CN104267716A - Distributed flight control system fault diagnosis design method based on multi-agent technology - Google Patents

Abstract

The invention relates to a distributed flight control system fault diagnosis design method based on the multi-agent technology. The method is characterized by including the steps that firstly, a multi-agent system connected graph with a leader is established and represented through an undirected graph and a Laplacian matrix L is acquired; secondly, a state equation and an output equation of each node of a flight control system are established; thirdly, according to each node, a distributed error equation and a global error equation based on the undirected graph are established; fourthly, according to the established undirected graph, the collected state equations of the flight control system, the collected output equations of the flight control system, and the established global error equations, a distributed fault diagnosis observer gain matrix of the flight control system can be acquired. According to the method, a multi-target distributed fault diagnosis observer is designed, online diagnosis can be conducted when any node in the system breaks down or multiple nodes break down simultaneously, and online fault diagnosis and real-time fault estimation can be conducted on the flight control system.

Description

A kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology

Technical field

The invention belongs to multi-agent system technical field, particularly relate to a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology.

Background technology

Multi-agent system (Multi-Agent Systems, MAS) refers to the system be made up of a series of individuality with local sensing ability, limited processing capacity and mutual communication capacity.Individuality in system can by with the communicating of other individualities, use respective ability mutually to cooperate, carried out common target.Nature has a lot of system to be considered as multi-agent system, such as aircraft formation flight, Distributed Calculation, robot cooperated etc.In recent years, the control problem of multi-agent system obtains the concern of more and more researchist.Single aircraft perception and executive capability limited, as in the face of large area region search etc. some comparatively heavy task time, efficiency is very low; For the task of some complexity, even cannot complete.According to aircraft formation flight, allow the collaborative work of multi rack aircraft, just effectively can overcome the defect of single aircraft, complete the aerial mission that complexity is heavy efficiently.Therefore, work in coordination with airmanship based on the Distributed Flight device of multi-agent system to be with a wide range of applications.

Chinese patent application 201310541339.8 proposes " a kind of diagnostic design method based on limited frequency domain flight control system gradual failure ", and the method is the state equation and the output equation that first gather this flight control system; Secondly instrument error equation, augmented error equation and fault diagnosis observer gain matrix; Then according to the error equation of the state equation of this flight control system collected and output equation and structure, augmented error equation and fault diagnosis observer gain matrix, a kind of fault diagnosis observer of discrete time flight control system is obtained.Utilize this Fault Estimation observer can carry out Fault Estimation to flight control system.The method, based on the lower feature of gradual failure frequency range, under the disturbance of extraneous high frequency, for flight control system model, devises the multiple constraint fault diagnosis observer based on limited frequency, reduces traditional conservative property in full frequency-domain method for designing.But the method also has the following disadvantages: one is the method is carry out design error failure diagnosis algorithm for single rack aircraft, be not suitable for the situation that when flight worked in coordination with by multi rack aircraft, multiple follower's system breaks down simultaneously; Two is that the error equation of the method structure only has the measurement using single rack aircraft to export data, not have to build the global error equation based on connection layout, not to be suitable for when flying to multiple follower's systematic collaboration the diagnosis of topological communication error information each other; Three is the method is design based on robust H_∞ performance, does not consider the transmission characteristic of system to energy bounded signal, so range of application is very restricted.

Summary of the invention

The present invention provides a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology for overcoming the deficiencies in the prior art, the present invention devises multiobject distributed diagnostics observer, inline diagnosis when fault that any one node in Distributed Flight Control System occurs or multiple node break down simultaneously can be realized, also can carry out on-line fault diagnosis and real-time Fault Estimation to flight control system.

According to a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology that the present invention proposes, it comprises following concrete steps:

The first step: structure has the multi-agent system connection layout of leader and represents with non-directed graph, draws Laplacian Matrix L:

Second step: state equation and the output equation of setting up each node flight control system:

3rd step: for each node, constructs the distributed error equation based on non-directed graph and global error equation:

4th step: according to the non-directed graph built, the global error equation of the state equation of the flight control system collected and output equation and structure, obtain a kind of distributed diagnostics observer gain matrix of flight control system, specific design is as follows:

Wherein:

The output of each node flight control system collected, output data are sent into above-mentioned fault diagnosis observer, obtains the Fault Estimation value of each node thus Fault Estimation is carried out to actuator of flight control system fault; Wherein: and y ₀t () is the fault diagnosis observer output vector of leader node respectively and measures output vector; with state vector and the measurement output vector of each follower's nodal fault diagnostics observer respectively, u _i(t) and y _it () is input vector and the output vector of each follower's node respectively; it is the actuator failures estimated value of each follower's node system, A, B, C are respectively state matrix, input matrix, the output matrix of described flight control system, matrix H is fault distribution matrix, and suitable dimension matrix R and F is described fault diagnosis observer gain matrix.

The further preferred version of the present invention is: the non-directed graph described in the first step of the present invention refers to that the every bar limit in multi-agent system connection layout is all do not establish closure.

The state equation of each node flight control system described in second step of the present invention and output equation, its implementation works online to flight control a little to carry out linearization and obtained.

Described in the present invention the 3rd step, the implementation method of distributed error equation is:

Suppose that the total state of leader node 0 can be surveyed, known based on this hypothesis, for i-th follower's node, order: state estimation error fault Estimation error output estimation error then the error equation of i-th follower's node represents:

$\begin{array}{c}{\stackrel{\·}{e}}_{\mathrm{xi}}\left(t\right)={\mathrm{Ae}}_{\mathrm{xi}}\left(t\right)+{\mathrm{He}}_{\mathrm{fi}}\left(t\right)-R[\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\ω}}_i\left(t\right)-{\mathrm{Ce}}_{\mathrm{xj}}\left(t\right)+D_2{\mathrm{\ω}}_j\left(t\right))+\\ g_j({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\ω}}_i\left(t\right))]-D_1{\mathrm{\ω}}_i\left(t\right)\end{array},$

$\begin{array}{c}{\stackrel{\·}{e}}_{\mathrm{fi}}\left(t\right)=-F[\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\ω}}_i\left(t\right)-{\mathrm{Ce}}_{\mathrm{xj}}\left(t\right)+D_2{\mathrm{\ω}}_j\left(t\right))+\\ g_j({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\ω}}_i\left(t\right))]-{\stackrel{\·}{f}}_i\left(t\right)\end{array};$

In formula, D ₁, D ₂be respectively the described input of every i follower's node flight control system, the distribution matrix of output disturbance; x _it state vector that () is the system failure, f _it () is system failure value, ω _it () is external disturbance vector; the differential of fault value;

For i-th follower's node, definition: error vector $\stackrel{\‾}{e_i}\left(t\right)=\left[\begin{array}{c}{e}_{\mathrm{xi}}\left(t\right)\\ e_{\mathrm{fi}}\left(t\right)\end{array}\right],$ $v_i\left(t\right)=\left[\begin{array}{c}{\mathrm{\ω}}_i\left(t\right)\\ {\stackrel{\·}{f}}_i\left(t\right)\end{array}\right],$ State matrix $\stackrel{\‾}{A}=\left[\begin{array}{cc}A& H\\ 0& 0\end{array}\right],$ Observer matrix $\stackrel{\‾}{R}=\left[\begin{array}{c}R\\ F\end{array}\right],$ Output matrix $\stackrel{\‾}{C}=\left[\begin{array}{cc}C& 0\end{array}\right],$ Perturbation matrix ${\stackrel{\‾}{D}}_1=\left[\begin{array}{cc}{D}_1& 1\\ 0& I\end{array}\right],$ ${\stackrel{\‾}{D}}_2=\left[\begin{array}{cc}{D}_2& 0\end{array}\right],$ And fault distribution matrix $\stackrel{\‾}{I_r}=\left[\begin{array}{c}0\\ I\end{array}\right],$

Then for i-th follower's node, following distributed error equation can be obtained

$\begin{array}{c}\stackrel{\·}{\stackrel{\‾}{e_i}}\left(t\right)=\stackrel{\‾}{A}{\stackrel{\‾}{e}}_i\left(t\right)-\stackrel{\‾}{R}[\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}(\stackrel{\‾}{C}\stackrel{\‾}{e_i}\left(t\right)-{\stackrel{\‾}{D}}_2{v}_i\left(t\right)-\stackrel{\‾}{C}{\stackrel{\‾}{e}}_j\left(t\right)+{\stackrel{\‾}{D}}_2{v}_j\left(t\right))+g_j(\stackrel{\‾}{C}\stackrel{\‾}{e_i}\left(t\right)-{\stackrel{\‾}{D}}_2{v}_i\left(t\right))]-{\stackrel{\‾}{D}}_1{v}_i\left(t\right)\end{array}$

$e_{\mathrm{fi}}\left(t\right)={\stackrel{\‾}{I}}_r^T\stackrel{\‾}{e_i}\left(t\right).$

Described in the present invention the 3rd step, the implementation method of global error equation is:

Definition global variable:

$\stackrel{\‾}{e}\left(t\right)={[{\stackrel{\‾}{e}}_1^T\left(t\right),{\stackrel{\‾}{e}}_2^T\left(t\right),...,{\stackrel{\‾}{e}}_N^T\left(t\right)]}^T,$

$v\left(t\right)={[v_1^T\left(t\right),v_2^T\left(t\right),...,v_N^T\left(t\right)]}^T,$

$e_f\left(t\right)={[e_{f1}^T\left(t\right),e_{f2}^T\left(t\right),...,e_{\mathrm{fN}}^T\left(t\right)]}^T,$

Global error equation can represent:

$\begin{array}{c}\stackrel{\·}{\stackrel{\‾}{e}}\left(t\right)=(I_N\⊗\stackrel{\‾}{A})\stackrel{\‾}{e}\left(t\right)-(I_N\⊗\stackrel{\‾}{R})[(L+G)\⊗\stackrel{\‾}{C}\stackrel{\‾}{e}\left(t\right)-(L+G)\⊗{\stackrel{\‾}{D}}_{2}v\left(t\right)]-\\ (I_N\⊗{\stackrel{\‾}{D}}_1)v\left(t\right)\\ =(I_N\⊗\stackrel{\‾}{A})\stackrel{\‾}{e}\left(t\right)-((L+G)\⊗\stackrel{\‾}{R}\stackrel{\‾}{C})\stackrel{\‾}{e}\left(t\right)+(L+G)\⊗\left(\stackrel{\‾}{R}{\stackrel{\‾}{D}}_2\right)v\left(t\right)-\\ (I_N\⊗{\stackrel{\‾}{D}}_1)v\left(t\right)\\ =[(I_N\⊗\stackrel{\‾}{A})-(L+G)\⊗\left(\stackrel{\‾}{R}\stackrel{\‾}{C}\right)]\stackrel{\‾}{e}\left(t\right)+[(L+G)\⊗\left(\stackrel{\‾}{R}{\stackrel{\‾}{D}}_2\right)-(I_N\⊗{\stackrel{\‾}{D}}_1)]v\left(t\right)\end{array},$

$e_f\left(t\right)=(I_N\⊗{\stackrel{\‾}{I}}_r^T)\stackrel{\‾}{e}\left(t\right),$

Wherein, represent Kronecker product.

Fault diagnosis observer gain matrix R and F described in the present invention the 4th step, obtains by solving following LMI: for given H ₂norm performance index γ and disc area if there is symmetric positive definite matrix symmetric matrix and matrix meet:

$\left[\begin{array}{cc}{I}_N\&CircleTimes;(\stackrel{\&OverBar;}{P}\stackrel{\&OverBar;}{A}+{\stackrel{\&OverBar;}{A}}^T\stackrel{\&OverBar;}{P})-(L+G)(\stackrel{\&OverBar;}{Y}\stackrel{\&OverBar;}{C}+{\stackrel{\&OverBar;}{C}}^T{\stackrel{\&OverBar;}{Y}}^T)& I_N\&CircleTimes;\stackrel{\&OverBar;}{I_r}\\ *& -I\end{array}\right]<0,$

$\left[\begin{array}{cc}-\stackrel{\&OverBar;}{Z}& (L+G)\&CircleTimes;{\left({\stackrel{\&OverBar;}{\mathrm{YD}}}_2\right)}^T-I_N\&CircleTimes;{\left(\stackrel{\&OverBar;}{P}{\stackrel{\&OverBar;}{D}}_1\right)}^T\\ *& I_N\&CircleTimes;(-\stackrel{\&OverBar;}{P})\end{array}\right]<0,$

$\mathrm{Trace}\left(\stackrel{\&OverBar;}{Z}\right)<{\mathrm{\&gamma;}}^2,$

$\left[\begin{array}{cc}{I}_N\&CircleTimes;(-\stackrel{\&OverBar;}{P})& I_N\&CircleTimes;(\stackrel{\&OverBar;}{P}\stackrel{\&OverBar;}{A}-\mathrm{\&alpha;}\stackrel{\&OverBar;}{P})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{Y}\stackrel{\&OverBar;}{C}\right)\\ *& I_N\&CircleTimes;(-{\mathrm{\&tau;}}^2\stackrel{\&OverBar;}{P})\end{array}\right]<0,$

Error dynamics system meets H ₂performance ${\left|\right|T_{v\left(t\right)e_f\left(t\right)}\left|\right|}_2<\mathrm{\&gamma;}$ With $[(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C}\right)]$ Characteristic root be positioned at then distributed observer matrix according to $\stackrel{\&OverBar;}{R}=\left[\begin{array}{c}R\\ F\end{array}\right]$ Obtain gain matrix R and F of described fault diagnosis observer; Above-mentioned matrix all meets the algorithm of matrix.

Above-mentioned distributed diagnostics observer of trying to achieve is utilized to carry out on-line fault diagnosis to the multiple agent actuator failures based on non-directed graph.

The present invention compared with prior art its remarkable advantage is: one is the present invention is directed to designing Multi-Agent system distributed diagnostics observer, overcome the deficiency of the fault diagnosis observer of flight control system modelling single at present, this is the unforeseeable a kind of breakthrough technological innovation in this area; Two is the present invention is output errors based on each node distributed, can estimate any one node system or the actuator failures that occurs of multiple node system simultaneously in real time online; Three is present invention employs based on H ₂performance and POLE PLACEMENT USING method for designing, transport function h ₂performance is in order to suppress the differential term of extraneous noise, disturbance and actuator failures, and POLE PLACEMENT USING will characteristic root be positioned at not only ensure the speed of convergence of Fault Estimation, and avoid distributed observer matrix numerical value is excessive; Four is global error dynamic equations that the present invention builds, and is conducive to carrying out online flight control system, Fault Estimation in real time.The present invention has important practical reference value for the real-time fault diagnosis of the formation flight control system of flight control system and accurate measurements.

Accompanying drawing explanation

Fig. 1 is the Distributed Flight Control System non-directed graph with 1 leader and 5 follower's nodes that the embodiment of the present invention is set up.

The Fault Estimation curve synoptic diagram of fault diagnosis observer during the 1st follower's one malfunctions that Fig. 2 surveys for the embodiment of the present invention be made up of Fig. 2-1 and Fig. 2-2, wherein: the curve in Fig. 2-1 represents estimated value; Curve in Fig. 2-2 represents actual value.

Fig. 3 for the embodiment of the present invention be made up of Fig. 3-1 and Fig. 3-2 survey when the 3rd, 4 follower's node breaks down simultaneously, the Fault Estimation curve synoptic diagram of the 3rd follower's nodal fault diagnostics observer, wherein: the curve in Fig. 3-1 represents estimated value; Curve in Fig. 3-2 represents actual value.

Fig. 4 for the embodiment of the present invention be made up of Fig. 4-1 and Fig. 4-2 survey when the 3rd, 4 follower's node breaks down simultaneously, the Fault Estimation curve synoptic diagram of the 4th follower's nodal fault diagnostics observer, wherein: the curve in Fig. 4-1 represents estimated value; Curve in Fig. 4-2 represents actual value.

Embodiment

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.

The present invention with the helicopter model control system vertical passage of certain vertical takeoff and landing for objective for implementation, for the actuator failures that rotor formation occurs in-flight, a kind of distributed diagnostics observer is proposed, this method for diagnosing faults not only can complete the Fault Estimation to single follower's node exactly, and can meet the diagnosis of the situation that simultaneously to break down to multiple follower's node;

For the aircraft vertical passage system of certain vertical takeoff and landing, as follows:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_i\left(t\right)={\mathrm{Ax}}_i\left(t\right)+{\mathrm{Bu}}_i\left(t\right)\\ y_i\left(t\right)={\mathrm{Cx}}_i\left(t\right)\end{array}\right..,$

Wherein, state vector be respectively helicopter flight speed along axis horizontal component and vertical component, pitch rate and the angle of pitch; Input vector is the variable of total distance variable and longitudinal periodicity displacement; Output vector be respectively flying speed along axis horizontal component and vertical component, the angle of pitch; Each matrix representation of system is as follows:

$A=\left[\begin{array}{cccc}-9.9477& -0.7476& 0.2632& 5.0337\\ 52.1659& 2.7452& 5.5532& -24.4221\\ 26.0922& 2.6361& -4.1975& -19.2774\\ 0& 0& 1& 0\end{array}\right],$ $B=\left[\begin{array}{cc}0.4422& 0.1761\\ 3.5446& -7.5922\\ -5.5200& 4.4900\\ 0& 0\end{array}\right],$

$C=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 0& 1\end{array}\right].$

Suppose this system generation actuator failures: because actuator failures occurs in control inputs passage, therefore make fault distribution matrix H=B; Assuming that the distribution matrix of the input of system, output disturbance is D respectively ₁=0.1 [1,1,1,1] ^tand D ₂=0.1 [1,1,1] ^t; For each follower's node, set up the out of order system model of tool as follows:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_i\left(t\right)={\mathrm{Ax}}_i\left(t\right)+{\mathrm{Bu}}_i\left(t\right)+{\mathrm{Hf}}_i\left(t\right)+D_1{\mathrm{\&omega;}}_i\left(t\right)\\ y_i\left(t\right)={\mathrm{Cx}}_i\left(t\right)+D_2{\mathrm{\&omega;}}_i\left(t\right)\end{array}\right.,$

As shown in Figure 1,0 in Fig. 1 represents leader, and 1-5 represents this non-directed graph and has 5 follower's nodes, wherein only have node 1 can with leader 0 communication; The adjacency matrix G of Laplacian Matrix L and leader as can be drawn from Figure 1:

$L=\left[\begin{array}{ccccc}2& -1& 0& 0& -1\\ -1& 2& -1& 0& 0\\ 0& -1& 2& -1& 0\\ 0& 0& -1& 2& -1\\ -1& 0& 0& -1& 2\end{array}\right],$ $G=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\end{array}\right]$

In order to suspected fault, the present invention devises the distributed diagnostics observer of following flight control system:

Wherein:

and y ₀t () is the fault diagnosis observer output vector of leader node respectively and measures output vector;

with state vector and the measurement output vector of each follower's nodal fault diagnostics observer respectively, u _i(t) and y _it () is input vector and the output vector of each follower's node respectively; it is the actuator failures estimated value of each follower's node system, A, B, C are respectively state matrix, input matrix, the output matrix of described flight control system, matrix H is fault distribution matrix, suitable dimension matrix R and F is described fault diagnosis observer gain matrix, obtains in accordance with the following methods:

Suppose that the total state of leader node 0 can be surveyed, known based on this hypothesis, can obtain

For i-th follower's node, order: state estimation error fault Estimation error $e_{\mathrm{ft}}\left(t\right)={\hat{f}}_i\left(t\right)-f_i\left(t\right),$ Output estimation error $e_{\mathrm{yi}}\left(t\right)={\hat{y}}_i\left(t\right)-y_i\left(t\right),$

The then state error the Representation Equation of i-th follower's node:

$\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_{\mathrm{xi}}\left(t\right)={\mathrm{Ae}}_{\mathrm{xi}}\left(t\right)+{\mathrm{He}}_{\mathrm{fi}}\left(t\right)-R[\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right)-{\mathrm{Ce}}_{\mathrm{xj}}\left(t\right)+D_2{\mathrm{\&omega;}}_j\left(t\right))+\\ g_j({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right))]-D_1{\mathrm{\&omega;}}_i\left(t\right)\end{array},$

$\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_{\mathrm{fi}}\left(t\right)=-F[\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right)-{\mathrm{Ce}}_{\mathrm{xj}}\left(t\right)+D_2{\mathrm{\&omega;}}_j\left(t\right))+\\ g_j({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right))]-{\stackrel{\&CenterDot;}{f}}_i\left(t\right)\end{array}$

In formula, D ₁, D ₂be respectively described each input of follower's node flight control system, the distribution matrix of output disturbance; x _it state vector that () is the system failure, ω _it () is external disturbance vector; the differential of fault value.

For i-th follower's node, definition: error vector $\stackrel{\&OverBar;}{e_i}\left(t\right)=\left[\begin{array}{c}{e}_{\mathrm{xi}}\left(t\right)\\ e_{\mathrm{fi}}\left(t\right)\end{array}\right],$ $v_i\left(t\right)=\left[\begin{array}{c}{\mathrm{\&omega;}}_i\left(t\right)\\ {\stackrel{\&CenterDot;}{f}}_i\left(t\right)\end{array}\right],$ State matrix $\stackrel{\&OverBar;}{A}=\left[\begin{array}{cc}A& E\\ 0_{2\&times;4}& I_2\end{array}\right],$ Observer matrix $\stackrel{\&OverBar;}{R}=\left[\begin{array}{c}R\\ F\end{array}\right],$ Output matrix $\stackrel{\&OverBar;}{C}=\left[\begin{array}{cc}C& 0_{3\&times;2}\end{array}\right],$ Perturbation matrix ${\stackrel{\&OverBar;}{D}}_1=\left[\begin{array}{cc}{D}_1& 0_{4\&times;2}\\ 0_{2\&times;1}& I_{2\&times;2}\end{array}\right],$ ${\stackrel{\&OverBar;}{D}}_2=\left[\begin{array}{cc}{D}_2& 0_{3\&times;2}\end{array}\right],$ And fault distribution matrix $\stackrel{\&OverBar;}{I_r}=\left[\begin{array}{c}{0}_{4\&times;2}\\ I_{2\&times;2}\end{array}\right],$

Then for i-th follower's node, following distributed error equation can be obtained

$\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e_i}}\left(t\right)=\stackrel{\&OverBar;}{A}{\stackrel{\&OverBar;}{e}}_i\left(t\right)-\stackrel{\&OverBar;}{R}[\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}(\stackrel{\&OverBar;}{C}\stackrel{\&OverBar;}{e_i}\left(t\right)-{\stackrel{\&OverBar;}{D}}_2{v}_i\left(t\right)-\stackrel{\&OverBar;}{C}{\stackrel{\&OverBar;}{e}}_j\left(t\right)+{\stackrel{\&OverBar;}{D}}_2{v}_j\left(t\right))+g_j(\stackrel{\&OverBar;}{C}\stackrel{\&OverBar;}{e_i}\left(t\right)-{\stackrel{\&OverBar;}{D}}_2{v}_i\left(t\right))]-{\stackrel{\&OverBar;}{D}}_1{v}_i\left(t\right)\end{array}$

$e_{\mathrm{fi}}\left(t\right)={\stackrel{\&OverBar;}{I}}_r^T\stackrel{\&OverBar;}{e_i}\left(t\right).$

Definition global variable:

$\stackrel{\&OverBar;}{e}\left(t\right)={[{\stackrel{\&OverBar;}{e}}_1^T\left(t\right),{\stackrel{\&OverBar;}{e}}_2^T\left(t\right),...,{\stackrel{\&OverBar;}{e}}_N^T\left(t\right)]}^T$

$v\left(t\right)={[v_1^T\left(t\right),v_2^T\left(t\right),...,v_N^T\left(t\right)]}^T$

$e_f\left(t\right)={[e_{f1}^T\left(t\right),e_{f2}^T\left(t\right),...,e_{\mathrm{fN}}^T\left(t\right)]}^T$

The expression of global error equation:

$\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}\left(t\right)=(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})\stackrel{\&OverBar;}{e}\left(t\right)-(I_N\&CircleTimes;\stackrel{\&OverBar;}{R})[(L+G)\&CircleTimes;\stackrel{\&OverBar;}{C}\stackrel{\&OverBar;}{e}\left(t\right)-(L+G)\&CircleTimes;{\stackrel{\&OverBar;}{D}}_{2}v\left(t\right)]-\\ (I_N\&CircleTimes;{\stackrel{\&OverBar;}{D}}_1)v\left(t\right)\\ =(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})\stackrel{\&OverBar;}{e}\left(t\right)-((L+G)\&CircleTimes;\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C})\stackrel{\&OverBar;}{e}\left(t\right)+(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{D}}_2\right)v\left(t\right)-\\ (I_N\&CircleTimes;{\stackrel{\&OverBar;}{D}}_1)v\left(t\right)\\ =[(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C}\right)]\stackrel{\&OverBar;}{e}\left(t\right)+[(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{D}}_2\right)-(I_N\&CircleTimes;{\stackrel{\&OverBar;}{D}}_1)]v\left(t\right)\end{array},$

$e_f\left(t\right)=(I_N\&CircleTimes;{\stackrel{\&OverBar;}{I}}_r^T)\stackrel{\&OverBar;}{e}\left(t\right),$

Wherein, represent Kronecker product;

For given norm H ₂performance index γ and disc area the transport function of global error equation meets H ₂performance ${\left|\right|T_{v\left(t\right)e_f\left(t\right)}\left|\right|}_2<\mathrm{\&gamma;}$ With $[(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C}\right)]$ Characteristic root be positioned at if there is symmetric positive definite matrix symmetric matrix and matrix meet:

$\left[\begin{array}{cc}{I}_N\&CircleTimes;(\stackrel{\&OverBar;}{P}\stackrel{\&OverBar;}{A}+{\stackrel{\&OverBar;}{A}}^T\stackrel{\&OverBar;}{P})-(L+G)(\stackrel{\&OverBar;}{Y}\stackrel{\&OverBar;}{C}+{\stackrel{\&OverBar;}{C}}^T{\stackrel{\&OverBar;}{Y}}^T)& I_N\&CircleTimes;\stackrel{\&OverBar;}{I_r}\\ *& -I\end{array}\right]<0$

$\left[\begin{array}{cc}-\stackrel{\&OverBar;}{Z}& (L+G)\&CircleTimes;{\left({\stackrel{\&OverBar;}{\mathrm{YD}}}_2\right)}^T-I_N\&CircleTimes;{\left(\stackrel{\&OverBar;}{P}{\stackrel{\&OverBar;}{D}}_1\right)}^T\\ *& I_N\&CircleTimes;(-\stackrel{\&OverBar;}{P})\end{array}\right]<0$

$\mathrm{Trace}\left(\stackrel{\&OverBar;}{Z}\right)<{\mathrm{\&gamma;}}^2,$

$\left[\begin{array}{cc}{I}_N\&CircleTimes;(-\stackrel{\&OverBar;}{P})& I_N\&CircleTimes;(\stackrel{\&OverBar;}{P}\stackrel{\&OverBar;}{A}-\mathrm{\&alpha;}\stackrel{\&OverBar;}{P})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{Y}\stackrel{\&OverBar;}{C}\right)\\ *& I_N\&CircleTimes;(-{\mathrm{\&tau;}}^2\stackrel{\&OverBar;}{P})\end{array}\right]<0$

Then distributed observer matrix according to $\stackrel{\&OverBar;}{R}=\left[\begin{array}{c}R\\ F\end{array}\right]$ Obtain gain matrix R and F of described fault diagnosis observer, thus obtain distributed fault estimation observer, utilize this Fault Estimation observer can obtain Fault Estimation value flight control system is carried out to the Fault Estimation of real-time online.

LMI tool box in application Matlab software solve above-mentioned in three conditions can obtain: disc area ask method of the present invention can calculate minimum H ₂performance index γ=8.7225, and distributed observer matrix

$\stackrel{\&OverBar;}{R}=\left[\begin{array}{ccc}-0.1316& -0.5638& 1.0379\\ 3.1256& 5.4782& -7.6165\\ -6.0783& -0.4983& 6.5317\\ -4.8659& -0.5290& 5.6864\\ 22.8329& 1.0478& -22.6637\\ 9.9677& -0.6247& -8.9171\end{array}\right].$

For verifying the effect of flight control system method for diagnosing faults of the present invention, following two emulation embodiment are adopted to verify.

Emulation embodiment I: suppose to only have the 1st follower's node to occur following actuator failures f (t)=[f ₁(t), f ₂(t)] ^t:

$f_1\left(t\right)=\left\{\begin{array}{cc}0& 0s\&le;t<50s\\ 1-e^{-0.1(t-50)}& 50s\&le;t\end{array}\right.,f_2\left(t\right)=0,$

Namely, when 50s, in variable, actuator failures is added total.

Emulation embodiment II: suppose that the 3rd, 4 follower's node breaks down simultaneously, as follows respectively:

The fault that 3rd follower's node occurs:

$f_1\left(t\right)=0,f_2\left(t\right)=\left\{\begin{array}{cc}0& 0s\&le;t<70s\\ \sin \left(0.05(t-70)\right)& 70s\&le;t\end{array}\right.,$

The fault that 4th follower's node occurs:

$f_1\left(t\right)=\left\{\begin{array}{cc}0& 0s\&le;t<50s\\ 1.5(-1+e^{-0.2(t-50)})& 50s\&le;t\end{array}\right.,f_2\left(t\right)=0,$

Namely the 3rd follower's node adds actuator failures when 70s in longitudinal periodicity displacement, and the 4th follower's node adds actuator failures total when 50s in variable.

As shown in Figure 2, in emulation I, only the 1st follower's node system breaks down is estimation curve, wherein: Fig. 2-1 is f ₁t () Fault Estimation curve, Fig. 2-2 is fault f ₁the actual value of (t).

For emulation II, when actuator failures appears in the 3rd, 4 follower's node system simultaneously, as shown in Figure 3, be the actuator failures estimation curve of follower's node 3, wherein: Fig. 3-1 is f ₂t () Fault Estimation curve, Fig. 3-2 is fault f ₂the actual value of (t); As shown in Figure 4, be the actuator failures estimation curve of the 4th follower's node, wherein: Fig. 4-1 is f ₁t () Fault Estimation curve, Fig. 4-2 is fault f ₁the actual value of (t).

Can draw from simulation result, when the system malfunctions of follower's node one or more in multi-agent system, the distributed diagnostics observer of the present invention's design can diagnose out the node system broken down, and can the fault that occurs of On-line Estimation, and there is good Fault Estimation performance.The present invention has important practical reference value for the real-time fault diagnosis of the formation flight control system of flight control system and accurate measurements.

In the specific embodiment of the present invention, all explanations do not related to belong to the known technology of this area, can be implemented with reference to known technology.

Above embodiment is the concrete support to a kind of Distributed Flight Control System Fault diagnosis design method and technology thought based on multi-agent Technology that the present invention proposes; protection scope of the present invention can not be limited with this; every technological thought proposed according to the present invention; any equivalent variations that technical solution of the present invention basis is done or the change of equivalence, all still belong to the scope of technical solution of the present invention protection.

Claims (6)

1., based on a Distributed Flight Control System Fault diagnosis design method for multi-agent Technology, it is characterized in that it comprises the steps:

The first step: structure has the multi-agent system connection layout of leader and represents with non-directed graph, draws Laplacian Matrix L:

Second step: state equation and the output equation of setting up each node flight control system:

3rd step: for each node, constructs the distributed error equation based on non-directed graph and global error equation:

4th step: according to the non-directed graph built, the global error equation of the state equation of the flight control system collected and output equation and structure, obtain a kind of distributed diagnostics observer gain matrix of flight control system, specific design is as follows:

Wherein:

The output of each node flight control system collected, output data are sent into above-mentioned fault diagnosis observer, obtains the Fault Estimation value of each node thus Fault Estimation is carried out to actuator of flight control system fault; Wherein: and y ₀t () is the fault diagnosis observer output vector of leader node respectively and measures output vector; with state vector and the measurement output vector of each follower's nodal fault diagnostics observer respectively, u _i(t) and y _it () is input vector and the output vector of each follower's node respectively; it is the actuator failures estimated value of each follower's node system, A, B, C are respectively state matrix, input matrix, the output matrix of described flight control system, matrix H is fault distribution matrix, and suitable dimension matrix R and F is described fault diagnosis observer gain matrix.

2. a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology according to claim 1, is characterized in that non-directed graph described in the first step refers to that the every bar limit in multi-agent system connection layout is all do not establish closure.

3. a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology according to claim 1, it is characterized in that state equation and the output equation of each node flight control system described in second step, its implementation works online to flight control a little to carry out linearization and obtained.

4. a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology according to claim 1, is characterized in that the implementation method of distributed error equation described in the 3rd step is:

Suppose that the total state of leader node 0 can be surveyed, known based on this hypothesis, for i-th follower's node, order: state estimation error fault Estimation error output estimation error then the error equation of i-th follower's node represents:

$\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_{\mathrm{xi}}\left(t\right)={\mathrm{Ae}}_{\mathrm{xi}}\left(t\right)+{\mathrm{He}}_{\mathrm{fi}}\left(t\right)-R[\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right)-{\mathrm{Ce}}_{\mathrm{xj}}\left(t\right)+D_2{\mathrm{\&omega;}}_j\left(t\right))+\\ g_j({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right))]-D_1{\mathrm{\&omega;}}_i\left(t\right)\end{array},$

$\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_{\mathrm{fi}}\left(t\right)=-F[\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right)-{\mathrm{Ce}}_{\mathrm{xj}}\left(t\right)+D_2{\mathrm{\&omega;}}_j\left(t\right))+\\ g_j({\mathrm{Ce}}_{\mathrm{xi}}\left(t\right)-D_2{\mathrm{\&omega;}}_i\left(t\right))]-{\stackrel{\&CenterDot;}{f}}_i\left(t\right)\end{array};$

In formula, D ₁, D ₂be respectively the described input of every i follower's node flight control system, the distribution matrix of output disturbance; x _it state vector that () is the system failure, f _it () is system failure value, ω _it () is external disturbance vector; the differential of fault value;

For i-th follower's node, definition: error vector $\stackrel{\&OverBar;}{e_i}\left(t\right)=\left[\begin{array}{c}{e}_{\mathrm{xi}}\left(t\right)\\ e_{\mathrm{fi}}\left(t\right)\end{array}\right],$ $v_i\left(t\right)=\left[\begin{array}{c}{\mathrm{\&omega;}}_i\left(t\right)\\ {\stackrel{\&CenterDot;}{f}}_i\left(t\right)\end{array}\right],$ State matrix $\stackrel{\&OverBar;}{A}=\left[\begin{array}{cc}A& H\\ 0& 0\end{array}\right],$ Observer matrix $\stackrel{\&OverBar;}{R}=\left[\begin{array}{c}R\\ F\end{array}\right],$ Output matrix $\stackrel{\&OverBar;}{C}=\left[\begin{array}{cc}C& 0\end{array}\right],$ Perturbation matrix ${\stackrel{\&OverBar;}{D}}_1=\left[\begin{array}{cc}{D}_1& 1\\ 0& I\end{array}\right],$ ${\stackrel{\&OverBar;}{D}}_2=\left[\begin{array}{cc}{D}_2& 0\end{array}\right],$ And fault distribution matrix $\stackrel{\&OverBar;}{I_r}=\left[\begin{array}{c}0\\ I\end{array}\right],$

Then for i-th follower's node, following distributed error equation can be obtained:

$\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e_i}}\left(t\right)=\stackrel{\&OverBar;}{A}{\stackrel{\&OverBar;}{e}}_i\left(t\right)-\stackrel{\&OverBar;}{R}[\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}(\stackrel{\&OverBar;}{C}\stackrel{\&OverBar;}{e_i}\left(t\right)-{\stackrel{\&OverBar;}{D}}_2{v}_i\left(t\right)-\stackrel{\&OverBar;}{C}{\stackrel{\&OverBar;}{e}}_j\left(t\right)+{\stackrel{\&OverBar;}{D}}_2{v}_j\left(t\right))+g_j(\stackrel{\&OverBar;}{C}\stackrel{\&OverBar;}{e_i}\left(t\right)-{\stackrel{\&OverBar;}{D}}_2{v}_i\left(t\right))]-{\stackrel{\&OverBar;}{D}}_1{v}_i\left(t\right)\end{array}$

$e_{\mathrm{fi}}\left(t\right)={\stackrel{\&OverBar;}{I}}_r^T\stackrel{\&OverBar;}{e_i}\left(t\right).$

5. a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology according to claim 1, is characterized in that the implementation method of global error equation described in the 3rd step is:

Definition global variable:

$\stackrel{\&OverBar;}{e}\left(t\right)={[{\stackrel{\&OverBar;}{e}}_1^T\left(t\right),{\stackrel{\&OverBar;}{e}}_2^T\left(t\right),...,{\stackrel{\&OverBar;}{e}}_N^T\left(t\right)]}^T,$

$v\left(t\right)={[v_1^T\left(t\right),v_2^T\left(t\right),...,v_N^T\left(t\right)]}^T,$

$e_f\left(t\right)={[e_{f1}^T\left(t\right),e_{f2}^T\left(t\right),...,e_{\mathrm{fN}}^T\left(t\right)]}^T,$

Global error equation can represent:

$\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}\left(t\right)=(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})\stackrel{\&OverBar;}{e}\left(t\right)-(I_N\&CircleTimes;\stackrel{\&OverBar;}{R})[(L+G)\&CircleTimes;\stackrel{\&OverBar;}{C}\stackrel{\&OverBar;}{e}\left(t\right)-(L+G)\&CircleTimes;{\stackrel{\&OverBar;}{D}}_{2}v\left(t\right)]-\\ (I_N\&CircleTimes;{\stackrel{\&OverBar;}{D}}_1)v\left(t\right)\\ =(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})\stackrel{\&OverBar;}{e}\left(t\right)-((L+G)\&CircleTimes;\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C})\stackrel{\&OverBar;}{e}\left(t\right)+(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{D}}_2\right)v\left(t\right)-\\ (I_N\&CircleTimes;{\stackrel{\&OverBar;}{D}}_1)v\left(t\right)\\ =[(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C}\right)]\stackrel{\&OverBar;}{e}\left(t\right)+[(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{D}}_2\right)-(I_N\&CircleTimes;{\stackrel{\&OverBar;}{D}}_1)]v\left(t\right)\end{array},$

$e_f\left(t\right)=(I_N\&CircleTimes;{\stackrel{\&OverBar;}{I}}_r^T)\stackrel{\&OverBar;}{e}\left(t\right),$

Wherein, represent Kronecker product.

6. a kind of Distributed Flight Control System Fault diagnosis design method based on multi-agent Technology according to claim 1, it is characterized in that fault diagnosis observer gain matrix R and F described in the 4th step, obtaining by solving following LMI: for given H ₂norm performance index γ and disc area if there is symmetric positive definite matrix symmetric matrix and matrix meet:

$\left[\begin{array}{cc}{I}_N\&CircleTimes;(\stackrel{\&OverBar;}{P}\stackrel{\&OverBar;}{A}+{\stackrel{\&OverBar;}{A}}^T\stackrel{\&OverBar;}{P})-(L+G)(\stackrel{\&OverBar;}{Y}\stackrel{\&OverBar;}{C}+{\stackrel{\&OverBar;}{C}}^T{\stackrel{\&OverBar;}{Y}}^T)& I_N\&CircleTimes;\stackrel{\&OverBar;}{I_r}\\ *& -I\end{array}\right]<0,$

$\left[\begin{array}{cc}-\stackrel{\&OverBar;}{Z}& (L+G)\&CircleTimes;{\left({\stackrel{\&OverBar;}{\mathrm{YD}}}_2\right)}^T-I_N\&CircleTimes;{\left(\stackrel{\&OverBar;}{P}{\stackrel{\&OverBar;}{D}}_1\right)}^T\\ *& I_N\&CircleTimes;(-\stackrel{\&OverBar;}{P})\end{array}\right]<0,$

$\mathrm{Trace}\left(\stackrel{\&OverBar;}{Z}\right)<{\mathrm{\&gamma;}}^2,$

$\left[\begin{array}{cc}{I}_N\&CircleTimes;(-\stackrel{\&OverBar;}{P})& I_N\&CircleTimes;(\stackrel{\&OverBar;}{P}\stackrel{\&OverBar;}{A}-\mathrm{\&alpha;}\stackrel{\&OverBar;}{P})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{Y}\stackrel{\&OverBar;}{C}\right)\\ *& I_N\&CircleTimes;(-{\mathrm{\&tau;}}^2\stackrel{\&OverBar;}{P})\end{array}\right]<0,$

Error dynamics system meets H ₂performance ${\left|\right|T_{v\left(t\right)e_f\left(t\right)}\left|\right|}_2<\mathrm{\&gamma;}$ With $[(I_N\&CircleTimes;\stackrel{\&OverBar;}{A})-(L+G)\&CircleTimes;\left(\stackrel{\&OverBar;}{R}\stackrel{\&OverBar;}{C}\right)]$ Characteristic root be positioned at then distributed observer matrix according to $\stackrel{\&OverBar;}{R}=\left[\begin{array}{c}R\\ F\end{array}\right]$ Obtain gain matrix R and F of described fault diagnosis observer; Above-mentioned matrix all meets the algorithm of matrix.