CN113985915A - High-order group system multi-leader clustering formation tracking control method - Google Patents
High-order group system multi-leader clustering formation tracking control method Download PDFInfo
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Abstract
The invention belongs to the field of group system formation control, and particularly relates to a high-order group system multi-leader clustering formation tracking control method. Step 1: establishing a multi-leader clustering formation tracking control problem model of a high-order group system; step 2: on the basis of the problem model established in the step 1, establishing communication connection relations among clusters and in clusters of the high-order group system; and step 3: and (3) establishing a high-order group system multi-leader clustering formation tracking control method on the basis of the communication connection relation established in the step (2). According to the invention, the intelligent agent cluster is divided into M subgroups, and under the action of control cooperation, the large-scale cluster has a diversified sub-module formation function. Each submodule has autonomy and also has an integral target; the system has the advantages of division of labor and cooperation, and greatly enhances the capability of the group system in processing complex formation tracking tasks. The method can be applied to multi-leader formation tracking control of multi-agent systems covering unmanned aerial vehicle clusters, ground robot clusters, unmanned ships, underwater submergers and the like.
Description
Technical Field
The invention belongs to the field of group system formation control, and particularly relates to a high-order group system multi-leader clustering formation tracking control method.
Background
Group system formation control has caused extensive research enthusiasm in academic circles in recent years, and related application development is carried out in multiple fields of markets, including network system synchronous control, mobile robot cooperative work, multi-unmanned aerial vehicle cooperative execution reconnaissance search tasks, sea surface naval vessel formation cruising sea areas and the like.
Most of the existing group system formation control only considers that all intelligent bodies form a formation together, however, in many practical application scenes, a group system needs to be divided into a plurality of groups to execute different subtasks, for example, in the plant protection industry of unmanned aerial vehicles, for farmlands spliced in block areas of a plurality of different shapes, when pesticide spraying tasks in the air are executed, the unmanned aerial vehicle cluster needs to be divided into a plurality of subgroups to form different formations according to the characteristics of respective spraying areas, and meanwhile, the whole unmanned aerial vehicle flies to a destination area from a departure area, so that spraying routes effectively cover all farmlands, and pesticide spraying is omitted or repeated. In the missile cluster remote combat, the missile cluster is generally required to be divided into a plurality of subgroups, a plurality of waves are separated for a certain time to cooperatively attack a high-value target with strong defense force of an enemy, and the missile cluster with the first waves is utilized to suppress and consume the firepower of the enemy, so that the missile cluster is in an overload state and cannot withstand the attack of the subsequent waves.
In these application contexts, the group system both has an overall formation tracking objective and needs to complete the subgroup formation task under the organization of the respective subgroup leader. The division cooperation mode can greatly improve the execution efficiency of complex tasks and has wide application prospect in the fields of military and civil use. From the existing research results, no public technology is disclosed to describe a group system multi-leader clustering formation tracking control method.
Disclosure of Invention
Aiming at the defects of the large complex task executed by the current group system formation, the invention provides a tracking control method for the cluster formation of multiple leaders of the group system, aiming at constructing a tracking control protocol for the cluster formation of the multiple leaders, and providing conditions required to be met by communication between clusters and in the clusters, a formation cooperative control gain matrix and a tracking control gain matrix solving method, thereby designing a tracking control algorithm for the cluster formation of the multiple leaders of the group system.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a high-order group system multi-leader clustering formation tracking control method comprises the following steps:
step 1: establishing a multi-leader clustering formation tracking control problem model of a high-order group system;
step 2: on the basis of the problem model established in the step 1, establishing communication connection relations among clusters and in clusters of the high-order group system;
and step 3: and (3) establishing a high-order group system multi-leader clustering formation tracking control method on the basis of the communication connection relation established in the step (2).
Preferably, the step 1 comprises:
step 1.1: establishing a state differential equation of each agent in the high-order group system:
where t represents a time variable, i represents the number of agents in the group system, xi(t) is the state variable of the agent, ui(t) is the control input of the agent, A and B represent the system matrix and input matrix of the agent respectively, and N is the number of agents in the high-order group system;
step 1.2: in step 1.1, N agents form a formation cluster, the formation cluster is divided into subsystems comprising M clusters according to task needs, each cluster is provided with a cluster head leader agent as a cluster leader, and the rest are follower agent agents in the clusterLet the number of agents in each cluster be d1+1,d2+1,…,dM+1, i.e.
wherein ,dmIndicates the number of followers in the mth cluster (M ═ 1,2, … M), dm+1 represents the number of clustered heavy agents, d, after the leader is addedMRepresenting the number of followers in the Mth cluster, the state vector in each cluster is marked as:
wherein ,sm0(t) (M ═ 1,2, …, M), representing the cluster head leader agent for each cluster, smj(t)(j∈{1,2,…,dmThe j < th > intelligent agent of the mth clustering is represented by M < th > element belonging to the {1,2 …, …, M }), an upper italic T represents a vector transposition symbol, the left side of the formula is used for numbering the intelligent agents according to the clustering condition, and the right side is used for sequentially numbering all the intelligent agents together;
step 1.3: the control target forms a desired formation with the respective leader as a core for each cluster, and meanwhile, the leader of each cluster forms a desired formation to track a specified target, namely:
wherein ,f0(t) is the target tracked by the leader agent of the cluster head, and f is the target of the dynamic state0(t) is a time varying function; at static target, f0(t) is a constant, hm0(t), M is 1,2, …, M is a leader queuing function, hmj(t),j∈{1,2,…,dmIs the follower formation function, M ∈ {1,2, …, M }.
Preferably, the specific operation of step 2 includes:
step 2.1: constructing a communication topology G between a target and multiple leaderso，GoThe method comprises the steps of (1) including a spanning tree taking a target as a root node;
step 2.2: constructing a communication topology G between the leader and the follower within each clusteri(i＝1,2,…,M)，GiThe tree contains a spanning tree with the leader as a root node.
Preferably, the communication connection relationship between the inter-cluster agents and the intra-cluster agents in step 2 satisfies the following condition:
1): communication exists among cluster head leaders of all clusters, and communication topology is communicated;
2): followers and followers of any two clusters cannot communicate with each other;
3): the leader does not receive the information of the follower, namely is not influenced by the working state of the follower;
4): the intra-cluster follower cannot receive other cluster leader information.
Preferably, the step 3 of establishing the multi-leader clustering formation tracking control method of the high-order group system specifically comprises the following steps:
step 3.1: setting values of a system matrix A and an input matrix B according to the dynamic characteristics of the agent;
step 3.2: the sub-systems are divided into M clusters according to the requirement of a formation tracking task, each cluster is provided with a cluster head leader agent as a cluster leader, and the rest cluster follower agents form a motion equation of a tracking target to meet the requirement of a formation tracking task
wherein ,f0(t) is the trajectory of the targetThe equations are set forth in the form of,
is the derivative of the track equation of the target, a cluster head leader agent carries a sensing device, and observes the target f needing to be tracked of a high-order cluster system0(t), the follower agent in the cluster cannot acquire target information due to the limitation of the performance of the follower agent;
3.3, constructing a leader formation function h according to the formation required to be kept or the movement requirement relative to the target when the leader agent tracks the targetm0(t),m∈{1,2，…,M}；
Step 3.4, constructing a follower formation function h according to the formation required to be kept by each cluster or the movement requirement of each leadermj(t),j∈{1,2,…,dm},m∈{1,2…，…,M}；
Step 3.5, the requirement is met
Is non-zero matrix of
Judging whether the formation function satisfies the condition
wherein 
Is a formation function hmj(t) the derivative, if the condition is met, continuing with the next step; if the conditions cannot be met, the state differential equation (1) of the high-order group system cannot realize h under the action of the control protocol 1 and the control protocol 2mj(t) determining the tracking control of the multi-leader clustering formation, and at this time, skipping back to step 1 to re-specify the system matrix A and the input matrix B or skipping back to step 3.4 and step 3.5 to re-specify the formation function hmj(t)；
Step 3.6 setting communication topology G between leadersoAnd guarantee an inter-leader communication topology GoAre connected;
step (ii) of3.7 setting the Intra-Cluster communication topology G of each clusteriAnd guarantee intra-cluster communication topology GiThe cluster leader can not only transmit state quantity information to followers, but also transmit control quantity information to the followers;
and 3.8, controlling the cluster head leader intelligent agent and the cluster follower intelligent agent in the cluster system by using a control protocol.
Preferably, in step 3.8, each cluster has a cluster head leader agent as a cluster leader agent, and the rest are cluster follower agents, so that the formation cluster agents are divided into two types: the cluster head leader agent intelligent agent and the cluster follower agent, the clustering formation tracking control protocol corresponding to the two types of intelligent agents is as follows:
protocol 1: if agent i is the cluster head node of the mth cluster, that is
The control protocol is as follows:
wherein ,ui(t) represents a control input of the agent,
is a neighbor set of agent i, wm0·n0Representing the connection weight between a cluster head agent and other clustered cluster head agents, K1Term is leader cooperative control gain, K2Term leader tracking control gain by adjusting K1,K2The rate at which leaders form a formation and the rate at which tracking is achieved can be controlled, w when there is communication between agents m0 and n0m0·n01, otherwise, wm0·n0＝0；
Satisfy the requirement of
Where I is an identity matrix of suitable dimensions, hm0(t) represents a time-varying formation function of the formation of the cluster head intelligent agent, and meets the requirements
Is to satisfy
Is non-zero matrix of, and
is of full rank;
protocol 2: agent i is the jth follower of the mth cluster, i.e., agent i
The control protocol is as follows:
wherein ,K3Is the follower control gain, the rate at which the followers form the formation and the rate at which tracking is achieved, wmj·mkRepresenting the weight of the connection between the jth follower and the kth follower of the mth cluster, w when there is communication between agents mk and mjmj·mk1, otherwise, wmj·mk＝0，wmj·m0Representing the connection weight between the jth follower of the mth cluster and the cluster head agent thereof, the value and the wmj·mkSimilarly.
Preferably, the control gain matrix K is chosen1,K2,K3When the following conditions are satisfied:
(i)
is a Hurwitz matrix;
(ii)
m is an element of {1,2, …, M } is a Hurwitz matrix;
wherein ,
is the eigenvalue of the laplacian matrix corresponding to the communication topology between the leaders,
and M is the eigenvalue of the Laplace matrix corresponding to the communication topology in each cluster {1,2, …, M }.
Compared with the prior art, the invention has the beneficial effects that:
by dividing the intelligent agent cluster into M subgroups and under the action of control protocols 1 and 2, the large-scale cluster has a diversified sub-module formation function. Each submodule has certain autonomy and also has an integral target; the system has the advantages of division of labor and cooperation, and greatly enhances the capability of the group system in processing complex formation tracking tasks. The potential application covers multi-leader formation tracking control of multi-agent systems such as unmanned aerial vehicle clusters, ground robot clusters, unmanned ships, underwater submergers and the like.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
In the drawings:
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a communication topology under the general situation of cluster formation by multiple leaders of the group system of the present invention;
FIG. 3 is a flowchart of a cluster formation tracking control algorithm for multiple leaders of the group system according to the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
Example (b):
referring to fig. 1-3, a method for tracking and controlling multi-leader cluster formation in a high-order group system includes the following steps:
step 1: establishing a multi-leader clustering formation tracking control problem model of a high-order group system, which specifically comprises the following steps:
step 1.1: establishing a state differential equation of each agent in the high-order group system:
where t represents a time variable, i represents the number of agents in the group system, xi(t) is the state variable of the agent, ui(t) is the control input of the agent, A and B represent the system matrix and input matrix of the agent respectively, and N is the number of agents in the high-order group system;
step 1.2: 1.1, N agents form a formation cluster, the formation cluster is divided into subsystems comprising M clusters according to task needs, each cluster is provided with a cluster head leader agent as a cluster leader, the rest are follower agents in the cluster, and the number of the agents in each cluster is d1+1,d2+1,…,dM+1, i.e.
wherein ,dmIndicates the number of followers in the mth cluster (M ═ 1,2, … M), dm+1 represents the number of clustered heavy agents, d, after the leader is addedMRepresenting the number of followers in the Mth cluster, the state vector in each cluster is marked as:
wherein, the left side of the formula is to number the agents according to the clustering condition, the right side is to number all the agents together in sequence, sm0(t) (M ═ 1,2, …, M), representing the cluster head leader agent for each cluster, smj(t)(j∈{1,2,…,dmM belongs to {1,2, …, M }), represents the jth agent of the mth cluster, and the upper italic letter T represents a vector transposition symbol;
if the actual tasks only need to form one formation to execute the same type of tasks, then M is 1, that is, the single-leader formation tracking control is a special case of the present invention, and the group system multi-leader clustering formation tracking control method provided by the present invention has generality in the field of formation control of the group system, and can execute a single formation control task and also can complete a large-scale clustering multi-type formation control task.
Step 1.3: the control target forms a desired formation with the respective leader as a core for each cluster, and meanwhile, the leader of each cluster forms a desired formation to track a specified target, namely:
wherein ,f0(t) is the target tracked by the leader agent of the cluster head, and f is the target of the dynamic state0(t) is a time varying function; at static target, f0(t) is a constant, hm0(t), M is 1,2, …, M is a leader queuing function, hmj(t),j∈{1,2,…,dmIs the follower formation function, M ∈ {1,2, …, M }.
Clustering leader as described in the present inventionThe follower is the only agent in the cluster which is not influenced by the states of other agents, the follower refers to the agents except the leader, and the follower is directly or indirectly influenced by the state of the leader. The leaders mutually influence each other and form a desired formation by taking the tracking target as a center. Formula (2) depicts key features for implementing multi-leader clustering formation tracking, wherein the first formula requires each cluster leader to be in a target state f0(t) is a central implementation of hm0(t) formation of a definite formation, the second equation requiring each clustered follower to have its own leader sm0(t) is a central implementation of hmj(t) the determined formation.
Step 2: on the basis of the problem model established in the step 1, establishing communication connection relations among clusters and in clusters of the high-order cluster system, and specifically comprising the following operations:
step 2.1: constructing a communication topology G between a target and multiple leaderso，GoThe method comprises the steps of (1) including a spanning tree taking a target as a root node;
step 2.2: constructing a communication topology G between the leader and the follower within each clusteri(i＝1,2,…,M)，GiThe tree contains a spanning tree with the leader as a root node.
The communication connection relation between the inter-cluster agents and the intra-cluster agents in the step 2 meets the following requirements:
1): communication exists among cluster head leaders of all clusters, and communication topology is communicated;
2): followers and followers of any two clusters cannot communicate with each other;
3): the leader does not receive the information of the follower, namely is not influenced by the working state of the follower;
4): the intra-cluster follower cannot receive other cluster leader information.
And step 3: on the basis of the communication connection relation constructed in the step 2, a high-order group system multi-leader clustering formation tracking control method is established, and the specific steps are as follows:
step 3.1: setting values of a system matrix A and an input matrix B according to the dynamic characteristics of the agent;
step 3.2: tracking task needs according to formationFor a subsystem comprising M clusters, each cluster is provided with a cluster head leader agent as a cluster leader, and the rest are follower agents in the clusters, a motion equation of a tracking target is constructed to meet the requirements
wherein ,f0(t) is the trajectory equation for the target,
is the derivative of the track equation of the target, a cluster head leader agent carries a sensing device, and observes the target f needing to be tracked of a high-order cluster system0(t), the follower agent in the cluster cannot acquire target information due to the limitation of the performance of the follower agent;
the cluster leader of the invention leads the followers to realize the given formation tracking task, and the cluster formed by the cluster leader realizes the overall formation cooperative control under the guidance of the target. The distributed cooperation mode enables a large-scale cluster to have diversified sub-module functions, and meanwhile, the overall strict organization and cooperation capability are kept.
3.3, constructing a leader formation function h according to the formation required to be kept or the movement requirement relative to the target when the leader agent tracks the targetm0(t),m∈{1,2，…,M}；
Step 3.4, constructing a follower formation function h according to the formation required to be kept by each cluster or the movement requirement of each leadermj(t),j∈{1,2,…,dm},m∈{1,2…，…,M}；
Step 3.5, the requirement is met
Is non-zero matrix of
Judging whether the formation function satisfies the condition
wherein 
Is a formation function hmj(t) the derivative, if the condition is met, continuing with the next step; if the conditions cannot be met, the state differential equation (1) of the high-order group system cannot realize h under the action of the control protocol 1 and the control protocol 2mj(t) determining the tracking control of the multi-leader clustering formation, and at this time, skipping back to step 1 to re-specify the system matrix A and the input matrix B or skipping back to step 3.4 and step 3.5 to re-specify the formation function hmj(t)；
Step 3.6 setting communication topology G between leadersoAnd guarantee an inter-leader communication topology GoAre connected;
step 3.7 setting the intra-cluster communication topology G of each clusteriAnd guarantee intra-cluster communication topology GiThe cluster leader can not only transmit state quantity information to followers, but also transmit control quantity information to the followers; the communication networking mode is a basic condition for realizing the multi-leader clustering formation tracking control of the group system.
And 3.8, controlling the cluster head leader intelligent agent and the cluster follower intelligent agent in the cluster system by using a control protocol.
In step 3.8, each cluster has a cluster head leader agent as a cluster leader agent, and the rest are cluster follower agents, so that the formation cluster agents are divided into two types: the cluster head leader agent intelligent agent and the cluster follower agent, the clustering formation tracking control protocol corresponding to the two types of intelligent agents is as follows:
protocol 1: if agent i is the cluster head node of the mth cluster, that is
The control protocol is as follows:
wherein ,ui(t) control input for agent，
Is a neighbor set of agent i, wm0·n0Representing the connection weight between a cluster head agent and other clustered cluster head agents, K1Term is leader cooperative control gain, K2Term leader tracking control gain by adjusting K1,K2The rate at which leaders form a formation and the rate at which tracking is achieved can be controlled, w when there is communication between agents m0 and n0m0·n01, otherwise, wm0·n0＝0；
Satisfy the requirement of
Where I is an identity matrix of suitable dimensions, hm0(t) represents a time-varying formation function of the formation of the cluster head intelligent agent, and meets the requirements
Is to satisfy
Is non-zero matrix of, and
is of full rank; u. ofi(t) is the leader control input message received by the follower, indicating that the leader, via the communications network, not only passed status information to the follower, but also passed control input ui(t) information to the follower.
Protocol 2: agent i is the jth follower of the mth cluster, i.e., agent i
The control protocol is as follows:
wherein ,K3Is the follower control gain, the rate at which the followers form the formation and the rate at which tracking is achieved, wmj·mkRepresenting the weight of the connection between the jth follower and the kth follower of the mth cluster, w when there is communication between agents mk and mjmj·mk1, otherwise, wmj·mk＝0。wmj·m0Representing the connection weight between the jth follower of the mth cluster and the cluster head agent thereof, the value and the wmj·mkSimilarly.
Selecting a control gain matrix K1,K2,K3When the following conditions are satisfied:
(i)
is a Hurwitz matrix;
(ii)
m is an element of {1,2, …, M } is a Hurwitz matrix;
wherein ,
m ∈ {1,2, …, M } is the eigenvalue of the Laplacian matrix corresponding to the communication topology between the leaders,
j∈{1,2,…,dmand the M belongs to {1,2, …, M } is an eigenvalue of a Laplace matrix corresponding to the communication topology in each cluster.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A high-order group system multi-leader clustering formation tracking control method is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing a multi-leader clustering formation tracking control problem model of a high-order group system;
step 2: on the basis of the problem model established in the step 1, establishing communication connection relations among clusters and in clusters of the high-order group system;
and step 3: and (3) establishing a high-order group system multi-leader clustering formation tracking control method on the basis of the communication connection relation established in the step (2).
2. The method for tracking and controlling the multi-leader cluster formation of the high-order group system according to claim 1, wherein: the step 1 comprises the following steps:
step 1.1: establishing a state differential equation of each agent in the high-order group system:
where t represents a time variable, i represents the number of agents in the group system, xi(t) is the state variable of the agent, ui(t) is the control input of the agent, A and B represent the system matrix and input matrix of the agent respectively, and N is the number of agents in the high-order group system;
step 1.2: 1.1, N agents form a formation cluster, the formation cluster is divided into subsystems comprising M clusters according to task needs, each cluster is provided with a cluster head leader agent as a cluster leader, the rest are follower agents in the cluster, and the number of the agents in each cluster is d1+1,d2+1,…,dM+1, i.e.
wherein ,dmIndicates the number of followers in the mth cluster (M ═ 1,2, … M), dm+1 represents the number of clustered heavy agents, d, after the leader is addedMRepresenting the number of followers in the Mth cluster, the state vector in each cluster is marked as:
wherein ,sm0(t) (M ═ 1,2, …, M), representing the cluster head leader agent for each cluster, smj(t)(j∈{1,2,…,dmThe j < th > intelligent agent of the mth clustering is represented by M < th > element belonging to the {1,2, …, M }), an upper italic body T represents a vector transposition symbol, the left side of the formula is used for numbering the intelligent agents according to the clustering condition, and the right side is used for sequentially numbering all the intelligent agents together;
step 1.3: the control target forms a desired formation with the respective leader as a core for each cluster, and meanwhile, the leader of each cluster forms a desired formation to track a specified target, namely:
wherein ,f0(t) is the target tracked by the leader agent of the cluster head, and f is the target of the dynamic state0(t) is time-varyingA function; at static target, f0(t) is a constant, hm0(t), M is 1,2, …, M is a leader queuing function, hmj(t),j∈{1,2,…,dmIs the follower formation function, M ∈ {1,2, …, M }.
3. The method for tracking and controlling the multi-leader cluster formation of the high-order group system according to claim 2, wherein: the specific operation of the step 2 comprises:
step 2.1: constructing a communication topology G between a target and multiple leaderso，GoThe method comprises the steps of (1) including a spanning tree taking a target as a root node;
step 2.2: constructing a communication topology G between the leader and the follower within each clusteri(i＝1,2,…,M)，GiThe tree contains a spanning tree with the leader as a root node.
4. The method for tracking and controlling the multi-leader cluster formation of the high-order group system according to claim 3, wherein: the communication connection relation between the inter-cluster agents and the intra-cluster agents in the step 2 meets the following requirements:
1): communication exists among cluster head leaders of all clusters, and communication topology is communicated;
2): followers and followers of any two clusters cannot communicate with each other;
3): the leader does not receive the information of the follower, namely is not influenced by the working state of the follower;
4): the intra-cluster follower cannot receive other cluster leader information.
5. The method for tracking and controlling the multi-leader cluster formation of the high-order group system according to claim 4, wherein: the step 3 of establishing the multi-leader clustering formation tracking control method of the high-order group system comprises the following specific steps:
step 3.1: setting values of a system matrix A and an input matrix B according to the dynamic characteristics of the agent;
step 3.2: dividing the system into subsystems comprising M clusters according to the requirement of a formation tracking task, wherein each cluster is divided into M clustersAll the cluster head leader agents serve as cluster leaders, and the rest cluster follower agents serve as cluster follower agents to construct a motion equation of a tracking target, so that the requirements of the motion equation of the tracking target are met
wherein ,f0(t) is the trajectory equation for the target,
is the derivative of the track equation of the target, a cluster head leader agent carries a sensing device, and observes the target f needing to be tracked of a high-order cluster system0(t), the follower agent in the cluster cannot acquire target information due to the limitation of the performance of the follower agent;
3.3, constructing a leader formation function h according to the formation required to be kept or the movement requirement relative to the target when the leader agent tracks the targetm0(t),m∈{1,2，…,M}；
Step 3.4, constructing a follower formation function h according to the formation required to be kept by each cluster or the movement requirement of each leadermj(t),j∈{1,2,…,dm},m∈{1,2，…,M}；
Step 3.5, the requirement is met
Is non-zero matrix of
Judging whether the formation function satisfies the condition
wherein 
Is a formation function hmj(t) the derivative, if the condition is met, continuing with the next step; if the conditions cannot be met, the state differential equation (1) of the high-order group system cannot realize h under the action of the control protocol 1 and the control protocol 2mj(t) the determined collarLeader clustering formation tracking control, at this time, a jump is required to return to the step 1 to give the system matrix A and the input matrix B again or to return to the step 3.4 and the step 3.5 to give the formation function h againmj(t)；
Step 3.6 setting communication topology G between leadersoAnd guarantee an inter-leader communication topology GoAre connected;
step 3.7 setting the intra-cluster communication topology G of each clusteriAnd guarantee intra-cluster communication topology GiThe cluster leader can not only transmit state quantity information to followers, but also transmit control quantity information to the followers;
and 3.8, controlling the cluster head leader intelligent agent and the cluster follower intelligent agent in the cluster system by using a control protocol.
6. The method of claim 5, wherein the method comprises the steps of: in step 3.8, each cluster has a cluster head leader agent as a cluster leader agent, and the rest are cluster follower agents, so that the formation cluster agents are divided into two types: the cluster head leader agent intelligent agent and the cluster follower agent, the clustering formation tracking control protocol corresponding to the two types of intelligent agents is as follows:
protocol 1: if agent i is the cluster head node of the mth cluster, that is
The control protocol is as follows:
wherein ,ui(t) represents a control input of the agent,
is a neighbor set of agent i, wm0·n0Agent for representing cluster head and other clustersWeight of connection between cluster head agents, K1Term is leader cooperative control gain, K2Term leader tracking control gain by adjusting K1,K2The rate at which leaders form a formation and the rate at which tracking is achieved can be controlled, w when there is communication between agents m0 and n0m0·n01, otherwise, wm0·n0＝0；
Satisfy the requirement of
Where I is an identity matrix of suitable dimensions, hm0(t) represents a time-varying formation function of the formation of the cluster head intelligent agent, and meets the requirements
Is to satisfy
Is non-zero matrix of, and
is of full rank;
protocol 2: agent i is the jth follower of the mth cluster, i.e., agent i
The control protocol is as follows:
wherein ,K3Is the follower control gain, the rate at which the followers form the formation and the rate at which tracking is achieved, wmj·mkJ-th heel representing m-th clusterWeight of connection between follower and kth follower, w when there is communication between Agents mk and mjmj·mk1, otherwise, wmj·mk＝0，wmj·m0Representing the connection weight between the jth follower of the mth cluster and the cluster head agent thereof, the value and the wmj·mkSimilarly.
7. The method of claim 6, wherein the method comprises the steps of: selecting a control gain matrix K1,K2,K3When the following conditions are satisfied:
(i)
is a Hurwitz matrix;
(ii)
is a Hurwitz matrix;
wherein ,
is the eigenvalue of the laplacian matrix corresponding to the communication topology between the leaders,
is the eigenvalue of the laplacian matrix corresponding to the communication topology within each cluster.
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