Stratospheric airship distributed time-varying formation control method based on affine transformation

Abstract

The invention discloses a stratospheric airship distributed time-varying formation control method based on affine transformation, and belongs to the technical field of formation control, and the method comprises the following steps: 1, measuring the motion state of an airship through a sensor, 2, generating an expected formation, and transmitting the expected formation to a navigator in a cluster, 3, setting a communication structure for the interior of the airship cluster, 4, calculating an expected attitude of the follower airship, 5, setting an aided design system for the follower airship to obtain a virtual control law saturation compensation amount and an execution mechanism saturation compensation value, 6, setting an adaptive law for the follower airship to obtain an adaptive estimated value, and 7, calculating an expected attitude of the follower airship. And 7, calculating the control quantity of the expected formation and attitude of the follower airship by using a reverse distribution controller according to the results in the steps 3-5. By adopting the method, the time-varying formation control of the stratospheric airship can be realized under the condition that global information is not needed; and the state of the airship in the formation maneuvering process of the airship cluster can be ensured to be within a limited range.

Description

Technical Field

[0001] The invention relates to the technical field of formation control, and in particular to a distributed time-varying formation control method for stratospheric airships based on affine transformation. Background Art

[0002] As one of the ideal platforms for near-space exploration, stratospheric airships have great application value. At the same time, stratospheric airship clusters have more advantages than single flights in reconnaissance, observation, communication relay and regional coverage. The above tasks usually require stratospheric airship clusters to perform formation cruise and maneuvering in a complex stratospheric environment, which means that the airship formation needs to have sufficient flexibility. Distributed formation control, as the core technology of airship formation application, has received widespread attention in recent years. However, few people have studied how to improve the flexibility of the airship system's formation.

[0003] In recent years, formation maneuver control has become an effective method to improve the flexibility of formation maneuvers. In order to achieve formation maneuver control, in the early stage, three formation control algorithms were proposed by imposing constant constraints on relative displacement, distance and azimuth. Considering that the constraints describing the formation are not universally applicable to all maneuvers, the displacement-based method only allows translational maneuvers, the distance-based method also allows rotational maneuvers, and the azimuth-based method can further realize scaling maneuvers. It is worth mentioning that the above methods still have an irreplaceable role in certain specific scenarios. For example, the agent using the distance-based method can measure the required signal through local sensors without pre-calibrating the coordinate system, which is suitable for environments without positioning signals. However, their inflexibility still limits the ability to complete complex tasks. In the field of stratospheric airship cluster control, there are still few results related to improving the flexibility of formations, and how to improve the flexibility of stratospheric airship formations still needs to be studied urgently.

[0004] Another issue that cannot be ignored in the formation control of a stratospheric airship cluster is error constraints. During formation maneuvers, certain position and attitude errors must be maintained to simultaneously perform observation or communication tasks. Error constraints include position error constraints related to the coverage area, attitude error constraints related to target observation, and speed and angular velocity error constraints related to structural strength. Exceeding the error limit may lead to communication interruption, failure to observe the predetermined area, damage to the platform structure, or other unforeseen consequences. Therefore, during the formation maneuver, the state error of the cluster system must be controlled within an acceptable range. Based on this, the present invention proposes a distributed time-varying formation control method for stratospheric airships based on affine transformation. Summary of the invention

[0005] The purpose of the present invention is to provide a distributed time-varying formation control method for stratospheric airships based on affine transformation. Based on the affine transformation theory, a formation maneuvering control method for stratospheric airships is designed, which can realize the time-varying formation control of stratospheric airships without the need for global information. At the same time, based on the obstacle Lyapunov theory, the state restriction problem of the airship is converted into a saturation error problem, and is solved by introducing an auxiliary design system method, so as to ensure that the state of the airship is within the restriction range during the formation maneuvering of the airship cluster.

[0006] To achieve the above object, the present invention provides a distributed time-varying formation control method for stratospheric airships based on affine transformation, comprising the following steps:

[0007] S1. Use sensors to measure the motion state of the airship;

[0008] S2, generate the desired formation and send it to the leader in the cluster;

[0009] S3, after the leader obtains the desired formation, it sets up the communication structure within the airship cluster;

[0010] S4. After the communication structure is set, the expected attitude of the follower airship is calculated;

[0011] S5. After obtaining the expected posture of each follower airship, an auxiliary design system is set for the follower airship to obtain the saturation compensation amount of the virtual control law and the saturation compensation value of the actuator;

[0012] S6, setting an adaptive law for the follower airship to obtain an adaptive estimation value;

[0013] S7. Use the anti-cloth controller to calculate the control amount of the desired formation and attitude of the follower airship according to the results in S3 to S5.

[0014] Preferably, the motion state of the airship in S1 includes position, speed, attitude angle and attitude angular velocity, and the data is transmitted to the backstepping controller.

[0015] Preferably, the process of generating the desired formation in S2 is as follows:

[0016] S21. Set the initial nominal configuration r, which is expressed as:

[0017] r=[r1,...,r N ];

[0018] ν l ={1,...,N l ];

[0019] v f = {N l +1,...,N};

[0020] Where N represents the number of airships, N l represents the number of pilot airships, v l represents the set of pilot airships, v f represents the collection of follower airships;

[0021] S22. Use affine transformation to obtain the desired formation p for the initial nominal configuration * (t), the process is as follows:

[0022]

[0023]

[0024] Among them I N ∈R N×N represents the identity matrix, represents the maneuver matrix representing the rotation, scaling, and shearing of the formation, b(t)R 3×1 represents the maneuver matrix representing the formation translation, represents the expected position of the i-th airship, 1 N represents the N-order identity matrix;

[0025] S23. Decompose the expected formation to obtain:

[0026]

[0027] in represents the desired formation of the pilot airship, Indicates the formation of follower airships;

[0028] S24, transmitting the desired formation of the navigator to the navigator to obtain the actual formation of the navigator p l :

[0029]

[0030] Preferably, the process of setting the communication structure in S3 is:

[0031] S31. Set a topology matrix

[0032] S32. Use the topology matrix in S31 to define the communication structure within the airship cluster, expressed as:

[0033]

[0034] where ω ij represents the corresponding topological gain between airship i and airship j;

[0035] like Indicates that there is no communication between airship i and airship j. If Indicates that airship i and airship j are neighbors;

[0036] S33. Install communications structures for all airships prior to flight.

[0037] Preferably, the process of calculating the expected posture of the follower airship in S4 is:

[0038] S41, deploying an expected attitude generator on each follower airship, and using the expected attitude generator to obtain the flight attitude of each follower airship at this time;

[0039] S42, calculate the follower blocks according to the topology matrix in S3, the calculation process is:

[0040]

[0041] in Represents the matrix after the topological matrix is ​​multiplied by the third-order matrix, and represents the follower block, I3 represents the third-order identity matrix;

[0042] S43, calculating the expected attitude of the follower airship, the calculation process is as follows:

[0043]

[0044] in represents the desired posture of the i-th follower airship, φ * ,θ * and ψ * Indicates the flight attitude of the follower airship. represents the expected position of the ith follower airship, z pj represents the distributed position error of each neighbor of the follower airship, ω k,j represents the corresponding topological gain between airship k and airship j, p j represents the expected position of the jth airship, j∈N i , p k represents the expected position of the kth airship, k∈N j .

[0045] Preferably, the process of obtaining the virtual control law saturation compensation amount and the actuator saturation compensation value in S5 is as follows:

[0046] S51. Arrange a first-order auxiliary design system and a second-order auxiliary design system on each follower airship;

[0047] S52, calculating the current virtual control law of the follower airship, the calculation process is as follows:

[0048]

[0049] The saturation error of the virtual control law is calculated according to the virtual control law: in:

[0050]

[0051] in represents the inverse of the transformation matrix that transforms the angular velocity of the airship from the body axis system to the earth axis system, α i =diag{α i1 ,α i2 ,α i3 ,α i4 ,α i5 ,α i6} represents the control law parameters to be selected, α ij >0,j=1,2,…,6,ω ij represents the corresponding topological gain between airship i and airship j, z 1i represents the first-order distributed error, ξ ξi It represents the saturation compensation of the virtual control law output by the first-order auxiliary design system. represents the derivative of the position of airship j;

[0052] S53, input the virtual control law and the first-order distributed error into the first-order auxiliary design system, and obtain the saturation compensation amount of the virtual control law through the formula, which is as follows:

[0053]

[0054] in Both represent the backstepping controller parameters to be designed, b ξj represents the first-order distributed error limit b ξ Elements of z 1ij Represents the element of the first-order distributed error, z 1i =[z 1i1 ,...,z 1i6 ], express The derivative of the output intermediate variable is the saturation compensation of the virtual control law;

[0055] S54, input the actuator saturation value and the second-order distributed error into the second-order auxiliary design system to obtain the actuator saturation compensation value, and the calculation process is as follows:

[0056]

[0057] in are the backstepping controller parameters to be designed. represents the saturation error of the control law, z 2ij is the second-order distributed error z 2i The element z 2i =[z 2i1 ,...,z 2i6 ], yes The derivative of the output intermediate variable is the actuator saturation compensation value;

[0058] S55, inputting the virtual control law saturation compensation amount and the actuator saturation compensation value into the backstepping controller.

[0059] Preferably, the dynamic model of the stratospheric airship is used, and the six-degree-of-freedom dynamic model is as follows:

[0060]

[0061] where ζ i =[x i ,y i ,z i ,φ i ,θ i ,ψ i ] T represents the three-dimensional coordinates and attitude angle of the stratospheric airship, represents the projection of the airship's velocity in the body axis system and the projection of the airship's angular velocity in the body axis system, f1(ζ i ) represents the coordinate transformation matrix that transforms the airship state quantity in the body axis system to the earth axis system. represents the aerodynamic force and aerodynamic moment of the airship, B represents the inverse of the airship mass and inertia matrix, τ' i =[τ'1,τ'2,τ'3,τ'4,τ'5,τ'6] T , represents the control amount of airship i, δ i =[δ u ,δ v ,δ w ,δ p ,δ q ,δ r ] represents the unknown uncertainty in the airship model consisting of unknown external disturbances and unmodeled dynamics, i∈N.

[0062] Preferably, the process of obtaining the adaptive estimated value in S6 is as follows:

[0063] S61. An adaptive law is arranged on each follower airship;

[0064] S62, input the second-order distributed error of the follower airship into the adaptive law to obtain an adaptive estimated value, the process is as follows:

[0065]

[0066] in represents the adaptive estimate, γ i,j >0,γ i0 >0 indicates the controller parameters to be designed, yes The derivative of j represents a diagonal matrix, I1=diag{1,0,0,0,0,0}, I2=diag{0,1,0,0,0,0}, ..., I6=diag{0,0,0,0,0,6}, represents the backstepping controller parameters to be designed.

[0067] Preferably, the process of calculating the control amount of the desired formation and attitude of the follower airship in S7 is as follows:

[0068] S71, inputting the current motion state, expected posture, virtual control law saturation compensation amount, actuator saturation compensation value and adaptive law estimation value of the follower airship into the backstepping controller;

[0069] S72, using the backstepping controller to calculate the attitude control value τ of the follower airship i , the process is as follows:

[0070]

[0071] where β i =diag{β i1 ,...,β i6}, β ij >0 indicates the controller parameters to be designed;

[0072] S73, obtaining a desired formation of the follower airship tracking time-varying according to the attitude control amount of the follower airship;

[0073] S74. Obtain a distributed time-varying formation of stratospheric airships according to the expected formation of the leader airship and the expected formation of the follower airships tracking the time-varying formation.

[0074] Therefore, the present invention adopts a stratospheric airship distributed time-varying formation control method based on affine transformation with the above structure, which has the following advantages:

[0075] 1. Based on the affine transformation theory, a formation maneuvering control method for stratospheric airships is designed, which can realize the time-varying formation control of stratospheric airships without the need for global information, thus improving the flexibility of the formation;

[0076] 2. Based on the obstacle Lyapunov theory, the problem of airship state limitation is converted into a saturation error problem, and solved by introducing the method of auxiliary design system to ensure that the state of the airship is within the limit during the formation maneuver of the airship cluster;

[0077] 3. No need to transmit global information to each airship, reducing the requirement for communication bandwidth;

[0078] 4. The auxiliary design system is used to deal with the saturation problem, which improves the actuator saturation problem;

[0079] 5. Adopting adaptive law to estimate unknown disturbances of the environment and uncertainties in the model, and passing the estimated values ​​to the backstepping sliding mode controller, the airship can still track the desired trajectory under the influence of external disturbances.

[0080] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a diagram of the execution process of a distributed time-varying formation control method of stratospheric airships based on affine transformation of the present invention;

[0082] Figure 2 The present invention is a flow chart of a distributed time-varying formation control method for stratospheric airships based on affine transformation. DETAILED DESCRIPTION

[0083] Example

[0084] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0085] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0087] In the description of the present invention, it should be noted that the terms "upper", "lower", "inside", "outside", etc. indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, or are directions or positional relationships in which the product of the invention is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present invention.

[0088] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "setting", "installation" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0089] Some embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0090] like Figure 1 and Figure 2 As shown, the present invention provides a distributed time-varying formation control method for stratospheric airships based on affine transformation, comprising the following steps:

[0091] S1, using sensors to measure the motion state of the airship, including position, velocity, attitude angle and attitude angular velocity, and transmit the data to the backstepping controller;

[0092] S2, generate the desired formation and send it to the leader in the cluster;

[0093] S21. Set the initial nominal configuration r, which is expressed as:

[0094] r=[r1,...,r N ];

[0095] ν l ={1,...,N l};

[0096] v f = {N l +1,...,N};

[0097] Where N represents the number of airships, N l represents the number of pilot airships, v l represents the set of pilot airships, v f represents the collection of follower airships;

[0098] S22. Use affine transformation to obtain the desired formation p for the initial nominal configuration * (t), the process is as follows:

[0099]

[0100]

[0101] Among them I N ∈R N×N represents the identity matrix, represents the maneuver matrix representing the rotation, scaling, and shearing of the formation, b(t)R 3×1 represents the maneuver matrix representing the formation translation, represents the expected position of the i-th airship, 1 N represents the N-order identity matrix;

[0102] S23. Decomposing the expected formation can yield:

[0103]

[0104] in represents the desired formation of the pilot airship, Indicates the formation of follower airships;

[0105] S24, transmitting the desired formation of the navigator to the navigator to obtain the actual formation of the navigator p l :

[0106]

[0107] S3, after the leader obtains the desired formation, it sets up the communication structure within the airship cluster;

[0108] S31. Set a topology matrix

[0109] S32. Use the topology matrix in S31 to define the communication structure within the airship cluster, expressed as:

[0110]

[0111] where ω ij represents the corresponding topological gain between airship i and airship j;

[0112] like Indicates that there is no communication between airship i and airship j. If Indicates that airship i and airship j are neighbors;

[0113] S33. Install communications structures for all airships prior to flight.

[0114] S4. After the communication structure is set, the expected attitude of the follower airship is calculated;

[0115] S41, deploying an expected attitude generator on each follower airship, and using the expected attitude generator to obtain the flight attitude of each follower airship at this time;

[0116] S42, calculate the follower blocks according to the topology matrix in S3, the calculation process is:

[0117]

[0118] in Represents the matrix after the topological matrix is ​​multiplied by the third-order matrix, and represents the follower block, I3 represents the third-order identity matrix;

[0119] S43, calculating the expected attitude of the follower airship, the calculation process is as follows:

[0120]

[0121]

[0122] in represents the desired posture of the i-th follower airship, φ * ,θ * and ψ * Indicates the flight attitude of the follower airship. represents the expected position of the ith follower airship, z pj represents the distributed position error of each neighbor of the follower airship, ω k,j represents the corresponding topological gain between airship k and airship j, p j represents the expected position of the jth airship, j∈N i represents the neighbors of the i-th airship, p k represents the expected position of the kth airship, k∈N j denotes the neighbors of the j-th airship.

[0123] S5. After obtaining the expected posture of each follower airship, an auxiliary design system is set for the follower airship to obtain the saturation compensation amount of the virtual control law and the saturation compensation value of the actuator;

[0124] S51. Arrange a first-order auxiliary design system and a second-order auxiliary design system on each follower airship;

[0125] S52, calculating the current virtual control law of the follower airship, the calculation process is as follows:

[0126]

[0127] The saturation error of the virtual control law is calculated according to the virtual control law: in:

[0128]

[0129] in represents the inverse of the transformation matrix that transforms the angular velocity of the airship from the body axis system to the earth axis system, α i =diag{α i1 ,α i2 ,α i3 ,α i4 ,α i5 ,α i6} represents the control law parameters to be selected, α ij >0,j=1,2,…,6,ω ij represents the corresponding topological gain between airship i and airship j, z 1i represents the first-order distributed error, It represents the saturation compensation of the virtual control law output by the first-order auxiliary design system. represents the derivative of the position of airship j;

[0130] S53, input the virtual control law and the first-order distributed error into the first-order auxiliary design system, and obtain the saturation compensation amount of the virtual control law through the formula, which is as follows:

[0131]

[0132] in Both represent the backstepping controller parameters to be designed, b ξj represents the first-order distributed error limit b ξ Elements of z 1ij Represents the element of the first-order distributed error, z 1i =[z 1i1 ,...,z 1i6 ], express The derivative of the output intermediate variable is the saturation compensation of the virtual control law;

[0133] S54, input the actuator saturation value and the second-order distributed error into the second-order auxiliary design system to obtain the actuator saturation compensation value, and the calculation process is as follows:

[0134]

[0135] in are the backstepping controller parameters to be designed. represents the saturation error of the control law, z 2ij is the second-order distributed error z 2i The element z 2i =[z 2i1 ,...,z 2i6 ], yes The derivative of the output intermediate variable is the actuator saturation compensation value;

[0136] S55, inputting the virtual control law saturation compensation amount and the actuator saturation compensation value into the backstepping controller.

[0137] S6, setting an adaptive law for the follower airship to obtain an adaptive estimation value;

[0138] S61. An adaptive law is arranged on each follower airship;

[0139] S62, input the second-order distributed error of the follower airship into the adaptive law to obtain an adaptive estimated value, the process is as follows:

[0140]

[0141] in represents the adaptive estimate, γ i,j >0,γ i0 >0 indicates the controller parameters to be designed, yes The derivative of j represents a diagonal matrix, I1=diag{1,0,0,0,0,0}, I2=diag{0,1,0,0,0,0}, ..., I6=diag{0,0,0,0,0,6}, represents the backstepping controller parameters to be designed.

[0142] S7, using the anti-cloth controller to calculate the control amount of the desired formation and attitude of the follower airship according to the results in S3 to S5;

[0143] S71, inputting the current motion state, expected posture, virtual control law saturation compensation amount, actuator saturation compensation value and adaptive law estimation value of the follower airship into the backstepping controller;

[0144] S72, using the backstepping controller to calculate the attitude control value τ of the follower airship i , the process is as follows:

[0145]

[0146] where β i =diag{β i1 ,...,βi6}, β ij >0 indicates the controller parameters to be designed;

[0147] S73, according to the attitude control amount of the follower airship, the desired formation of the follower airship tracking time variation can be obtained;

[0148] S74. Obtain a distributed time-varying formation of stratospheric airships according to the expected formation of the leader airship and the expected formation of the follower airships tracking the time-varying formation.

[0149] The present invention uses the dynamic model of the stratospheric airship, and the six-degree-of-freedom dynamic model is as follows:

[0150]

[0151] where ζ i =[x i ,y i ,z i ,φ i ,θ i ,ψ i ] T represents the three-dimensional coordinates and attitude angle of the stratospheric airship, represents the projection of the airship's velocity in the body axis system and the projection of the airship's angular velocity in the body axis system, f1(ζ i ) represents the coordinate transformation matrix that transforms the airship state quantity in the body axis system to the earth axis system. represents the aerodynamic force and aerodynamic moment of the airship, B represents the inverse of the airship mass and inertia matrix, τ' i =[τ'1,τ'2,τ'3,τ'4,τ'5,τ'6] T , represents the control amount of airship i, δ i =[δ u ,δ v ,δ w ,δ p ,δ q ,δ r ] represents the unknown uncertainty in the airship model consisting of unknown external disturbances and unmodeled dynamics, i∈N.

[0152] The principle of this method is: the sensor measures the motion state of the airship and transmits the position, speed, attitude angle, and attitude angular velocity to the control system. At the same time, the airship will communicate with its neighbors according to the pre-set topological structure to obtain the distributed error and position information of the neighbors. The entire control system consists of a first-order auxiliary design system, a second-order auxiliary design system, an adaptive law, and a backstepping controller. After the airship obtains the information of the sensor and the neighbors, it will first calculate its expected attitude according to the information of the neighbors, and then calculate the first-order distributed error according to the expected attitude and its own position. Then the first-order auxiliary design system outputs the virtual control law saturation compensation according to the virtual control law and the first-order distributed error and inputs it to the backstepping controller. The second-order auxiliary design system calculates the actuator saturation compensation value according to the actuator saturation value and the second-order distributed error and inputs it to the backstepping controller. The adaptive law calculates the estimated value of the uncertainty according to the second-order distributed error and outputs it to the backstepping controller. Finally, the backstepping controller calculates the control amount and transmits it to the actuator to control the airship to form a formation.

[0153] Therefore, the present invention discloses a distributed time-varying formation control method for stratospheric airships based on affine transformation. Based on the affine transformation theory, a formation maneuvering control method for stratospheric airships is designed, which can realize the time-varying formation control of stratospheric airships without global information, thereby improving the flexibility of the formation. At the same time, based on the barrier Lyapunov theory, the problem of airship state restriction is converted into a saturation error problem, which is solved by introducing an auxiliary design system. In the process of realizing the formation maneuvering of the airship cluster, the state of the airship is ensured to be within the restriction range. There is no need to transmit global information to each airship, thereby reducing the requirement for communication bandwidth. The auxiliary design system is used to process the saturation problem, thereby improving the actuator saturation problem. Finally, an adaptive law is used to estimate the unknown disturbance of the environment and the uncertain terms in the model, and the estimated value is transmitted to the backstepping sliding mode controller, thereby enabling the airship to track the desired trajectory under the influence of external disturbances.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A distributed time-varying formation control method for stratospheric airships based on affine transformation, characterized in that: The following steps are involved: S1. Use sensors to measure the motion state of the airship; S2, generating a desired formation and sending the desired formation to the leader airship in the cluster; S3, after the leader airship obtains the desired formation, it sets up a communication structure within the airship cluster; S4. After the communication structure is set, the expected attitude of the follower airship is calculated; S5. After obtaining the expected posture of each follower airship, an auxiliary design system is set for the follower airship to obtain the saturation compensation amount of the virtual control law and the saturation compensation value of the actuator; S6, setting an adaptive law for the follower airship to obtain an adaptive estimation value; S7. Use the anti-cloth controller to calculate the control amount of the desired formation and attitude of the follower airship according to the results in S3 to S5.

2. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 1, characterized in that: The motion state of the airship in S1 includes position, velocity, attitude angle and attitude angular velocity, and the data is transmitted to the backstepping controller.

3. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 2, characterized in that: The process of generating the desired formation in S2 is as follows: S21. Set the initial nominal configuration r, which is expressed as: r＝[r1,...,r N ]； v l ={1,...,N l }; v f ={N l +1,...,N}; Where N represents the number of airships, N l represents the number of pilot airships, v l represents the set of pilot airships, v f represents the collection of follower airships; S22. Use affine transformation to obtain the desired formation p for the initial nominal configuration * (t), the process is as follows: Among them I N ∈R N×N represents the identity matrix, represents the maneuver matrix representing the rotation, scaling, and shearing of the formation, b(t)R 3×1 represents the maneuver matrix representing the formation translation, represents the expected position of the i-th airship, 1 N represents the N-order identity matrix; S23. Decompose the expected formation to obtain: in represents the desired formation of the pilot airship, Indicates the formation of follower airships; S24, transmitting the desired formation of the navigator to the navigator to obtain the actual formation of the navigator p l :

4. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 3, characterized in that: The process of setting the communication structure in S3 is: S31. Set a topology matrix S32. Use the topology matrix in S31 to define the communication structure within the airship cluster, expressed as: where ω ij represents the corresponding topological gain between airship i and airship j; like Indicates that there is no communication between airship i and airship j. If Indicates that airship i and airship j are neighbors; S33. Install communications structures for all airships prior to flight.

5. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 4, characterized in that: The process of calculating the expected attitude of the follower airship in S4 is: S41, deploying an expected attitude generator on each follower airship, and using the expected attitude generator to obtain the flight attitude of each follower airship at this time; S42, calculate the follower blocks according to the topology matrix in S3, the calculation process is: in Represents the matrix after the topological matrix is ​​multiplied by the third-order matrix, and represents the follower block, I3 represents the third-order identity matrix; S43, calculating the expected attitude of the follower airship, the calculation process is as follows: in represents the desired posture of the i-th follower airship, φ * ,θ * and ψ * Indicates the flight attitude of the follower airship. represents the expected position of the ith follower airship, z pj represents the distributed position error of each neighbor of the follower airship, ω k,j represents the corresponding topological gain between airship k and airship j, p j represents the expected position of the jth airship, j∈N i , p k represents the expected position of the kth airship, k∈N j .

6. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 5, characterized in that: The process of obtaining the virtual control law saturation compensation amount and the actuator saturation compensation value in S5 is as follows: S51. Arrange a first-order auxiliary design system and a second-order auxiliary design system on each follower airship; S52, calculating the current virtual control law of the follower airship, the calculation process is as follows: The saturation error of the virtual control law is calculated according to the virtual control law: in: in represents the inverse of the transformation matrix that transforms the angular velocity of the airship from the body axis system to the earth axis system, α i =diag{α i1 ,α i2 ,α i3 ,α i4 ,α i5 ,α i6 } represents the control law parameters to be selected, α ij >0,j=1,2,…,6,ω ij represents the corresponding topological gain between airship i and airship j, z 1i represents the first-order distributed error, ξ ξi It represents the saturation compensation of the virtual control law output by the first-order auxiliary design system. represents the derivative of the position of airship j; S53, input the virtual control law and the first-order distributed error into the first-order auxiliary design system, and obtain the saturation compensation amount of the virtual control law through the formula, which is as follows: in Both represent the backstepping controller parameters to be designed, b ξj represents the first-order distributed error limit b ξ The element b ξ =[b ξ1 ,...,b ξ6 ] T , z 1ij Represents the element of the first-order distributed error, z 1i =[z 1i1 ,...,z 1i6 ], express The derivative of the output intermediate variable is the saturation compensation of the virtual control law; S54, input the actuator saturation value and the second-order distributed error into the second-order auxiliary design system to obtain the actuator saturation compensation value, and the calculation process is as follows: in are the backstepping controller parameters to be designed. represents the saturation error of the control law, z 2ij is the second-order distributed error z 2i The element z 2i =[z 2i1 ,...,z 2i6 ], yes The derivative of the output intermediate variable is the actuator saturation compensation value; S55, inputting the virtual control law saturation compensation amount and the actuator saturation compensation value into the backstepping controller.

7. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 6, characterized in that: The dynamic model of the stratospheric airship is used, and the six-degree-of-freedom dynamic model is as follows: where ζ i =[x i ,y i ,z i ,φ i ,θ i ,ψ i ] T represents the three-dimensional coordinates and attitude angle of the stratospheric airship, represents the projection of the airship's velocity in the body axis system and the projection of the airship's angular velocity in the body axis system, f1(ζ i ) represents the coordinate transformation matrix that transforms the airship state quantity in the body axis system to the earth axis system. represents the aerodynamic force and aerodynamic moment of the airship, B represents the inverse of the airship mass and inertia matrix, τ' i =[τ'1,τ'2,τ'3,τ'4,τ'5,τ'6] T , represents the control amount of airship i, δ i =[δ u ,δ v ,δ w ,δ p ,δ q ,δ r ] represents the unknown uncertainty in the airship model consisting of unknown external disturbances and unmodeled dynamics, i∈N.

8. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 7, characterized in that: The process of obtaining the adaptive estimated value in S6 is as follows: S61. An adaptive law is arranged on each follower airship; S62, input the second-order distributed error of the follower airship into the adaptive law to obtain an adaptive estimated value, the process is as follows: in represents the adaptive estimate, γ i,j >0,γ i0 >0 indicates the controller parameters to be designed, yes The derivative of j represents a diagonal matrix, represents the backstepping controller parameters to be designed.

9. The method for controlling a distributed time-varying formation of stratospheric airships based on affine transformation according to claim 8, characterized in that: The process of calculating the control amount of the desired formation and attitude of the follower airship in S7 is as follows: S71, inputting the current motion state, expected posture, virtual control law saturation compensation amount, actuator saturation compensation value and adaptive law estimation value of the follower airship into the backstepping controller; S72, using the backstepping controller to calculate the attitude control value τ of the follower airship i , the process is as follows: where β i =diag{β i1 ,...,β i6 }, β ij >0 indicates the controller parameters to be designed; S73, obtaining a desired formation of the follower airship tracking time-varying according to the attitude control amount of the follower airship; S74. Obtain a distributed time-varying formation of stratospheric airships according to the expected formation of the leader airship and the expected formation of the follower airships tracking the time-varying formation.

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