CN110109351B - Multi-agent consistency control method based on designated performance - Google Patents
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Abstract
The invention discloses a multi-agent consistency control method based on specified performance, which comprises the following steps: establishing a communication topology by taking a plurality of agents as communication nodes; acquiring neighbor nodes and self state information according to the communication topology; the status information includes location and velocity; calculating a tracking error of the leader according to the state information; performing specified performance transformation on the tracking error by designing a performance function to obtain a transformed error model; according to the transformed error model, an event trigger adaptive controller of a follower is designed by utilizing a back-stepping method and a dynamic surface technology, and an event trigger mechanism is designed, so that multi-agent consistency control based on specified performance is realized. The invention can make the system obtain the expected transient performance and steady-state error in the control process, and has the advantages of rapidity, high precision and the like; in addition, the invention can also reduce the communication cost between the intelligent agents, and has wider application range and application value.
Description
Technical Field
The invention relates to the field of unmanned system control, in particular to multi-agent consistency event triggering adaptive control based on designated performance.
Background
With the development of industrial and military applications, more and more work needs to be completed by a plurality of intelligent agents in a coordinated manner, so that the distributed cooperative control technology of the plurality of intelligent agents is rapidly developed. The distributed cooperative control of the multiple intelligent agents only needs to receive local information among the intelligent agents, so that the communication cost and energy consumption are greatly reduced, and the distributed cooperative control system has better flexibility and robustness, and is widely applied to the fields of robot teams, unmanned aerial vehicle formation, sensor networks and the like. The distributed cooperative control mainly comprises a consistency problem, a clustering problem, a formation problem and the like. The consistency tracking problem is a basic problem of cooperative control, and is a research hotspot in recent years.
In practical applications of multi-agent coherency tracking, the microprocessor of each agent typically has limited computational power and digital bandwidth. Therefore, the event trigger mechanism which can further reduce the communication cost and reduce the calculation pressure is added in the consistency tracking control, and the method has more important research value. Event-triggered control is a non-periodic control scheme, in which the controller updates the control signal only when a certain performance index specified in the system reaches a certain threshold. In event-triggered control, avoiding the occurrence of the knowless phenomenon is an important issue, namely ensuring that a triggering event is not triggered numerous times within a limited time. Studies have shown that the event-triggered mechanism does not produce the knoop phenomenon when external disturbances or measurement noise are absent, whereas the knoop phenomenon is likely to occur.
In addition, in practical engineering application, the system is required to be capable of running stably, and certain requirements are generally provided for performance indexes such as convergence rate, maximum overshoot, steady-state error and the like. Therefore, adding specified performance to the controller design has significant application value.
In summary, although the conventional multi-agent event triggering control can further reduce the communication cost between agents and reduce the energy consumption, the capability of achieving the desired performance indexes such as the convergence rate, the maximum overshoot, and the steady-state error is still lacking. Therefore, multi-agent event-triggered control techniques with specified capabilities are a problem that those skilled in the art are demanding to solve.
Disclosure of Invention
Aiming at the problem of consistency control of a multi-agent class, the invention provides an event-triggered self-adaptive control method based on designated performance to overcome the defects of the prior art, so that the communication cost between agents is further reduced, the rapidity and the accuracy of the control process can be improved, the system performance is optimized, and the expected transient performance and steady-state error are obtained.
In order to achieve the above purpose, the invention provides the following technical scheme:
a multi-agent consistency control method based on specified performance, comprising:
establishing a communication topology by taking a plurality of agents as communication nodes, wherein one agent is a leader and the other agents are followers;
the followers communicate with each other according to the communication topology, so as to acquire the state information of the neighbor nodes; the status information includes location and velocity;
each follower calculates the tracking error of the leader according to the state information of the follower and the state information of the neighbor nodes, and performs specified performance transformation on the tracking error through a designed performance function to obtain a transformed error model;
according to the transformed error model, an event trigger adaptive controller of a follower is designed by utilizing a back-stepping method and a dynamic surface technology, and an event trigger mechanism is designed, so that multi-agent consistency control based on specified performance is realized.
Further, the multi-agent is an unmanned vehicle, a drone or a robot.
Optionally, the establishing a communication topology includes:
determining a directed topology graph according to a communication protocol;
and determining an adjacency matrix, an in-degree matrix and a Laplace matrix according to the directed topological graph.
Further, the directed topology graph is determined according to the communication protocol; determining an adjacency matrix, an in-degree matrix and a Laplace matrix according to the directed topology graph, comprising:
the directed topology graph is denoted as ζ ═ (V, E, a), where V ═ 1,2, …, N is the number of nodes, N denotes the number of agents,
is an edge of a node, A ═ ai,j]∈RN×NIs a contiguous matrix, ai,jRepresenting a communication relationship; the edges of nodes j to i are denoted as (V)j,Vi) E, representing that the agent i can receive the information of the agent j; set of neighbor nodes of agent i is denoted as Ni；
Defining the degree of entry of node i as
Diagonal matrix D ═ diag (D)1,d2,…,dN) For the in-degree matrix, the laplacian matrix of the directed topology graph ζ is L ═ D-a.
Optionally, the tracking error and the specified performance function are respectively:
the tracking error is defined as:
yisystem output signal, y, representing the ith followerdA system output signal representing a leader;
the specified performance function is described by the following inequality:
δminand deltamaxIs an adjustable parameter, the performance function μ is bounded and monotonically decreases; the performance function is designed as follows:
wherein t is time, mu0＞μ∞V are all positive real numbers, μ0,μ∞The value of μ is given when t is 0 and t is infinity.
Further, the performing the specified performance transformation to obtain the transformed error model includes:
performing the equivalent transformation as follows:
wherein
In order to transform the error, the error is transformed,
in the formula:
in the formula
The transformed error model is then:
optionally, the event-triggered adaptive controller is designed as follows:
in the formula of alphai,nFor virtual control signals, si,nFor virtual error planes, epsilon, defined in the backstepping method and dynamic plane techniquei，σiAnd
are all positive design parameters;
is an estimate of all unknown parameters, τi,nIn order to adjust the function of the adjustment,
is an adaptive law.
Optionally, the designing an event trigger mechanism according to the requirement includes:
determining a fixed threshold condition triggered by an event according to application requirements;
and judging whether the measurement error of the control signal reaches a fixed threshold condition, if so, updating the control signal, and otherwise, keeping the control signal unchanged.
Further, the event trigger mechanism is designed as follows:
tk+1＝inf{t∈R||ei(t)|≥mi},t1＝0
wherein ei(t)＝wi(t)-ui(t) represents a control signal measurement error, inf { } is an infimum boundary, miIs a fixed threshold value, and
tkfor the event trigger time, wi(t) denotes a control signal, ui(t) and wi(tk) The control signal is updated for the event trigger time.
Compared with the prior art, the invention has the following technical characteristics:
the method comprises the steps of providing fixed threshold event trigger self-adaptive control aiming at the problems of large information demand, large calculation pressure and the like of the existing multi-agent consistency control technology; aiming at the defect of lack of rapid and high-precision control capability with specified performance, a performance function is designed to carry out specified performance transformation on the tracking error, and the expected convergence rate, the maximum overshoot and other transient performance and steady-state errors can be obtained. Greatly increases the application value and the application range of the prior art, reduces the economic cost and obtains better control effect.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a communication topology diagram consisting of 4 followers and 1 leader multi-agent system as provided by an embodiment of the present invention;
FIG. 3 is a graph of the response of each multi-agent output signal provided by the embodiment;
FIG. 4 shows the tracking error for a given performance condition according to an embodiment;
FIG. 5 is a control signal of an event-triggered adaptive controller according to an embodiment;
FIG. 6 illustrates follower agent u within 0-50 seconds according to an exemplary embodiment1、u2The event triggering time interval and the counted event triggering times;
FIG. 7 illustrates the embodiment providing each follower agent u within 0-50 seconds1、u2The event trigger time interval and the counted number of event triggers.
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.
The invention aims to provide a multi-agent consistency control method based on specified performance, which can further reduce the communication cost and energy consumption between agents, improve the rapidity and accuracy of a control process, optimize the system performance and obtain expected transient performance and steady-state error.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
FIG. 1 is a flowchart of a multi-agent consistency control method based on specified performance according to an embodiment of the present invention. As shown in fig. 1, the specific implementation steps of the present invention are as follows:
The multi-agent can be equipment such as unmanned vehicles, unmanned planes, robots and the like; the state information of the leader can be directly acquired by only part of followers, but at least one path of the communication topology can reach all other nodes from the leader node, and all the followers can track the leader by the control method of the scheme, so that consistency is realized.
The establishing of the communication topology comprises:
determining a directed topology graph according to a communication protocol;
and determining an adjacency matrix, an in-degree matrix and a Laplace matrix according to the directed topological graph.
The multi-agent system acquires the state information of other agents through mutual communication among the agents, and the communication relation among the agents can be described by an algebraic graph. The directed graph between agents is denoted as ζ ═ (V, E, a), where V ═ is (1,2, …, N) the number of nodes, indicating that the system contains N agents.
Is an edge of a node, A ═ ai,j]∈RN×N(R is the real number field) is the adjacency matrix. For adjacency matrix A, if the information of node j can be received by node i, then note ai,j1, otherwise ai,j0, i.e. ai,jRepresenting the communication relationship. The edges of nodes j to i are denoted as (V)j,Vi) E, representing that the agent i can receive the information of the agent j, namely the agent j is a neighbor node of the agent i; the set of neighbor nodes of agent i is defined as Ni＝{Vj|(Vj,Vi)∈E,i≠j}。
Defining the degree of entry of node i as
Diagonal matrix D ═ diag (D)1,d2,…,dN) Is an in-degree matrix. The laplacian matrix of the directed graph ζ is L ═ D-a. Definition expander graph
Wherein
0 denotes a leader, and likewise, a when node i is able to receive the signal of leader 0i,01, otherwise ai,0＝0。
The communication topology diagram of the multi-agent system composed of 4 followers and 1 leader provided by the embodiment of the invention is shown in fig. 2.
The state tracking error of the follower to the leader is defined as:
yi、yjthe system output signal representing the i, j followers (including speed and position information, i.e. said status information), ydThe system output signal (including the desired speed and location information) representing the leader.
The specified performance function is described by the following inequality:
δminand deltamaxIs an adjustable parameter, the performance function μ is bounded and monotonically decreases; the performance function is designed as follows:
wherein t is time, mu0＝μ(0),μ0＞μ∞And v are both positive and real numbers. Performing the equivalent transformation as follows:
wherein
In order to transform the error, the error is transformed,
in the formula:
in the formula
The transformed error model is:
In the formula
And
are respectively as
And the derivative of μ.
The error tracking error can be made to converge to a specified range within a specified time by the above specified performance transformation, thereby obtaining the desired transient performance and steady state error.
The tracking error satisfying the specified performance condition provided by the embodiment of the invention is shown in fig. 4. Wherein the values of the parameters are as follows: deltamin＝0.15；δmax＝0.18；μ0＝1；μ∞＝0.001；v＝0.05。
And 4, designing an event triggering adaptive controller of a follower into the following form by utilizing a backstepping method and a dynamic surface technology according to the transformed error model:
in the formula of alphai,nFor virtual control signals, si,nFor virtual error planes, epsilon, defined in the backstepping method and dynamic plane techniquei，σiAnd
are all positive design parameters;
is an estimate of all unknown parameters in the system (including non-linear terms in the system, etc., determined from the particular system model), τi,nFor the adjustment function (the adjustment function is derived by a back-stepping method),
is an adaptive law. The values of the parameters in the embodiment of the invention are as follows: epsiloni＝1.5；σi＝0.001；
determining a fixed threshold condition triggered by an event according to application requirements;
and judging whether the measurement error of the control signal reaches a fixed threshold condition, if so, updating the control signal, and otherwise, keeping the control signal unchanged.
The event trigger mechanism is designed into the following form:
tk+1＝inf{t∈R||ei(t)|≥mi},t1＝0
wherein ei(t)＝wi(t)-ui(t) represents a control signal measurement error, inf { } is an infimum boundary, miIs a fixed threshold value, and
tkfor the event trigger time, wi(t) denotes a control signal, ui(t) and wi(tk) The control signal updated at the event triggering moment is called as a triggering event when the measurement error of the control signal reaches a fixed threshold value, namely the control signal is updated by the controller of the follower when the measurement error of the control signal reaches the fixed threshold value, otherwise, the control signal is kept unchanged.
The control signal of the event triggered adaptive controller provided by the embodiment of the present invention is shown in fig. 5, where mi0.02; the event triggering times of each follower agent within 0-50 seconds provided by the embodiment of the invention are shown in fig. 6 and 7.
And 6, storing the event-triggered adaptive controller in each follower, wherein the controller controls the state of the follower to continuously reduce the tracking error between the follower and the leader, and finally converging the tracking error in a specified range within a specified time, thereby realizing the consistency control of the multi-agent.
Each follower output signal y provided by the embodiment of the inventioni(i ═ 1,2,3,4) and leader output signal ydAs shown in fig. 3. It can be seen from fig. 3-4 that the embodiments provided by the present invention achieve consistency control of multiple agents and meet specified performance.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The above specification provides a detailed description of the multi-agent consistency control method based on specified performance provided by the present invention. The above description of the embodiments is only intended to facilitate the understanding of the method of the invention and its core idea. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
Claims (5)
1. A multi-agent consistency control method based on specified performance, comprising:
establishing a communication topology by taking a plurality of agents as communication nodes, wherein one agent is a leader and the other agents are followers;
the followers communicate with each other according to the communication topology, so as to acquire the state information of the neighbor nodes; the status information includes location and velocity;
each follower calculates the tracking error of the leader according to the state information of the follower and the state information of the neighbor nodes, and performs specified performance transformation on the tracking error through a designed performance function to obtain a transformed error model;
according to the transformed error model, an event trigger adaptive controller of a follower is designed by utilizing a back-stepping method and a dynamic surface technology, and an event trigger mechanism is designed, so that multi-agent consistency control based on specified performance is realized;
the establishing of the communication topology comprises:
determining a directed topology graph according to a communication protocol;
determining an adjacency matrix, an in-degree matrix and a Laplace matrix according to the directed topological graph;
determining a directed topology graph according to a communication protocol; determining an adjacency matrix, an in-degree matrix and a Laplace matrix according to the directed topology graph, comprising:
the directed topology graph is denoted as ζ ═ (V, E, a), where V ═ 1,2, …, N is the number of nodes, N denotes the number of agents,
is an edge of a node, A ═ ai,j]∈RN×NIs a contiguous matrix, ai,jRepresenting a communication relationship; the edges of nodes j to i are denoted as (V)j,Vi) E, representing that the agent i can receive the information of the agent j; set of neighbor nodes of agent i is denoted as Ni；
Defining the degree of entry of node i as
Diagonal matrix D ═ diag (D)1,d2,…,dN) The Laplace matrix of the directed topology graph zeta is L ═ D-A;
the tracking error and the specified performance function are respectively as follows:
the tracking error is defined as:
yisystem output signal, y, representing the ith followerdA system output signal representing a leader; 0 denotes a leader, and when a node i can receive a signal of the leader 0, ai,01, otherwise, ai,0＝0；
The specified performance function is described by the following inequality:
δminand deltamaxIs an adjustable parameter, the performance function μ is bounded and monotonically decreases; the performance function is designed as follows:
μ＝(μ0-μ∞)e-vt+μ∞
wherein t is time, mu0＞μ∞V are all positive real numbers, μ0,μ∞The value of mu is t ═ 0, and t ∞;
the step of performing the specified performance transformation to obtain the transformed error model comprises the following steps:
performing the equivalent transformation as follows:
wherein
In order to transform the error, the error is transformed,
in the formula:
in the formula
The transformed error model is then:
2. the multi-agent consistency control method based on specified performances as recited in claim 1, wherein the multi-agent is an unmanned vehicle, a drone or a robot.
3. The multi-agent consistency control method based on specified capabilities as claimed in claim 1, wherein said event-triggered adaptive controller is designed in the form of:
in the formula of alphai，nFor the virtual control signal, Si，nFor virtual error planes, epsilon, defined in the backstepping method and dynamic plane techniquei，σiAnd
are all positive design parameters;
is an estimate of all unknown parameters, τi，nIn order to adjust the function of the adjustment,
is an adaptive law.
4. The multi-agent consistency control method based on specified capabilities as claimed in claim 1, wherein said designing event trigger mechanism comprises:
determining a fixed threshold condition triggered by an event according to application requirements;
and judging whether the measurement error of the control signal reaches a fixed threshold condition, if so, updating the control signal, and otherwise, keeping the control signal unchanged.
5. A multi-agent consistency control method based on specified capabilities as claimed in claim 3, characterized in that said event triggering mechanism is designed in the form of:
tk+1＝inf{t∈R||ei(t)|≥mi}，t1＝0
wherein ei(t)＝wi(t)-ui(t) represents a control signal measurement error, inf { } is an infimum boundary, miIs a fixed threshold value, and
tkfor the event trigger time, wi(t) denotes a control signal, ui(t) and wi(tk) The control signal is updated for the event trigger time.
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| CN108983734B (en) * | 2018-08-29 | 2021-07-20 | 燕山大学 | Finite time control method considering teleoperation system under triangular structure |
| CN109333529B (en) * | 2018-09-20 | 2022-08-23 | 南京邮电大学 | Multi-single-arm manipulator output consistent controller with predefined performance and design method |
| CN109379125B (en) * | 2018-09-30 | 2020-06-12 | 北京航空航天大学 | Multi-agent formation control method and system |
| CN109031958B (en) * | 2018-10-16 | 2021-07-27 | 廊坊师范学院 | Iterative learning control method for tracking consistency of fractional order multi-agent |
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