Unmanned aerial vehicle cluster flight attitude adaptive consensus control method based on directed support tree

Abstract

The present application relates to the unmanned aerial vehicle cluster flight attitude adaptive consistency control method based on the directed support tree, including the construction about the multi-agent system of unmanned aerial vehicle;Definition multi-agent system on the directed connected graph is interacted and the directed connected graph contains a directed support tree;The design of the multi-agent system determines the equivalent controller;The equivalent controller is extended to the time-varying coupling gain;The parameter design of time-varying coupling equivalent controller is carried out;The breadth-first search algorithm is used to find the directed support tree from the directed connected graph;The undirected version of the directed support tree is constructed;The system state is updated in cycles through the directed connected graph and the undirected support tree, and the unmanned aerial vehicle cluster flight attitude adaptive consistency control is realized.The present application realizes the adaptive leaderless consistency of multi-agent on the directed support tree, overcomes the problem caused by the uncertainty in the communication graph in the model, and realizes the unmanned aerial vehicle cluster flight attitude adaptive consistency control.

Description

Technical Field

[0001] This invention relates to the field of adaptive control technology, and in particular to an adaptive consistency control method for the flight attitude of unmanned aerial vehicle (UAV) swarms based on directed support trees. Background Technology

[0002] With the rapid development of modern society, multi-agent systems have shown great application potential in many fields, and multi-agent consensus has gradually become a research hotspot in the field of automatic control. Unmanned aerial vehicle (UAV) technology has begun to be widely used in areas such as farmland sowing and forest search and rescue. Unmanned aerial vehicle (UAV) group consensus control is an important part of the autonomous cooperative control of multi-agent systems. Starting from an initial attitude, the UAV group uses a certain control algorithm and exchanges information among itself to update its state, gradually adjusting to achieve the desired attitude consistency to cope with different environments.

[0003] Leaderless consensus in multi-agent systems is a classic problem, as all agents must coordinate autonomously due to the lack of a unified leader. Generally, the graph used in leaderless consensus algorithms in multi-agent systems is assumed to be undirected, implying symmetric communication flow. However, in real-world networks such as web pages, social networks, and one-way traffic networks, directed information flow is prevalent. Directed graphs treat undirected graphs as a special case, describing their characteristics by decomposing each undirected edge into two directed edges. Uncertain systems, which contain factors that cannot be described by deterministic quantities or present uncertain information, present challenges due to the asymmetric propagation of uncertainty in the communication graph. Therefore, the adaptive consensus control problem in uncertain multi-agent systems on directed graphs remains a worthy area of ​​research. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides an adaptive consensus control method for UAV swarm flight attitude based on directed support trees. This method solves the challenge of adaptive consensus control of uncertain multi-agent systems on directed graphs caused by the asymmetric propagation of uncertainty in the communication graph, which is a problem in traditional leaderless scenarios.

[0005] To achieve the above technical objectives, the present invention provides the following technical solution: an adaptive consistency control method for UAV swarm flight attitude based on directed support trees, comprising the following steps:

[0006] S1. Construct a roll attitude dynamics model of the UAV swarm and abstract it into a multi-agent network with parameter uncertainty to build a multi-agent system;

[0007] S2. Define a multi-agent system that interacts on a directed connected graph with UAVs as nodes, wherein the directed connected graph contains a directed support tree;

[0008] S3. Based on S2 and the coupling gain condition, design a deterministic equivalent controller for the multi-agent system; the deterministic equivalent controller updates the control input based on the estimated parameters, and the estimated parameters remain bounded.

[0009] S4. Extend the coupling gain in the deterministic equivalent controller to the time-varying coupling gain to obtain the time-varying coupling deterministic equivalent controller; the time-varying coupling deterministic equivalent controller updates the control input based on the estimated parameters and the time-varying coupling gain, and its estimated parameters and time-varying coupling gain remain bounded;

[0010] S5. Based on the coupling gain condition, design the time-varying coupling gain, select an arbitrary positive definite gain matrix, and then solve for the state feedback gain and the symmetric positive definite matrix to complete the parameter design of the time-varying coupled deterministic equivalent controller.

[0011] S6. Using the breadth-first search algorithm, starting from the root node, find the directed support tree from the directed connected graph;

[0012] S7. Construct an undirected version of the directed support tree so that nodes can exchange information with each other.

[0013] S8. By updating the control input in the time-varying coupled deterministic equivalent controller through the directed connected graph and updating the estimated parameters in the time-varying coupled deterministic equivalent controller through the undirected version of the directed support tree, the cyclic update of the UAV system state is realized, and the adaptive consistency control of the UAV swarm flight attitude is achieved.

[0014] Optionally, the roll attitude dynamics model of the UAV swarm is expressed by the following formula:

[0015] ;

[0016] in, The roll angle of the drone. The roll rate of the drone. Parameterizable nonlinear dynamics For the control input to be designed, This indicates the roll angle trajectory of the drone. This represents the roll rate trajectory of the drone.

[0017] Optionally, the multi-agent system is expressed by the following formula:

[0018] ;

[0019] in, For the first The system status of a drone, including roll angle and roll rate. The state matrix, For the control matrix, For the first An unknown parameter array for a UAV, symbol... Indicates matrix transpose. For nodes The corresponding known bounded and Lipzig-continuous regression function, For the first The control input for a drone The total number of drones, Indicates time, Indicates the first The system status trajectory of the drone.

[0020] Optionally, the deterministic equivalent controller is mathematically represented as follows:

[0021] ;

[0022] ;

[0023] in, For the first The control input of the nth node, i.e., the nth node Control inputs for a drone; This is the coupling gain; The state feedback gain and satisfying ,symbol Indicates matrix transpose. For the control matrix, It is a symmetric positive definite matrix and satisfies ; Represents nodes in a directed connected graph , The weight of the edges between them; Represents a node The system status; For nodes The estimated parameters; For nodes The corresponding known bounded and Lipsitz continuous regression function; Represents a node The derivative of the estimated parameters; Let be an arbitrary positive definite gain matrix; For nodes In the set of in-neighbor nodes in a directed connected graph For nodes The set of ingress neighbor nodes in a directed support tree; For nodes The set of out-neighbor nodes in a directed support tree; Represents a node Incoming neighbor nodes in a directed connected graph; Represents a node Neighboring nodes in a directed support tree.

[0024] Optionally, for the multi-agent system, considering the deterministic equivalent controller, let ,in This is the formula The only solution is that which satisfies step S2 and the coupling gain. Under these conditions, all agents in a multi-agent system can asymptotically reach consensus, and all estimated parameters... Maintaining boundedness; where The state matrix, Represents the Laplacian matrix of a directed connected graph. express The second smallest eigenvalue, Indicates taking the real part, express An identity matrix of order 1. Indicates the order.

[0025] Optionally, the time-varying coupled deterministic equivalent controller is expressed by the following formula:

[0026] ;

[0027] ;

[0028] ;

[0029] in, Indicates the time-varying coupling gain. Indicates time The time-varying coupling gain; Represents the connection nodes in a directed connected graph. , The edge, This represents the set of edges in a directed support tree. Indicates the gain to be designed. The derivative of the time-varying coupling gain. This represents the gain matrix to be determined.

[0030] Considering the time-varying coupled deterministic equivalent controller for the multi-agent system, where let In a multi-agent system, all agents achieve asymptotic consistency, and all estimated parameters... and time-varying coupling gain Keep it bounded.

[0031] Optionally, the solution for the state feedback gain and the symmetric positive definite matrix includes:

[0032] Solve the following two equations to obtain the symmetric positive definite matrix. and state feedback gain :

[0033] ;

[0034] .

[0035] Optionally, the construction of the undirected version of the directed support tree includes:

[0036] Draw at most from the directed support tree Given an edge, we can obtain its undirected version. This represents the total number of nodes, i.e., the total number of drones.

[0037] The present invention also provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute the aforementioned UAV swarm flight attitude adaptive consistency control method based on directed support tree.

[0038] The present invention also provides a computer-readable storage medium storing computer instructions, which are used to cause a processor to implement the aforementioned adaptive consistency control method for UAV swarm flight attitude based on directed support tree when executed.

[0039] By employing the above technical solution, the present invention provides an adaptive consistency control method for the flight attitude of UAV swarms based on directed support trees, which has at least the following beneficial effects:

[0040] (1) This invention focuses on solving the problem of uncertain multi-agent adaptive leaderless consensus. By designing a deterministic equivalent controller, parameter uncertainty can be perfectly eliminated without the need to introduce an additional reference model layer, providing an efficient tool for achieving leaderless consensus.

[0041] (2) The deterministic equivalent controller designed in this invention inherits a structural design similar to that of undirected networks, namely, it includes a consensus term and an uncertainty equivalent compensation term, eliminating the additional components such as the reference model used in traditional methods, thereby providing an effective method for achieving leaderless consensus among multi-agent agents with parameter uncertainty.

[0042] (3) This invention not only successfully proposed a design scheme for the controller under fixed coupling gain to achieve consistency among multiple agents, but also ensured that the multi-agent system can achieve consistent results through rigorous theoretical proof. This not only provides a solid theoretical foundation for the research method, but also emphasizes the reliability and effectiveness of the proposed technology.

[0043] (4) The present invention further extends the deterministic equivalent controller to time-varying coupled gain, optimizes the controller design, and not only achieves an important breakthrough in theory, but also shows wide applicability in practical applications. Attached Figure Description

[0044] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0045] Figure 1 This is a flowchart of the adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to the present invention.

[0046] Figure 2 This is a schematic diagram illustrating the process of constructing a directed support tree in a directed connected graph based on breadth-first search according to the present invention.

[0047] Figure 3 This is a schematic diagram illustrating the process of cyclically updating the control input, estimated parameters, and system state according to the present invention.

[0048] Figure 4 This is a schematic diagram of the directed support tree constructed in an embodiment of the present invention;

[0049] Figure 5 This is a schematic diagram illustrating the time-varying coupling gain obtained by the rewritten deterministic equivalent controller in an embodiment of the present invention as a function of time.

[0050] Figure 6 This is a schematic diagram illustrating the time-varying parameters of the rewritten deterministic equivalent controller in an embodiment of the present invention.

[0051] Figure 7 This is a schematic diagram illustrating the change of system state with respect to time obtained by the rewritten deterministic equivalent controller in an embodiment of the present invention. Detailed Implementation

[0052] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0053] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0054] Please refer to Figures 1-7 This document illustrates a specific implementation of this embodiment. This embodiment constructs a multi-agent system through theoretical modeling; designs a deterministic equivalent controller; provides the deployment process of the deterministic equivalent controller and the solution steps for the closed-loop system; extends the deterministic equivalent controller to time-varying coupled gain; verifies the above method using simulation, validating its effectiveness and reliability in practical applications; achieves adaptive leaderless consensus among multi-agents on a directed support tree, while overcoming the challenges posed by uncertainties in the communication graph, thus realizing adaptive consensus control of UAV swarm flight attitude.

[0055] Please refer to Figure 1 This embodiment proposes an adaptive consistency control method for the flight attitude of UAV swarms based on directed support trees. The method includes:

[0056] A roll attitude dynamics model of a drone swarm is constructed and abstracted into a multi-agent network with parameter uncertainty, thus constructing a multi-agent system.

[0057] Specifically, consider the roll attitude dynamics model of a class of drone swarms as follows:

[0058] ;(Formula 1)

[0059] in, The roll angle of the drone. The roll rate of the drone. Parameterizable nonlinear dynamics is used to describe uncertain disturbances such as airflow effects. For the control input to be designed, This indicates the roll angle trajectory of the drone. This represents the roll rate trajectory of the drone.

[0060] Consider containing To facilitate derivation and explanation, the attitude consistency control problem of a swarm system of drones can be abstracted from the above roll attitude dynamics model into a multi-agent network with parameter uncertainties. Consider the following multi-agent network with parameter uncertainties:

[0061] ;(Formula 2)

[0062] in, Indicates the first The system status of a drone, such as the numbered... The roll angle and roll rate of the drone Indicates the first The system status trajectory of a drone The state matrix, For the control matrix, the system matrix pair It is known and stable. For the first The unknown parameters of the UAV (a constant matrix, but unknown for control design purposes), with symbols... Indicates matrix transpose. For nodes The corresponding known bounded and Lipsitz continuous regression function ( , Indicates the initial time, symbol (represents mapping). For the first The control input for a drone The total number of drones, Indicates time, For the real number space, , , They represent , , Dimensions.

[0063] In existing research, for the leaderless consensus problem in a communication graph, it is assumed that the multi-agent system (Equation 2) is in a directed connected graph. Interact with the intelligent agent. At this time, the intelligent agent... The deterministic equivalent controller (using drones as agents in a multi-agent system) can be designed as follows:

[0064] ;(Formula 3)

[0065] ; (Formula 4)

[0066] State feedback gain ,and This is the formula The only solution Represents nodes in a directed connected graph , The weight of the edges between them. Represents a node The derivative of the estimated parameters, It is an arbitrarily positive definite gain matrix, and the coupling gain is... It is a constant and represents the global gain for all agents. express for neighboring nodes ( (This represents the set of neighboring nodes). To achieve leaderless consensus, coupling gain... Need to obtain a sufficiently large ( ),in Represents the Laplacian matrix of a directed connected graph. express The second smallest eigenvalue. For the more general case of directed graphs, the design of deterministic equivalent controllers has been previously unclear, which is the problem this application aims to address.

[0067] Define a multi-agent system that interacts on a directed connected graph with drones as nodes, and satisfy Assumption 1: the directed connected graph contains a directed support tree.

[0068] Specifically, for a multi-agent system (Equation 2), assume a directed connected graph. It contains a directed spanning tree (DST). The theoretical basis of the parameter adaptation law is the directed connected graph. We will study a directed support tree structure. Let's arbitrarily select a directed support tree, denoted as [example tree]. Without loss of generality, relabel the nodes in the directed support tree so that the root node is 1. For all nodes in the directed support tree... ,set up Represents a node exist The unique parent node (incoming neighbor node) in the directed spanning tree is represented by the Laplace matrix as follows: ,node exist The set of neighbor nodes in the is represented as ,in The in / out symbols correspond to their in / out edges, satisfying And when hour, .

[0069] First, consider the following assumptions:

[0070] Assumption 1: Directed connected graph It contains a directed support tree (DST).

[0071] A directed support tree is an important concept in graph theory. It refers to a tree structure formed in a directed graph by selecting some edges, which contains all the nodes in the original graph, and each node has one and only one parent node except for the root node. Assumption 1 is general and is a necessary condition for achieving multi-agent consensus under static communication topologies.

[0072] Based on Assumption 1 and the coupling gain condition, a deterministic equivalent controller is designed for a multi-agent system, and a theorem regarding the boundedness of its estimated parameters is obtained, which is referred to as Theorem 1.

[0073] Specifically, for multi-agent systems (Equation 2), the following deterministic equivalent controller is designed:

[0074] ;(Formula 5)

[0075] ;(Formula 6)

[0076] Among them, the state feedback gain Similar to the design method in Formula 3, the matrix It is an arbitrary positive definite gain matrix. For the first The control input of the nth node, i.e., the nth node Control inputs for a drone; It is a symmetric positive definite matrix and satisfies ; Represents a node The system status; For nodes In the set of in-neighbor nodes in a directed connected graph, For nodes The set of ingress neighbor nodes in a directed support tree; For nodes The set of out-neighbor nodes in a directed support tree; Represents a node In a directed connected graph, the in-neighbor node; Represents a node Neighboring nodes in a directed support tree.

[0077] Based on assumption 1, the following conclusions can be drawn:

[0078] Theorem 1: For a multi-agent system (Equation 2), consider a deterministic equivalent controller of the form above (Equation 5), let ,in This is the formula The only solution is given by Assumption 1 and coupling gain. Under these conditions, all agents in a multi-agent system (Equation 2) can asymptotically reach consensus, and all estimated parameters... Maintaining boundedness; where Indicates taking the real part, express An identity matrix of order 1. Indicates the order.

[0079] The proof of Theorem 1 is given below:

[0080] Theorem 1 can be derived by analyzing directed support trees. This is proven by examining the consistency error within the model. For ease of proof, we first use... The edges are defined by two matrices: the edge node incidence matrix and the edge node incidence matrix. Sum of subtree cumulative difference matrix Edge node association matrix Defined in the following form:

[0081] ;(Formula 7)

[0082] Edge node association matrix Each row represents a directed support tree. A directed edge in the network, the origin of which is the parent node. The endpoint (child node) is 1. The value is -1.

[0083] Subtree cumulative difference matrix for:

[0084] ;(Formula 8)

[0085] in Represented by node The set of nodes in the subtree rooted at the root. express The nodes in. Let. , These represent finding the minimum and second smallest eigenvalues, respectively. Describe the null space of the matrix. Let represent the span of vectors. Then, under assumption 1, it is obvious that... , , , Represents a vector consisting entirely of 1s. In the Laplace matrix middle The value at that location, In the Laplace matrix middle The value at that location.

[0086] The above defines two matrices , Multiply At that time, they have a commutative relationship. That is:

[0087] ;(Formula 9)

[0088] Substituting the proposed deterministic equivalent controller (Equation 5) into the multi-agent system (Equation 2), we obtain:

[0089] ;(Formula 10)

[0090] in To account for the parameter estimation error, the above equation can be written in a compact form:

[0091] ;(Formula 11)

[0092] in ; , representing the parameter estimation error matrix; ; Indicates the system status. Let the regression function be known to be bounded and Lipsitz continuous. Vectorization is represented. Indicates diagonal matrixing, express The derivative of express identity matrix of order 1, symbol It represents the Kronecker product.

[0093] Define consistency error If and only if for All states An agreement was reached at this time Then, according to formulas 9 and 11, The dynamics can be described as follows:

[0094] ;(Formula 12)

[0095] in This represents the consistency error trajectory.

[0096] Consider a Lyapunov function :

[0097] ;(Formula 13)

[0098] in Represents the trace of a matrix. express The inverse matrix.

[0099] Along the consistency error trajectory (Equation 12) Finding the time derivative and substituting it into Equation 6, we get:

[0100] ;(Formula 14)

[0101] in express The derivative with respect to time.

[0102] The first equation uses The design was obtained, and the second equation was obtained by using the invariance of the trace operator under cyclic permutation.

[0103] First, one can notice the matrix. eigenvalues So, given Under the condition of auxiliary matrix All eigenvalues ​​lie in the left half of the complex plane, that is... It is semi-negative definite, that is:

[0104] ;(Formula 15)

[0105] Secondly, it needs to be proven that the last two terms of Equation 14 cancel each other out. According to Equation 16... From the definition of a matrix, it is not difficult to see It is an unweighted and undirected support tree The Laplacian matrix, that is, by unifying the edge weights and ignoring the basis... The graph obtained by considering the edge directions. In fact, yes The in-degree matrix, multiplied by its transpose, yields... The Laplace matrix. Therefore, we can obtain:

[0106] ;(Formula 16)

[0107] in represent Middle node The set of neighboring nodes.

[0108] Therefore, according to formulas 14, 15, and 16, we can obtain:

[0109] ;(Formula 17)

[0110] Therefore, we can obtain In other words , It is bounded. At this point, all estimated parameters... It is also bounded. Because It is bounded, so the function It is uniformly continuous. Integrating both sides of Equation 17 toward infinity further demonstrates that... The integrability of [the property]. Finally, according to the famous Barbalat lemma, we can derive [the property]. It converges to 0, that is:

[0111] ;(Formula 18)

[0112] The proof is now complete, and Theorem 1 holds true. The following section will provide the specific steps for implementing the control law algorithm.

[0113] This invention focuses on solving the uncertain multi-agent adaptive leaderless consensus problem. By designing a deterministic equivalent controller, it perfectly eliminates parameter uncertainty without introducing an additional reference model layer, providing an efficient tool for achieving leaderless consensus. The deterministic equivalent controller designed in this invention inherits a structural design similar to undirected networks, namely, it includes a consensus term. and uncertainty equivalent compensation item This eliminates the need for additional components such as reference models used in traditional methods, thus providing an effective method for achieving leaderless consensus among multi-agent agents with parameter uncertainty.

[0114] Based on the coupling gain condition, the coupling gain of the deterministic equivalent controller can be designed. By selecting an arbitrary positive definite gain matrix, the state feedback gain and the symmetric positive definite matrix can be solved to complete the parameter design of the deterministic equivalent controller.

[0115] Specifically, this step solves for the required parameters, including the coupling gain. State feedback gain arbitrarily positive definite gain matrix Symmetric positive definite matrix .

[0116] Firstly, according to (Coupling gain condition) Design Next, select any positive definite gain matrix. Then solve using the following two equations. , :

[0117] ;(Formula 19)

[0118] ;(Formula 20)

[0119] Using the above methods, the parameters required for a deterministic equivalent controller can be designed.

[0120] Next, using the breadth-first search algorithm, starting from the root node, we find the directed support tree in the directed connected graph.

[0121] Finding a directed support tree from a directed connected graph generally involves breadth-first search (BFS) and depth-first search (DFS). This invention employs BFS to achieve this goal. BFS uses a queue as its core. Its search process starts from the initial node, searches for a legally feasible node reachable in one step, adds it to the queue, then pops the initial node, and repeats the search operation on each node in the queue until the queue is empty. For a directed connected graph... Performing a breadth-first search starting from the root node yields a directed support tree. For detailed steps, please refer to Figure 2 First, initialize a queue, setting V0 as the initial node. Visit V0 and set its flag, then enqueue V0. At this point, check if the queue is empty. If the queue is empty, end the search. If it is not empty, dequeue the head node V, find V's adjacent node w, and check if w exists. If w does not exist, return to the step of "checking if the queue is empty" and re-execute the subsequent steps. If w exists, check if w has been visited. If w has been visited, set V's next adjacent node to w, return to the step of "checking if w exists", check if the next w exists, and re-execute the subsequent steps. If w has not been visited, visit w and set its flag, enqueue w, and set V's next adjacent node to w. Then, return to the step of "checking if w exists" to check if the next w exists, until the queue is empty, then end the search.

[0122] Construct an undirected version of the directed support tree so that nodes can exchange information with each other.

[0123] Specifically, by introducing at most A directed support tree is obtained by using edges. Undirected version This enables nodes to exchange information with each other. It can be used to update Formula 6.

[0124] The control input in the deterministic equivalent controller (Equation 5) is updated by updating the directed connected graph. ; through directed support trees Estimated parameters in the undirected version update deterministic equivalent controller (Equation 5) This will update the system status. .

[0125] Specifically, this step implements the algorithm through a loop; for details, please refer to [link to relevant documentation]. Figure 3 First, perform system initialization. Assign a value of 1, then check. Check if the condition is true; if not, end the loop; if true, then... Assign a value of 1 to solve for the control input. Update the estimated parameters Finally, a consistent attitude is achieved for the drone, meaning the roll angle and roll rate are aligned; and further judgment is made. Is it true or false? If not, then... Increment the value by 1; if true, then Increment the value by 1, then roll back to "Solve Control Input". The process of repeating the cycle continues until... The loop terminates if the condition is not met. Indicates the number of updates. Indicates the time step. Indicates the end time.

[0126] Based on the above steps and theoretical proof, the coupling gain in the deterministic equivalent controller can be further extended to the time-varying coupling gain, avoiding the solution of the eigenvalues ​​of the Laplace matrix, thus obtaining the time-varying coupled deterministic equivalent controller. This leads to the theorems on the bounded estimation parameters and bounded time-varying coupling gain of the time-varying coupled deterministic equivalent controller, which are referred to as Theorem 2.

[0127] To simplify the explanation, the same directed support tree as mentioned earlier is used here. For directed connected graphs Each edge in Randomly initialize a scalar variable As the initial time-varying coupling gain, the deterministic equivalent controller (Equations 5 and 6) is then rewritten as:

[0128] ;(Formula 21)

[0129] ;(Formula 22)

[0130] ;(Formula 23)

[0131] in Indicates the time-varying coupling gain. Indicates time The time-varying coupling gain; Represents the connection nodes in a directed connected graph. , The edge, Represents the set of edges in a directed support tree; This indicates the gain to be designed, which needs to be set according to the actual situation. ( (representing the space of positive real numbers); The derivative of the time-varying coupling gain; This represents the undetermined gain matrix, which needs to be set according to the actual situation. Clearly, it only occurs when the edge... Appears in directed support tree China Times, That is time-varying. At this moment, existence... ,make and ,but Represented as .also, The update law also depends on its end nodes. and And all of them .

[0132] Theorem 2: For a multi-agent system (Equation 2), consider a rewritten deterministic equivalent controller of the form above (Equations 21, 22, and 23), where let ,and The design is consistent with Theorem 1. Under Assumption 1, all agents in the multi-agent system (Equation 2) achieve asymptotic consistency, and all estimated parameters... and time-varying coupling gain Keep it bounded.

[0133] The proof of Theorem 2 is given below:

[0134] Based on time-varying coupling gain A generalized pseudo-Laplace matrix can be defined. :

[0135] ;(Formula 24)

[0136] ;(Formula 25)

[0137] in Represents a node With nodes The generalized pseudo-Laplace matrix, Represents a node Its own generalized pseudo-Laplace matrix.

[0138] Generalized pseudo-Laplace matrix It can be divided into two parts, such as , For directed support trees The generalized pseudo-Laplace matrix, It is a constant matrix.

[0139] Define the same edge node incidence matrix as in Formula 7. Simultaneously define the cumulative difference matrix of the pseudo-subtree. :

[0140] ;(Formula 26)

[0141] in, The cumulative difference matrix of pseudo-subtrees is represented in The value at that location, Represented by node The set of nodes in the subtree rooted at the root. express The nodes in Represents a constant matrix exist The value at that location, Represents a constant matrix exist The value at that location, The cumulative difference matrix of the constant pseudo-subtree is in The value at that location, The cumulative difference matrix of the generalized pseudo-subtrees of the directed support tree is shown in The value at that location, Represents the generalized pseudo-Laplace matrix exist The value at that location, Represents the generalized pseudo-Laplace matrix exist The value at that location.

[0142] Clearly, the cumulative difference matrix of the constant pseudo-subtree It is invariant and is the cumulative difference matrix of the generalized pseudo-subtrees of the directed support tree. satisfy:

[0143] ;(Formula 27)

[0144] in Represents a node To the node The time-varying coupling gain between them Represents nodes in a directed connected graph To the node The weight of the edges between them. Represents a node exist The only parent node (incoming neighbor node) in the node.

[0145] Because the equation This always holds true, therefore the new consistency error The dynamics can be written as:

[0146] ;(Formula 28)

[0147] in This is the new consistency error trajectory.

[0148] Based on Equation 13, construct a new Lyapunov function. :

[0149] ;(Formula 29)

[0150] Among the adjustment parameters , is an undetermined constant. It is obtained along the trajectory (Equation 28). time derivative :

[0151] ;(Formula 30)

[0152] Note , According to formula 25, we can obtain:

[0153] ;(Formula 31)

[0154] in, Represents nodes in a directed connected graph To the node The weight of the edges between them. Represents a node To the node The time-varying coupling gain between them , Representing nodes respectively , The corresponding new consistency error, Represents a node In the directed support tree, the out-neighbor node ( That is, its set).

[0155] Similarly, define the subtree cumulative difference structure matrix:

[0156] ;(Formula 32)

[0157] in Represents the position in the subtree cumulative difference structure matrix The value at that point. According to formulas 28, 29, and 30, we can derive:

[0158] ;(Formula 33)

[0159] Define the comprehensive coupling strength matrix , This represents the cumulative difference matrix of constant pseudo-subtrees. This represents the subtree cumulative difference structure matrix, and the subscript sym indicates that the matrix is ​​a symmetric matrix.

[0160] definition This represents finding eigenvalues, and according to the Ky-Fan inequality for summing Hermitian matrices, a partial order relation exists. ,so Among them, due to the matrix It remains unchanged and can be adjusted by changing the parameters. make Take one that is arbitrarily large. Make At this time, the matrix All eigenvalues ​​of are located in the left half of the complex plane, thus we obtain:

[0161] ;(Formula 34)

[0162] At this point, all agents in the multi-agent system (Equation 2) can asymptotically reach a consensus, and all estimated parameters... and time-varying coupling gain It remains bounded.

[0163] The proof is complete, and Theorem 2 holds true.

[0164] Based on the above theoretical foundation, the coupling gain in the deterministic equivalent controller is extended to the time-varying coupling gain to obtain the time-varying coupling deterministic equivalent controller. The same method as the deterministic equivalent controller is used to design parameters, find directed support trees, construct undirected support trees, and update control inputs and estimated parameters, thereby realizing the cyclic update of the UAV system state and finally completing the adaptive consistency control of UAV swarm flight attitude.

[0165] This invention further extends the deterministic equivalent controller to time-varying coupled gain, optimizing the controller design. This represents a significant theoretical breakthrough and demonstrates broad applicability in practical applications. The invention not only successfully proposes a controller design scheme for fixed coupled gain to achieve consistency among multiple agents, but also ensures, through rigorous theoretical proof, that the multi-agent system can achieve consistent results. This provides a solid theoretical foundation for the research methodology and emphasizes the reliability and effectiveness of the proposed technology.

[0166] To enable researchers in the field to better understand the implementation of this invention, the following simulation verification is also provided in this embodiment.

[0167] This invention utilizes Matlab software for simulation. Specific information about the simulation software is as follows:

[0168] Software Name: MATLAB;

[0169] Version information: 9.8.0.1380330 (R2020a) Update 2;

[0170] License number: 919961;

[0171] Operating system: Microsoft Windows 10, Home Chinese Edition, Version 10.0 (Build 19042);

[0172] Java version: Java 1.8.0_202-b08 with Oracle Corporation Java HotSpot (TM) 64-Bit Server VM mixed mode;

[0173] Special toolboxes: Statistics and Machine Learning Toolbox-11.7 (R2020a), Aircraft Control Toolbox-1.0.

[0174] This embodiment is based on a type of multi-agent unmanned aerial vehicle (UAV) system, considering actual dynamics (Equation 1) and forms such as Figure 4 The directed support tree is represented by red arrows, and the directed connected graph is represented by black arrows. As the roll angle of the drone in this embodiment, As the roll rate, the system contains a total of six drones (corresponding to...) Figure 4 The roll attitude dynamics model of nodes 1 to 6 is as follows:

[0175] ;(Formula 35)

[0176] Unknown dynamics Among them, the unknown parameters of each category Represented as , recorded as ,category In this embodiment, the values ​​for each category of unknown parameters are assigned as follows: .

[0177] Design a symmetric positive definite matrix State feedback gain as follows:

[0178] .

[0179] Figure 5This demonstrates the time-varying coupling gain obtained by the rewritten deterministic equivalent controller in Theorem 2 with respect to time. The changes. Figure 5 middle Indicates drone , Time-varying coupling gain between them This represents an edge in a directed connected graph that does not exist in a directed support tree. The corresponding drone , The time-varying coupling gain between them. Figure 5 It can be seen that the rewritten deterministic equivalent controller can keep the time-varying coupling gain bounded.

[0180] Figure 6 This demonstrates the estimated parameters for each category obtained from the rewritten deterministic equivalent controller in Theorem 2. About time The changes. From Figure 6 It can be seen that the rewritten deterministic equivalent controller can keep the estimated parameters bounded at all times.

[0181] Figure 7 This demonstrates the state of the leaderless agent (i.e., drone) system with respect to time t, obtained by the rewritten deterministic equivalent controller in Theorem 2. The changes. From Figure 7 It can be seen that the rewritten deterministic equivalent controller can enable all agents to reach a consensus.

[0182] This application also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the UAV swarm flight attitude adaptive consistency control method based on directed support tree.

[0183] This application also provides a computer-readable storage medium storing computer instructions, which are used to cause a processor to implement the aforementioned adaptive consistency control method for UAV swarm flight attitude based on directed support tree when executed.

[0184] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0185] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0186] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for adaptive consistency control of UAV swarm flight attitude based on directed support tree, characterized in that, include: S1. Construct a roll attitude dynamics model of the UAV swarm and abstract it into a multi-agent network with parameter uncertainty to build a multi-agent system; The multi-agent system is mathematically represented as follows: ； in, For the first The system status of a drone, including roll angle and roll rate. The state matrix, For the control matrix, For the first An unknown parameter array for a UAV, symbol Indicates matrix transpose. For nodes The corresponding known bounded and Lipzig-continuous regression function, For the first The control input for a drone The total number of drones, Indicates time, Indicates the first The system status trajectory of the drone; S2. Define a multi-agent system that interacts on a directed connected graph with UAVs as nodes, wherein the directed connected graph contains a directed support tree; S3. Based on S2 and the coupling gain condition, design a deterministic equivalent controller for the multi-agent system; the deterministic equivalent controller updates the control input based on the estimated parameters, and the estimated parameters remain bounded. S4. Extend the coupling gain in the deterministic equivalent controller to the time-varying coupling gain to obtain the time-varying coupling deterministic equivalent controller; the time-varying coupling deterministic equivalent controller updates the control input based on the estimated parameters and the time-varying coupling gain, and its estimated parameters and time-varying coupling gain remain bounded; The time-varying coupled deterministic equivalent controller is mathematically represented as: ； ； ； in, For the first The control input of the nth node, i.e., the nth node Control inputs for a drone; This is the coupling gain; For state feedback gain, sign Indicates matrix transpose. For the control matrix, It is a symmetric positive definite matrix and satisfies ; Represents nodes in a directed connected graph , The weight of the edges between them; Represents a node The system status; For nodes The estimated parameters; For nodes The corresponding known bounded and Lipsitz continuous regression function; Represents a node The derivative of the estimated parameters; Let be an arbitrary positive definite gain matrix; For nodes In the set of in-neighbor nodes in a directed connected graph, For nodes The set of ingress neighbor nodes in a directed support tree; For nodes The set of out-neighbor nodes in a directed support tree; Represents a node Incoming neighbor nodes in a directed connected graph; Represents a node Neighboring nodes in a directed support tree; Indicates the time-varying coupling gain. Indicates time The time-varying coupling gain; Represents the connection nodes in a directed connected graph. , The edge, This represents the set of edges in a directed support tree. Indicates the gain to be designed. The derivative of the time-varying coupling gain, This represents the gain matrix to be determined. S5. Based on the coupling gain condition, design the time-varying coupling gain, select an arbitrary positive definite gain matrix, and then solve for the state feedback gain and the symmetric positive definite matrix to complete the parameter design of the time-varying coupled deterministic equivalent controller. S6. Using the breadth-first search algorithm, starting from the root node, find the directed support tree from the directed connected graph; S7. Construct an undirected version of the directed support tree so that nodes can exchange information with each other. S8. By updating the control input in the time-varying coupled deterministic equivalent controller through the directed connected graph and updating the estimated parameters in the time-varying coupled deterministic equivalent controller through the undirected version of the directed support tree, the cyclic update of the UAV system state is realized, and the adaptive consistency control of the UAV swarm flight attitude is achieved.

2. The adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to claim 1, characterized in that: The roll attitude dynamics model of the drone swarm is mathematically represented as follows: ； in, The roll angle of the drone. The roll rate of the drone. Parameterizable nonlinear dynamics For the control input to be designed, This indicates the roll angle trajectory of the drone. This represents the roll rate trajectory of the drone.

3. The adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to claim 1, characterized in that: The deterministic equivalent controller is mathematically represented as follows: ； ； in, For the first The control input of the nth node, i.e., the nth node Control inputs for a drone; This is the coupling gain; The state feedback gain and satisfying ,symbol Indicates matrix transpose. For the control matrix, It is a symmetric positive definite matrix and satisfies ; Represents nodes in a directed connected graph , The weight of the edges between them; Represents a node The system status; For nodes The estimated parameters; For nodes The corresponding known bounded and Lipsitz continuous regression function; Represents a node The derivative of the estimated parameters; Let be any positive definite gain matrix; For nodes In the set of in-neighbor nodes in a directed connected graph, For nodes The set of ingress neighbor nodes in a directed support tree; For nodes The set of out-neighbor nodes in a directed support tree; Represents a node Incoming neighbor nodes in a directed connected graph; Represents a node Neighboring nodes in a directed support tree.

4. The adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to claim 3, characterized in that: Considering the deterministic equivalent controller in the multi-agent system, let ,in This is the formula The only solution is that which satisfies step S2 and the coupling gain. Under these conditions, all agents in a multi-agent system can asymptotically reach consensus, and all estimated parameters... Maintaining boundedness; where The state matrix, Represents the Laplacian matrix of a directed connected graph. express The second smallest eigenvalue, Indicates taking the real part, express An identity matrix of order 1. Indicates the order.

5. The adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to claim 4, characterized in that: Considering the time-varying coupled deterministic equivalent controller for the multi-agent system, where let In a multi-agent system, all agents achieve asymptotic consistency, and all estimated parameters... and time-varying coupling gain Keep it bounded.

6. The adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to claim 5, characterized in that: The solution to the state feedback gain and the symmetric positive definite matrix includes: Solve the following two equations to obtain the symmetric positive definite matrix. and state feedback gain : ； 。 7. The adaptive consistency control method for UAV swarm flight attitude based on directed support tree according to claim 1, characterized in that: The undirected version of constructing the directed support tree includes: Draw at most from the directed support tree Given an edge, we can obtain its undirected version. This represents the total number of nodes, i.e., the total number of drones.

8. An electronic device, characterized in that, The electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute the UAV swarm flight attitude adaptive consistency control method based on directed support tree as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the adaptive consistency control method for UAV swarm flight attitude based on a directed support tree, as described in any one of claims 1-7.

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