CN107888412A - Multi-agent network finite time contains control method and device - Google Patents

Multi-agent network finite time contains control method and device Download PDF

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CN107888412A
CN107888412A CN201711062636.9A CN201711062636A CN107888412A CN 107888412 A CN107888412 A CN 107888412A CN 201711062636 A CN201711062636 A CN 201711062636A CN 107888412 A CN107888412 A CN 107888412A
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following
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季向阳
于镝
陈孝罡
高山
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Tsinghua University
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    • H04W4/02—Services making use of location information
    • H04W4/025—Services making use of location information using location based information parameters
    • H—ELECTRICITY
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/025—Services making use of location information using location based information parameters
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Abstract

The invention provides a kind of multi-agent network finite time to contain control method and device, including：Obtain the minimum geometric space that navigator's intelligent body is formed by verifying Obstacle Position；According to multi-agent network topological structure and navigate intelligent body position and velocity information, it is determined that desired locations and speed when following the intelligent body to operate in the space；According to the Topology connection situation followed between intelligent body, the relative position and speed followed between intelligent body intelligent body adjacent thereto is obtained, and the finite-time control agreement of intelligent body is followed according to relative position and speed designs；Follow intelligent body to enter minimal safe region according to finite-time control protocol integrated test system, and make to follow intelligent body to move according to its desired locations and speed.The present invention ensures the coordination security control of multi-agent network by a small number of navigator's intelligent bodies for being equipped with sensor；Controlled using the second nonlinear based on intelligent body position and speed, effectively improve rapidity and stability that Nonlinear Intelligent body group coordinates control.

Description

Multi-agent network limited time containing control method and device
Technical Field
The invention belongs to the technical field of multi-agent network control, and particularly relates to a multi-agent network limited time tolerance control method and device.
Background
A multi-agent network is a large system of groups of agents with computing, sensory communication, and mobility capabilities linked by network communication. The intelligent agents carry out information transmission through the network and adopt a more convenient and flexible distributed control method. Multi-agent coordinated control has been successfully applied in many engineering fields, such as agent aggregation, unmanned aerial vehicle fire rescue, communication network congestion control, sensor network positioning, and the like. In general, an agent refers to a robot, a drone, and the like.
In practical application, when a plurality of agents with different performances execute a coordination task, only part of the agents are required to be provided with sensors to detect dangerous obstacles, the agents are designated as navigation agents, and the other agents are following agents. By ascertaining the location of the dangerous obstacle, the piloting agent can form a safe moving area, and if the following agent always moves in the safe area formed by the piloting agent, the group of agents can safely and smoothly reach the destination. However, in practical applications, the agents in the multi-agent network are described in a nonlinear dynamic manner and are affected by nonlinear disturbances such as model uncertainty and random disturbance, and the existing agent control method cannot realize fast finite-time containment control of the agents.
Disclosure of Invention
To solve the above technical problem, embodiments of the present invention provide a method and an apparatus for controlling a multi-agent network with a limited time tolerance.
In one aspect, an embodiment of the present invention provides a method for controlling a multi-agent network with a finite time tolerance, where the multi-agent network includes a plurality of leading agents and following agents, and the method includes:
step 1, acquiring a minimum geometric space formed by a piloting intelligent agent through finding the position of an obstacle;
step 2, determining an expected position and an expected speed when the following agent runs in the minimum geometric space according to the topological structure of the multi-agent network and the position information and the speed information of the piloting agent;
step 3, acquiring the relative position and relative speed between the following agent and the adjacent agent according to the topological connection condition between the following agents, and designing a limited time control protocol of the following agent according to the relative position and relative speed;
and 4, controlling the following intelligent agent to enter the minimum safety area according to the limited time control protocol, and controlling the following intelligent agent to move in the minimum safety area according to the expected position and the expected speed.
In one aspect, an embodiment of the present invention further provides a device for controlling a multi-agent network with a finite time tolerance, where the multi-agent network includes a plurality of leading agents and following agents, and the device includes:
the minimum geometric space acquisition unit is used for acquiring a minimum geometric space formed by the piloting intelligent agent by finding the position of the barrier;
the expected track calculation unit is used for determining an expected position and an expected speed when the following intelligent agent runs in the minimum geometric space according to the topological structure of the multi-intelligent-agent network and the position information and the speed information of the piloting intelligent agent;
and the control unit is used for acquiring the relative position and the relative speed between the following intelligent agent and the adjacent intelligent agent according to the topological connection condition between the following intelligent agents, designing a limited time control protocol of the following intelligent agent according to the relative position and the relative speed, controlling the following intelligent agent to enter the minimum safety area according to the limited time control protocol, and controlling the following intelligent agent to move according to the expected position and the expected speed.
In another aspect, embodiments of the present invention also provide a computer-readable storage medium storing computer-readable instructions that, when executed, cause a processor to perform at least the operations of the multi-agent network limited-time inclusion control method.
On the other hand, an embodiment of the present invention further provides an electronic device, where the electronic device includes:
the sensor module is used for acquiring position information and speed information of the piloting agent and the following agent;
a memory for storing program instructions and data;
and the processor is connected with the sensor module and the memory and is used for executing the program instructions in the memory and processing the position information and the speed information of the piloting agent and the following agent according to the steps in the multi-agent network limited time containment control method.
The method for controlling the limited time inclusion of the multi-agent network provided by the embodiment of the invention can implement the limited time inclusion control on the following agent network on the premise that the piloting agent forms a safe area, thereby improving the rapidity and the stability of the multi-agent network coordination control. Compared with the asymptotic convergence characteristic, the finite time control enables the system to have the advantages of high response speed, good robustness, strong disturbance resistance and the like. In addition, the embodiment of the invention has the following beneficial effects: sensing the surrounding environment and forming a safe area for moving the intelligent agent through a few piloting intelligent agents provided with sensors, and ensuring the coordinated safety control of a multi-intelligent-agent network; by adopting second-order nonlinear control based on the position and the speed of the intelligent agent, the rapidity and the stability of the nonlinear intelligent agent group coordination control can be effectively improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a multi-agent network time-limited containment control method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a multi-agent network time-limited containment control method provided by an embodiment of the invention;
FIG. 3 is a network topology diagram of a multi-agent network following an agent's undirected connectivity;
FIG. 4 is a diagram of the movement trajectories of all network individuals in a two-dimensional space when the control protocol (4) is adopted following the undirected connectivity of the agents in the embodiment of the present invention;
FIG. 5 is a diagram of the movement traces of all network individuals in a two-dimensional space when the control protocol (5) is adopted following the undirected connection of the agents;
FIG. 6 is a network topology diagram of a multi-agent network following agent directed strong connectivity;
FIGS. 7A and 7B are diagrams of the movement trajectories of all agents in a two-dimensional space when a control protocol (6) is adopted following the direction strong communication of the agents, respectively;
FIG. 8 is a schematic structural diagram of a finite time-containment control device of an intelligent agent network according to an embodiment of the present invention;
fig. 9 is a schematic structural diagram of a desired trajectory calculation unit 802 provided in an embodiment of the present invention;
fig. 10 is a schematic structural diagram of a control unit 803 provided in an embodiment of the present invention;
fig. 11 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the practical application of the prior art, the agents in the network can be described in a nonlinear dynamic manner and are generally influenced by nonlinear disturbances such as model uncertainty and random disturbance, and the existing agent control method cannot realize the fast finite time-contained control of the multi-agent network. In order to realize the fast finite time-tolerant control of the multi-agent network, the embodiment of the invention researches and simulates the control protocol of the nonlinear multi-agent network subjected to bounded disturbance. The intelligent agent in the embodiment of the invention can be a robot, an unmanned aerial vehicle or other intelligent agents capable of moving.
Containment control is a typical situation in navigation-following coordination control, and essentially means that a group of following agents keep moving in a minimum geometric space (convex hull) surrounded by navigation agents under the guidance of a plurality of navigation agents, so that the following agents can safely and smoothly reach a destination. The embodiment of the invention provides a multi-agent network limited time containment control method. The flow diagram of the method is shown in fig. 1, and mainly comprises the following steps:
step 1, acquiring a minimum geometric space (namely a convex hull) formed by a piloting agent by detecting the position of an obstacle.
Generally, the piloting intelligent agent forms a safe moving area by ascertaining the position of a dangerous obstacle, and the piloting intelligent agent moves in a safe area formed by the piloting intelligent agent, so that the safe moving of an intelligent agent group can be ensured. The piloting agent may send information to the following agent, which is responsible for receiving the information but not sending the information to the piloting agent.
And 2, determining an expected position and an expected speed when the following agent runs in the convex hull according to the topological structure of the multi-agent network and the position information and the speed information of the piloting agent.
And 3, acquiring the relative position and the relative speed between the following agent and the adjacent agent according to the topological connection condition between the following agents, and designing a limited time control protocol of the following agent according to the relative position and the relative speed.
And 4, controlling the following intelligent agent to enter the minimum safety area according to the limited time control protocol, and controlling the following intelligent agent to move in the minimum safety area according to the expected position and the expected speed.
FIG. 2 is a schematic diagram of a multi-agent network time-limited containment control method according to an embodiment of the present invention. As shown, 1 denotes an obstacle, 2 denotes a piloting agent, 3 denotes a following agent, 4 denotes a safety zone (i.e., convex hull) formed by the piloting agent, 5 denotes a motion trajectory of the piloting agent, and 6 denotes a center line of the convex hull formed by the piloting agent. After obtaining the corresponding finite time control protocol according to the corresponding steps in fig. 1, the following agent can be controlled to enter the convex hull and move along the desired position and the desired velocity.
Fig. 2 is only a schematic illustration of the embodiment, and is not intended to limit the present invention, and in the specific implementation, the number of the leading agents and the number of the following agents are not limited, but the number of the leading agents is usually not less than 4. The piloting agent constitutes the top layer structure, and follows the agent and constitute the substructure to form the coordinated control structure of double-deck agent network, when the top layer piloting agent realizes effectual obstacle avoidance, form the bottom and follow the agent finite time and contain the control. For each following agent, at least one lead agent communicates with it.
The method for controlling the limited time inclusion of the multi-agent network provided by the embodiment of the invention can implement the limited time inclusion control on the following agent network on the premise that the piloting agent forms a safe area, thereby improving the rapidity and the stability of the multi-agent network coordination control. Compared with the asymptotic convergence characteristic, the finite time control enables the system to have the advantages of high response speed, good robustness, strong disturbance resistance and the like.
Consider a group of agents sigma consisting of a plurality of agents i I =1, \8230, N + M, N being the number of following agents, M being the number of piloting agents, with the corresponding topology being G (V, epsilon, a). Let the following agent set and the piloting agent set in the agent group be respectively represented by F = {1, \8230, N } and L = { N +1, \8230, N + M }, then the vertex set V = { ν } of the whole agent group network 1 ,…,ν N+M V set of following agent nodes f ＝{ν i I ∈ F } and a set of piloting agent nodes V l ＝{ν i I ∈ L }. In an embodiment of the present invention, i.e., taking into account the location and velocity changes of all agents in the agent network, the dynamics of an individual agent in a multi-agent network is described by a second order nonlinear equation as shown below:
wherein x is i ＝[x i1 ,x i2 ,…,x ip ] T ∈R p ,v i ∈R p ,u i ∈R p ,i＝1,…,N+M；Respectively represent x i 、v i A derivative of (a); when i ∈ F, x i ,v i ,u i Respectively representing position information, velocity information and control vector of the following agent i, f (x) i ,v i )∈R p And ρ i ∈R p Respectively representing a nonlinear dynamic vector and a disturbance vector acting on a following agent i, and | | ρ i || ∞ Not more than sigma, sigma is following the nonlinearity that the intelligent body receivesThe upper bound of the perturbation. Order to F＝[f T (x 1 ,v 1 ),f T (x 2 ,v 2 ),…,f T (x N ,v N )] T Andrespectively representing the position information, the speed information, the control vector, the nonlinear dynamic vector and the received nonlinear disturbance vector of the following agent; the position information, the speed information and the control vector of the piloting intelligent agent are respectively made of And (4) showing. The nonlinear dynamic vector acting on the piloting agent is G = [ G ] T (x N+1 ,v N+1 ),g T (x N+2 ,v N+2 ),…,g T (x M ,v M )] T Is represented, and | | | g (x) i ,v i )|| ∞ Tau is less than or equal to, i belongs to L, and tau represents the upper bound of the control action of the piloting intelligent body. The position information and the speed information are usually vector information, and if the dimension p of the vector is 2, the position information of a certain agent includes x-axis coordinates and y-axis coordinates, and similarly, the speed information includes a speed in the x-axis direction and a speed in the y-axis direction.
In an embodiment of the invention, x is the position information and the speed information of all following agents i ,x j ,v i ,v j I belongs to F, j belongs to F, and all the constants are nonnegative constants l 1 And l 2 So that the following holds: | f (x) i ,v i )-f(x j ,v j )||≤l 1 ||x i -x j ||+l 2 ||v i -v j L. In thatIn practical application, the relative position error and the relative speed error between the agents are bounded, so that the nonlinear dynamic f (x) of the agents is followed i ,v i ) Is also bounded.
In an embodiment, when the expected position and the expected speed of the following agent in the convex hull formed by the piloting agent are obtained in step 2, the topological structures of the piloting agent and the following agent in the multi-agent network need to be obtained first, and the Laplacian matrix L of the multi-agent network topology is determined. Generally, the Laplacian matrix L of the multi-agent network topology can also be written in the form of a block matrix:
wherein, gamma is 1 Matrix gamma corresponding to topological connection relation between following intelligent bodies in Laplacian matrix L representing multi-intelligent network topology 1 ∈R N×N ；Γ 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M 。
Then, according to the Laplacian matrix L and the position information and the speed information of the piloting agent, respectively calculating a convex weighted average value x of the position of the piloting agent d And a convex weighted average v of the velocity d ：
In the embodiment of the invention, the convex weighted average of the positions of the piloting agents is used as the expected position of the following agent, and the convex weighted average of the speeds of the piloting agents is used as the expected speed of the following agent, so that the finite time containing control of the following agent is realized.
In embodiments of the present invention, the control action on the following agent is based on network errors, which are based on the relative position and relative velocity between the following agent and its neighbors. And the control action following the agent is related to the value range of the control gain parameter.
To more clearly illustrate the technical solution in the above embodiment, based on the relative position and relative speed information between the agents, the position error and the speed error of the network of the multi-agent are defined as follows:
wherein e is 1j Is the position error of an agent in a multi-agent network; e.g. of the type 2j Is the speed error of an agent in a multi-agent network; a is ij Is an element in an adjacency matrix corresponding to a multi-agent network topology, a ij A 1 indicates that the following agent i communicates with its neighbor agent j, a ij A value of 0 indicates that the following agent i does not communicate with its neighbor agent j.
The error dynamics of the entire multi-agent network can be described as:
wherein,
in the multi-agent network, each piloting agent is not communicated with each other, and each following agent is communicated with at least one piloting agent, so that the topological structure of the multi-agent network is easily obtained. Furthermore, according to the topological structure of the multi-agent network, the matrix gamma is known no matter the following agents are in undirected connection or directed strong connection 1 Are all strong diagonal dominant M-matrices, so their inverseExists and is positively determined, thenA non-negative matrix and a row random matrix. Order toAndwherein a convex weighted average of the position and velocity of the piloting agent is usedRespectively representing a desired position vector and a desired velocity vector of the following agent, whereinx di ∈R p ,v di ∈R p ,i∈F。x d 、v d Respectively representing the desired position and desired velocity, x, of the following agent f 、v f Respectively representing real-time position information and real-time velocity information of the following agent,representing the position error and velocity error of the following agent, respectively. In order for the following agent to converge into the convex hull formed by the piloting agent and move at the desired speed in the convex hull, thenFormed by a matrix F 1 Is not singularity of when E 1 =0 and E 2 When =0, x f ＝x d ，v f ＝v d I.e. following the arrival of the agent and keeping it in its desired position, in the convex hull formed by the piloting agent and moving at the desired speed.
From the above analysis, it can be seen that if E is the case when there is no directional communication between the following agents and there is at least one lead agent communicating with each following agent 1 ＝0，E 2 =0, then the following agent can converge to the convex formed by the piloting agentIn the package and along the desired trajectory.
Consider the nonlinear agent population described in dynamics (1), if x is for all initial states i (0),v i (0) I ∈ F, there is T' (x) i (0),v i (0))&Infinity so that there is x for all T ≧ T i (t)＝x di (t)，v i (t)＝v di And (t) is established, the intelligent agent group network (1) is called to realize the finite time containing control. The method is the definition of precise limited time containing control, namely, the intelligent agent is followed to enter a convex hull formed by the navigation intelligent agent under the action of a control protocol, and then the intelligent agent moves according to an expected track.
In addition, consider the nonlinear agent population described by dynamics (1), if for all initial states: x is the number of i (0),v i (0) I ∈ F, presence of T' (x) i (0),v i (0))&Infinity so that there is x for all T ≧ T i (t)∈Co(X L )，v i (t)∈Co(V L ) And wherein:
the multi-agent network (1) is said to achieve a limited time fast containment control. Co (X) L ) Representing a convex hull, θ, bounded by the positions of M piloting agents i A convex weighting factor representing each piloting agent position information. That is, as long as the following agent is caused to enter the convex hull and remain moving in the convex hull, it is not required to be caused to move according to its desired trajectory, so that faster finite-time containment control can be achieved.
In the embodiment of the invention, when following agents in the multi-agent network are connected in an undirected way, the following control protocol can be adopted to realize the limited time control of the following agents:
wherein u is fi Is a control vector acting on the following agent i; a is ij Is an adjacency matrix element corresponding to the multi-agent network topology; x is a radical of a fluorine atom i 、v i Respectively position information and velocity information, x, following agent i j 、v j Respectively position information and speed information of an agent j adjacent to a following agent i, wherein i belongs to {1, \8230;, N }, j belongs to {1, \8230;, N + M }, N is the number of following agents in the multi-agent network, and M is the number of piloting agents; (x) i －x j ) Representing the relative position between a following agent i and its neighboring agent j, (v) i －v j ) Representing the relative velocity between a following agent i and its neighboring agent j; 1 p The column vector with the p-dimensional elements of 1 is adopted, and p is a space dimension; sgn (·) is a sign function,α 1 、β 1 、γ、κ 1 and kappa 2 Is a control parameter for a multi-agent network.
In the control protocol (4), the control parameter α is 1 、β 1 、γ、κ 1 And kappa 2 The following conditions are satisfied:
wherein tau is the upper bound of the control action of the piloting agent; gamma-shaped 1 The Laplacian matrix L representing the topology of multiple intelligent networks is the matrix corresponding to the topological connection between the agents, gamma 1 ∈R N×N ，Γ 2 Indicating the Laplacian matrix, gamma, in the Laplacian matrix L corresponding to the topological connection between the agent and the piloting agent 2 ∈R N×M ；λ min (Γ 1 ) Is a matrix gamma 1 The minimum eigenvalue of (c).
When following agents are connected in a multi-agent network in an undirected mode, the following control protocols can be adopted to realize the limited time containing control of the following agents:
wherein u is fi I belongs to {1, \ 8230;, N } for the control vector acting on the following agent i, N being the number of following agents in the multi-agent network; a is a ij J belongs to {1, \ 8230;, N + M }, wherein M is the number of piloting agents; x is the number of i 、v i Respectively position information and speed information of the following agent i; x is the number of j 、v j Respectively, position information and velocity information of agent j adjacent to following agent i; (x) i －x j ) Representing the relative position between a following agent i and its neighboring agent j, (v) i －v j ) Representing the relative velocity between a following agent i and its neighboring agent j; sgn (·) is a sign function,m 1 and m 2 Is a control parameter for a multi-agent network.
In the control protocol (5), the control parameter m 1 And m 2 The following conditions are satisfied:
wherein eta is any normal number; μ is an upper bound following the nonlinear dynamics of the agent; tau is the upper bound of the control action on the piloting agent and sigma is the upper bound following the nonlinear disturbance on the agent; gamma-shaped 1 The matrix corresponding to the topological connection relation between the following intelligent agents in the Laplacian matrix L representing the multi-intelligent network topology, and the Laplacian matrixΓ 1 ∈R N×N ，Γ 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；λ max (Γ 1 ) Is a matrix gamma 1 The maximum eigenvalue of (d); lambda [ alpha ] min (Γ 1 ) Is a matrix F 1 The minimum eigenvalue of (c); p is the spatial dimension.
When there is a directed strong connection between following agents in a multi-agent network, the following control protocol may be employed to achieve a finite time control of the following agents:
wherein u is fi Is a control vector acting on the following agent i; t is ij A matrix gamma corresponding to the topological connection relation between the following intelligent agents in a Laplacian matrix L of a multi-intelligent network topology 1 Of inverse matrix Γ 1 ﹣1 Element of (D), F 1 ﹣1 ＝[T ij ]∈R N×N Laplacian matrixΓ 1 ∈R N×N ，Γ 2 Showing the Laplacian matrix, gamma, corresponding to the topological connection between the following agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；sig α (x) For a non-smooth function, for a vector x = [ x = 1 ,x 2 ,…,x n ] T sig α (x)＝[|x 1 | α sgn(x 1 ),|x 2 | α sgn(x 2 ),…,|x n | α sgn(x n )] T ；α 2 、β 2 、γ 1 、γ 2 、k 1 、k 2 、χ 1 Hexix- 2 Control parameters for a multi-agent network; sgn (. Cndot.) is a symbolThe function of the function is that of the function,Φ i and Ω i As an intermediate process variable, [ phi ] i ＝[x i1 sgn(s i1 ),x i2 sgn(s i2 ),…,x ip sgn(s ip )] T ，Ω i ＝[v i1 sgn(s i1 ),v i2 sgn(s i2 ),…,v ip sgn(s ip )] T ；s j In order to be a sliding-mode error vector,e 1j is the position error of an agent in a multi-agent network; e.g. of a cylinder 2j Is the speed error of an agent in a multi-agent network.
In the control protocol (6), the control parameter α is 2 、β 2 、γ 1 、γ 2 、k 1 、k 2 、χ 1 Hexix- 2 The following conditions are satisfied:
α 2 >0,β 2 >0,k 1 >0,k 2 >0,1<γ 2 <2,γ 1 >γ 2 and x 1 >l 1 ,χ 2 >l 2 ,
Wherein i, j is equal to {1, \8230;, N }, x i 、v i Respectively representing position information and speed information of the following agent i; x is the number of j 、v j Respectively representing location information and velocity information of agent j adjacent to following agent i; (x) i －x j ) Representing the relative position between the following agent i and the following agent j, (v) i －v j ) Representing the relative velocity between the following agent i and the following agent j.
Under two conditions of undirected communication and directed strong communication, the embodiment of the invention selects a Lyapunov function based on a network error to analyze the finite time stability of a network system according to the theorem of finite time stability, then constructs a control protocol meeting the conditions of the theorem, and simultaneously gives a reasonable value range of control parameters. To demonstrate the above control protocols (4) - (6), the embodiments of the present invention introduce the following arguments:
introduction 1 [1] Consider a system
Wherein, f is U 0 ×R + →R n Open neighborhood U at origin 0 The inner phase is continuously differentiable with respect to x. It is assumed that there is a continuously differentiable positive definite function V (x, t) (V:wherein) Real number 1>α&gt, 0 and c&gt, 0, such thatIn thatThe upper half is determined negatively, the origin of the system is stable in a finite time, and the rest time depends on the initial time value x (t) of the system state 0 ) With an upper boundary of
Introduction 2 [2] An extended Lyapunov description of finite time stability can be written as follows
Wherein the parameter alpha>0，β>0，1<γ 2 <2，γ 1 >γ 2 V (x, t) is a continuously differentiable positive definite function with respect to system state and time, the dynamic finite time is stable and the system's rest time depends on the system state initial time value x (t) 0 ) And is that:
wherein F (-) is a Gaussian hypergeometric function.
The invention divides the second-order nonlinear agent group with nonlinear dynamics and bounded disturbance into a pilot agent and a following agent to carry out the finite time containing control of the agent network. Construction is based on network error E when following undirected connectivity between agents 1 And E 2 And then the derivative of the Lyapunov function V with respect to time is obtained. Adopts a variable structure control idea to construct a switching control protocol so as to meet the lemma 1 [1] InIn such a way that a suitable range of parameters in the control protocol is determined such that V =0, i.e. E, is achieved within a limited time 1 ＝0,E 2 =0, so the entire network achieves a limited time containment control under the action of this control protocol. When following the strong communication between the intelligent agents, the idea of sliding mode control can be adopted, and firstly, the network error E is defined 1 And E 2 Of a sliding mode error vectorAnd constructing a Lyapunov function V related to the sliding mode error vector S, and then solving a derivative of the Lyapunov function V related to timeFurther, the distributed control protocol is constructed so as to satisfy lemma 1 [1] InAnd determining suitable ranges of parameters in the control protocol such that V =0 is achieved in a limited time, i.e. the system moves onto the sliding mode surface S =0. Further according to the lemma 2 [2] Can obtain the network error E within a limited time 1 ＝0,E 2 And =0, therefore, under the action of the control protocol, the whole network realizes the limited time containment control, thereby improving the rapidity and the stability of the coordination control of the nonlinear agent group.
In order to more clearly illustrate the present invention, the following two examples are provided to illustrate the technical solution of the present invention.
Example 1
In this embodiment, consider a network of 8 agents, including 4 leading agents and 4 following agents, whose network topology is shown in FIG. 3, L 1 ～L 4 Representing 4 piloting agents, F 1 ～F 4 Representing 4 following agents. As can be seen from fig. 3, there is no directional connectivity between the following agents, and for each following agent there is at least one lead agent in communication with it. Let nonlinear dynamics and nonlinear disturbances be:
g(x i ,v i )＝(0,-0.158sin(0.1256t)) T ,i∈L
ρ i ＝[0.5sin(x i1 )+0.5sin(v i1 ),0.5cos(x i2 )+0.5cos(v i2 )] T ,i∈F
and (3) designing two control schemes based on the relative position and relative speed information between the intelligent agents by adopting a variable structure control idea, wherein the two control schemes are respectively shown as a control protocol (4) and a control protocol (5).
When adoptingIn the case of controlling the protocol (4), in order to enable the nonlinear network to implement the finite-time containment control, that is, to converge into the dynamic convex hull surrounded by the piloting agent within the finite time following the agent, the upper bound of the control action of the piloting agent and the upper bound of the disturbance are respectively τ =1 and σ =1, and in the allowable value range of the control parameters of the control protocol (4), the following values are respectively assigned to the control parameters: alpha (alpha) ("alpha") 1 ＝1，β 1 ＝2，γ＝0.6，κ 1 ＝0.9，κ 2 =0.9, and the motion trace of the agent is shown in fig. 4. The solid star represents the initial position of the following intelligent agent, the solid square represents the position of the piloting intelligent agent, the solid round dots represent the expected positions of the following intelligent agent in the convex hull, the thick solid lines represent the motion tracks of 4 piloting intelligent agents, the other four groups of thin dotted lines, dotted lines and solid lines represent the motion tracks of the following intelligent agents, and the solid line frame surrounded by the piloting intelligent agents represents the convex hull surrounded by the piloting intelligent agents when t =0s,20s and 40s. According to the embodiment, based on the switching control law, the following agent in the multi-agent network can enter the convex hull formed by the piloting agent after about 7 seconds, and can move at the expected speed along the expected track after about 12 seconds, namely, the finite-time fast containing control is realized.
Fig. 5 is a diagram of the motion trail of all network individuals in a two-dimensional space when the control protocol (5) is adopted following the undirected connection of the intelligent agent. When the control protocol (5) is adopted, in this embodiment, in order to enable the nonlinear network to realize the finite-time containment control, that is, the following agent converges in a dynamic convex hull surrounded by the piloting agent within a finite time, the nonlinear dynamic upper bound and the disturbance upper bound of the following agent are μ =7 and σ =1, respectively, the upper bound for control of the piloting agent is τ =1, and within an allowable value range of the control parameters of the control protocol (5), the control parameters are respectively set as follows: m is a unit of 1 =42 and m 2 =32, the motion track of the multi-agent network is obtained as shown in fig. 5. Wherein solid star represents the initial position of the following agent, solid square represents the position of the piloting agent, solid dots represent the expected position of the following agent in the convex hull, thick solid line represents 4The motion trail of each piloting intelligent agent, the rest four groups of thin dotted lines, dotted lines and solid lines represent the motion trail of the following intelligent agent, and the solid line frame enclosed by the piloting intelligent agents represents a convex hull enclosed by the piloting intelligent agents when t =0s,20s and 40s. It can be seen from this embodiment that, based on the action of the switching control law, the multi-agent network can enter the convex hull formed by the piloting agents for about 8s, and can move at a desired speed along a desired track for about 12s, that is, the limited-time fast inclusion control is realized.
Example 2
In order to relax the limitation on the network topology, in this embodiment, the following strong connection condition between the agents is studied.
Consider a directed network topology consisting of 10 agents, including 4 piloting agents L 1 ～L 4 And 6 following agents F 1 ～F 6 The network topology is as shown in fig. 6, following agents have strong communication, and for each following agent, at least one piloting agent is in communication with the following agent. In example 2, the same intrinsic nonlinear dynamics and nonlinear perturbation as in example 1 are used, following the Laplacian matrix Γ corresponding to the network topology connection between agents 1 Is a non-singular matrix but is asymmetrically positive.
Designing a non-smooth discontinuous control protocol to realize the finite time containment control of the non-linear network, and defining a sliding mode error vector as follows:
wherein s is i ＝[s i1 ,s i2 ,…,s ip ] T ，α 2 、β 2 For controlling control parameters in protocol (6), for vector x = [ x ] 1 ,x 2 ,…,x n ] T Sigo function α (x)＝[|x 1 | α sgn(x 1 ),|x 2 | α sgn(x 2 ),…,|x n | α sgn(x n )] T 。
In the embodiment, when the distributed nonsingular rapid terminal control protocol (6) is adopted to control the movement of the following intelligent body, the control parameter alpha of the control protocol (6) 2 、β 2 、γ 1 、γ 2 、k 1 、k 2 、χ 1 Hexix- 2 Need to satisfy alpha 2 >0，β 2 >0，k 1 >0,k 2 >0，1<γ 2 <2，γ 1 >γ 2 χ 1 >l 1 ,χ 2 >l 2 ,
Fig. 7A and 7B are diagrams of the movement trajectories of all agents in a two-dimensional space when the control protocol (6) is used when following the agent direction strong connection, respectively. FIG. 7A shows following agent F 1 、F 3 、F 6 Fig. 7B shows and follows agent F 2 、F 4 、F 5 The motion trajectory of (2). In fig. 7A and 7B, a solid star represents an initial position of the following agent, a solid square represents a position of the navigating agent, a solid dot represents a desired position of the following agent in the convex hull, a thick solid line represents a motion trajectory of 4 pilots, three groups of thin dotted lines, and solid lines represent motion trajectories of the following agent, and a solid line frame surrounded by pilots represents a convex hull surrounded by pilots at t =0s,20s, and 40s. When the control protocol (6) is adopted, in order to enable the nonlinear network to realize the finite time containment control, namely, the following intelligent agents converge into a dynamic convex hull surrounded by the piloting intelligent agents within finite time, the upper control action bound and the upper disturbance bound of the piloting intelligent agents are tau =1 and sigma =1 respectively, and in the allowable value range of the control parameters of the control protocol (6), the control parameters are respectively set as follows: l 1 =42 and l 2 ＝32，α＝5，β＝0.08，γ 1 ＝1.5，γ 2 ＝1.2，χ 1 =0.9 and χ 2 ＝0.9The movement locus of the agent is shown in fig. 7A and 7B. It can be seen that in the present embodiment, based on the action of the switching control law, the multi-agent network achieves the limited-time fast-inclusive control after about 7s, and achieves the limited-time inclusive control after 10 s.
In embodiment 1 and embodiment 2, no matter the following agents in the multi-agent network are connected in an undirected manner or in a directed manner, the network error corresponding to the following agents in the system can be converged to zero quickly in a limited time by adopting any one of the control protocols (4) to (6), and no singularity occurs in the whole process.
Based on the same inventive concept as the multi-agent network limited time containment control method shown in fig. 1, the embodiment of the present invention further provides a multi-agent network limited time containment control device, as described in the following embodiments. Since the principle of the device for solving the problem is similar to the control method in fig. 1, the implementation of the device can refer to the implementation of the multi-agent network limited-time containment control method in fig. 1, and repeated details are not repeated.
In another embodiment, the present invention further provides a multi-agent network limited-time containment control device, the structure of which is substantially as shown in fig. 8, the device mainly comprising: a minimum geometric space acquisition unit 801, a desired trajectory calculation unit 802, and a control unit 803. The minimum geometric space acquiring unit 801 is configured to acquire a minimum geometric space formed by the piloting agent by ascertaining the position of the obstacle; the expected trajectory calculation unit 802 is configured to determine an expected position and an expected speed when the following agent runs in the minimum geometric space according to the topology structure of the multi-agent network and the position information and speed information of the piloting agent; the control unit 803 is configured to obtain a relative position and a relative speed between the following agent and its neighbor according to a topological connection condition between the following agents, design a finite time control protocol of the following agent according to the relative position and the relative speed, control the following agent to enter the minimum security area according to the finite time control protocol, and control the following agent to move along the desired position and the desired speed.
In an embodiment, the expected trajectory calculation unit 802 specifically includes: the topology matrix determining module 901 and the calculating module 902 are schematically shown in fig. 9. The topology matrix determining module 901 is configured to obtain a topology structure of a piloting agent and a following agent in a multi-agent network, and determine a Laplacian matrix L of a multi-agent network topology:
the calculating module 902 is configured to calculate a convex weighted average of the position and a convex weighted average of the speed of the piloting agent according to the Laplacian matrix L and the position information and the speed information of the piloting agent, and take the convex weighted average of the position and the convex weighted average of the speed of the piloting agent as an expected position and an expected speed of the following agent, respectively:
wherein the multi-agent network comprises following agents and pilot agents to form an agent group sigma i I =1, \8230;, N + M; f = {1, \8230;, N } and L = { N +1, \8230;, N + M } respectively represent the following agent set and the piloting agent set, N is the number of following agents, and M is the number of piloting agents; gamma-shaped 1 A matrix, Γ, representing the Laplacian matrix L corresponding to the topological connection between the agents that follow it 1 ∈R N×N ，Is gamma 1 The inverse matrix of (d); gamma-shaped 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；x l 、v l Respectively position information and speed information of the piloting agent; x is the number of d 、v d Convex being respectively the position of piloting agentA weighted average and a convex weighted average of velocity.
In an embodiment, the control unit 803 specifically includes a first control protocol module 1001 (see fig. 10). The first control protocol module 1001 is configured to control the movement of the following agent using a control protocol (4) when there is no directional communication between the following agents.
In one embodiment, the control unit 803 further comprises a second control protocol module 1002 for controlling the movement of the following agent using the control protocol (5) when there is no directional communication between said following agents.
In an embodiment, the control unit 803 further comprises a second control protocol module 1003 for controlling the movement of the following agent using the following control protocol when there is a strong communication between said following agents.
In one embodiment, the multi-agent network comprises at least 4 piloting agents for detecting obstacles.
In one embodiment, the dynamics of the following agent and the lead agent in a multi-agent network are described using second-order nonlinear equations shown in equation (1), respectively.
The invention divides the second-order nonlinear agent group with nonlinear dynamics and bounded disturbance into a pilot agent and a following agent to carry out finite time containment control of the agent network. When following the undirected communication between the agents, a variable structure control idea is adopted, and based on the relative position and relative speed information of the agents, a switching item (symbolic function) is introduced into a distributed control protocol to realize the finite time containment control. When following the strong communication between the agents, a proper distributed control protocol is designed to realize the control purpose, and the rapidity and the stability of the coordination control of the nonlinear agent groups are improved through the finite time containing control of the second-order nonlinear agent groups.
The embodiment of the invention also provides electronic equipment, which can be a desktop computer and the like, and the embodiment is not limited to the electronic equipment. In this embodiment, the electronic device may refer to the implementation of the method shown in fig. 1 and the implementation of the apparatus shown in fig. 8, and the contents thereof are incorporated herein, and repeated descriptions are omitted.
Fig. 11 is a schematic block diagram of a system configuration of an electronic apparatus according to an embodiment of the present invention. As shown in fig. 11, the electronic device may include a processor 1101, a memory 1102, and a sensor module 1103, the memory 1102, the sensor module 1103 each coupled to the processor 1101. It is noted that this figure is exemplary and that other types of structures may be used in addition to or in place of this structure to implement communications, processing functions, or other functions. The sensor module 1103 is mainly used for acquiring position information and speed information of the piloting agent and the following agent. The memory is used primarily for storing program instructions. The processor 1101 is primarily configured to execute program instructions in the memory to process the position information and velocity information of the lead agent and the following agent according to the steps shown in fig. 1.
In one embodiment, program instructions to perform the following operations may be integrated into the processor 1101: step 1, acquiring a minimum geometric space formed by a piloting intelligent agent by detecting the position of an obstacle; step 2, determining an expected position and an expected speed when the following agent runs in the minimum geometric space according to the topological structure of the multi-agent network and the position information and the speed information of the piloting agent; step 3, acquiring the relative position and relative speed between the following agent and the neighbor thereof according to the topological connection condition between the following agents, and designing a limited time control protocol of the following agent according to the relative position and relative speed; and 4, controlling the following intelligent agent to enter the minimum safety area according to the limited time control protocol, and controlling the following intelligent agent to move in the minimum safety area according to the expected position and the expected speed.
In step 2, the processor 1101 may be further configured to perform the following control: acquiring topological structures of a piloting agent and a following agent in a multi-agent network, and determining a Laplacian matrix L of a multi-agent network topology; and respectively calculating a convex weighted average value of the position of the piloting intelligent agent and a convex weighted average value of the speed according to the Laplacian matrix L and the position information and the speed information of the piloting intelligent agent, taking the convex weighted average value of the position of the piloting intelligent agent as an expected position of the following intelligent agent, and taking the convex weighted average value of the speed of the piloting intelligent agent as an expected speed of the following intelligent agent. The expression of the matrix L, the convex weighted average of the position and velocity of the piloting agent are described with reference to the method embodiment in fig. 1.
Wherein, when there is no directional connectivity between the following agents, the processor 1101 is configured to control the following agents using the control protocol (4) to achieve limited time containment control.
Additionally, when there is no directional connectivity between the following agents, the processor 1101 may be further configured to control the following agents using a control protocol (5) to achieve limited time containment control.
When there is strong communication between the following agents, the processor 1101 is configured to control the following agents using a control protocol (6) to achieve limited-time containment control.
The multi-agent network studied in the embodiment of the present invention comprises at least 4 pilot agents.
In addition, the following agent and the navigation agent in the multi-agent network studied by the embodiment of the invention are respectively described by a second-order nonlinear equation shown in formula (1).
As shown in fig. 11, the electronic device may further include: a display unit 1104 and a power supply 1105. It is noted that the electronic device does not necessarily have to include all of the components shown in fig. 11. Furthermore, the electronic device may also comprise components not shown in fig. 11, reference being made to the prior art.
As shown in fig. 11, the processor 1101, which is sometimes referred to as a controller or operational control, may include a microprocessor or other processor device and/or logic device, the processor 1101 receives inputs and controls the operation of the various components of the electronic device.
The memory 1102 may be, for example, one or more of a buffer, a flash memory, a hard drive, a removable medium, a volatile memory, a non-volatile memory, or other suitable device, and may store one or more of configuration information of the processor 1101, instructions executed by the processor 1101, recorded sensor data, and the like. The processor 1101 may execute the program stored in the memory 1102 to realize information storage or processing, or the like. In one embodiment, memory 1102 also includes buffer memory (i.e., buffers) therein to store intermediate process information.
The display unit 1104 is used for displaying a display object such as an image or a character, and the display unit may be, for example, an LCD display, but the present invention is not limited thereto. The power supply 1105 is used to provide power to the electronic device.
Embodiments of the present invention also provide a storage medium having computer-readable instructions stored thereon, wherein the computer-readable instructions cause an electronic device to perform a method of limited-time containment control for a multi-agent network as shown in fig. 1.
It should be understood that, in various embodiments of the present invention, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principle and the implementation mode of the invention are explained by applying specific embodiments in the invention, and the description of the embodiments is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (22)

1. A multi-agent network finite time containment control method, wherein the multi-agent network comprises a plurality of leading agents and following agents, the method comprising:
step 1, acquiring a minimum geometric space formed by a piloting intelligent agent through finding the position of an obstacle;
step 2, determining an expected position and an expected speed when the following agent runs in the minimum geometric space according to the topological structure of the multi-agent network and the position information and the speed information of the piloting agent;
step 3, acquiring the relative position and relative speed between the following agent and the adjacent agent according to the topological connection condition between the following agents, and designing a limited time control protocol of the following agent according to the relative position and relative speed;
and 4, controlling the following intelligent agent to enter the minimum safety area according to the limited time control protocol, and controlling the following intelligent agent to move in the minimum safety area according to the expected position and the expected speed.
2. The multi-agent network finite time containment control method of claim 1, wherein the dynamics of the following agents and the leading agent in the multi-agent network are described using the following second order nonlinear equations, respectively:
wherein,respectively represent x i 、v i A derivative of (a); f = {1, \8230;, N } and L = { N +1, \8230;, N + M } represent the following agent set and the piloting agent set, respectively, N is the number of following agents, and M is the number of piloting agents; when i ∈ F, x i ,v i ,u i Respectively representing position information, velocity information and control vector, f (x) of the following agent i i ,v i )∈R p And ρ i ∈R p Respectively representing the nonlinear dynamics of the following agent i and the nonlinear disturbance vector acting on the following agent i, and | | ρ i || ∞ Not more than sigma, sigma being non-linear disturbance to the following agentA moving upper bound; when i ∈ L, x i ,v i Respectively representing the position vector and velocity vector, g (x), of the piloting agent i i ,v i ) Representing the nonlinear dynamics of the piloting agent i; for all x i ,x j ,v i ,v j I belongs to F, j belongs to F, and all the constants are nonnegative constants l 1 And l 2 Such that: i | f (x) i ,v i )-f(x j ,v j )||≤l 1 ||x i -x j ||+l 2 ||v i -v j ||。
3. The multi-agent network limited-time containment control method according to claim 2, wherein the step 2 specifically comprises:
acquiring topological structures of a piloting agent and a following agent in a multi-agent network, and determining a Laplacian matrix L of a multi-agent network topology:
respectively calculating a convex weighted average value of the position and a convex weighted average value of the speed of the piloting intelligent agent according to the Laplacian matrix L and the position information and the speed information of the piloting intelligent agent:
taking the convex weighted average of the position of the piloting agent as the expected position of the following agent, and taking the convex weighted average of the speed of the piloting agent as the expected speed of the following agent;
wherein, gamma is 1 A matrix, Γ, representing the Laplacian matrix L corresponding to the topological connection between the agents 1 ∈R N ×N ，Is gamma-shaped 1 The inverse matrix of (d); gamma-shaped 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；x l 、v l Respectively position information and speed information of the piloting agent; x is a radical of a fluorine atom d 、v d Respectively a convex weighted average of the piloting agent position and a convex weighted average of the velocity.
4. The multi-agent network finite time containment control method of claim 2, wherein when there is no directional connectivity between the following agents, the finite time control protocol of the following agents is:
wherein u is fi Is a control vector acting on the following agent i; a is a ij As elements in an adjacency matrix corresponding to a multi-agent network topology, a ij To 1 indicates that following agent i communicates with adjacent agent j, a ij A value of 0 indicates that the following agent i does not communicate with the adjacent agent j; here, i ∈ {1, \8230;, N }, j ∈ {1, \8230;, N + M }, x ∈ {1, \\ 8230;, X;, and M } i 、v i Respectively position information and velocity information, x, following agent i j 、v j Respectively, position information and velocity information of agent j adjacent to following agent i; (x) i －x j ) Representing the relative position between a following agent i and an adjacent agent j, (v) i －v j ) Representing the relative velocity between the following agent i and the adjacent agent j; 1 p The column vector with the p-dimensional elements of 1 is adopted, and p is a space dimension; sgn (·) is a sign function,α 1 、β 1 、γ、κ 1 and kappa 2 Is a control parameter of the multi-agent network.
5. The multi-agent network limited-time containment control method according to claim 4, wherein the control parameters of the multi-agent network satisfy the following conditions:
wherein tau is the upper bound of the control action of the piloting agent; gamma-shaped 1 The matrix corresponding to the topological connection relation between the following intelligent agents in the Laplacian matrix L representing the multi-intelligent network topology, and the Laplacian matrixΓ 1 ∈R N×N ，Γ 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；λ min (Γ 1 ) Is a matrix F 1 The minimum eigenvalue of (c).
6. The multi-agent network finite time containment control method of claim 2, wherein when there is no directional connectivity between the following agents, the finite time control protocol of the following agents is:
wherein u is fi Acting on a control vector following an agent i, i belongs to {1, \8230;, N }; j belongs to {1, \ 8230;, N + M }, a ij Is an element in an adjacency matrix corresponding to a multi-agent network topology, a ij A 1 indicates that the following agent i communicates with the adjacent agent j, a ij A value of 0 indicates that the following agent i does not communicate with the adjacent agent j; here, i ∈ {1, \8230;, N }, j ∈ {1, \8230;, N + M }, x ∈ j 、v j Respectively, position information and velocity information of agent j adjacent to following agent i; (x) i －x j ) Representing the relative position between a following agent i and an adjacent agent j, (v) i －v j ) Representing the relative velocity between the following agent i and the adjacent agent j; sgn (·) is a sign function,m 1 and m 2 Is a control parameter for a multi-agent network.
7. The multi-agent network limited-time containment control method according to claim 6, wherein the control parameters of the multi-agent network satisfy the following conditions:
wherein η is a constant greater than 0; μ is an upper bound following the nonlinear dynamics of the agent; tau is the upper bound of the control action of the piloting agent; gamma-shaped 1 The matrix corresponding to the topological connection relation between the following intelligent agents in the Laplacian matrix L representing the multi-intelligent network topology, and the Laplacian matrixΓ 1 ∈R N×N ，Is gamma 1 The inverse matrix of (d); gamma-shaped 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；λ max (Γ 1 ) Is a matrix gamma 1 The maximum eigenvalue of (d); lambda [ alpha ] min (Γ 1 ) Is a matrix gamma 1 The minimum eigenvalue of (c); p is the spatial dimension。
8. The multi-agent network finite time containment control method of claim 2, wherein when there is strong connectivity between the following agents, the finite time control protocol of the following agents is:
wherein u is fi Is a control vector acting on the following agent i; t is a unit of ij A matrix gamma corresponding to the topological connection relation between the following intelligent agents in a Laplacian matrix L of a multi-intelligent network topology 1 Of inverse matrix Γ 1 ﹣1 Of (b), gamma 1 ﹣1 ＝[T ij ]∈R N×N Laplacian matrixΓ 1 ∈R N×N ，Γ 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；sig α (x) For a non-smooth function, for a vector x = [ x ] 1 ,x 2 ,…,x n ] T sigα(x)＝[|x 1 |αsgn(x 1 ),|x 2 |αsgn(x 2 ),…,|x n |αsgn(x n )] T ；α 2 、β 2 、γ 1 、γ 2 、k 1 、k 2 、χ 1 Hexix 2 Control parameters for a multi-agent network; sgn (·) is a sign function,Φ i and Ω i As an intermediate process variable, [ phi ] i ＝[x i1 sgn(s i1 ),x i2 sgn(s i2 ),…,x ip sgn(s ip )] T ，Ω i ＝[v i1 sgn(s i1 ),v i2 sgn(s i2 ),…,v ip sgn(s ip )] T ；s j Is a sliding-mode error vector and is,e 1j is the position error of an agent in a multi-agent network; e.g. of the type 2j Is the speed error of an agent in a multi-agent network.
9. The multi-agent network limited time containment control method of claim 8, wherein the control parameters of the multi-agent network satisfy the following conditions:
α 2 >0,β 2 >0,k 1 >0,k 2 >0,1<γ 2 <2,γ 1 >γ 2 and is
χ 1 >l 1 ,χ 2 >l 2 ,
Wherein, i, j ∈ {1, \8230;, N }, x i 、v i Respectively representing position information and speed information of the following agent i; x is the number of j 、v j Respectively representing position information and velocity information of a following agent j adjacent to the following agent i; (x) i －x j ) Representing the relative position between a following agent i and an adjacent following agent j, (v) i －v j ) Representing the relative velocity between a following agent i and an adjacent following agent j.
10. The multi-agent network limited-time containment control method of claim 1, wherein the multi-agent network comprises at least 4 lead agents.
11. A multi-agent network limited-time containment control apparatus, said multi-agent network comprising a plurality of lead agents and following agents, said apparatus comprising:
the minimum geometric space acquisition unit is used for acquiring a minimum geometric space formed by the piloting intelligent agent by finding the position of the obstacle;
the expected track calculation unit is used for determining an expected position and an expected speed when the following intelligent agent runs in the minimum geometric space according to the topological structure of the multi-intelligent-agent network and the position information and the speed information of the piloting intelligent agent;
and the control unit is used for acquiring the relative position and the relative speed between the following intelligent agent and the adjacent intelligent agent according to the topological connection condition between the following intelligent agents, designing a limited time control protocol of the following intelligent agent according to the relative position and the relative speed, controlling the following intelligent agent to enter the minimum safe area according to the limited time control protocol, and controlling the following intelligent agent to move according to the expected position and the expected speed.
12. The multi-agent network finite time tolerance control device of claim 11, wherein the dynamics of the following and lead agents in the multi-agent network are described using the following second order nonlinear equations, respectively:
wherein,respectively represent x i 、v i A derivative of (a); f = {1, \8230;, N } and L = { N +1, \8230;, N + M } represent the following agent set and the piloting agent set, respectively, N is the number of following agents, and M is the number of piloting agents; when i ∈ F, x i ,v i ,u i Are respectively provided withIndicating position information, velocity information and control vector, f (x) of the following agent i i ,v i )∈R p And ρ i ∈R p Respectively representing the nonlinear dynamics of the following agent i and the nonlinear disturbance vector acting on the following agent i, and | | ρ i || ∞ Sigma is less than or equal to sigma, and sigma is an upper bound following nonlinear disturbance borne by the agent; when i ∈ L, x i ,v i Respectively representing the position vector and velocity vector, g (x), of the piloting agent i i ,v i ) Representing the nonlinear dynamics of the piloting agent i; for all x i ,x j ,v i ,v j I belongs to F, j belongs to F, and all the constants are nonnegative 1 And l 2 Such that: i | f (x) i ,v i )-f(x j ,v j )||≤l 1 ||x i -x j ||+l 2 ||v i -v j ||。
13. The multi-agent network limited-time containment control device as claimed in claim 12, wherein said desired trajectory calculation unit comprises in particular:
the topology matrix determining module is used for acquiring the topological structures of the piloting agent and the following agents in the multi-agent network and determining a Laplacian matrix L of the multi-agent network topology:
a calculating module, configured to calculate a convex weighted average of the position and a convex weighted average of the speed of the piloting agent according to the Laplacian matrix L and the position information and the speed information of the piloting agent, and take the convex weighted average of the position and the convex weighted average of the speed of the piloting agent as an expected position and an expected speed of the following agent, respectively:
wherein,the multi-agent network comprises following agents and navigation agents which form an agent group sigma i ,i＝1,…,N+M；Γ 1 A matrix, Γ, representing the Laplacian matrix L corresponding to the topological connection between the agents that follow it 1 ∈R N×N ，Is gamma 1 The inverse matrix of (d); gamma-shaped 2 Indicating the Laplacian matrix, gamma, in the Laplacian matrix L corresponding to the topological connection between the agent and the piloting agent 2 ∈R N×M ；x l 、v l Respectively position information and speed information of the piloting agent; x is the number of d 、v d Respectively a convex weighted average of the position of the piloting agent and a convex weighted average of the speed.
14. The multi-agent network limited-time containment control device of claim 12, wherein the control unit comprises a first control protocol module for controlling movement of a following agent when there is no directional connectivity between the following agents, using a control protocol that:
wherein u is fi Is a control vector acting on the following agent i; a is ij Is an element in an adjacency matrix corresponding to a multi-agent network topology, a ij A 1 indicates that the following agent i communicates with the adjacent agent j, a ij A value of 0 indicates that the following agent i does not communicate with the adjacent agent j; here, i ∈ {1, \8230;, N }, j ∈ {1, \8230;, N + M }, x ∈ {1, \\ 8230;, X;, and M } i 、v i Respectively position information and velocity information, x, following agent i j 、v j Respectively, position information and velocity information of agent j adjacent to following agent i; (x) i －x j ) Representing the relative position between a following agent i and an adjacent agent j, (v) i －v j ) Show the heelWith the relative velocity between agent i and the adjacent agent j; 1 p The column vector with the p-dimensional elements of 1 is adopted, and p is a space dimension; sgn (·) is a sign function,α 1 、β 1 、γ、κ 1 and kappa 2 Is a control parameter for a multi-agent network.
15. The multi-agent network limited-time containment control device of claim 14, wherein the control parameters of the multi-agent network satisfy the following conditions:
κ 1 >l 1 ,κ 2 >l 2 ,β 1 >σ||Γ 1 || 1 +τ||Γ 2 || 1 ，
wherein tau is the upper bound of the control action borne by the piloting agent; gamma-shaped 1 The matrix corresponding to the topological connection relation between the following intelligent agents in the Laplacian matrix L representing the multi-intelligent network topology, and the Laplacian matrixΓ 1 ∈R N×N ，Γ 2 Indicating the Laplacian matrix, gamma, in the Laplacian matrix L corresponding to the topological connection between the agent and the piloting agent 2 ∈R N×M ；λ min (Γ 1 ) Is a matrix gamma 1 The minimum eigenvalue of (c).
16. The multi-agent network limited-time containment control device of claim 12, wherein the control unit further comprises a second control protocol module for controlling the movement of the following agents when there is no directional communication between the following agents, using the following control protocol:
wherein u is fi For a control vector acting on a following agent i, i belongs to {1, \8230;, N }; j belongs to {1, \8230;, N + M }; a is ij Is an element in an adjacency matrix corresponding to a multi-agent network topology, a ij To 1 indicates that following agent i communicates with adjacent agent j, a ij A value of 0 indicates that the following agent i does not communicate with the adjacent agent j; here, i ∈ {1, \8230;, N }, j ∈ {1, \8230;, N + M }, x ∈ i 、v i Respectively position information and speed information of the following agent i; x is the number of j 、v j Respectively, position information and velocity information of agent j adjacent to following agent i; (x) i －x j ) Representing the relative position between a following agent i and an adjacent agent j, (v) i －v j ) Representing the relative velocity between the following agent i and the adjacent agent j; sgn (·) is a sign function,m 1 and m 2 Is a control parameter of the multi-agent network.
17. The multi-agent network limited time containment control device of claim 16, wherein the control parameters of the multi-agent network satisfy the following conditions:
wherein η is a constant greater than 0; μ is an upper bound following the nonlinear dynamics of the agent; tau is the upper bound of the control action borne by the piloting agent; gamma-shaped 1 Representing multiple intelligent network topologiesThe Laplacian matrix L is a matrix corresponding to the topological connection relation between the following intelligent agents, and the Laplacian matrixΓ 1 ∈R N×N ，Is gamma 1 The inverse matrix of (d); gamma-shaped 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；λ max (Γ 1 ) Is a matrix gamma 1 The maximum eigenvalue of (c); lambda min (Γ 1 ) Is a matrix gamma 1 The minimum eigenvalue of (c); p is the spatial dimension.
18. The multi-agent network limited-time containment control device of claim 12, wherein the control unit further comprises a third control protocol module for controlling the movement of the following agents when there is strong communication between the following agents using a control protocol:
wherein u is fi Is a control vector acting on the following agent i; t is a unit of ij A matrix gamma corresponding to the topological connection relation between the following intelligent agents in a Laplacian matrix L of a multi-intelligent network topology 1 Of inverse matrix Γ 1 ﹣1 Element of (D), F 1 ﹣1 ＝[T ij ]∈R N×N Laplacian matrixΓ 1 ∈R N×N ，Γ 2 Indicating the Laplacian matrix, gamma, corresponding to the topological connection relationship between the agent and the piloting agent in the Laplacian matrix L 2 ∈R N×M ；sig α (x) For a non-smooth function, for a vector x = [ x = 1 ,x 2 ,…,x n ] T sig α (x)＝[|x 1 | α sgn(x 1 ),|x 2 | α sgn(x 2 ),…,|x n | α sgn(x n )] T ；α 2 、β 2 、γ 1 、γ 2 、k 1 、k 2 、χ 1 Hexix- 2 Control parameters for a multi-agent network; sgn (·) is a sign function,Φ i and Ω i As an intermediate process variable, [ phi ] i ＝[x i1 sgn(s i1 ),x i2 sgn(s i2 ),…,x ip sgn(s ip )] T ，Ω i ＝[v i1 sgn(s i1 ),v i2 sgn(s i2 ),…,v ip sgn(s ip )] T ；s j Is a sliding-mode error vector and is,e 1j is the position error of an agent in a multi-agent network; e.g. of a cylinder 2j Is the speed error of an agent in a multi-agent network.
19. The multi-agent network limited-time containment control device of claim 18, wherein the control parameters of the multi-agent network satisfy the following conditions:
α 2 >0,β 2 >0,k 1 >0,k 2 >0,1<γ 2 <2,γ 1 >γ 2 and is provided with
χ 1 >l 1 ,χ 2 >l 2 ,
Wherein, i, j ∈ {1, \8230;,N}，x i 、v i respectively representing position information and speed information of a following agent i; x is the number of j 、v j Respectively representing position information and velocity information of a following agent j adjacent to the following agent i; (x) i －x j ) Represents the relative position between a following agent i and an adjacent following agent j, (v) i －v j ) Representing the relative velocity between a following agent i and an adjacent following agent j.
20. The multi-agent network limited-time containment control device of claim 11, wherein the multi-agent network comprises at least 4 lead agents.
21. A computer-readable storage medium having computer-readable instructions stored thereon that, when executed, cause a processor to perform at least the operations of claim 1.
22. An electronic device, characterized in that the electronic device comprises:
the sensor module is used for acquiring position information and speed information of the piloting agent and the following agent;
a memory for storing program instructions;
a processor coupled to the sensor module and the memory for executing program instructions in the memory for processing the position information and velocity information of the lead agent and the following agent according to the steps of claim 1.
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