CN106444701B - Leader-follower type multi-agent system finite time Robust Fault Diagnosis design method - Google Patents
Leader-follower type multi-agent system finite time Robust Fault Diagnosis design method Download PDFInfo
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Abstract
The invention discloses a kind of leader-follower type multi-agent system finite time Robust Fault Diagnosis design methods, building is had the multi-agent system connection figure of leader and is indicated with digraph first, obtains the Laplacian matrix L of follower and the adjacency matrix G of leader；The state equation and output equation of each node flight control system are resettled, and is new vector by state vector and fault vectors augmentation；For each node, according to the digraph of building, construct distributed error equation and global error equation based on digraph, and it is based on finite time robust control, the finite time fault diagnosis observer for constructing flight control system carries out finite time fault diagnosis to the multiple agent actuator failures based on digraph.The present invention is to the effectively accurate finite time inline diagnosis of implementation when the failure of any one node appearance or multiple nodes break down simultaneously in control system and Fault Estimation.
Description
Technical Field
The invention belongs to the technical field of multi-agent systems, and particularly relates to a finite-time robust fault diagnosis design method of a leader-follower type multi-agent system.
Background
For control systems, stability of a system is a priority during analysis or design. This depends on the unstable system, which is not practical in practice. In general, the stabilities that we often say in the control field, such as Lyapunov stabilization and BIBO (bound-input-bound-output) stabilization, are asymptotic stabilities. The essence of asymptotic stability is to observe whether the system state can approach the equilibrium point infinitely after the system is disturbed in the initial state and when the time t approaches infinity. It should be noted that the above conventional stability theory, and the system behavior of interest, are discussed for an infinitely long time interval. The state of the system is not limited to one boundary as long as it is bounded. That is, these conventional stability theories characterize only the steady-state performance of the system, and do not really require transient performance. This results, for example, in a system that is asymptotically stable, but has poor transient performance and thus cannot be used at all in a project, and its infinite convergence time will limit its application to a situation where a quick maneuvering control is required in a real project.
The term "finite-time stability", FTS (finite-time stability), is used in this patent, and is a stability concept that is different from the conventional stability, and is provided with emphasis on the transient performance and convergence performance of the system. The FTS specifies a finite time interval within which the state of the control system will remain within a specified limit and may converge to a stable equilibrium point within a finite time relative to an infinitely long time interval. For finite time stabilization, there are three factors, including (1) a finite time interval, (2) a limit for initial conditions and (3) a limit at which the system state is expected to remain at all times.
With the development of flight control Systems, there are many situations that require multiple intelligent agents to cooperatively complete tasks, and research based on the Multi-Agent Systems (MAS) technology of the Multi-Agent system has also gained more and more attention and research. The precise and complex characteristics of MAS naturally make more attention paid to the theoretical research of fault diagnosis. The fault diagnosis technology can be divided into three parts of fault detection, fault separation and fault estimation. Fault diagnosis techniques are mainly used to improve the reliability of system operation and reduce the risk of system operation. The method and the device judge whether a fault occurs by monitoring the operating condition of the system and determine specific information of the fault, such as time, position, size and the like. Since the formation flight of the multi-agent system, especially the flight control system, is a high-cost and high-investment technology, the fault diagnosis technology for the multi-agent system needs to have accuracy and rapidity. This places a demand on both transient performance and convergence performance of fault diagnosis. The leader-follower multi-agent system finite time robust fault diagnosis design method provided by the patent is just a research completed aiming at the situation, and has very important theoretical research value and wide application prospect.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a finite time robust fault diagnosis design method of a leader-follower type multi-agent system for solving the existing problems, and designs a finite time distributed fault diagnosis observer by a finite time robust control method, which can theoretically restrain the influence of external time-varying interference on fault diagnosis and can ensure the transient performance and convergence performance of fault diagnosis, namely, effective and accurate finite time online diagnosis and fault estimation are carried out when a fault appears on any node or a plurality of nodes in a control system simultaneously appear faults.
The technical scheme is as follows: the specific technical scheme of the invention is as follows:
a method for designing finite time robust fault diagnosis of a leader-follower type multi-agent system comprises the following specific steps:
the first step is as follows: constructing a multi-agent system connection graph with a leader, and representing the multi-agent system connection graph by a directed graph to obtain a Laplacian matrix L of the follower and an adjacent matrix G of the leader;
the second step is that: establishing a state equation and an output equation of each node flight control system, and increasing a state vector and a fault vector into a new vector;
the third step: aiming at each node, constructing a distributed error equation and a global error equation based on the directed graph according to the constructed directed graph, and constructing a finite time fault diagnosis observer of the flight control system based on finite time robust control;
the fourth step: and carrying out finite time fault diagnosis on the fault of the multi-agent actuator based on the directed graph by using the obtained finite time fault diagnosis observer.
Further, in the first step, a specific method for obtaining the Laplacian matrix L of the follower and the adjacency matrix G of the leader is as follows:
setting a complete leader-follower directed graph consisting of a plurality of vertexes v and a plurality of edges epsilon, wherein the vertex v is0Represents leader 0; vertex viRepresents the ith follower, i belongs to (1-N); side (v)i,νj) The information used for indicating that the follower j can receive the information of the follower i, and otherwise, the information cannot be received;
definition a ═ aij]∈Rn×nA weighted adjacency matrix representing the directed graph, wherein aijRepresenting the weight of each edge; if (v)i,νj) E is epsilon, then aij> 0, otherwise aij＝0；aii＝0；
The adjacency matrix that defines the leader of the directed graph is G, where G ═ diag (G)1,…,gN),
Define the Laplacian matrix L of the follower as G-a.
Further, the directed graph in the first step means that each edge in the multi-agent system connection graph has a connection direction.
Further, in the second step, the specific method is to establish a system model with a fault and augment for each follower node:
dynamic equation for leader 0:
dynamic equation for follower i:
in the above equation, xi(t) and yi(t) are the state vector and output vector, u, of each follower node, respectivelyi(t) is the control input vector for each follower node; A. b, C are respectively the state matrix, input matrix and output matrix of the flight control system, matrix H is fault distribution matrix and matrix D1A distribution matrix of input disturbances for each i follower node flight control system; f. ofi(t) is a system fault, ωi(t) is an external time-varying disturbance vector, and for any omega (t), there is omegaT(t)ω(t)≤d1(d1≥0)；Is a differential of the fault and is arbitraryIs provided with(d2Not less than 0), wherein d1、d2Two non-negative scalars;
for the augmented equation of state, the new state vector isState matrix Input disturbance matrixFault distribution matrix
Furthermore, the state equation and the output equation of the flight control system of each node in the second step are obtained by linearizing the online working point of the nonlinear flight control system.
Further, in the third step, a finite time fault diagnosis observer of the flight control system is constructed as follows:
wherein,
wherein y is0(t) andthe fault diagnosis observer of the leader node measures an output vector and estimates the output vector respectively;is the measurement output vector of each follower node fault diagnosis observer;
observer matrixWherein, the adaptive matrixes R and F are gain matrixes of the fault diagnosis observer;
augmented observer state vectorSending the collected output data of the flight control system of each node to the fault diagnosis observer to obtain the state vector of the observer, thereby obtaining the fault estimation value of each nodeThus, the fault of the flight control system actuator is estimated on line; whereinIs the state vector of each follower node fault diagnosis observer,is an actuator fault estimate for each follower node system.
Further, the specific design method of the adaptive matrices R and F is as follows:
first, assume thatEstimate error of order stateError of fault estimationOutput estimation error
Then for the ith follower node, the local augmented state estimation error vector is:
then the local augmented state estimation error equation for the ith follower node is expressed as:
secondly, orderThen:
then, the local error equation is converted into a global error equation, and a global variable is defined:
the global augmented state estimates the error vector as
Global output estimation error vector of
The global disturbance vector is
The global fault estimation error vector is
Based on the directed graph theory, a kronecker product is introduced, and the obtained global error state space expression is as follows:
wherein INIs an N × N identity matrix.
Further, the global error dynamic system satisfies:
1) when v (t) is 0, the system is time-limited stable, i.e. for the time-limited parameter (c)1,c2,T,R0,d1,d2) Wherein c is1＜c2,R0＞0，c1,c2,d1,d2Are all scalar quantities, R0For a given matrix, an identity matrix may be taken; the system is satisfyingUnder the conditions of (a):
2) when v (t) ≠ 0, it is determined by summing any ω (t)Has omegaT(t)ω(t)≤d1， And getThe system is bounded in time at this point, and there is a scalar γ > 0, T > 0, which makes the system satisfy:
further, the gain matrices R and F of the finite time robust fault diagnosis observer are obtained by solving the following linear matrix inequality:
for a given finite time parameter (c)1,c2,T,R0＝I,d1,d2) And scalar gamma > 0, α > 0, lambda1＞0，λ2＞0，λ3> 0 and β > 0 if a symmetric positive definite matrix Q exists1∈R(n+r)×(n+r)Symmetric positive definite matrix Q2∈R(n+r)×(n+r)A sum matrixSatisfies the following conditions:
λ1I＜Q1＜I (17)
λ2I＜Q2＜λ3I (18)
said formulaThe following linear matrix inequalities are converted:
wherein
According toAnd obtaining gain matrixes R and F of the fault diagnosis observer.
Has the advantages that: compared with the prior art, the leader-follower type multi-agent system finite time robust fault diagnosis design method provided by the invention has the remarkable advantages that:
the method has the advantages that firstly, the finite time control technology is applied to the fault diagnosis process of the multi-agent system, the transient performance of the diagnosis process is optimized, a limit is defined for the fault estimated by the observer, and the time-varying interference and the fault differential item received by the system when the fault of the actuator occurs are well inhibited in the fault estimation process by combining the used robust control, so that the fault diagnosis accuracy is improved;
secondly, the invention adds e in the solving process-αTIn the form ofCompared withThe method is easier to obtain, so that the conservatism of the solution result can be reduced, and the solution meeting the conditions is more likely to be obtained for a complex multi-agent system;
thirdly, the invention applies the finite time control technology to the fault diagnosis process of the multi-agent system, improves the convergence performance of the system, is different from the convergence performance of the asymptotic stability performance in an infinite time interval, and can enable the fault diagnosis observer to carry out online diagnosis and fault estimation on the faults of the multi-agent system in a finite time.
The method has important practical reference value for real-time fault diagnosis and accurate monitoring of the formation flight control system of the flight control system.
Drawings
FIG. 1: FIG. 1 is a directed graph of a distributed flight control system with 1 leader and 4 follower nodes created by an example of the validation implementation of the present invention.
FIG. 2: fig. 2-1 is a schematic diagram of a fault estimation curve of a fault diagnosis observer of 4 follower nodes 2 (agents 1, 2, 3, and 4) when 1 st and 4 th follower nodes (agent 1 and agent 4) have faults simultaneously according to embodiment 1 of the present invention; fig. 2-2 is a schematic diagram of a comparison curve between a fault estimation value and a fault true value measured by a fault diagnosis observer of a follower node 1 (agent 1) when both of the 1 st and 4 th follower nodes (agent 1 and agent 4) have faults, which are measured in embodiment 1 of the present invention; fig. 2 to 3 are schematic diagrams of comparison curves between a fault estimation value and a fault true value measured by a fault diagnosis observer of the follower node 4 (the agent 4) when the 1 st and 4 th follower nodes (the agent 1 and the agent 4) both have faults, which are measured in embodiment 1 of the present invention.
FIG. 3: fig. 3-1 is a schematic diagram of a fault estimation curve of a fault diagnosis observer of 4 follower nodes 2 (agents 1, 2, 3, and 4) when 2 nd and 3 rd follower nodes (agent 2 and agent 3) have faults simultaneously according to embodiment 2 of the present invention; fig. 3-2 is a schematic diagram of a comparison curve between a fault estimation value and a fault true value measured by a fault diagnosis observer of a follower node 2 (agent 2) when both of the 2 nd and 3 rd follower nodes (agent 2 and agent 3) have faults, which are measured in embodiment 2 of the present invention; fig. 3-3 are schematic diagrams of comparison curves between a fault estimation value and a fault true value measured by a fault diagnosis observer of a follower node 3 (agent 3) when 2 nd and 3 rd follower nodes (agent 2 and agent 3) both have faults, which are measured in embodiment 2 of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings.
The invention provides a finite time robust fault diagnosis design method of a leader-follower type multi-agent system, which comprises the following specific steps:
the first step is as follows: constructing a multi-agent system connection graph with a leader and representing the multi-agent system connection graph by a directed graph to obtain a Laplacian matrix L of the follower and an adjacent matrix G of the leader:
and a complete leader-follower directed graph is formed by a plurality of vertexes v and a plurality of edges epsilon. Vertex v0Represents leader 0; vertex viIndicates the ith follower, i ∈ (1 to N). Side (v)i,νj) The information used to indicate that follower j can receive the information of follower i, but not vice versa, because the communication between the followers may be one-way.
Definition a ═ aij]∈Rn×nA weighted adjacency matrix representing the directed graph, wherein aijRepresenting the weight of each edge; if (v)i,νj) E is epsilon, then aij> 0, otherwise aij0. And for the directed graph used by the invention, the connectivity of the node itself, namely a, is not consideredii＝0。
Define the field of the directed graphThe adjacency matrix of the leader is G, wherein G ═ diag (G)1,…,gN),Define the Laplacian matrix L of the follower as G-a.
The second step is that: establishing a state equation and an output equation of the flight control system of each node, and increasing the state vector and the fault vector into a new vector:
dynamic equation for leader 0:
dynamic equation for follower i:
in the above equation, xi(t) and yi(t) are the state vector and output vector, u, of each follower node, respectivelyi(t) is the control input vector for each follower node; A. b, C are respectively the state matrix, input matrix and output matrix of the flight control system, matrix H is fault distribution matrix and matrix D1A distribution matrix of input disturbances for each i follower node flight control system; f. ofi(t) is the system fault (considered here is the actuator additive fault), ωi(t) is an external time-varying disturbance vector, and for any omega (t), there is omegaT(t)ω(t)≤d1(d1≥0)；Is a differential of the fault and is arbitraryIs provided withFor the augmented equation of state, the new state vector isState matrixOutput matrixInput disturbance matrixFault distribution matrix
The third step: for each node, according to the constructed directed graph, a distributed error equation and a global error equation based on the directed graph are constructed, and based on the finite time robust control, the following finite time fault diagnosis observer of the flight control system is constructed:
in the above-mentioned dynamic equations,
wherein y is0(t) andrespectively, a measured output vector of the leader node (which can be measured by setting the full state of the leader) and an estimated output vector of the leader node, and an augmented observer state vectorAll collected sectionsThe output data of the point flight control system is sent to the fault diagnosis observer to obtain the state vector of the observer, so that the fault estimation value of each node is obtainedTherefore, the fault of the flight control system actuator is estimated on line.
Is the fault diagnosis observer output vector of the leader node;andrespectively a state vector and a measurement output vector of each follower node fault diagnosis observer,is an actuator fault estimate for each follower node system.
Observer matrixThe adaptive matrices R and F are the gain matrices of the fault diagnosis observer and are also unknown matrices which are needed to be designed in the key point of the invention, and the specific design method is as follows:
from the second step, it is known that, in the present invention, assuming that the full state of the leader node 0 is measurable, the estimated output vector of the leader, that is, the originally measured output vector, can be known, that is:based on this assumption, let the state estimation error beError of fault estimation isOutput an estimation error of
Then for the ith follower node, the local augmented state estimation error vector is:
then the local augmented state estimation error equation for the ith follower node can be expressed as:
order toThen:
converting a local error equation into a global error equation, and firstly defining a global variable:
the global augmented state estimates the error vector as
Global output estimation error vector of
The global disturbance vector is
The global fault estimation error vector is
Based on the directed graph theory, the kronecker product is introduced (used)Representation), the obtained global error state space expression is:
wherein INIs an N × N identity matrix.
In order to solve the dimension-adaptive unknown gain matrix needing to be designed, namely gain matrices R and F of the finite time robust fault diagnosis observer, the invention requires that the global error dynamic system meets the following requirements:
1) when v (t) is 0, the system is time-limited stable, i.e. for the time-limited parameter (c)1,c2,T,R0,d1,d2) Wherein
c1＜c2,R0＞0，c1,c2,d1,d2Are all scalar quantities, R0For a given matrix, an identity matrix may be taken; the system is satisfyingUnder the conditions of (a):
2) when v (t) ≠ 0, it is determined by summing any ω (t)Has omegaT(t)ω(t)≤d1， And getThe system is bounded in time at this point, and there is a scalar γ > 0, T > 0, which makes the system satisfy:
wherein,
in the third step of the invention, the gain matrices R and F of the finite time robust fault diagnosis observer can be obtained by solving the following linear matrix inequality: for a given finite time parameter (c)1,c2,T,R0＝I,d1,d2) Andscalar gamma > 0, α > 0, lambda1＞0，λ2＞0，λ3> 0 and β > 0 if a symmetric positive definite matrix Q exists1∈R(n+r)×(n+r)Symmetric positive definite matrix Q2∈R(n +r)×(n+r)A sum matrixSatisfies the following conditions:
λ1I＜Q1＜I (37)
λ2I＜Q2＜λ3I (38)
for easy solution, in the above formulaThe following linear matrix inequalities are converted:
whereinAccording toObtaining gain matrixes R and F of the fault diagnosis observer; the above matrices all satisfy the algorithm of the matrix.
And carrying out finite-time fault diagnosis on the fault of the multi-agent actuator based on the directed graph by using the obtained distributed fault diagnosis observer.
The further preferable scheme of the invention is as follows: the directed graph in the first step of the invention means that each edge in the multi-agent system connection graph has a connection direction, and the undirected graph means that each edge in the multi-agent system communication topology connection graph has no connection direction. An undirected graph is a special case of a directed graph, which is more general.
The state equation and the output equation of each node flight control system in the second step of the invention are obtained by linearizing the online working point of the nonlinear flight control system.
The present invention will be better understood from the following examples. However, those skilled in the art will readily appreciate that the specific material ratios, process conditions and results thereof described in the examples are illustrative only and should not be taken as limiting the invention as detailed in the claims.
Examples
The invention provides a finite time distributed fault diagnosis observer by taking a certain type civil aircraft longitudinal motion equation as an implementation object and aiming at the faults of an actuator in formation flight, and the fault diagnosis method can improve the transient performance and the convergence performance of fault diagnosis;
consider the following equation for the longitudinal motion of a certain type of civil aircraft:
wherein, the state vector x (t) is the pitch angle rate q (rad/s), the vacuum speed Vtas(m/s), angle of attack α (rad) andpitch angle θ (rad). Control input u (t) is elevator yaw angle δe(rad) and thrust T (10)5N). The various matrices of the system are represented as follows:
assuming the system experiences an actuator failure: in view of the fact that actuator faults occur in the control input portion, the fault distribution matrix H of the present invention is B; assume that the distribution matrix of the input disturbances of the system is D1＝0.1[1,1,1,1]T(ii) a As shown in FIG. 1, agent 0 in FIG. 1 represents a leader, and agent 1, agent 2, agent 3, and agent 4 represent that the directed graph has 4 follower nodes, of which only node 1 can communicate with leader 0; from fig. 1, the Laplacian matrix L of the follower and the adjacency matrix G of the leader can be derived:
and carrying out finite-time fault diagnosis on the fault of the multi-agent actuator based on the directed graph by using the obtained distributed fault diagnosis observer.
Using the CVX tool box in Matlab software, directly matching c2，λ3And β, solving the above conditions can obtain when c is taken1When T is 1, c can be obtained2129.0068, β, 0.8590, thus obtainingThe other distributed observer matrices obtained are as follows:
in order to verify the effect of the fault diagnosis method of the flight control system, the following two simulation embodiments are adopted for verification, and in both embodiments, noise is added into a system model as disturbance.
Example 1
Suppose that the 1 st and 4 th follower nodes have failed simultaneously:
failure of 1 st follower node
Failure of 4 th follower node
That is, the 1 st follower node has failed at 20s, and the 4 th follower node has failed at 50 s. The experimental simulation results are shown in fig. 2. Fig. 2-1 is a schematic diagram of a fault estimation curve of a fault diagnosis observer of 4 follower nodes 2 (agents 1, 2, 3, and 4) when 1 st and 4 th follower nodes (agent 1 and agent 4) have faults simultaneously according to embodiment 1 of the present invention; fig. 2-2 is a schematic diagram of a comparison curve between a fault estimation value and a fault true value measured by a fault diagnosis observer of a follower node 1 (agent 1) when both of the 1 st and 4 th follower nodes (agent 1 and agent 4) have faults, which are measured in embodiment 1 of the present invention; fig. 2 to 3 are schematic diagrams of comparison curves between a fault estimation value and a fault true value measured by a fault diagnosis observer of the follower node 4 (the agent 4) when the 1 st and 4 th follower nodes (the agent 1 and the agent 4) both have faults, which are measured in embodiment 1 of the present invention.
Example 2
Suppose that the 2 nd and 3 rd follower nodes fail simultaneously:
failure of 2 nd follower node
Failure of the 3 rd follower node
That is, the actuator failure occurred at 10s for the 2 nd follower node, and the actuator failure occurred at 40s for the 3 rd follower node. The results of the experimental simulation are shown in fig. 3.
Fig. 3-1 is a schematic diagram of a fault estimation curve of a fault diagnosis observer of 4 follower nodes 2 (agents 1, 2, 3, and 4) when 2 nd and 3 rd follower nodes (agent 2 and agent 3) have faults simultaneously according to embodiment 2 of the present invention; fig. 3-2 is a schematic diagram of a comparison curve between a fault estimation value and a fault true value measured by a fault diagnosis observer of a follower node 2 (agent 2) when both of the 2 nd and 3 rd follower nodes (agent 2 and agent 3) have faults, which are measured in embodiment 2 of the present invention; fig. 3-3 are schematic diagrams of comparison curves between a fault estimation value and a fault true value measured by a fault diagnosis observer of a follower node 3 (agent 3) when 2 nd and 3 rd follower nodes (agent 2 and agent 3) both have faults, which are measured in embodiment 2 of the present invention.
As shown in the drawings, as can be seen from fig. 2-1 and 3-1, when a system fails, the observer can diagnose in real time on which agent the failure occurred. 2-2, 2-3, 3-2 and 3-3, the fault estimated by the observer can simulate the true value of the fault within a limited time, and the observer has good robustness as seen by small fluctuation of a curve.
From the simulation result, when one or more follower node systems in the multi-agent system have faults, the extended limited-time fault diagnosis observer designed by the invention can diagnose the failed node systems within limited time, estimate the fault size within limited time, has better fault estimation performance and has good inhibition effect on added disturbance and fault differential items. The method has important practical reference value for fault diagnosis and accurate monitoring of the formation flight control system of the flight control system within a limited time.
The embodiments of the present invention are described in detail with reference to the prior art, and the description thereof is not limited thereto.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A method for designing finite time robust fault diagnosis of a leader-follower type multi-agent system is characterized by comprising the following steps: the method comprises the following specific steps:
the first step is as follows: constructing a multi-agent system connection graph with a leader, and representing the multi-agent system connection graph by a directed graph to obtain a Laplacian matrix L of the follower and an adjacent matrix G of the leader; the specific method comprises the following steps:
setting a complete leader-follower directed graph consisting of a plurality of vertexes v and a plurality of edges epsilon, wherein the vertex v is0Represents leader 0; vertex viIndicating the ith followingI belongs to (1-N); side (v)i,νj) The information used for indicating that the follower j can receive the information of the follower i, and otherwise, the information cannot be received;
definition a ═ aij]∈Rn×nA weighted adjacency matrix representing the directed graph, wherein aijRepresenting the weight of each edge; if (v)i,νj) E is epsilon, then aij> 0, otherwise aij＝0；aii＝0；
The adjacency matrix that defines the leader of the directed graph is G, where G ═ diag (G)1,…,gN),
Defining Laplacian matrix L of the follower as G-A;
the directed graph means that each edge in the multi-agent system connection graph has a connection direction.
The second step is that: establishing a state equation and an output equation of each node flight control system, and increasing a state vector and a fault vector into a new vector; the specific method is that for each follower node, a system model with faults is established and is expanded:
dynamic equations for the leader:
dynamic equation for follower i:
in the above equations (1) and (2), xi(t) and yi(t) are the state vector and output vector, u, of each follower node, respectivelyi(t) is the control input vector for each follower node; A. b, C are respectively the state matrix, input matrix and output matrix of the flight control system, matrix H is fault distribution matrix and matrix D1A distribution matrix of input disturbances for each i follower node flight control system; f. ofi(t) is a system fault, ωi(t) is an external time-varying disturbance vector, and for any omega (t), there is omegaT(t)ω(t)≤d1，d1≥0；Is a differential of the fault and is arbitraryIs provided withd2Not less than 0, wherein d1、d2Two non-negative scalars;
for the augmented equation of state, the new state vector isState matrix Input disturbance matrixFault distribution matrix
The third step: for each node, constructing a distributed error equation and a global error equation based on the directed graph according to the constructed directed graph, and constructing a finite time robust fault diagnosis observer of the flight control system based on finite time robust control; the finite time robust fault diagnosis observer for constructing the flight control system comprises the following steps:
wherein,
wherein y is0(t) anda measurement output vector and an estimation output vector of the fault diagnosis observer which are the leader node respectively;is the measurement output vector of each follower node fault diagnosis observer;
observer matrixThe adaptive matrixes R and F are gain matrixes of the finite time robust fault diagnosis observer;
augmented observer state vectorSending the collected output data of the flight control system of each node to the fault diagnosis observer to obtain the state vector of the observer, thereby obtaining the fault estimation value of each nodeThus, the fault of the flight control system actuator is estimated on line; whereinIs the state vector of each follower node fault diagnosis observer,is an actuator of each follower node systemA barrier estimate value;
the fourth step: and carrying out finite time fault diagnosis on the fault of the multi-agent actuator based on the directed graph by using the obtained finite time robust fault diagnosis observer.
2. The lead-follow multi-agent system time-limited robust troubleshooting design method of claim 1 characterized by: and the second step is that the state equation and the output equation of each node flight control system are obtained by linearizing the online working point of the nonlinear flight control system.
3. The lead-follow multi-agent system time-limited robust troubleshooting design method of claim 1 characterized by: the specific design method of the dimension-adaptive matrixes R and F is as follows:
first, assume thatEstimate error of order stateError of fault estimationOutput estimation error
Then for the ith follower node, the local augmented state estimation error vector is:
then the local augmented state estimation error equation for the ith follower node is expressed as:
secondly, orderThen:
then, the local error equation is converted into a global error equation, and a global variable is defined:
the global augmented state estimates the error vector as
Global output estimation error vector of
The global disturbance vector is
The global fault estimation error vector is
Based on the directed graph theory, a kronecker product is introduced, and the obtained global error state space expression is as follows:
wherein INIs an N × N identity matrix.
4. The lead-follow multi-agent system time-limited robust troubleshooting design method of claim 3 characterized by: the global error dynamic system satisfies:
1) when v (t) is 0, the system is time-limited stable, i.e. for the time-limited parameter (c)1,c2,T,R0,d1,d2) Wherein c is1＜c2,R0＞0，c1,c2,d1,d2Are all scalar quantities, R0For a given matrix, an identity matrix may be taken; the system is satisfyingUnder the conditions of (a):
2) when v (t) ≠ 0, it is determined by summing any ω (t)Has omegaT(t)ω(t)≤d1， And getThe system is bounded in time at this point, and there is a scalar γ > 0, T > 0, which makes the system satisfy:
5. the lead-follow multi-agent system time-limited robust troubleshooting design method of claim 1 characterized by: the finite time robust fault diagnosis observer gain matrixes R and F are obtained by solving the following linear matrix inequality:
for a given finite time parameter c1,c2,T,R0＝I,d1,d2And scalar gamma > 0, α > 0, lambda1＞0，λ2＞0，λ3> 0 and β > 0 if a symmetric positive definite matrix Q exists1∈R(n+r)×(n+r)Symmetric positive definite matrix Q2∈R(n+r)×(n+r)A sum matrixSatisfies the following conditions:
λ1I＜Q1＜I (17)
λ2I＜Q2＜λ3I (18)
said formulaThe following linear matrix inequalities are converted:
wherein
According toAnd obtaining gain matrixes R and F of the fault diagnosis observer.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB2346461B (en) * | 1999-02-04 | 2003-06-18 | Mitel Corp | Semantic error diagnostic process for multi-agent systems |
| CN102890449A (en) * | 2012-09-20 | 2013-01-23 | 河北工业大学 | Wind turbine generator system variable-pitch controller design method based on finite time robust stability |
| CN105093934A (en) * | 2015-08-17 | 2015-11-25 | 哈尔滨工业大学 | Distributed finite time tracking control method for multi-robot system in view of interference and model uncertainty |
-
2016
- 2016-09-14 CN CN201610824378.2A patent/CN106444701B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB2346461B (en) * | 1999-02-04 | 2003-06-18 | Mitel Corp | Semantic error diagnostic process for multi-agent systems |
| CN102890449A (en) * | 2012-09-20 | 2013-01-23 | 河北工业大学 | Wind turbine generator system variable-pitch controller design method based on finite time robust stability |
| CN105093934A (en) * | 2015-08-17 | 2015-11-25 | 哈尔滨工业大学 | Distributed finite time tracking control method for multi-robot system in view of interference and model uncertainty |
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