following operations:

[0087] First consider the following transformation:

[0088]

[0089] The system equations can be transformed into the following more stable form:

[0090]

[0091] calculate:

[0092]

[0093] in, and They are Differentiate with respect to x and with respect to t.

[0094]

[0095] Consider the following Lyapunov-Krasovskii function:

[0096]

[0097] Here, λ is a positive constant, and we will choose its specific value later. It is a positive definite matrix and is a solution to the following equation:

[0098]

[0099] in It is a positive definite matrix.

[0100] To prove the stability of the multi-agent system, we differentiate equation (20) and obtain:

[0101]

[0102] choose

[0103]

[0104] in

[0105]

[0106] N i (t) is a bounded function, and so The system satisfies Lyapunov stability. This also indicates that the system output can follow the changes in the given signal very well, and the controller effectively solves the leader-follower consistency problem in the presence of input time delay.

[0107] To verify the correctness of this method, the following parameter d=100 was selected for system simulation. Figure 2 To estimate the leader's state using an adaptive distributed observer, the dashed lines in the figure represent the leader, and the straight lines represent the followers. The figure shows that each follower accurately observes the leader's state, proving the correctness of the second equation in formula (3) and providing a valid basis for designing a controller using the observations. The leader's state matrix is... c = [0 2]. A second-order follower equation is chosen:

[0108]

[0109] Initial state: x1(0) = [5,6] T x2(0) = [2, -2] T x3(0) = [4,3] T x4(0) = [5,3] T .

[0110] Get as Figure 3The results shown are obtained through Figure 3 It can be seen that the position of the followers successfully tracks the output of the leader, that is, the position of each follower follows the output of the leader.

[0111] S4: Control the multi-agent system through the controller so that its output follows the changes of the given signal in a timely manner.

[0112] The beneficial effects of this invention are:

[0113] 1. The complex consensus problem of high-order multi-agent systems is transformed into a stabilization problem of low-order systems (Equations 1, 4, 5). An adaptive distributed observer is used to estimate the leader's state and state matrix, so that each follower can observe the leader's information, thereby designing a distributed controller using the observations.

[0114] 2. The input delay of the multi-agent system is modeled by transmitting PDE (partial differential equations) (Equation (6)), and the multi-agent system is mapped to the ODE-PDE target system (Equation (7), Equation (14)). The stability of the quality is analyzed by using the Lyapunov-Krasovskii function, so that the output of the agent system can follow the changes of the given signal well and in a timely manner. The designed controller solves the problem of leader-follower consistency in the system with input delay.

[0115] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a multi-UAV leader-follower controller with input time delay, characterized in that: include: S1: Construct a multi-drone system; the multi-drone system includes one leader and... N One follower; S2: Design an observer for followers to observe leaders in a multi-UAV system; S3: Design the controller in the followers based on the observer's observations of the leader's state and the state matrix; S4: Control the followers in multiple drones through the designed controller, so that N followers can follow the leader's output in a timely manner; The dynamic equations of the follower in the multi-UAV system are: in, For the state of a single follower, , N Indicates the number of followers. s , r Both represent the order. Representing vectors x i The expression for each of the first r-1 orders; It is the position of the follower. It is the speed of the followers. a Representing vectors x i The r The order is the negative of the sum of the previous orders plus the control. U i ( td ), It has a time delay The follower input, i.e., the follower's controller; The dynamic equation of the leader is: in, For the leader's state, It is the leader's state matrix. c It is the output matrix of the leader's state equation. It is the leader's output; The observer is an adaptive distributed observer, and its formula is: in, Indicates the first i The first follower and the first j Each follower's observation of the leader's state and Two positive numbers, This indicates the communication relationships between the followers. They represent the first i The first follower and the first j Estimation of the leader's state matrix by each follower. , , , N Indicates the number of followers; The controller is: in, r Indicates the order, Indicates time delay, and These are the forms of the partial differential equations used to handle input time delays. c It is the output matrix of the leader's state equation. Indicates the first The observations of each follower on the leader's state matrix. They represent the first Observations of the leader's state matrix by each follower The power of sum The power, where , Indicates the first i An observation of the leader's state by a follower. .

2. The design method of a multi-UAV leader-follower controller with input time delay as described in claim 1, characterized in that: The designed controller needs to meet the following requirements: in, It is the position of the follower. It is the leader's output.

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