A quad-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant control method

Abstract

The application discloses a kind of four-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant control methods, belong to unmanned aerial vehicle control technical field;The application includes: the four-rotor unmanned aerial vehicle cluster dynamics model including unconstrained interference (including unbounded interference) and multiple faults is established;Augmented system enhances the representation ability of system to compound uncertainty;Distributed unknown input observer is constructed, and four-rotor unmanned aerial vehicle state, sensor fault and unconstrained collective interference are observed simultaneously;Four-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant controller is constructed;The application can realize four-rotor unmanned aerial vehicle cluster in multiple faults concurrent, unbounded disturbance coupling, keep good fault estimation accuracy, disturbance suppression capacity and collaborative control performance, enhance the flight safety and task reliability of four-rotor unmanned aerial vehicle cluster in complex environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle control, and particularly relates to a method for anti-interference and fault-tolerant control of a quad-rotor unmanned aerial vehicle cluster under multiple faults and unconstrained interference (including unbounded interference). BACKGROUND

[0002] In recent years, with the continuous progress of new materials, micro-electro-mechanical systems and control technology, quad-rotor unmanned aerial vehicle clusters have been widely used in disaster prevention and rescue, environmental exploration, police security and protection, cluster combat and many other fields due to their functional diversity and wide range of applications. However, quad-rotor unmanned aerial vehicle clusters are extremely susceptible to strong interference such as measurement noise, electromagnetic interference, weather changes, wind field disturbances and the like when performing tasks in harsh environments, which may in turn cause navigation deviation, loss of flight control, communication damage and the like, seriously affecting the overall performance and task completion of the quad-rotor unmanned aerial vehicle cluster system. Therefore, anti-interference control in the presence of external interference has achieved many excellent results, including sliding mode control methods, adaptive control methods, control methods based on disturbance observers and control methods based on filters. However, the above-mentioned anti-interference control methods often require that the interference or its derivative satisfy the boundedness condition, while in engineering practice, there are often unconstrained interference forms such as unbounded ramp interference and unbounded derivative square wave interference, which makes the traditional anti-interference method have obvious limitations in such unbounded interference scenarios. Although in recent years, there have been many research results on anti-interference strategies based on anti-interference observers, estimators and predictive control for unbounded interference, but often need to assume that the interference derivative is bounded, satisfies the Lipschitz constraint, and satisfies certain distribution characteristics, thus making the existing anti-interference control strategy unable to solve the completely unconstrained interference (including unbounded interference) problem.

[0003] In extreme and complex operating environments, quad-rotor unmanned aerial vehicle clusters often face high-intensity and long-duration task execution, which gradually increases the probability of physical component failure. In particular, key components such as actuators, sensors and control systems are susceptible to multiple failures caused by external factors. However, existing fault-tolerant control methods often target a single type of fault, such as individual actuator additive / multiplicative faults, sensor faults or process faults, and most require that the process fault amplitude be bounded, the derivative be bounded or the upper and lower bounds of the multiplicative fault factor be known. In actual systems, multiple fault phenomena such as actuator and sensor process faults, additive and multiplicative faults often exist simultaneously, and are easily coupled with external disturbances, component aging and other dynamic uncertainties, leading to complex fault characteristics. More seriously, when unconstrained interference (including unbounded interference) and multiple faults are coupled, the large amplitude characteristics of unconstrained interference (including unbounded interference) significantly amplify the influence of faults, making traditional fault-tolerant control methods ineffective.

[0004] Based on the above analysis, in order to ensure the robustness and fault tolerance of the quad-rotor unmanned aerial vehicle cluster under the condition of unconstrained disturbance (including unbounded disturbance) and multiple faults, the application proposes a new anti-interference fault-tolerant control method based on an unknown input observer. SUMMARY

[0005] The application aims to provide a quad-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant control method to solve the problems mentioned in the background art. The application innovatively solves the problems of unconstrained disturbance (including unbounded disturbance) and multiple faults which are difficult to handle by traditional methods, and realizes safe and reliable flight control of unmanned aerial vehicles under the coupling action of multiple faults and unconstrained disturbance (including unbounded disturbance).

[0006] In order to achieve the above application purpose, the application provides the following technical scheme:

[0007] A quad-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant control method, comprising the following steps:

[0008] S1, establishing a quad-rotor unmanned aerial vehicle cluster dynamics model containing unconstrained disturbance (including unbounded disturbance) and multiple faults;

[0009] S2, establishing an augmented system based on the dynamics model in S1 to enhance the representation ability of the dynamics model to complex uncertainties;

[0010] S3, designing a distributed unknown input observer, and using the observer to simultaneously observe the quad-rotor unmanned aerial vehicle state, sensor fault and unconstrained lumped disturbance;

[0011] S4, based on the output of the observer in S3, constructing a quad-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant controller to realize stable cooperative control of the unmanned aerial vehicle cluster under the condition of disturbance and fault.

[0012] Preferably, S1 specifically includes the following contents:

[0013] The kinematics model of a single quad-rotor unmanned aerial vehicle under unconstrained disturbance (including unbounded disturbance) is expressed as:

[0014]

[0015] Where x, y and z represent the position of the quad-rotor unmanned aerial vehicle in the inertial coordinate system; φ, θ and ψ represent the roll angle, pitch angle and yaw angle of the unmanned aerial vehicle, respectively; x , I y and I z represent the moment of inertia of the quad-rotor unmanned aerial vehicle along each axis of the body coordinate system; I r represents the moment of inertia of the propeller; u z represents the total thrust generated by the four propellers; u φ , uθ and u ψ denote the roll moment, pitch moment and yaw moment of the quadrotor, respectively; d h (h = 1, 2,..., 4) denote unbounded disturbances; m denotes the mass of the quadrotor; g denotes the gravity acceleration; Ω r denotes the differential angular velocity of the quadrotor's propellers.

[0016] It is assumed that the quadrotor is moving in a near hover state, which means that in the vertical direction u z ≈ mg, the pitch angle and roll angle are small enough to satisfy sin φ ≈ φ and sin θ ≈ θ, and the quadrotor does not produce yaw motion (ψ = 0) during flight. Therefore, the linearization of equation (1) can be performed, and the simplified linear model is:

[0017]

[0018] Let x = [x, y, z, φ, θ, ψ] as the system state vector, u = [u z , u φ , u θ , u ψ ] T ∈ R p as the control input vector, d = [d1, d2, d3, d4] T ∈ R q as the external disturbance vector, y = [x, y, z, φ, θ, ψ] T ∈ R m as the measurement output vector, then the linear dynamics model of the quadrotor can be expressed as:

[0019]

[0020] where:

[0021]

[0022] G = [0 0 0 0 0 -1 0 0 0 0 0 0] T

[0023] The propulsion system of the quadrotor UAV is composed of four identical brushless motors and four fixed-pitch propellers. Since the motor or propeller may fail, resulting in the actuator unable to operate normally, this will significantly reduce the safety and reliability of the quadrotor UAV. At the same time, accurate path tracking relies on the reliable measurement of sensors. However, the harsh environment in which the UAV cluster is located and the aging of the sensors themselves make the UAV cluster vulnerable to interference and sensor failure. Since Gg is a constant matrix, it can be regarded as the interference part. Thus, based on equation (3), the mathematical model of the ith UAV in the quadrotor UAV cluster under multiple failures and unconstrained interference (including unbounded interference) is described as:

[0024]

[0025] where N represents the number of UAVs in the quadrotor UAV cluster; i represents the actuator additive fault, i represents the sensor fault, The input of the system contains multiplicative faults, which can be specifically represented as:

[0026]

[0027] where l represents the lth actuator channel, ρ il represents the actuator efficiency loss factor. Consider the following cases: if ρ il (t) = 0, the lth actuator has no actuator multiplicative fault; if 0 < ρ il (t) < 1, the lth actuator has a partial efficiency loss fault; if ρ il (t) < 0, it indicates that the lth actuator has an overload fault. Let u i (t) = [u i1 (t), …, u i4 (t)] T , and the actuator efficiency loss factor ρ i (t) = diag(ρ i1 (t), …, ρ i4 (t)), the compact model of the control input containing actuator multiplicative faults can be described as:

[0028]

[0029] Preferably, the S2 specifically includes the following content:

[0030] An augmented system containing the state of the quadrotor UAV and the actuator fault is established:

[0031]

[0032] where C1 = [C E]

[0033] Aggregate disturbance w in augmented system i (t) is expressed as:

[0034] w i (t) = -p i (t)u i (t) + f a,i (t) + d i (t) (8)

[0035] It can be seen that the aggregate disturbance covers the unbounded disturbance, multiplicative and additive actuator faults, so that it is very challenging to accurately estimate such aggregate disturbance.

[0036] Preferably, the S3 specifically comprises the following contents:

[0037] Design a novel unknown input observer:

[0038]

[0039] wherein, and are the estimates of the system state x i (t) and the sensor fault f s,i (t) respectively; and are the estimates of the system output and the aggregate disturbance respectively; is the first derivative of the system output, and S, R are the gain matrices of the unknown input observer.

[0040] Define as the estimation error of the augmented state of the UAV, and it can be obtained that:

[0041]

[0042] wherein, is the estimation error of the aggregate disturbance.

[0043] Preferably, the S4 specifically comprises the following contents:

[0044] Construct a fault-tolerant controller:

[0045] In combination with the observer design part of S3, the controller is designed as:

[0046]

[0047] wherein, is the consensus error of the quadrotor UAV cluster system state. K is the controller gain, which can be obtained by solving the following linear matrix inequality:

[0048]

[0049] wherein,

[0050]

[0051] wherein, Q1 and Q2 are positive definite matrices, Q3 = Q2S is a matrix of appropriate dimension, L is the Laplacian matrix of the quadrotor UAV swarm, λ max (·) and λ min (·) represent the maximum and minimum eigenvalues of the matrix respectively, is a symmetric matrix, 1 N is an N-dimensional all-1 vector, I is a unit matrix of appropriate dimension, R and S are gain matrices of the unknown input observer, R is also solved by the linear matrix inequality described in equation (11). The expression of S is:

[0052]

[0053] Compared with the prior art, the beneficial effects of the present application are:

[0054] 1) The present application establishes a new type of lumped interference model, which covers unconstrained interference (including unbounded interference) and multiplicative / additive actuator faults. The method of the present application eliminates the assumptions that the existing methods require the derivative of the interference to be bounded, satisfy the Lipschitz condition, be normally distributed, etc., and is suitable for more complex scenarios.

[0055] 2) The present application uses an augmented system that contains state information and sensor fault information to design a new type of unknown input observer, reducing the design difficulty and computational complexity of the observer. Further, the simultaneous online estimation of system state, sensor fault and unconstrained lumped interference (including unbounded interference) is realized, improving the performance of the UAV in complex scenarios.

[0056] 3) The present application formulates a fault-tolerant control strategy by using real-time estimation information obtained by the observer and designs a distributed fault-tolerant controller based on a disturbance compensation mechanism, which can achieve anti-interference and fault-tolerant control of the quadrotor UAV swarm. In addition, the fault-tolerant control method based on the unknown input observer realizes the decoupling of the lumped interference and the error system, reducing the complexity of solving the observer gain matrix. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 is a flow chart of the anti-interference and fault-tolerant control method for the quadrotor UAV swarm of the present application. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application.

[0059] The present application provides a quad-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant control method, so that the quad-rotor unmanned aerial vehicle cluster can realize accurate decoupling estimation of the quad-rotor unmanned aerial vehicle state and fault under the coupling action of unconstrained interference (including unbounded interference) and multiple faults, and a distributed fault-tolerant control strategy with strong robustness is constructed, so as to break through the strict constraints of existing methods on interference and fault types, and improve the overall performance of the quad-rotor unmanned aerial vehicle cluster in complex environments. The quad-rotor unmanned aerial vehicle cluster anti-interference and fault-tolerant control method proposed in the present application will be described below in combination with related drawings and specific examples, and the specific content is as follows.

[0060] Embodiment 1:

[0061] As shown in Figure 1 , the present application provides a quad-rotor unmanned aerial vehicle fault estimation and fault-tolerant control method, which comprises:

[0062] S101, a quad-rotor unmanned aerial vehicle cluster dynamics model containing unconstrained interference (including unbounded interference) and multiple faults is established, which specifically comprises the following contents:

[0063] The kinematic model of a single quad-rotor unmanned aerial vehicle under unconstrained interference (including unbounded interference) is expressed as:

[0064]

[0065] Wherein, x, y and z represent the position of the quad-rotor unmanned aerial vehicle in the inertial coordinate system; φ, θ and ψ represent the roll angle, pitch angle and yaw angle of the unmanned aerial vehicle respectively; I x , I y and I z represent the moment of inertia of the quad-rotor unmanned aerial vehicle along each axis of the body coordinate system; I r represents the moment of inertia of the propeller; u z represents the total thrust generated by the four propellers; u φ , u θ and u ψ represent the roll moment, pitch moment and yaw moment of the quad-rotor unmanned aerial vehicle respectively; d h (h = 1, 2, …, 4) represents external unconstrained interference (including unbounded interference); m represents the mass of the quad-rotor unmanned aerial vehicle; g represents the gravitational acceleration; Ω r represents the differential angular velocity of the propeller of the quad-rotor unmanned aerial vehicle.

[0066] It is assumed that the quad-rotor unmanned aerial vehicle moves in an approximate hovering state, which means that in the vertical direction uz ≈mg, the pitch angle and roll angle are small enough to satisfy sinφ≈φ and sinθ≈θ, and the quadrotor UAV does not generate yaw motion (ψ = 0) during flight. Therefore, Equation (1) can be linearized, and the simplified linear model is:

[0067]

[0068] Taking as the system state vector, u = [u z , u φ , u θ , u ψ T ∈R p as the control input vector, d = [d1, d2, d3, d4] T ∈R q as the external disturbance vector, y = [x, y, z, φ, θ, ψ] T ∈R m as the measurement output vector, then the linear dynamic model of the quadrotor UAV can be expressed as:

[0069]

[0070] In the formula:

[0071]

[0072]

[0073] G = [0 0 0 0 0 -1 0 0 0 0 0 0] T

[0074] The propulsion system of the quadrotor UAV consists of four identical brushless motors and four fixed-pitch propellers. Due to possible failures of the motors or propellers, the actuators may not operate properly, which will significantly reduce the safety and reliability of the quadrotor UAV. At the same time, precise path tracking depends on reliable measurements of sensors. However, due to the harsh environment in which the UAV swarm is located and the aging of the sensors themselves, the UAV swarm is vulnerable to interference and sensor failures. Since Gg is a constant matrix, it can be regarded as the interference part. Thus, based on Equation (3), the mathematical model description of the i-th UAV in the quadrotor UAV swarm under multiple faults and unconstrained disturbances (including unbounded disturbances) is:

[0075]

[0076] where N represents the number of UAVs in the quadrotor UAV swarm; 尻, i represents the actuator additive fault; 尻, i represents the sensor fault, [[ID=5S]] ​To include the input with multiplicative actuator faults, it can be expressed as:

[0077]

[0078] where l represents the lth actuator channel, ρ il represents the actuator efficiency loss factor.

[0079] If ρ il (t) = 0, the lth actuator has no actuator multiplicative fault; if 0 < ρ il (t) < 1, the lth actuator has partial efficiency loss fault; if ρ il (t) < 0, it means that the lth actuator has overload fault. Denote u i (t) = [u i1 (t), …, u i4 (t)] T , and the actuator efficiency loss factor ρ i (t) = diag(ρ i1 (t), …, ρ i4 (t)), the control input compact model with actuator multiplicative fault can be described as:

[0080]

[0081] S102, an augmented system is established, the state of the quadrotor unmanned aerial vehicle and the sensor fault form an augmented state vector, the representation ability of the system to the compound uncertainty is enhanced, and the specific contents include the following:

[0082] An augmented system including the state of the quadrotor unmanned aerial vehicle and the actuator fault is established:

[0083]

[0084] wherein, C1 = [C E];

[0085] The lumped disturbance w i (t) in the augmented system is expressed as:

[0086] w i (t) = -ρ i (t)u i (t) + f a,i (t) + d i (t) (8)

[0087] It can be seen that the lumped disturbance covers the unbounded disturbance, multiplicative and additive actuator faults, so that it is very challenging to accurately estimate such lumped disturbance.

[0088] S103, design a distributed unknown input observer, which can not only observe the system state and sensor fault simultaneously, but also observe the lumped disturbance, including actuator additive fault, actuator partial loss fault and unconstrained disturbance (including unbounded disturbance). Specifically, it includes the following contents:

[0089] Construct a novel unknown input observer:

[0090]

[0091] Where, And are the estimates of the system state x i (t) and sensor fault f s,i (t), respectively; And are the estimates of the system output and the lumped disturbance, respectively; is the first derivative of the system output, and S and R are the gain matrices of the unknown input observer.

[0092] Define as the estimation error of the augmented state of the UAV, which can be obtained as:

[0093]

[0094] Where, is the estimation error of the lumped disturbance, which can be derived as:

[0095]

[0096] Where, (C1B1) + (C1B1) = I. If the following constraint condition is satisfied Then the estimation error of the lumped disturbance can be simplified as:

[0097]

[0098] Then the estimation error (10) of the augmented system can be simplified as:

[0099]

[0100] S104, based on the state / fault estimation information of the observer output, design a robust controller with disturbance compensation characteristics to ensure the robustness and safety of the quadrotor UAV cluster, which includes the following contents:

[0101] The fault-tolerant controller can be established as:

[0102]

[0103] Where, is the consensus error of the quadrotor UAV swarm system, is the estimation of the lumped disturbance, which can be obtained by the observer. The solution of the controller gain matrix K is based on Lyapunov stability theory, which guarantees the asymptotic stability of the system by ensuring the derivative of the Lyapunov function of the closed-loop system to be negative definite.

[0104] Substituting the designed controller (14) into equation (4) gives

[0105]

[0106] By introducing the Kronecker product, the above equation can be written in a compact matrix form as

[0107]

[0108] Define and Further, we have and where L is the Laplacian matrix of the system.

[0109] Therefore, the consensus error of the quadrotor UAV swarm system is

[0110]

[0111] The present application provides the following verification steps to verify that the fault-tolerant controller obtained in S104 meets the requirements of the quadrotor UAV system described in the present application to still be able to operate stably in the presence of multiple faults and disturbances. The specific content is as follows:

[0112] According to the system error state equation (13) and the consensus error equation (17), a suitable Lyapunov function is constructed:

[0113]

[0114] where, Q1,Q2 are symmetric positive definite matrices.

[0115] Taking the derivative of the above Lyapunov function gives

[0116]

[0117] where,

[0118]

[0119] where, λ max (·) and λ min (·) represent the maximum and minimum eigenvalues of the matrix respectively, is a symmetric matrix, 1N is a N-dimensional all-one vector, and I is a unit matrix with appropriate dimension.

[0120] For the convenience of solving linear matrix inequality, let Q3=Q2S, and the decoupled matrix is obtained as follows:

[0121]

[0122] wherein,

[0123]

[0124] When the above linear matrix inequality is established, V i (t)<0, which proves the stability of the system and guarantees the robustness and safety of the quad-rotor unmanned aerial vehicle cluster.

[0125] The application aims at the anti-interference and fault-tolerant control problem of quad-rotor unmanned aerial vehicle cluster, and proposes a new fault-tolerant control scheme based on an unknown input observer. The application realizes the synchronous and accurate estimation of the system state, sensor fault and unbounded disturbance by innovatively designing an unknown input observer, and breaks through the assumption limit of the known upper bound of disturbance of the existing method. Based on the output information of the observer, a fault-tolerant control strategy is constructed, which ensures the flight stability of the closed-loop system under the action of multiple concurrent faults and unbounded disturbance.

[0126] It should be noted that in the present application, the relationship terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between the entities or operations.

[0127] The above is only the preferred embodiment of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can make equivalent replacement or change according to the technical solution and inventive concept of the present application within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for anti-interference and fault-tolerant control of quadrotor unmanned aerial vehicle (UAV) swarms, characterized in that, Includes the following steps: S1. Establish a dynamic model of a quadrotor UAV swarm, including unconstrained disturbances, unbounded disturbances, and multiple faults; specifically, it includes the following: The kinematic model of a single quadcopter UAV under unconstrained disturbance, including unbounded disturbance, is represented as: (1) in, x, y and z This indicates the position of the quadcopter drone in the inertial coordinate system; , θ and ψ These represent the roll angle, pitch angle, and yaw angle of the UAV, respectively. I x , I y and I z These represent the moments of inertia of the quadrotor UAV along each axis of the body coordinate system; I r This represents the moment of inertia of the propeller. u z This represents the total thrust generated by the four propellers; , and These represent the roll moment, pitch moment, and yaw moment of a quadcopter drone, respectively. d h This indicates unconstrained interference, h=1,2,…,4; m This indicates the mass of the quadcopter drone; g Represents gravitational acceleration; This represents the differential angular velocity of the propeller of a quadcopter drone; Assuming a quadcopter drone moves in a near-hovering state, its vertical direction u z ≈mg, pitch angle and roll angle satisfy and Furthermore, the quadcopter UAV did not exhibit yaw motion during flight; based on this, equation (1) is linearized, and the simplified linear model is: (2) Will As the system state vector; As a control input vector; As an external interference vector; As a measurement output vector; Based on the above, the linear dynamics model of the quadcopter UAV can be expressed as follows: (3) In the formula: Therefore, based on equation (3), the fourth in the quadcopter drone swarm is... i The mathematical model of a UAV under multiple faults and unconstrained disturbances including unbounded disturbances is described as follows: (4) in, N This indicates the number of drones in a quadcopter drone swarm; f a,i This indicates an additive fault in the actuator; f s,i This indicates a sensor malfunction; For inputs to a system containing multiplicative faults, specifically: (5) in, l Indicates the first l One actuator channel; ρ il This represents the actuator efficiency loss factor; if ρ il ( t If )=0, then the first l There are no actuator multiplication faults in any actuator; if 0 < ρ il ( t If ) < 1, then the first l One actuator experiences a partial efficiency loss failure; if ρ il ( t If ) < 0, then it means the first digit is 0. l One actuator experienced an overload failure; remember u i ( t )=[ u i1 ( t ),…, u i4 ( t )] T And the actuator efficiency loss factor ρ i ( t =diag( ρ i1 ( t ),…, ρ i4 ( t The compact model of control inputs containing actuator multiplicative faults is described as follows: (6) S2. Construct an augmented system based on the dynamic model described in S1 to enhance the dynamic model's ability to represent complex uncertainties; specifically, this includes the following: Establish an augmented system that includes the status of quadcopter UAVs and actuator malfunctions: (7) in, , , , ; Lumped interference in the augmented system w i ( t ) is represented as: (8) S3. Design a distributed unknown input observer to simultaneously observe the state of a quadcopter UAV, sensor failures, and unconstrained lumped interference. S4. Based on the output of the observer described in S3, construct a quadcopter UAV swarm anti-interference and fault-tolerant controller to achieve stable and coordinated control of the UAV swarm under interference and fault conditions.

2. The anti-interference and fault-tolerant control method for quadrotor UAV swarms according to claim 1, characterized in that, S3 specifically includes the following: The distributed unknown input observer is designed as follows: (9) in, , and Representing the system state respectively x i ( t ) and sensor failure f s,i ( t The estimate; These represent the estimates of the system output and lumped disturbance, respectively. This represents the first derivative of the system output; S , R This represents the gain matrix of the unknown input observer.

3. The anti-interference and fault-tolerant control method for quadcopter UAV swarms according to claim 1, characterized in that, S4 specifically includes the following: The fault-tolerant controller is designed as follows: (10) in, For the state consistency error of the quadcopter drone swarm system; K The controller gain is obtained by solving the following linear matrix inequality: (11) in, (12) in, Q 1 and Q 2 is a positive definite matrix. Q 3= Q 2 S For a matrix of appropriate dimension, L For the Laplace matrix of a quadcopter drone swarm, λ max (·)and λ min (·) represent the maximum and minimum eigenvalues ​​of the matrix, respectively. It is a symmetric matrix, 1 N for N A 1-dimensional vector; I An identity matrix of appropriate dimension; S , R Let be the gain matrix of the unknown input observer; where, S The solution formula is: (13) R The solution is obtained by using the linear matrix inequality in equation (11).

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