CN108803316A - For the Active Fault-tolerant Control Method of multi-agent system actuator failures - Google Patents
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Abstract
The invention discloses a kind of Active Fault-tolerant Control Methods for multi-agent system actuator failures.A kind of distributed fault observer is constructed, fault value is estimated using improved adaptive algorithm, conventional failure observer is overcome and is only capable of the defect of estimation constant value failure, and improve robustness.Fault message based on acquisition, and the opposite output information between intelligent body is combined, active tolerant control device is devised, the complexity of tolerant fail algorithm is effectively reduced, improves the ability of faults-tolerant control.Using the lower output information design observer of dimension and control law, communication bandwidth has effectively been saved.Active tolerant control of the present invention for a kind of multi-agent system with actuator failures.
Description
Technical Field
The invention relates to a fault-tolerant control method of a multi-agent system based on a distributed fault observer, and belongs to the field of multi-agent system control.
Background
Inspired by the phenomenon of biological clustering, american scholars Minsky originally proposed the concept of an agent, called an agent with certain behaviours and adaptivity as hardware, software, or other entities. A plurality of intelligent agents with signal acquisition, operation and communication capabilities realize information interaction and cooperation through a network to complete a preset task, and therefore the multi-agent system is formed. The fact that each intelligent agent can normally operate is a precondition for the multi-intelligent-agent system to realize tasks, and once one or more intelligent agents fail to operate, the control law cannot be completely executed, so that the overall task fails. Due to the mutual connection of the intelligent agents, the fault of a single intelligent agent can possibly influence the whole system, even lead to the breakdown of the whole system, and can not complete the task, thereby causing economic loss and even casualties. The research on the fault-tolerant control method of the multi-intelligent system has important practical significance for improving the reliability and safety of a complex large system.
Currently, many scholars study active fault-tolerant control by adopting the idea of control law reconstruction. And the control law reconstruction is to reconstruct the parameters of the controller on line according to the fault information determined by the fault diagnosis unit so as to ensure the performance of the system. The method has the advantages that the controller can be reconstructed according to the fault information, and the method has great flexibility. The fault diagnosis module in the active fault-tolerant control can acquire fault information in real time, so that for different types of faults, the controller has different reconstruction schemes, and the dynamic performance of the system is ensured. The cheng gang of Chongqing university and the like have designed a fault detection unit for a second-order multi-agent system, and when a fault is detected, an auxiliary module for handling the fault is activated. The northeast university of foley et al estimates state and actuator faults by constructing an observer and designing an auxiliary controller to handle the faults. In a distributed multi-agent system, where interconnection topology exists between agents, the design of the observer should be considered globally and information interaction between agents cannot be ignored. Therefore, it is of great significance to research the active fault-tolerant control of the distributed observer-based multi-agent system.
Disclosure of Invention
The purpose of the invention is as follows: the invention relates to a fault-tolerant control method of a multi-agent system based on a distributed fault observer, and belongs to the field of multi-agent system control.
The technical scheme is as follows: an active fault-tolerant control method of a multi-agent system based on a distributed fault observer is provided by combining a fault diagnosis technology when an actuator of the multi-agent system has a fault. A distributed fault observer is provided based on relative output information, and an output feedback fault-tolerant control method is provided based on fault estimation, and comprises the following specific steps:
step 1) determining a model and parameters thereof of a piloting-following multi-agent system, comprising the following steps:
step 1.1) determining a motion model of a pilot, as shown in formula (1):
wherein,andrespectively the state of the pilotVariables, input variables and output variables; d (t) is belonged to RrSatisfies | d for the external disturbance of the piloti(t)||∞A, B, D is a real matrix, C is a full rank matrix, D satisfies the matching condition D is BH, H is a constant matrix;
step 1.2) determining a motion model of the ith follower, as shown in formula (2):
wherein,andstate variables, input variables and output variables of the ith follower are respectively; di(t)∈RrSatisfies | d for the external disturbance of the ith followeri(t)||∞α ≦ α, α being a known constant, fi(t)∈RrRepresenting the actuator fault function occurring at the ith follower as an unknown function of time; A. b, D is a real matrix, C and E are full rank matrices, matrix D satisfies the matching condition D ═ BH, H is a constant matrix; e is a fault distribution matrix which represents the fault effect of the follower system;
step 2) determining the communication topological structure of the multi-agent system:
navigation-following multi-agent system under undirected graph communication topology, graphRepresenting the information interaction situation between all nodes including follower and pilotRepresenting all node setsIn the synthesis process, the raw materials are mixed,representing a collection of communication links between the nodes,representing an adjacency matrix; assuming that the multi-agent system has n followers, a subgraph G ═ V, E, a represents a communication topology network between followers, where V ═ 1, 2.Representing a set of communication links between followers,an adjacency matrix representing diagram G; note the bookFor the Laplacian matrix of FIG. G, defineWherein lijIs as defined in formula (3):
the adjacency matrix between the pilot and the follower is defined asIf there is an undirected edge e between the pilot 0 and the ith follower0i＝(0，i)∈E0Then bi1 is ═ 1; otherwise, bi0; it is clear that,
step 3) designing a distributed fault observer, which comprises the following steps:
step 3.1) designing a fault observer for each follower, as shown in formula (4):
wherein,a state variable representing a fault observer,in order to output the variable, the output variable,is fi(t) estimated value, R represents the fault observer gain matrix, ξi(t) is the relative output estimation error of the ith follower, which is defined as shown in equation (5):
wherein,is the jth following output vector estimate, aijRepresenting the weight of the connection between the ith and jth followers, biRepresenting the weight of the connection between the i-th follower and the pilot, NiA set of neighbors representing the ith follower; since the pilot is a formation command generator, it is assumed that the state of the pilot is known, i.e. the pilot is a member of the formation command generatorIs established, thenIf true;
step 3.2) definitionThe error is estimated for the ith following state,for the fault estimation error, the ith following state estimation error equation is derived, as shown in equation (6):
step 3.3) designing a self-adaptive fault estimation algorithm, as shown in formula (7):
whereinIs fi(ii) an estimate of the value of (t),is a parameter matrix to be designed, and a fault estimation error equation is derived according to the parameter matrix, and is shown in a formula (8):
step 3.4) constructing an error amplification system, as shown in formula (9):
wherein,
to be considered from a distributed global perspective, the following global variables are defined:
obtaining a global estimation error system dynamic equation as shown in equation (10):
step 3.5) there are positive definite symmetric matrix Q and matrix S satisfying
Wherein,the gain matrix of the amplification can be obtained by calculationThereby ensuring a state estimation error exAnd error of fault estimation efConverge to zero;
step 4) designing a fault-tolerant controller, which comprises the following steps:
step 4.1) obtaining a fault estimation value according to the fault observer, as shown in formula (12):
wherein, tfIs the trigger time;
step 4.2) defining the relative output information v that the ith follower can obtainiAs shown in formula (13):
step 4.3) calculating the matrixSo that B*Satisfies formula (14);
(In-BB*)E＝0 (14)
wherein, InIs an n-order identity matrix;
step 4.4) designing a fault-tolerant control law for the ith follower, wherein the form is shown as a formula (15):
where K is the feedback gain to be designed, λ is the fixed coupling weight,is a fault estimation value;
and 4.5) substituting the formula (15) into the formula (2) to obtain a dynamic equation of the follower system, as shown in the formula (16):
defining a tracking error variable ei＝xi(t)-x0(t), disturbance variableObtaining a closed loop system dynamic equation as shown in equation (17):
the following global variables are defined:
and (3) rewriting the formula (17) into a vector form to obtain a closed-loop tracking error system, as shown in a formula (18):
step 4.6), selecting proper parameters to complete fault-tolerant control on the parameters, wherein a positive definite matrix P exists, and the matrix K and the parameter lambda satisfy the formula (19):
the matrix K and the parameter lambda can be obtained through calculation, so that the closed-loop tracking system is ensured to be asymptotically stable.
Has the advantages that: the invention provides an active fault-tolerant control method of a multi-agent system based on a distributed fault observer, which combines fault diagnosis technology when an actuator of the multi-agent system has faults, provides the distributed fault observer based on relative output information between agents, and provides an output feedback fault-tolerant control method based on fault estimation, and has the following specific advantages:
(1) the output information with lower dimensionality is selected to design a fault observer and a fault-tolerant controller, so that the heavy burden of system communication and calculation caused by overhigh system state dimensionality is avoided;
(2) the fault observer can quickly and accurately estimate constant and time-varying faults, the fault-tolerant controller can effectively process faults of the actuator, and the fault observer and the fault-tolerant controller have good robustness to external disturbance;
(3) the fault observer and the fault-tolerant controller are separately designed, and the performances of the fault observer and the fault-tolerant controller are considered at the same time, so that the design process is optimized, and the parameters in the fault observer and the fault-tolerant controller can be conveniently solved;
the method provided by the invention is an active fault-tolerant control method for a system containing actuator faults and external disturbance, has certain application significance, is easy to realize, good in real-time performance and high in accuracy, can effectively improve the safety of the control system, is strong in operability, saves time, is higher in efficiency, and can be widely applied to actuator fault-tolerant control of a multi-agent system.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is an experimental set-up Qball-X4 quad-rotor craft developed by Quanser corporation;
FIG. 3 is a multi-aircraft system communication topology;
FIG. 4 is a failure estimate for the 3 rd aircraft under the failure observer;
FIG. 5 is a failure estimate for the 2 nd aircraft under the failure observer;
FIG. 6 is a position tracking error for a multiple aircraft system;
FIG. 7 is a velocity tracking error for a multiple aircraft system.
Detailed Description
The invention is further explained below with reference to the drawings.
As shown in fig. 1, an active fault-tolerant control method for a multi-agent system based on a distributed fault observer provides an active fault-tolerant control method in combination with a fault diagnosis technology when an actuator fault exists in the multi-agent system. A distributed fault observer is provided based on relative output information, and an output feedback fault-tolerant control method is provided based on fault estimation, and comprises the following specific steps:
step 1) determining a model and parameters thereof of a piloting-following multi-agent system, comprising the following steps:
step 1.1) determining a motion model of a pilot, as shown in formula (1):
wherein,andrespectively a state variable, an input variable and an output variable of a pilot; d (t) eRrSatisfies | d for the external disturbance of the piloti(t)||∞A, B, D is a real matrix, C is a full rank matrix, D satisfies the matching condition D is BH, H is a constant matrix;
step 1.2) determining a motion model of the ith follower, as shown in formula (2):
wherein,andstate variables, input variables and output variables of the ith follower are respectively; di(t)∈RrSatisfies | d for the external disturbance of the ith followeri(t)||∞α ≦ α, α being a known constant, fi(t)∈RrRepresenting the actuator fault function occurring at the ith follower as an unknown function of time; A. b, D is a real matrix, C and E are full rank matrices, matrix D satisfies the matching condition D ═ BH, H is a constant matrix; e is a fault distribution matrix which represents the fault effect of the follower system;
step 2) determining the communication topological structure of the multi-agent system:
navigation-following multi-agent system under undirected graph communication topology, graphRepresenting the information interaction situation between all nodes including follower and pilotA set of all the nodes is represented,representing a collection of communication links between the nodes,representing an adjacency matrix; assuming that the multi-agent system has n followers, a subgraph G ═ V, E, a represents a communication topology network between followers, where V ═ 1, 2.Representing a set of communication links between followers,an adjacency matrix representing diagram G; note the bookFor the Laplacian matrix of FIG. G, defineWherein lijIs as defined in formula (3):
the adjacency matrix between the pilot and the follower is defined asIf there is an undirected edge e between the pilot 0 and the ith follower0i＝(0，i)∈E0Then bi1 is ═ 1; otherwise, bi0; it is clear that,
step 3) designing a distributed fault observer, which comprises the following steps:
step 3.1) designing a fault observer for each follower, as shown in formula (4):
wherein,a state variable representing a fault observer,in order to output the variable, the output variable,is fi(t) estimated value, R represents the fault observer gain matrix, ξi(t) is the relative output estimation error of the ith follower, which is defined as shown in equation (5):
wherein,is the jth following output vector estimate, aijRepresenting the weight of the connection between the ith and jth followers, biRepresenting the weight of the connection between the i-th follower and the pilot, NiA set of neighbors representing the ith follower; since the pilot is a formation command generator, it is assumed that the state of the pilot is known, i.e. the pilot is a member of the formation command generatorIs established, thenIf true;
step 3.2) definitionThe error is estimated for the ith following state,for the fault estimation error, the ith following state estimation error equation is derived, as shown in equation (6):
step 3.3) designing a self-adaptive fault estimation algorithm, as shown in formula (7):
whereinIs fi(ii) an estimate of the value of (t),is a parameter matrix to be designed, and a fault estimation error equation is derived according to the parameter matrix, and is shown in a formula (8):
step 3.4) constructing an error amplification system, as shown in formula (9):
wherein,
to be considered from a distributed global perspective, the following global variables are defined:
obtaining a global estimation error system dynamic equation as shown in equation (10):
step 3.5) there are positive definite symmetric matrix Q and matrix S satisfying
Wherein,the gain matrix of the amplification can be obtained by calculationThereby ensuring a state estimation error exAnd error of fault estimation efConverge to zero;
step 4) designing a fault-tolerant controller, which comprises the following steps:
step 4.1) obtaining a fault estimation value according to the fault observer, as shown in formula (12):
wherein, tfIs the trigger time;
step 4.2) defining the relative output information v that the ith follower can obtainiAs shown in formula (13):
step 4.3) calculating the matrixSo that B*Satisfies formula (14);
(In-BB*)E＝0 (14)
wherein, InIs an n-order identity matrix;
step 4.4) designing a fault-tolerant control law for the ith follower, wherein the form is shown as a formula (15):
where K is the feedback gain to be designed, λ is the fixed coupling weight,is a fault estimation value;
and 4.5) substituting the formula (15) into the formula (2) to obtain a dynamic equation of the follower system, as shown in the formula (16):
defining a tracking error variable ei＝xi(t)-x0(t), disturbance variableObtaining a closed loop system dynamic equation as shown in equation (17):
the following global variables are defined:
and (3) rewriting the formula (17) into a vector form to obtain a closed-loop tracking error system, as shown in a formula (18):
step 4.6), selecting proper parameters to complete fault-tolerant control on the parameters, wherein a positive definite matrix P exists, and the matrix K and the parameter lambda satisfy the formula (19):
the matrix K and the parameter lambda can be obtained through calculation, so that the closed-loop tracking system is ensured to be asymptotically stable.
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.
The effectiveness of the implementation is illustrated in the following by a practical case simulation.
Qball-X4 quad-rotor aircraft flight control system actuators, developed by Quanser, Canada, were used as the subject of the application study. The Qball-X4 experimental subject is shown in FIG. 2. The Qball-X4 four-rotor aircraft has six-dimensional variables (X, Y, Z, psi, theta, phi), wherein X, Y and Z are position variables, psi is yaw angle, theta is pitch angle and phi is roll angle. The simulation of the case selects the channel signal in the forward direction of the x axis as a research object.
The motion of the body about the x-axis is affected by the total thrust and roll angle phi/pitch angle theta. Assuming a yaw angle ψ of 0, the dynamic equation for the x-axis is described as follows:
wherein M isgThe mass of the machine body is shown, and X is the position in the X-axis direction. F is the thrust generated by the rotor:
wherein, KgPositive gain, ω actuator bandwidth. Define v as actuator dynamics:
the state space expression is as follows:
in the x-axis position control model, the pitch angle theta is coupled with the x-axis position control model, the integral control can be divided into two stages, one is a pitch angle control stage, and the second stage, namely the position control stage, is started after the pitch angle is controlled to a preset value. And when the position reaches the set position, the pitch angle theta is reset to zero through the pitch angle control channel. Under the condition that theta is smaller, a model of an x-axis direction under an ideal condition without external disturbance, parameter perturbation and time-varying time lag is obtained through linearization, and the model is as follows:
consider a multi-aircraft system comprising 4 followers and 1 pilot, all of which are Qball-X4 quad-rotor aircraft, with the pilot labeled 0 and the followers labeled i (i ═ 1, 2, 3, 4). Assuming that in the x-axis position control stage, the pitch angle is set as 0.035rad, and the kinematics equation of the pilot aircraft is as follows:
considering actuator faults and external disturbance, the kinematic equation of the ith follower aircraft is as follows:
wherein,x represents the displacement in the X-axis direction,linear velocity in the x-axis direction is indicated and v indicates actuator dynamics. u (t) is the control input, d (t) is the external disturbance, fi(t) is an actuator failure function for the ith follower aircraft. The parameter value of the unmanned aerial vehicle can be subjected to actuator failure through the unmanned aerial vehicle, and the failure distribution matrix E is B. D is the disturbance distribution matrix, the value of which will be given in the simulation. The values of each matrix in the system are as follows:
C＝[1 0 0]，
the communication topology is shown in fig. 3. Then, the Laplacian matrixAnd adjacency matrixComprises the following steps:
suppose the disturbance distribution matrix is D ═ 003]TThe external disturbance function is di(t) 0.01sin (t). In the simulation, a time-varying fault is injected into a control input channel of the 2 nd aircraft, and the description of the fault is as follows:
injecting a constant fault into a control input channel of the 3 rd aircraft, wherein the fault is described as follows:
simulated sampling period Ts0.01s, pilot control input u0(t) sin (t), the initial state quantity of the system is:
x0(0)＝[0.2125，1.0527，0.358]T，
x1(0)＝[0.1125，3.5527，-2.142]T，
x2(0)＝[1.087，0.6527，0.9651]T，
x3(0)＝[0.3682，1.8712，-0.153]T，
x4(0)＝[3.1125，-1.4473，-2.142]T。
the gain matrix of the fault observer can be obtained by calculation as follows:
external disturbance di(t) and control input u0the upper limit of (t) is selected from α ═ 0.5, β ═ 2, and λ ═ 2.5, | | | H | | | | 0.2, K | | 8.3289, B are calculated, respectively*＝[0 0 0.0667]。
Fig. 4 is a fault estimation curve of the 3 rd aircraft, and it can be seen that the fault estimation curve 5s can achieve complete estimation of fault information, and the fault observer can rapidly achieve accurate estimation of a constant fault. Fig. 5 is a fault estimation curve for the 2 nd aircraft, when a time-varying fault occurs, the fault observer can almost completely estimate the actual fault information. Therefore, the fault observer can effectively realize the on-line estimation of the sudden change constant fault and the time-varying fault.
The system state quantity isWherein X represents a displacement in the X-axis direction,indicating the linear velocity in the x-axis direction. Defining the tracking error of the ith aircraft as exi＝xi(t)-x0(t), then exiIs the position tracking error in the x-axis direction; the second component is the velocity tracking error in the x-direction.
Fig. 6 is a plot of position tracking error versus time under the controller of the present disclosure, and fig. 7 is a plot of velocity tracking error versus time.
As is clear from fig. 6 and 7, the tracking errors of the 1 st and 4 th aircraft, which have no actuator failure, can be converged to zero quickly, although the 3 rd aircraft has a constant failure in the initial stage, the tracking error can also be converged to zero. And after the 2 nd aircraft has time-varying fault, the tracking error can be kept within a certain small range, and finally the tracking error converges to zero.
Claims (1)
1. An active fault-tolerant control method for multi-agent system actuator faults is characterized in that: when the multi-agent system has an actuator fault, an active fault-tolerant control method is provided by combining a fault diagnosis technology, so that the multi-agent system can normally operate after the actuator fault occurs; a distributed fault observer is constructed, a self-adaptive algorithm is designed to estimate a fault value, an active fault-tolerant controller is designed based on acquired fault information and combined with relative output information between intelligent agents, and the method comprises the following specific steps:
step 1) determining a model and parameters thereof of a piloting-following multi-agent system, comprising the following steps:
step 1.1) determining a motion model of a pilot, as shown in formula (1):
wherein,andrespectively a state variable, an input variable and an output variable of a pilot; d (t) is belonged to RrSatisfies | d for the external disturbance of the piloti(t)||∞A, B, D is a real matrix, C is a full rank matrix, D satisfies the matching condition D is BH, H is a constant matrix;
step 1.2) determining a motion model of the ith follower, as shown in formula (2):
wherein,andstate variables, input variables and output variables of the ith follower are respectively; di(t)∈RrSatisfies | d for the external disturbance of the ith followeri(t)||∞α ≦ α, α being a known constant, fi(t)∈RrRepresenting the actuator fault function occurring at the ith follower as an unknown function of time; A. b, D is a real matrix, C and E are full rank matrices, matrix D satisfies the matching condition D ═ BH, H is a constant matrix; e is failure scoreA distribution matrix representing the effect of failure of the follower system;
step 2) determining the communication topological structure of the multi-agent system:
navigation-following multi-agent system under undirected graph communication topology, graphRepresenting the information interaction situation between all nodes including follower and pilotA set of all the nodes is represented,representing a collection of communication links between the nodes,representing an adjacency matrix; assuming that the multi-agent system has n followers, a subgraph G ═ V, E, a represents a communication topology network between followers, where V ═ 1, 2.Representing a set of communication links between followers,an adjacency matrix representing diagram G; note the bookFor the Laplacian matrix of FIG. G, defineWherein lijIs as defined in formula (3):
the adjacency matrix between the pilot and the follower is defined asIf there is an undirected edge e between the pilot 0 and the ith follower0i＝(0，i)∈E0Then bi1 is ═ 1; otherwise, bi0; it is clear that,
step 3) designing a distributed fault observer, which comprises the following steps:
step 3.1) designing a fault observer for each follower, as shown in formula (4):
wherein,a state variable representing a fault observer,in order to output the variable, the output variable,is fi(t) estimated value, R represents the fault observer gain matrix, ξi(t) is the relative output estimation error of the ith follower, which is defined as shown in equation (5):
wherein,is the jth following output vector estimate, aijRepresenting the weight of the connection between the ith and jth followers, biRepresenting the weight of the connection between the i-th follower and the pilot, NiA set of neighbors representing the ith follower; since the pilot is a formation command generator, it is assumed that the state of the pilot is known, i.e. the pilot is a member of the formation command generatorIs established, thenIf true;
step 3.2) definitionThe error is estimated for the ith following state,for the fault estimation error, the ith following state estimation error equation is derived, as shown in equation (6):
step 3.3) designing a self-adaptive fault estimation algorithm, as shown in formula (7):
whereinIs fi(ii) an estimate of the value of (t),is a parameter matrix to be designed, and a fault estimation error equation is derived according to the parameter matrix, and is shown in a formula (8):
step 3.4) constructing an error amplification system, as shown in formula (9):
wherein,
to be considered from a distributed global perspective, the following global variables are defined:
obtaining a global estimation error system dynamic equation as shown in equation (10):
step 3.5) there are positive definite symmetric matrix Q and matrix S satisfying
Wherein,can be augmented by calculationBenefit matrixThereby ensuring a state estimation error exAnd error of fault estimation efConverge to zero;
step 4) designing a fault-tolerant controller, which comprises the following steps:
step 4.1) obtaining a fault estimation value according to the fault observer, as shown in formula (12):
wherein, tfIs the trigger time;
step 4.2) defining the relative output information v that the ith follower can obtainiAs shown in formula (13):
step 4.3) calculating the matrixSo that B*Satisfies formula (14);
(In-BB*)E＝0 (14)
wherein, InIs an n-order identity matrix;
step 4.4) designing a fault-tolerant control law for the ith follower, wherein the form is shown as a formula (15):
where K is the feedback gain to be designed, λ is the fixed coupling weight,is a fault estimation value;
and 4.5) substituting the formula (15) into the formula (2) to obtain a dynamic equation of the follower system, as shown in the formula (16):
defining a tracking error variable ei＝xi(t)-x0(t), disturbance variableObtaining a closed loop system dynamic equation as shown in equation (17):
the following global variables are defined:
and (3) rewriting the formula (17) into a vector form to obtain a closed-loop tracking error system, as shown in a formula (18):
step 4.6), selecting proper parameters to complete fault-tolerant control on the parameters, wherein a positive definite matrix P exists, and the matrix K and the parameter lambda satisfy the formula (19):
the matrix K and the parameter lambda can be obtained through calculation, so that the closed-loop tracking system is ensured to be asymptotically stable.
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