CN118226748B - Multi-agent sliding mode fault-tolerant control method under finite time observer - Google Patents
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Abstract
本发明公开了有限时间观测器下的多智能体滑模容错控制方法。针对存在未知扰动和执行器故障的二阶非线性多智能体系统，通过提出一种有限时间观测器，实现对智能体受到的扰动和故障信息的实时观测。根据多智能体之间的相对状态信息，定义了一致性误差变量。然后提出了一种新颖的滑模面，通过和人工势函数相结合，设计了分布式自适应滑模容错方法。本发明可以排除故障和未知扰动对系统的影响，在多智能体系统到达状态一致的同时，实现连通性保存。
The present invention discloses a multi-agent sliding mode fault-tolerant control method under a finite-time observer. For a second-order nonlinear multi-agent system with unknown disturbances and actuator faults, a finite-time observer is proposed to achieve real-time observation of the disturbance and fault information suffered by the agent. According to the relative state information between the multi-agents, the consistency error variable is defined. Then a novel sliding surface is proposed, and a distributed adaptive sliding mode fault-tolerant method is designed by combining it with an artificial potential function. The present invention can eliminate the influence of faults and unknown disturbances on the system, and realize connectivity preservation when the multi-agent system reaches a consistent state.
Description
Technical Field
The invention relates to a multi-agent sliding mode fault-tolerant control method under a limited time observer, belonging to the technical field of fault-tolerant consistency control of a multi-agent system.
Background
With the rapid development of society, communication, artificial intelligence, etc., multi-agent systems have become a research hotspot in the field of control engineering. Due to the cooperation and coordination of individuals among the agents, the intelligent agent can complete complex tasks which are difficult to be completed by the individuals. Since the concept of multi-agent systems was born, their practicality, flexibility, and efficiency in engineering applications have raised intense attention. In order to ensure the stability and safety of the multi-agent system in practical application, the robustness of the system is first improved, and the consistency goal of the multi-agent system is one of the most basic problems. The consistency target is that in the running process of the multi-agent system, the information interaction between the agents can be realized under the action of a certain control law, and finally the same expected value is reached. The consistency research is embodied in a plurality of engineering fields such as robot cooperation, unmanned aerial vehicle formation, mobile sensor networks and the like, and has important research significance.
However, in practical engineering applications, since the multi-agent is a multiplication of a single agent on a hardware scale, the likelihood of it being subject to unknown disturbances and faults is correspondingly multiplied. Taking unmanned aerial vehicle cluster system as an example, in the process of unmanned aerial vehicle formation execution task, every unmanned aerial vehicle can all receive the noise interference of different degree, and these disturbances can influence the gesture of individual self on the one hand, and on the other hand can influence its and other information interaction between the individual, and then influence the control of entire system. Therefore, how to quickly and effectively realize the consistency of the multi-agent system, and it is important to design a more efficient controller to improve the robustness of the system.
It is worth noting that in practical applications, the range of perception and communication between adjacent agents is always limited due to the limitation of transmission power. That is, the connectivity of the communication topology network can only be maintained for a limited distance. To address this problem, it is necessary to combine the artificial potential function with the control rate, further considering the reality factors.
Disclosure of Invention
Aiming at the research background, the invention provides a multi-agent sliding mode fault-tolerant control method under a limited time observer. A finite time observer capable of realizing rapid and accurate estimation of unknown disturbance and fault information is designed, an artificial potential function is designed, connectivity preservation is realized, a distributed self-adaptive sliding mode controller is designed by combining relative state errors among intelligent agents, and fault tolerance consistency control of a multi-intelligent agent system is realized within finite time.
The technical scheme is as follows:
the multi-agent sliding mode fault-tolerant control method under the limited time observer comprises the following specific steps:
Step 1), determining a dynamics model of a multi-agent system, wherein the multi-agent system comprises a leader and n followers;
step 2), determining a communication topological structure of the multi-agent system;
Step 3), constructing a finite time observer;
And 4) designing a consistency control method, and verifying that the multi-agent system realizes the finite time consistency under the action of the designed consistency control method according to the Lyapunov stability theory.
Preferably, the implementation process of step 1) is as follows:
step 1.1) determining a kinetic model of the leader as shown in (1):
Wherein, Representing the position and speed status of the leader, respectively; m is the space dimension, t is the time variable;
step 1.2) determining a kinetic model of follower i (i=1, 2,..n) with unknown disturbances and actuator faults as shown in (2):
Wherein, Representing the position and speed status of the ith follower, respectively; The control input for the ith follower, f i(xi(t),vi (t), t) representing the inherent nonlinear dynamic function of the ith follower, w i (t) representing the sum of the unknown disturbance of the ith follower and the actuator fault, defined as a lumped fault;
step 1.3) assume for the intrinsic nonlinear dynamic function f i(xi(t),vi (t), t) and the aggregate fault w i (t):
Wherein, AndAll are non-negative constants, and I represent two norms.
Preferably, the implementation process of step 2) is as follows:
in a multi-agent system, the leader is marked 0, the follower is marked i (i=1, 2,..n), the communication topology between the followers is represented by a topology graph g= (V, E, a), where v= {1,2,..n } represents a set of nodes, Representing an edge set, a= [ a ij]n×n ] representing an adjacency matrix, a ij being used to determine whether an edge exists between node i and node j, if (i, j) E, then there is a direct path between node i and node j, a ij =1, otherwise a ij =0, and defining the degree of node i asThe degree matrix of the topology graph G is denoted as d=diag { D 1,d2,…,di,…dn }, the laplace matrix is denoted as l= [ L ij]n×n＝D-A,lij ] j-th row of the laplace matrix, where L ij＝di when i=j, L ij＝-aij when i+.j, the adjacency matrix between the leader and the follower is defined as b=diag { B 1,b2,…,bi,…bn},bi for judging whether the follower i can accept the information of the leader, B i =1 if the follower i can directly obtain the information from the leader, otherwise B i =0, the neighborhood of the follower i is denoted as N i = { j| (j, i) ∈e }.
Preferably, the implementation process of step 3) is as follows:
Step 3.1) first, a finite time observer as shown in (4) is designed for each follower:
Wherein, H i (t) is an auxiliary variable, a and c i are normal numbers, and the sum fault estimated value of the ith follower is expressedParameter α satisfies 0< α <1;
step 3.2) defining an estimation error of the lumped fault As shown in (5):
Step 3.3) constructing two auxiliary variables h i (t) and q i (t), designing the auxiliary variable h i (t) with the aid of q i (t) as an estimation error for lumped faults Is integrated with:
adjusting the values of a, c i, α so that the error is estimated The final consistent bounded and multi-agent system is stable for a limited time, namely:
Wherein T 1 is the finite convergence time, V 1 (0) is the value of the selected Lyapunov function at t=0, and the values of a, c i, alpha are adjusted to estimate the error Adjusted to a minimum value of 0.
Preferably, the implementation process of the step 4) is as follows:
Step 4.1) defining a consistent tracking position error variable e xi (t) and a consistent tracking speed error variable e vi (t) in the form:
Defining position errors Speed errorDefining a set of vectorsVector setVector setVector set
Wherein, Is the position error between follower and leaderIs set of vectors of (a) to (b),Is the velocity error between follower and leaderE x is a vector set of the consistency tracking position error variable e xi (t), e v is a vector set of the consistency tracking speed error variable e vi (t), then (8) is rewritten to a vector form as shown in (9):
Wherein I m represents an m-dimensional identity matrix;
step 4.2) designing a sliding mode surface function s i (t) as shown in (10):
Wherein k 1,k2,k3 is a normal number, a function The parameter ζ satisfies 0< ζ <0.2;
step 4.3) designing an artificial potential function J i (t) as shown in (11):
Wherein, For any arbitraryAll have ||x i(t)-xj (t) ||r hold, N i is the neighborhood of follower i, R is the upper bound of the distance between the ith follower and the jth follower that can transfer information;
combining the artificial potential function J i (t) with the sliding mode surface, the obtained sliding mode surface function s i (t) is shown as (12):
step 4.3) designing a consistency control method for the multi-agent system as shown in (13):
Where k 4, iota, ρ and k 5 are positive constants, The method is a self-adaptive parameter, and verifies that the multi-agent system realizes the finite time consistency under the action of a designed consistency control method according to the Lyapunov stability theory.
The intelligent multi-agent sliding mode fault-tolerant control method has the beneficial effects that a novel multi-agent sliding mode fault-tolerant control method under a limited time observer is designed aiming at a nonlinear multi-agent system with unknown disturbance and actuator faults. A limited time observer is designed, and the rapid estimation and compensation of disturbance and fault information can be realized. According to the estimated value obtained by the observer, a distributed self-adaptive sliding mode controller is designed by combining with an artificial potential function, and a limited time consistency control target is realized. In general, the present invention has the following advantages:
① A limited time observer is designed, and the rapid estimation and compensation of disturbance and fault information can be realized.
② The novel sliding mode surface is designed, the need for fractional order and sign functions is eliminated, the communication burden is reduced, and buffeting is eliminated.
③ The distributed self-adaptive sliding mode control method combines the artificial potential function with the novel sliding mode surface, and can solve the problem of realizing the consistency of a nonlinear multi-agent system with unknown disturbance and actuator faults. The method can ensure that the system completes convergence within a bounded time, improves the efficiency of equipment to a certain extent, reduces the cost, enhances the robustness and stability of the system, and realizes connectivity preservation;
the multi-agent sliding mode fault-tolerant control method under the limited time observer provided by the invention has the advantages of high accuracy, strong safety, high efficiency, less harsh hardware requirements, certain application significance and wide application in the problem of realizing the consistency of a nonlinear multi-agent system with unknown disturbance and actuator faults.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a communication topology network of a multiple Qball-X4 quad-rotor helicopter system;
FIG. 3 is an estimated plot of disturbance and failure of follower 2 by two observers;
FIG. 4 is a graph of position tracking error under the control method of the present invention;
FIG. 5 is a graph of velocity tracking error under the control method of the present invention;
FIG. 6 is a graph of position tracking error under a conventional sliding mode control method;
FIG. 7 is a graph of velocity tracking error under a conventional sliding mode control method;
FIG. 8 is a graph of the response distance between agents under the control method of the present invention;
Fig. 9 is a graph showing the response distance between agents in the conventional sliding mode control method.
Detailed Description
The invention is further explained below with reference to the drawings.
As shown in fig. 1, a limited time observer is designed for the condition of second-order system interference and unknown actuator faults, so that the disturbance and fault information of an intelligent agent are observed in real time. On the basis of designing a novel sliding mode surface, connectivity preservation is realized by combining the intelligent agent perception range limiting problem with an artificial potential function. Compared with the conventional sliding mode control, the control law has the advantages of higher convergence speed, limited convergence time and higher robustness. Aiming at multi-agent sliding mode fault-tolerant control under a limited time observer, the method comprises the following specific steps:
step 1) determining a multi-agent system dynamics model, comprising the steps of:
step 1.1) determining a kinetic model of the leader as shown in (1):
Wherein, Representing the position and speed status of the leader, respectively; Control input for the leader;
step 1.2) determining a kinetic model of follower i (i=1, 2,..n) with unknown disturbances and actuator faults as shown in (2):
Wherein, Representing the position and speed status of the ith follower, respectively; The method comprises the steps of providing a control input for an ith follower, f i(xi(t),vi (t), w i (t) representing the sum of external disturbance and actuator injection faults of the ith follower and defining the sum as a lumped fault, wherein f i(xi(t),vi (t), t represents an inherent nonlinear dynamic function of the ith follower;
Step 1.3) reasonable assumptions are made about the inherent nonlinear dynamic function f i(xi(t),vi (t), t) and the aggregate fault w i (t):
Wherein, AndAre all non-negative constants;
step 2) determining the communication topology of the multi-agent system:
in a multi-agent system, the leader is marked 0, the follower is marked i (i=1, 2,..n), the communication topology between the followers is represented by a topology graph g= (V, E, a), where v= {1,2,..n } represents a set of nodes, Representing an edge set, a= [ a ij]n×n ] representing an adjacency matrix, a ij being used to determine whether an edge exists between node i and node j, if (i, j) E, then there is a direct path between node i and node j, a ij =1, otherwise a ij =0, and defining the degree of node i asThe degree matrix of the topology graph G is denoted as d=diag { D 1,d2,…,di,…dn }, the laplace matrix is denoted as l= [ L ij]n×n＝D-A,lij ] j-th row of the laplace matrix, where L ij＝di when i=j, L ij＝-aij when i+.j, the adjacency matrix between the leader and the follower is defined as b=diag { B 1,b2,…,bi,…bn},bi for judging whether the follower i can accept the information of the leader, B i =1 if the follower i can directly obtain the information from the leader, otherwise B i =0, the neighborhood of the follower i is denoted as N i = { j| (j, i) ∈e }.
Step 3) constructing a finite time fault observer, comprising the steps of:
step 3.1) first, a finite time observer as shown in (4) is designed for each follower:
Wherein, A, c i is a normal number, 0< alpha <1,
Step 3.2) defining the estimation error of the lumped fault as shown in (5):
Step 3.3) constructing two auxiliary variables, the auxiliary variable h i (t) being designed as an integral of the lumped fault estimation error:
by choosing the appropriate parameters, the estimation error (5) is eventually consistent and the system is stable for a finite time, i.e.:
Wherein T 1 is the finite convergence time, V 1 (0) is the value of the selected Lyapunov function at t=0, and the estimation error can be adjusted to a minimum value by selecting a proper value for a, c i and alpha;
step 4) a design consistency control method, which comprises the following steps:
Step 4.1) defining a consistency tracking position error variable e xi (t) and a speed error variable e vi (t) according to neighbor information acquired by the ith agent, wherein the consistency tracking position error variable e xi (t) and the speed error variable e vi (t) are as follows:
Definition of the definition Then (8) can be rewritten as a vector form as shown in (9):
Wherein I m represents an m-dimensional identity matrix;
step 4.2) designing a sliding mode surface function s i (t) as shown in (10):
Wherein k 1,k2,k3 is a normal number, a function The parameter ζ satisfies 0< ζ <0.2;
step 4.3) designing an artificial potential function J i (t) as shown in (11):
Wherein, For any arbitraryAll have the significance of I x i(t)-xj (t) I which is less than or equal to R, and combining the artificial potential function J i (t) with a sliding mode surface to obtain a sliding mode surface function s i (t) as shown in (12):
step 4.3) designing a consistency control method for the multi-agent system as shown in (13):
Where k 4, iota, ρ and k 5 are positive constants, The method is a self-adaptive parameter, and according to the Lyapunov stability theory, the second-order nonlinear multi-agent system consisting of the components (1) and (2) can be verified to realize the finite time consistency under the action of a control law (13).
The effectiveness of the embodiments is described below in a practical case simulation.
A Qball-X4 quadrotor helicopter flight control system developed by Quanser, canada was used as the subject of application. A multi-agent system consisting of a 5-frame Qball-X4 quad-rotor helicopter, with communication topology shown in fig. 2, containing a leader labeled 0 and a follower labeled i (i=1, 2,3, 4). And setting the weight of each edge in the communication topological graph to be 1, and calculating the concrete expression of the Laplace matrix L and the adjacent matrix B according to the communication topological structure, wherein the concrete expression is as follows:
for the model of the multi-agent system, the dynamics model of the leader is described as follows:
wherein, the initial state value of the leader is x 0(0)＝0.5,v0 (0) =0.2;
The kinetic model of follower i (i=1, 2,3, 4) is described as follows:
Wherein the inherent nonlinear dynamic f i(xi(t),vi(t),t)＝-cos(xi(t))-cos(vi (t)), the apparent I F i(xi(t),vi (t), t I is less than or equal to 2, and the initial state values of the followers are respectively x1(0)＝2.2,x2(0)＝2.55,x3(0)＝0.7,x4(0)＝-2.4,v0(0)＝0.2,v1(0)＝3.2,v2(0)＝1.98,v3(0)＝-2.1,v4(0)＝1.8.
To illustrate the effectiveness and superiority of the fault-tolerant control method of the present invention in solving the problem of consistent control of a multi-agent system with unknown disturbances and actuator faults, it is assumed that follower 2 is experiencing a fault and the remaining followers are not, but all are experiencing disturbances. Wherein the lumped fault equation for follower 2 is described as:
w2(t)=0.1sin(0.125πt)+0.1+0.2sin(0.5πt)
The lumped fault equations for the remaining followers are described as:
wi(t)=0.1+0.2sin(0.5πt)i=1,3,4
the observer parameters were chosen as a=1, c i =0.6, α=0.5. In order to better embody the rapidity and accuracy of the observer designed by the invention in disturbance and fault estimation, a traditional observer is selected for comparison, and a comparison curve of the observer and the traditional observer in disturbance and fault estimation is shown in figure 3. Compared with the traditional observer, the observer designed by the invention has the advantages of higher convergence speed, smoother curve and lower peak value. Therefore, the observer designed by the invention has better effect.
The controller parameters were chosen to be k 1＝3,k2＝0.1,k3＝1,k4＝0.5,k5 =2, ζ=0.1, iota=1, ρ=2, r=5. In order to better embody that the distributed self-adaptive sliding mode controller designed by the invention has higher robustness, the traditional sliding mode controller is selected for comparison. Fig. 4 and 5 are graphs of the position and velocity errors of the follower under the action of the controller designed according to the present invention, and fig. 6 and 7 are graphs of the position and velocity errors of the follower under the action of the conventional sliding mode controller, respectively. The curve shows that the two methods can realize the consistent convergence goal of the multi-agent system under disturbance and fault, but obviously, the controller designed by the invention has shorter convergence time, better robustness and better influence of the fault and disturbance on the system. Fig. 8 and fig. 9 show the response distances between agents under two control methods, respectively, both of which can achieve connectivity preservation. In summary, this case can indicate that the control method is effective.
The method designs a sliding mode fault-tolerant control method for processing a second-order nonlinear multi-agent system with unknown disturbance and actuator faults. The method is characterized in that a limited time observer is designed for the condition of second-order system interference and unknown actuator faults, and the disturbance and fault information of the intelligent body are observed in real time. On the basis of designing a novel sliding mode surface, connectivity preservation is realized by combining the intelligent agent perception range limiting problem with an artificial potential function. Compared with the conventional sliding mode control, the control law has the advantages of higher convergence speed, limited convergence time and higher robustness.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (1)
1. The multi-agent sliding mode fault-tolerant control method under the limited time observer is characterized by comprising the following specific steps:
Step 1), determining a dynamics model of a multi-agent system, wherein the multi-agent system comprises a leader and n followers;
step 1.1) determining a kinetic model of the leader as shown in (1):
Wherein, Representing the position and speed status of the leader, respectively; m is the space dimension, t is the time variable;
Step 1.2): determining a kinetic model of the follower with unknown disturbance and actuator failure i=1, 2,..n is shown in (2):
Wherein, Representing the position and speed status of the ith follower, respectively; The control input for the ith follower, f i(xi(t),vi (t), t) representing the inherent nonlinear dynamic function of the ith follower, w i (t) representing the sum of the unknown disturbance of the ith follower and the actuator fault, defined as a lumped fault;
step 1.3) assume for the intrinsic nonlinear dynamic function f i(xi(t),vi (t), t) and the aggregate fault w i (t):
Wherein, AndAll are non-negative constants, and I represent two norms;
step 2), determining a communication topological structure of the multi-agent system;
In a multi-agent system, a leader is marked 0, a follower is marked i=1, 2..n, the communication topology between followers is represented by a topology graph g= (V, E, a), where v= {1, 2..n } represents a set of nodes, Representing an edge set, a= [ a ij]n×n ] representing an adjacency matrix, a ij being used to determine whether an edge exists between node i and node j, if (i, j) E, then there is a direct path between node i and node j, a ij =1, otherwise a ij =0, and defining the degree of node i asThe degree matrix of the topology graph G is denoted as d=diag { D 1,d2,…,di,…dn }, the laplace matrix is denoted as l= [ L ij]n×n＝D-A,lij is the ith row j column of the laplace matrix, where L ij＝di when i=j, L ij＝-aij when i+.j, the adjacency matrix between the leader and the follower is defined as b=diag { B 1,b2,…,bi,…bn},bi for judging whether the follower i can accept the information of the leader, B i =1 if the follower i can directly obtain the information from the leader, otherwise B i =0, the neighborhood of the follower i is denoted as N i = { j| (j, i) ∈e };
Step 3), constructing a finite time observer;
Step 3.1) first, a finite time observer as shown in (4) is designed for each follower:
Wherein, H i (t) is an auxiliary variable, a and c i are normal numbers, and the sum fault estimated value of the ith follower is expressedParameter α satisfies 0< α <1;
step 3.2) defining an estimation error of the lumped fault As shown in (5):
Step 3.3) constructing two auxiliary variables h i (t) and q i (t), designing the auxiliary variable h i (t) with the aid of q i (t) as an estimation error for lumped faults Is integrated with:
adjusting the values of a, c i, α so that the error is estimated The final consistent bounded and multi-agent system is stable for a limited time, namely:
Wherein T 1 is the finite convergence time, V 1 (0) is the value of the selected Lyapunov function at t=0, and the values of a, c i, alpha are adjusted to estimate the error Adjusting to a minimum value of 0;
Step 4), designing a consistency control method, and verifying that the multi-agent system realizes the finite time consistency under the action of the designed consistency control method according to the Lyapunov stability theory;
Step 4.1) defining a consistent tracking position error variable e xi (t) and a consistent tracking speed error variable e vi (t) in the form:
Defining position errors Speed errorDefining a set of vectorsVector setVector setVector set
Wherein, Is the position error between follower and leaderIs set of vectors of (a) to (b),Is the velocity error between follower and leaderE x is a vector set of the consistency tracking position error variable e xi (t), e v is a vector set of the consistency tracking speed error variable e vi (t), then (8) is rewritten to a vector form as shown in (9):
Wherein I m represents an m-dimensional identity matrix, L is a Laplacian matrix, and B is an adjacency matrix between a leader and a follower;
step 4.2) designing a sliding mode surface function s i (t) as shown in (10):
Wherein k 1,k2,k3 is a normal number, a function The parameter ζ satisfies 0< ζ <0.2;
step 4.3) designing an artificial potential function J i (t) as shown in (11):
Wherein, For any arbitraryAll have ||x i(t)-xj (t) ||r hold, N i is the neighborhood of follower i, R is the upper bound of the distance between the ith follower and the jth follower that can transfer information;
combining the artificial potential function J i (t) with the sliding mode surface, the obtained sliding mode surface function s i (t) is shown as (12):
step 4.3) designing a consistency control method for the multi-agent system as shown in (13):
Where k 4, iota, ρ and k 5 are positive constants, The method is a self-adaptive parameter, and verifies that the multi-agent system realizes the finite time consistency under the action of a designed consistency control method according to the Lyapunov stability theory.
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