Distributed uniform circular formation-keeping control method for second-order multi-agent systems in two-dimensional plane

Abstract

The application discloses a kind of second-order multi-agent system in two-dimensional plane distributed uniform ring surrounding control method, first, establish surrounding target interval observer to obtain the estimated value of surrounding target state quantity;Second, establish agent interval observer to obtain the estimated value of agent state quantity;Finally, using the state quantity estimated value of surrounding target and agent, design its distributed uniform ring surrounding control strategy in two-dimensional plane, to realize the uniform ring surrounding of second-order multi-agent system in two-dimensional plane to surrounding target.This application obtains the estimated value of each state quantity by establishing interval observer to surrounding target and each agent respectively, reduces the influence caused by unknown disturbance to surrounding control strategy;By controlling two coordinates in two-dimensional plane respectively, avoid more complex complex function integral operation, reduce operation cost;In addition, the uniform ring surrounding achieved adapts to actual demand, has good application prospect.

Description

Technical Field

[0001] This invention relates to control technology for multi-agent systems, and in particular to a distributed uniform ring-encircling control method for a disturbed second-order multi-agent system based on an interval observer in a two-dimensional plane. Background Technology

[0002] In recent years, with the development of research on multi-agent systems, the modeling and simulation of migrating flocks of geese and schools of fish hunting in nature have been applied to practical problems such as UAV formations and wireless communication. These problems are mainly coordination and control issues between groups and individuals, and can generally be divided into the following four components: dynamic agent model, agent state information, communication relationships between agents, and local control strategies. In these research problems, agents exchange state information through communication topology networks and use local control strategies to adjust their states to achieve the desired control effect, such as formation and behavior. As research deepens, the study of multi-agent system coordination and control has incorporated the situation where there is a leader within the group, which can be divided into consistency problems, tracking control, and encirclement control.

[0003] Encirclement control, in particular, refers to the problem of designing distributed control strategies using state information and local network topology in a multi-agent system to encircle a target within a specific range. Encirclement control has many important applications in practical problems, such as the space orbiting flight and orbiting motion control of spacecraft, thus attracting considerable attention from the academic community. The encirclement control problem for multi-agent systems was initially proposed by Dimargoonas et al. in 2006. In recent years, with the deepening of research, it has mainly been divided into the following research problems: encirclement control based on local information, encirclement control using estimators, encirclement control in three-dimensional space, encirclement control under disturbance conditions, and event-driven encirclement control. In 2010, Deghat et al. designed a motion controller using angle information, solving the encirclement control problem of a single first-order agent for a single unknown target, and then extended it to the encirclement control problem of multiple encircling targets in 2015. In the same year, Shi et al. conducted in-depth research on encirclement models and target model formation. In 2013, Li et al. studied the encirclement control problem of a first-order multi-agent system with communication noise, and solved the encirclement control problem with communication delay the following year. Current research has not adequately addressed the encirclement control problem of disturbed second-order multi-agent systems in a two-dimensional plane. Summary of the Invention

[0004] Purpose of the invention: In view of the current research status and practical application background of the above-mentioned multi-agent system control technology, the present invention provides a distributed uniform ring encirclement control method for a disturbed second-order multi-agent system based on an interval observer in a two-dimensional plane.

[0005] Technical solution: The distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to the present invention includes the following steps:

[0006] For a target surrounded by unknown, bounded disturbances and measurement noise, its state space equation is established, and then an interval observer for the target surrounded is established to obtain the estimated values ​​of the target surrounded state variables, including its position, velocity and acceleration.

[0007] For each agent in a second-order multi-agent system affected by unknown and bounded disturbances, the state space equation of each agent is established, and an agent interval observer is further established to obtain the estimated values ​​of the agent state variables, including their position and velocity.

[0008] Using the state estimates of the surrounding target and the second-order agent obtained from the above two types of interval observers, a distributed uniform ring encirclement control strategy for the second-order multi-agent system in the two-dimensional plane is designed to achieve uniform ring encirclement of the surrounding target by the second-order multi-agent system in the two-dimensional plane.

[0009] Furthermore, the position coordinates of the surrounding target in the two-dimensional plane are represented as follows:

[0010]

[0011] Where p(t) represents the position coordinate vector of the target in the two-dimensional plane, p x (t) represents the x-axis coordinates of the target in the two-dimensional plane, p y (t) represents the y-coordinate of the target in the two-dimensional plane. It is a 2×1 dimensional real vector space;

[0012] The state-space equations surrounding the target are as follows:

[0013]

[0014] in, It is the first derivative of p(t), that is, the velocity vector surrounding the target in the two-dimensional plane; It is the system matrix surrounding the target. The unknown, bounded disturbances encountered by the target in order to surround it. To encompass the measurable output of the target system, The output matrix enclosing the target system.

[0015] Furthermore, the state-space equations surrounding the target satisfy the following conditions:

[0016] First, a known Lipschitz function must exist. ω (t) and Make the following inequality always true:

[0017]

[0018] in, The unknown, bounded disturbances encountered by the target in order to surround it. The lower bound of the unknown, bounded perturbations that surround the target. The upper bound of the unknown, bounded disturbances affecting the target;

[0019] Secondly, the initial position p(0) of the surrounding target is unknown, but a known vector must exist. p (0) and Make the following inequality always true:

[0020]

[0021] in, The initial position surrounding the target. This serves as the lower bound encompassing the initial position of the target. This is the upper bound surrounding the initial position of the target;

[0022] Finally, the system surrounding the target must be completely observable, i.e. (A p C p ) observable; It is the system matrix surrounding the target. The output matrix enclosing the target system.

[0023] Furthermore, an interval observer is established for the surrounding target as follows:

[0024]

[0025] in, It is the system matrix surrounding the target. The output matrix enclosing the target system, Let be the gain matrix that encloses the target interval observer. To encompass the measurable output of the target system, The lower bound of the unknown, bounded perturbations that surround the target. The upper bound of the unknown, bounded disturbances affecting the target; This is the estimated upper bound of the area surrounding the target location. This is the lower bound of the estimated target location. for The first derivative, for p The first derivative of (t); the resulting upper and lower bounds enclosing the target position always satisfy the following inequality:

[0026]

[0027] Based on the above interval observer data, an estimate of the location surrounding the target is obtained. as follows:

[0028]

[0029] Using this estimate, the estimated velocity of the surrounding target can be obtained. and acceleration in, for The first derivative, for The second derivative of .

[0030] Furthermore, the second-order multi-agent system moves in a two-dimensional plane, denoted as […]. Among them, a i Let N represent the i-th agent, and N be the number of agents. The position coordinates of the N agents in the two-dimensional plane are represented as follows:

[0031]

[0032] in, Let p be the position coordinate vector of the i-th agent in the two-dimensional plane. ix (t) represents the x-axis coordinate of the i-th agent in the two-dimensional plane, p iy (t) represents the y-axis coordinate of the i-th agent in the two-dimensional plane;

[0033] The dynamic equations of each agent are described as follows:

[0034]

[0035] in, For p i The first derivative of (t), Let v be the velocity vector of the i-th agent in the two-dimensional plane, where v ix (t) represents the x-axis velocity component of the i-th agent in the two-dimensional plane, v iy (t) represents the y-axis velocity component of the i-th agent in the two-dimensional plane. This is the position control input for the i-th agent; For v i The first derivative of (t), This is the speed control input for the i-th agent. The unknown, bounded perturbation experienced by the intelligent agent is the same as the perturbation experienced by the surrounding target;

[0036] Based on the above dynamic equations, the state-space equations of each agent are as follows:

[0037]

[0038] in, Let i be the augmented state variable of the i-th agent. For z i The first derivative of (t); Let be the system matrix of the i-th agent, 0 2×2 I represents a second-order zero matrix. 2×2 Represents a second-order identity matrix; For the augmented control input of the i-th agent, For the i-th agent, the augmented unknown and bounded perturbation; Let i be the measurable output of the i-th agent. Let be the output matrix of the i-th agent.

[0039] Furthermore, the state-space equations of each multi-agent agent need to satisfy the following conditions:

[0040] First, the disturbances experienced by each agent Unknown, but since ω(t) always has a known Lipschitz function. and ω (t) such that the following inequality always holds:

[0041]

[0042] Therefore, the disturbances experienced by the intelligent agent system always ensure that the following inequality holds:

[0043]

[0044] in, This is a lower bound function for the perturbation experienced by the agent. It is an upper bound function for the perturbation experienced by the agent;

[0045] Secondly, the initial positions and velocities of each agent are unknown, i.e., z i (0) Unknown, but a known vector must exist. and Make the following inequality always true:

[0046]

[0047] in, z i (0) is the lower bound of the initial position of the i-th agent. This is the upper bound of the initial position of the i-th agent;

[0048] Finally, the state-space equations of each agent must be fully observable, i.e. (A,C) observable; A is the system matrix of the i-th agent; C is the output matrix of the i-th agent.

[0049] Furthermore, interval observers are established for each agent as follows:

[0050]

[0051] in, Let be the gain matrix of the interval observer of the i-th agent; This is the upper bound of the estimated state variables of the agent. This is the lower bound of the estimated state variables of the agent; for The first derivative, for z i The first derivative of (t); u i The augmented control input is used for the i-th agent; the upper and lower bounds of the resulting agent's state variables always satisfy the following inequality:

[0052]

[0053] Based on the data obtained from the agent's interval observer, the estimated values ​​of the state variables of each agent are obtained. as follows:

[0054]

[0055] in, Let be the estimated location of the i-th agent. This is an estimate of the velocity of the i-th agent.

[0056] Furthermore, the augmented control inputs applied to each agent The specific format is as follows:

[0057]

[0058] in, This is an estimate of the location surrounding the target. and These are the estimated velocity and acceleration of the surrounding target, respectively; Used to determine the relative position of each agent to the surrounding target, ρ is the radius of the preset uniform ring, θ is the relative position of the i-th agent on the preset uniform ring to the surrounding target, and N is the number of agents. Let be the estimated location of the i-th agent. This is an estimate of the velocity of the i-th agent;

[0059] The uniform ring-shaped encirclement control achieved by applying this control strategy satisfies the following condition: there exists a positive real number δ such that the following inequality holds:

[0060]

[0061] in, Let be the position coordinate vector of the i-th agent in the two-dimensional plane.

[0062] Based on the same inventive concept, the second-order multi-agent system of the present invention provides a distributed uniform ring-encircling control system in a two-dimensional plane, comprising:

[0063] The enclosing target interval observer construction module is used to establish the state space equation of an enclosing target that is affected by unknown, bounded disturbances and measurement noise, and further establish an enclosing target interval observer to obtain the estimated values ​​of the enclosing target state variables, including its position, velocity and acceleration.

[0064] The agent interval observer construction module is used to establish the state space equation of each agent in a second-order multi-agent system affected by unknown and bounded disturbances, and further establish agent interval observers to obtain the estimated values ​​of agent state variables, including their position and velocity.

[0065] The control module is used to design a distributed uniform ring encirclement control strategy for the second-order multi-agent system in a two-dimensional plane by using the state quantity estimates of the encircling target and the second-order agent obtained from the above two types of interval observers, so as to realize the uniform ring encirclement of the encircling target by the second-order multi-agent system in a two-dimensional plane.

[0066] Based on the same inventive concept, the present invention provides a distributed uniform ring encirclement control device for a second-order multi-agent system in a two-dimensional plane, comprising a processor and a memory. The memory stores computer instructions, and the processor executes the computer instructions stored in the memory. When the computer instructions are executed by the processor, the electronic device implements the steps of the distributed uniform ring encirclement control method for a second-order multi-agent system in a two-dimensional plane as described above.

[0067] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0068] (1) The present invention controls two coordinates in a two-dimensional plane respectively, avoiding complex integral operations of complex functions and reducing computational costs;

[0069] (2) This invention reduces the impact of unknown disturbances on the encirclement control strategy by establishing interval observers for the encircling target and each intelligent agent under unknown and bounded disturbances respectively;

[0070] (3) The control strategy used in the method of the present invention achieves a uniform ring enclosure that meets actual needs and has good application prospects. Attached Figure Description

[0071] Figure 1 This is a flowchart of the method of the present invention;

[0072] Figure 2 It is a schematic diagram of a uniform enclosure in a two-dimensional plane;

[0073] Figure 3 It is a schematic diagram of uniform enclosure of the target estimate in a two-dimensional plane;

[0074] Figure 4 This is a diagram illustrating the effect of the method of the present invention in achieving uniform encirclement control in a two-dimensional plane. Detailed Implementation

[0075] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0076] The uniform ring encirclement control problem addressed in this invention refers to the problem in a two-dimensional plane where, under a given ring formation, various agents in a control system simultaneously move to encircle a target affected by a disturbance, maintaining their original shape and state after successfully forming a uniform ring encirclement. The resulting uniform encirclement effect is as follows: Figure 2 As shown in the diagram. First, for the target being surrounded by unknown, bounded disturbances, interval observers are established to obtain estimates of its position, velocity, acceleration, and other state variables. Then, for each agent in the second-order multi-agent system being surrounded by unknown, bounded disturbances, interval observers are established to obtain estimates of their position, velocity, and other state variables. Finally, using the state variable estimates of the target and the second-order agents obtained from the above two interval observers, a distributed uniform ring-shaped encirclement control strategy in the two-dimensional plane is designed to achieve uniform ring-shaped encirclement of the target by the second-order multi-agent system in the two-dimensional plane. The resulting uniform encirclement effect using the estimated values ​​of the target is shown in the diagram. Figure 3 As shown in the figure. The method obtains estimates of various state variables by establishing interval observers for the surrounding target and each agent under unknown and bounded disturbances, thereby reducing the impact of unknown disturbances on the surrounding control strategy. By controlling two coordinates in the two-dimensional plane separately, it avoids complex integral operations of complex functions and reduces computational costs. In addition, the uniform ring enclosure achieved by this control strategy meets practical needs and has good application prospects.

[0077] Example 1

[0078] like Figure 1 As shown, the distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to the present invention includes the following steps:

[0079] S1. For the enclosed target affected by unknown, bounded disturbances and measurement noise, establish its state space equation, and further establish an enclosed target interval observer to obtain estimates of its position, velocity, acceleration and other state quantities.

[0080] In this embodiment, the surrounding target can be either stationary or moving, and its position coordinates in the two-dimensional plane are represented as follows:

[0081]

[0082] Where p(t) represents the position coordinate vector of the target in the two-dimensional plane, p x (t) represents the x-axis coordinates of the target in the two-dimensional plane, p y (t) represents the y-coordinate of the target in the two-dimensional plane. It is a 2×1 dimensional real vector space.

[0083] The state-space equations surrounding the target are as follows:

[0084]

[0085] in, It is the first derivative of p(t), that is, the velocity vector surrounding the target in the two-dimensional plane. It is the system matrix surrounding the target. The unknown, bounded disturbances encountered by the target in order to surround it. To encompass the measurable output of the target system, The output matrix enclosing the target system.

[0086] The state-space equations surrounding the target must satisfy the following conditions:

[0087] First, a known Lipschitz function must exist. ω (t) and Make the following inequality always true:

[0088]

[0089] in, The lower bound of the unknown, bounded perturbations that surround the target. The upper bound of the unknown, bounded disturbances that surround the target.

[0090] Secondly, the initial position p(0) of the surrounding target is unknown, but a known vector must exist. p (0) and Make the following inequality always true:

[0091]

[0092] in, The initial position surrounding the target. This serves as the lower bound encompassing the initial position of the target. This is the upper bound surrounding the initial position of the target.

[0093] Finally, the system surrounding the target must be completely observable, i.e. (A p C p ) Observable.

[0094] Based on the state-space equations and conditions surrounding the target, the interval observer for the surrounding target is established as follows:

[0095]

[0096] in, Let be the gain matrix that encloses the target interval observer. To encompass the measurable output of the target system, This is the estimated upper bound of the area surrounding the target location. This is the lower bound of the estimated target location. for The first derivative, for p The first derivative of (t). To ensure that the obtained upper and lower bounds enclosing the target position always satisfy the following inequality:

[0097]

[0098] The following error systems must be positive systems: a system with state variable x(t) and input variable u(t) is called a positive system if, for any initial state x(0)≥0 and any input u(t)≥0 (t≥0), the system's state trajectory x(t) satisfies x(t)≥0 at any time t≥0.

[0099] The error between the estimate obtained by the observer and the true position surrounding the target is defined as:

[0100]

[0101] in, This is the error between the upper bound of the target's estimated location and the true location of the target. The error between the lower bound of the target's estimated location and the actual location of the target.

[0102] The error system is defined as:

[0103]

[0104] in, This is the derivative of the error between the upper bound of the target's estimated position and the true position of the target. It is the derivative of the error between the lower bound of the target location estimated by the observer and the true location of the target.

[0105] For continuous-time linear systems in If the system matrix A1 is a Metzler matrix Then for any t≥0, All This holds true. The Metzler matrix is ​​a square matrix with all non-negative off-diagonal elements.

[0106] Obviously, If (A) p -L p C p If A is a Metzler matrix, then the error system is non-negative. p -L p C p If the error system is both a Metzler matrix and a Hurwitz matrix, then the above error system is non-negative and stable. Therefore, the upper and lower bounds of the obtained position vectors surrounding the target can satisfy the required inequalities.

[0107] To obtain (A) a matrix that is both a Metzler matrix and a Hurwitz matrix p -L p C p The matrix is ​​needed to solve the following linear programming problem.

[0108] matrix A matrix is ​​both Metzler's and Hurwitz's if and only if there exists a strictly diagonal matrix whose diagonal elements are all positive real numbers. and Make:

[0109] i. It is a Metzler matrix;

[0110] ii.

[0111] Where n1 and p1 are the dimensions of the state variables and control inputs, respectively, the observer gain matrix is:

[0112] Based on the results obtained from the above interval observer, an estimate of the location surrounding the target can be obtained. as follows:

[0113]

[0114] Using this estimate, the estimated velocity of the surrounding target can also be obtained. and acceleration in, for The first derivative, for The second derivative of .

[0115] S2. For each agent in a second-order multi-agent system affected by unknown and bounded disturbances, establish the state space equation of each agent, and further establish an agent interval observer to obtain the estimated values ​​of its position, velocity and other state variables.

[0116] In this embodiment, the multi-agent system moves in a two-dimensional plane, and the multi-agent system is denoted as... Among them, a i Let N represent the i-th agent, and N be the number of agents. Next, the position coordinates of the N agents in the two-dimensional plane are represented as follows:

[0117]

[0118] in, Let p be the position coordinate vector of the i-th agent in the two-dimensional plane. ix (t) represents the x-axis coordinate of the i-th agent in the two-dimensional plane, p iy (t) represents the y-coordinate of the i-th agent in the two-dimensional plane.

[0119] The dynamic equations of each agent are described as follows:

[0120]

[0121] in, For p i The first derivative of (t), Let v be the velocity vector of the i-th agent in the two-dimensional plane, where v ix (t) represents the x-axis velocity component of the i-th agent in the two-dimensional plane, v iy (t) represents the y-axis velocity component of the i-th agent in the two-dimensional plane. This is the position control input for the i-th agent. For vi The first derivative of (t), This is the speed control input for the i-th agent. The unknown, bounded disturbances experienced by the intelligent agent are the same as the disturbances experienced by the surrounding target.

[0122] Based on the above dynamic equations, the state-space equations for each agent can be written as follows:

[0123]

[0124] in, Let i be the augmented state variable of the i-th agent. For z i The first derivative of (t). Let be the system matrix of the i-th agent, 0 2×2 I represents a second-order zero matrix. 2×2 It represents the second-order identity matrix. For the augmented control input of the i-th agent, For the i-th agent, there is an augmented unknown and a bounded perturbation. Let i be the measurable output of the i-th agent. Let be the output matrix of the i-th agent.

[0125] The state-space equations of each multi-agent agent need to satisfy the following conditions. First, the disturbances experienced by each agent... Unknown, but since ω(t) always has a known Lipschitz function. and ω (t) such that the following inequality always holds:

[0126]

[0127] Therefore, the disturbances experienced by the intelligent agent system always ensure that the following inequality holds:

[0128]

[0129] in, This is a lower bound function for the perturbation experienced by the agent. It is an upper bound function for the perturbation experienced by the agent.

[0130] Secondly, the initial positions and velocities of each agent are unknown, i.e., z i (0) Unknown, but a known vector must exist. and Make the following inequality always true:

[0131]

[0132] in,z i (0) is the lower bound of the initial position of the i-th agent. This is the upper bound of the initial position of the i-th agent.

[0133] Finally, the state-space equations of each agent must be fully observable, i.e., (A,C) observable.

[0134] For each agent, an interval observer is established as follows:

[0135]

[0136] in, Let be the gain matrix of the interval observer for the i-th agent. This is the upper bound of the estimated state variables of the agent. This is the lower bound of the estimated state variables of the agent. for The first derivative, for z i The first derivative of (t). The upper and lower bounds of the resulting agent's state variables always satisfy the following inequality:

[0137]

[0138] Then the following error system must be a positive system, where the error is defined as:

[0139]

[0140] in, The error between the upper bound of the agent's state variables estimated by the observer and the actual state variables. The error between the upper bound of the agent's state variables estimated by the observer and the actual state variables.

[0141] The error system is defined as:

[0142]

[0143] in, This is the derivative of the error between the upper bound of the agent's state variables estimated by the observer and the actual state variables. It is the derivative of the error between the upper bound of the agent's state variables estimated by the observer and the actual state variables.

[0144] Obviously, If (A-LC) is a Metzler matrix, then the error system is non-negative. If (A-LC) is both a Metzler matrix and a Hurwitz matrix, then the above error system is non-negative and stable. In this case, the upper and lower bounds of the state variables of the obtained agent system can satisfy the required inequalities.

[0145] To obtain an (A-LC) matrix that is both a Metzler matrix and a Hurwitz matrix, the same method is used to calculate the observer gain surrounding the target.

[0146] Based on the results obtained from the interval observers above, estimates of the state variables of each agent can be obtained. as follows:

[0147]

[0148] in, Let be the estimated location of the i-th agent. This is an estimate of the velocity of the i-th agent.

[0149] S3. Using the state estimates of the surrounding target and the second-order agent obtained from the above two types of interval observers, design a distributed uniform ring encirclement control strategy for the second-order multi-agent system in the two-dimensional plane, so as to realize the uniform ring encirclement of the target by the second-order multi-agent system in the two-dimensional plane.

[0150] Augmented control inputs applied to each agent The specific format is as follows:

[0151]

[0152] in, Used to determine the relative positions of each agent and the surrounding target, ρ is the radius of the preset uniform ring, and θ is the relative position of the i-th agent on the preset ring and the surrounding target.

[0153] The uniform ring-shaped encirclement control achieved by applying this control strategy satisfies the following condition: there exists a positive real number δ such that the following inequality holds:

[0154]

[0155] Example 2

[0156] A distributed uniform ring-encircling control system for a second-order multi-agent system in a two-dimensional plane includes:

[0157] The enclosing target interval observer construction module is used to establish the state space equation of an enclosing target that is affected by unknown, bounded disturbances and measurement noise, and further establish an enclosing target interval observer to obtain the estimated values ​​of the enclosing target state variables, including its position, velocity and acceleration.

[0158] The agent interval observer construction module is used to establish the state space equation of each agent in a second-order multi-agent system affected by unknown and bounded disturbances, and further establish agent interval observers to obtain the estimated values ​​of agent state variables, including their position and velocity.

[0159] The control module is used to design a distributed uniform ring encirclement control strategy for the second-order multi-agent system in a two-dimensional plane by using the state quantity estimates of the encircling target and the second-order agent obtained from the above two types of interval observers, so as to realize the uniform ring encirclement of the encircling target by the second-order multi-agent system in a two-dimensional plane.

[0160] Example 3

[0161] A distributed uniform ring-encirclement control device for a second-order multi-agent system in a two-dimensional plane includes a processor and a memory. The memory stores computer instructions, and the processor executes the computer instructions stored in the memory. When the computer instructions are executed by the processor, the electronic device implements the steps of the distributed uniform ring-encirclement control method for a second-order multi-agent system in a two-dimensional plane as described above.

[0162] The memory may include computer system readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The device may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the memory may be used to read and write non-removable, non-volatile magnetic media (commonly referred to as a "hard disk drive"). A program / utility having a set (at least one) of program modules may be stored in, for example, memory. Such program modules include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. The program modules typically perform the functions and / or methods described in the embodiments of the present invention.

[0163] The processor executes various functional applications and data processing by running programs stored in memory, such as the method provided in Embodiment 1 of the present invention.

[0164] Experimental simulation

[0165] The following section will use Simulink in MATLAB to model the above-mentioned two-dimensional plane second-order multi-agent system and the surrounding target, and use the method of this invention to verify the effectiveness of the uniform ring control achieved by the above-mentioned uniform ring control strategy.

[0166] To verify the effectiveness of the uniform loop control achieved by this control strategy, a more stringent disturbance can be selected for verification. This experiment uses sine waves of different amplitudes and frequencies to simulate stringent disturbances in real-world scenarios. For good visual simulation results, this experiment uses a multi-agent system with five agents as an example.

[0167] Selecting the system matrix surrounding the target C p =[-1,2], the disturbance received The upper and lower bounds of the disturbance are respectively and Let the initial position of the surrounding target be... Pick Using the YALMIP toolbox, solve the linear programming problem as shown above, and based on... Theorem 4 yields Therefore To ensure the complete observability of the dynamic system of each agent, the output matrix is ​​selected. Using the YALMIP toolbox and solving according to Theorem 4, we can obtain... Therefore The initial positions of each agent are selected as follows: and make p i =p i -Δ, where In this simulation experiment, the initial velocity vector v of each agent is... i Set all to 0 2×1 and make v i =v i -Δ, where The perturbations experienced by each agent are consistent with the perturbations experienced by the surrounding target. In this simulation, the radius of the surrounding ring is preset to ρ = 20, and the relative angle θ between the 5th agent on the ring and the surrounding target is preset to 3 / π. Therefore, for each agent: The control effect obtained by applying the control strategy described in this invention to each intelligent agent is as follows: Figure 4As shown, it can be seen that as time progresses, each intelligent agent is evenly distributed on a preset circular ring centered on the target, reaching a preset relative position. Combined with the time axis, it can be seen that each intelligent agent has a good following effect on the target moved by the disturbance, achieving the uniform circular encirclement control in a two-dimensional plane as expected by this invention.

Claims

1. A distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane, characterized in that, Includes the following steps: For a target surrounded by unknown, bounded disturbances and measurement noise, its state-space equation is established. Furthermore, an interval observer for the target surrounding is established to obtain estimates of the target's state variables, including its position, velocity, and acceleration. The interval observer for the target surrounding is as follows: ； in, It is the system matrix surrounding the target. The output matrix enclosing the target system, Let be the gain matrix that encloses the target interval observer. To encompass the measurable output of the target system, The lower bound of the unknown, bounded perturbations that surround the target. The upper bound of the unknown, bounded disturbances affecting the target; This is the estimated upper bound of the area surrounding the target location. This is the lower bound of the estimated target location. for The first derivative, for The first derivative; the resulting upper and lower bounds enclosing the target position always satisfy the following inequality: ； in, This represents the position coordinate vector of the target within a two-dimensional plane. Based on the above interval observer data, an estimate of the location surrounding the target is obtained. as follows: ； Using this estimate, the estimated velocity of the surrounding target can be obtained. and acceleration ;in, for The first derivative, for The second derivative; For each agent in a second-order multi-agent system affected by unknown, bounded perturbations, a state-space equation is established for each agent. Furthermore, an agent interval observer is established to obtain estimates of the agent's state variables, including its position and velocity. The agent interval observer is as follows: ； in, For the first Gain matrix of interval observers for each agent; This is the upper bound of the estimated state variables of the agent. This is the lower bound of the estimated state variables of the agent; for The first derivative, for The first derivative; For the first Augmented control input for individual agents For the first The system matrix of each agent, For the first The output matrix of each agent This is a lower bound function for the perturbation experienced by the agent. This is an upper bound function for the perturbations experienced by the agent. For the first The measurable output of an agent; the upper and lower bounds of the resulting agent's state variables always satisfy the following inequality: ； Based on the data obtained from the agent's interval observer, the estimated values ​​of the state variables of each agent are obtained. as follows: ； in, ; For the first The estimated location of each agent. For the first The estimated velocity of each agent is obtained. Using the state estimates of the surrounding target and the second-order agents obtained from the above two types of interval observers, a distributed uniform ring encirclement control strategy for the second-order multi-agent system in the two-dimensional plane is designed to achieve uniform ring encirclement of the surrounding target by the second-order multi-agent system in the two-dimensional plane.

2. The distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to claim 1, characterized in that, The position coordinates of the surrounding target in the two-dimensional plane are represented as follows: ； in, This represents the position coordinate vector of the target within a two-dimensional plane. To enclose the target in a two-dimensional plane Axis coordinates To enclose the target in a two-dimensional plane Axis coordinates for 3D real vector space; The state-space equations surrounding the target are as follows: ； in, for The first derivative, i.e., the velocity vector surrounding the target in the two-dimensional plane. The unknown, bounded disturbances experienced by the target.

3. The distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to claim 1, characterized in that, The state-space equations surrounding the target satisfy the following conditions: First, a known Lipschitz function must exist. and Make the following inequality always true: ； in, Unknown, bounded disturbances encountered in order to surround the target; Secondly, the initial position of the surrounded target. Unknown, but a known vector must exist. and Make the following inequality always true: ； in, The initial position surrounding the target. This serves as the lower bound encompassing the initial position of the target. This is the upper bound surrounding the initial position of the target; Finally, the system surrounding the target must be fully observable, i.e. Observable.

4. The distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to claim 1, characterized in that, A second-order multi-agent system moves in a two-dimensional plane. Let this second-order multi-agent system be denoted as […]. , ;in, Representing the An intelligent agent. For the number of intelligent agents, The position coordinates of an agent in a two-dimensional plane are represented as follows: ； in, For the first The position coordinate vector of an agent in a two-dimensional plane For the first An intelligent agent in a two-dimensional plane Axis coordinates For the first An intelligent agent in a two-dimensional plane Axis coordinates; The dynamic equations of each agent are described as follows: ； in, for The first derivative, For the first The velocity vectors of the agents in a two-dimensional plane, where For the first An intelligent agent in a two-dimensional plane axial velocity component, For the first An intelligent agent in a two-dimensional plane axial velocity component, For the first Position control input for each agent; for The first derivative, For the first Speed ​​control input for each agent The unknown, bounded perturbation experienced by the intelligent agent is the same as the perturbation experienced by the surrounding target; Based on the above dynamic equations, the state-space equations of each agent are as follows: ； in, For the first Augmented state variables of an agent for The first derivative; For the first The system matrix of each agent, Represents a second-order zero matrix. Represents a second-order identity matrix; For the first Augmented unknowns and bounded perturbations of individual agents; 5. The distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to claim 1, characterized in that, The state-space equations of each multi-agent agent need to satisfy the following conditions: First, the disturbances experienced by each agent Unknown, but due to There always exists a known Lipschitz function. and This ensures that the following inequality always holds: ； Therefore, the disturbances experienced by the intelligent agent system always ensure that the following inequality holds: ； Secondly, the initial positions and velocities of each agent are unknown, i.e. Unknown, but a known vector must exist. and Make the following inequality always true: ； in, For the first The lower bound of the initial position of each agent. For the first The upper bound of the initial position of each agent; Finally, the state-space equations of each agent must be completely observable, i.e. Observable.

6. The distributed uniform ring-encircling control method for a second-order multi-agent system in a two-dimensional plane according to claim 1, characterized in that, Augmented control inputs applied to each agent The specific format is as follows: ； in, This is an estimate of the location surrounding the target. and These are the estimated velocity and acceleration of the surrounding target, respectively; = , To predetermine the radius of a uniform ring, For the preset uniform ring on the first The relative positions of each agent and the surrounding target. The number of intelligent agents; For the first The estimated location of each agent. For the first Estimates of the speed of each agent; The uniform ring-shaped encirclement control achieved by applying this control strategy satisfies the following condition: there exists a positive real number. Make the following inequality true: ； in, For the first The position coordinate vector of an agent in a two-dimensional plane.

7. A distributed uniform ring-encircling control system for a second-order multi-agent system in a two-dimensional plane, characterized in that, include: The enclosing target interval observer construction module is used to establish the state-space equations of an enclosing target affected by unknown, bounded perturbations, and measurement noise. It then further establishes an enclosing target interval observer to obtain estimates of the enclosing target's state variables, including its position, velocity, and acceleration. The enclosing target interval observer is as follows: ； in, It is the system matrix surrounding the target. The output matrix enclosing the target system, Let be the gain matrix that encloses the target interval observer. To encompass the measurable output of the target system, The lower bound of the unknown, bounded perturbations that surround the target. The upper bound of the unknown, bounded disturbances affecting the target; This is the estimated upper bound of the area surrounding the target location. This is the lower bound of the estimated target location. for The first derivative, for The first derivative; the resulting upper and lower bounds enclosing the target position always satisfy the following inequality: ； Based on the above interval observer data, an estimate of the location surrounding the target is obtained. as follows: ； Using this estimate, the estimated velocity of the surrounding target can be obtained. and acceleration ;in, for The first derivative, for The second derivative; The agent interval observer construction module is used to establish the state-space equations of each agent in a second-order multi-agent system affected by unknown, bounded perturbations, and further establish agent interval observers to obtain estimates of the agent's state variables, including its position and velocity. The agent interval observer is as follows: ； in, For the first Gain matrix of interval observers for each agent; This is the upper bound of the estimated state variables of the agent. This is the lower bound of the estimated state variables of the agent; for The first derivative, for The first derivative; For the first Augmented control inputs for each agent For the first The measurable output of an agent; the upper and lower bounds of the resulting agent's state variables always satisfy the following inequality: ； Based on the data obtained from the agent's interval observer, the estimated values ​​of the state variables of each agent are obtained. as follows: ； in, ; For the first The estimated location of each agent. For the first Estimates of the velocity of each agent; The control module is used to design a distributed uniform ring encirclement control strategy for the second-order multi-agent system in a two-dimensional plane by using the state quantity estimates of the encircling target and the second-order agent obtained from the above two types of interval observers, so as to realize the uniform ring encirclement of the encircling target by the second-order multi-agent system in a two-dimensional plane.

8. A distributed uniform ring-encircling control device for a second-order multi-agent system in a two-dimensional plane, characterized in that, The device includes a processor and a memory, wherein the memory stores computer instructions, and the processor executes the computer instructions stored in the memory. When the computer instructions are executed by the processor, the electronic device implements the steps of the distributed uniform ring encirclement control method for a second-order multi-agent system in a two-dimensional plane as described in any one of claims 1 to 6.

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