Multi-unmanned aerial vehicle cooperative formation network stability controller design method, system, equipment and medium

Abstract

The invention provides a multi-unmanned aerial vehicle cooperative formation network stability controller design method, system and device and a medium, and belongs to the field of new energy inspection, and the method specifically comprises the steps: building a mathematical model of a multi-unmanned aerial vehicle cooperative formation network; derivation and expectation operation are carried out on the generic function, and an expectation expression is obtained; extracting an intermediate judgment condition of system synchronization stability; defining parameters related to upper and lower limits of time delay and state variables, constructing a diagonal matrix, carrying out pre-multiplication and post-multiplication on an intermediate judgment condition, and adjusting an expression form; and equivalently converting the inequality group which still comprises the nonlinear term after adjustment into a linear matrix inequality form, and completing the design of the stability controller of the multi-unmanned aerial vehicle autonomous cooperative formation network. Through accurately depicting complex environmental factors, optimizing a mathematical form of a stability determination condition and solving by means of a numerical tool, stable cooperation of the multi-unmanned aerial vehicle formation under complex interference is finally realized, and the reliability and adaptability of the formation in an inspection task are improved.

Description

Technical Field

[0001] This invention belongs to the field of new energy inspection, specifically involving a design method, system, equipment and medium for a multi-UAV collaborative formation network stability controller. Background Technology

[0002] In the field of new energy, using drones for site inspection is currently the mainstream engineering approach. Traditionally, drones are piloted by operators to inspect photovoltaic panels in photovoltaic power generation areas or wind turbines in wind farms using machine vision. Manual drone inspection is inefficient and costly, so many technology companies are now exploring multi-drone autonomous swarm flight methods to improve efficiency and optimize costs. In this process, the swarm of multiple drones can be viewed as a dynamic and complex network with the number of nodes that can be quickly added or removed.

[0003] To ensure real-time communication between drone swarms and guarantee their safety and operational efficiency, related technologies have failed to consider the combined effects of time-varying communication delays and control signal packet loss. This leads to a disconnect between stability analysis and actual inspection scenarios. Furthermore, when dealing with stability criteria containing nonlinear terms, these technologies do not utilize standard numerical tools to solve for the nonlinear terms often present in multi-drone systems. This prevents the transformation of these nonlinear terms into a solvable linear form, leaving the analysis results at the theoretical level and hindering their application to practical control strategies.

[0004] When designing judgment conditions for the nonlinear characteristics of inspection drones, the control law has poor adaptability. The dynamics of rotary-wing drones have a nonlinear relationship between aerodynamic drag and speed. Existing methods often assume a linear model, which leads to conservative stability judgment conditions. The designed control law is prone to overshoot or oscillation in actual flight, affecting the inspection accuracy. Summary of the Invention

[0005] This invention provides a design method for a stable controller for a multi-UAV cooperative formation network. Addressing the challenges of time-varying communication delays, control signal packet loss, and nonlinear dynamics faced by multiple UAVs in inspection scenarios, a framework from modeling to control law design is constructed. By accurately characterizing complex environmental factors, optimizing the mathematical form of stability judgment conditions, and utilizing numerical tools for solution, stable cooperative multi-UAV formations under complex interference are ultimately achieved, improving the reliability and adaptability of formations in inspection tasks.

[0006] The methods include: Step S101: Establish a mathematical model for a multi-UAV cooperative formation network; Step S102: Use Lyapunov–Krasovskii generalized functions as a stability analysis tool; Step S103: Differentiate the Lyapunov–Krasovskii functional and take the expectation to obtain the expected expression containing the system state derivative, time-varying time delay upper and lower limits, and random disturbance term; Step S104: Extract intermediate judgment conditions for system synchronization and stability from the result after taking the expectation through mathematical transformation. The intermediate judgment conditions consist of multiple inequalities including time-varying time delay upper and lower limits, state variables and control parameters. Step S105: Under the premise of synchronous asymptotic stability, define parameters related to the upper and lower limits of time delay and state variables, construct a diagonal matrix and multiply it by the intermediate decision conditions before and after, and adjust the expression form; Step S106: The system of inequalities that still contain nonlinear terms after adjustment is equivalently converted into linear matrix inequalities, solved using standard numerical calculation software, and the specific expression of the feedback control law is derived based on the transformed stability judgment conditions to complete the design of the stability controller for the multi-UAV autonomous cooperative formation network.

[0007] This application also provides a design system for a multi-UAV cooperative formation network stability controller, the system comprising: The model building module is used to establish mathematical models for multi-UAV cooperative formation networks; The framework analysis module uses Lyapunov–Krasovskii generalized functions as a stability analysis tool. The expectation derivation module is used to differentiate the Lyapunov–Krasovskii functional and perform expectation operations to obtain the expectation expression containing the system state derivative, time-varying time delay upper and lower limits, and random disturbance terms. The condition extraction module is used to extract intermediate judgment conditions for system synchronization and stability from the result of differentiation and expectation through mathematical transformation. The intermediate judgment conditions consist of multiple inequalities including time-varying time delay upper and lower limits, state variables and control parameters. The parameter adjustment module is used to define parameters related to the upper and lower limits of time delay and state variables under the premise of synchronous asymptotic stability, construct a diagonal matrix and multiply it by the intermediate judgment conditions before and after, and adjust the expression form. The formation design module is used to convert a system of inequalities that still contain nonlinear terms after adjustment into equivalent linear matrix inequalities, solve them using standard numerical calculation software, and derive the specific expression of the feedback control law based on the transformed stability judgment conditions, thus completing the design of the stability controller for a multi-UAV autonomous cooperative formation network.

[0008] According to another embodiment of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the multi-UAV cooperative formation network stability controller design method.

[0009] According to another embodiment of this application, a storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the design method for the multi-UAV cooperative formation network stability controller.

[0010] As can be seen from the above technical solutions, the present invention has the following advantages: This invention proposes a multi-UAV cooperative formation network stability controller design method. By incorporating time-varying communication delays, synchronization control signal packet loss, and the Lurie nonlinearity of rotary-wing UAVs, the physical behavior of multi-UAV cooperative formation is quantified into mathematical equations, clarifying the relationship between system state, disturbances, and control inputs. The use of Lyapunov–Krasovskii functionals accurately captures the impact of time-varying delays, rather than just fixed delays, on system stability, improving the specificity of stability analysis. Differentiation reflects the trend of system energy changes, and the expectation of random disturbance terms eliminates randomness, transforming the stability analysis of stochastic systems into deterministic analysis, providing a unified mathematical expression for extracting stability conditions. Mathematical transformations simplify complex expressions into a system of inequalities containing upper and lower limits of time delays and state variables, clarifying the constraints that system stability must satisfy, and providing clear target boundaries for controller design. By defining associated parameters and constructing a diagonal matrix, the intermediate conditions are structurally optimized, eliminating nonlinear factors that hinder the transformation into linear matrix inequalities (LMIs), reducing the difficulty of subsequent solutions. The nonlinear inequalities are equivalently transformed into LMIs, and the derived feedback control law is directly applied to multi-UAV formations, ensuring that theoretical analysis is translated into an executable control strategy. Ultimately, stable coordination of multi-UAV formations under complex interference is achieved, improving the reliability and adaptability of formations in inspection missions and solving the problems of inaccurate analysis, difficult solutions, and poor control law adaptability in complex scenarios encountered by traditional methods. Attached Figure Description

[0011] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 Flowchart of a design method for a stable controller for a multi-UAV cooperative formation network; Figure 2A schematic diagram illustrating the relationship between the control and formation network of a multi-UAV formation system; Figure 3 A schematic diagram of a system for designing a stable controller for a multi-UAV cooperative formation network; Figure 4 This is a schematic diagram of an electronic device. Detailed Implementation

[0013] The proposed design method for a stable controller in a multi-UAV cooperative formation network establishes a mathematical model of a complex network with multi-UAV formations exhibiting time-varying communication delays and packet loss of synchronization control signals. By constructing a Lyapunov–Krasovskii functional for system stability analysis, a controller design method is derived that can calculate the synchronous stability of the multi-UAV autonomous cooperative formation network in real time online. Thus, when the multi-UAV cooperative formation network loses synchronization stability, the corresponding UAV control algorithm is used to restore the overall formation network to synchronous stability.

[0014] The following describes in detail the design method of the multi-UAV cooperative formation network stability controller involved in this application. Specific details such as particular system structures and technologies are presented for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details.

[0015] It should be understood that, when used in this specification, the term "comprising" indicates the presence of the described feature, integral, step, operation, element, and / or component, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0016] The terms "one embodiment" or "some embodiments" used in this application mean that one or more embodiments of this application include the specific features, structures, or characteristics described in that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this application do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Please see Figure 1 The diagram shows a flowchart of a design method for a multi-UAV cooperative formation network stability controller in a specific embodiment. The method includes: Step S101: Establish a mathematical model for a multi-UAV cooperative formation network.

[0019] In some embodiments, when establishing a mathematical model for a multi-UAV cooperative formation network, it is necessary to first determine the dynamic model of each UAV, such as using a second-order linear model to describe its position and velocity changes, including physical parameters such as mass and damping coefficient. Then, the communication topology between UAVs is considered, using an adjacency matrix from graph theory to represent communication connections, clarifying which UAVs interact with each other. Next, the desired formation is defined, with the deviation between the actual and desired positions used as state variables. The effects of external environmental interference and communication delays are also introduced, ultimately representing the entire formation system as a state-space equation containing all UAV states, communication relationships, formation errors, and interference terms.

[0020] As can be seen, this embodiment abstracts the motion characteristics, interaction relationships and external influences of multiple UAVs, transforming the physical-level coordination problem into mathematical equations, thereby achieving a quantitative description of the system's dynamic behavior.

[0021] Step S102: Use Lyapunov–Krasovskii generalized functions as a stability analysis tool.

[0022] When using the Lyapunov–Krasovskii functional as a stability analysis tool in this embodiment, it is necessary to construct a suitable functional form. This functional should include the system's state variables, time-delay related integral terms, and positive definite terms reflecting the system's energy.

[0023] For example, the functional can be composed of a quadratic form of the current state, the integral of the state within the time delay interval, and auxiliary terms related to the time delay, ensuring that the functional itself has positive definiteness and can reflect the energy level of the system.

[0024] This embodiment utilizes Lyapunov stability theory, which states that a system is stable if its functional is positive definite and its derivative with respect to time is negative definite. For multi-UAV systems with time delays, the Lyapunov–Krasovskii functional, by including time-delay-related terms, can more accurately capture the impact of time delays on system stability. Advantages: Compared to traditional Lyapunov functions, it is more suitable for handling systems with time-varying time delays, enabling more precise analysis of system stability conditions and providing an effective analytical tool for ensuring stable coordination among multi-UAV formations.

[0025] Step S103: Differentiate the Lyapunov–Krasovskii functional and take the expectation to obtain the expectation expression containing the system state derivative, time-varying time delay upper and lower limits, and random disturbance term.

[0026] In some embodiments, when differentiating and taking the expectation of the Lyapunov–Krasovskii functional, the derivatives of each term in the functional are calculated separately according to the rules of differentiation in calculus. In particular, for integral terms containing time-varying delays, the influence of the rate of change of the delay on the derivative needs to be considered. After differentiation, due to the presence of random disturbance terms in the system, the expectation of the derivative result needs to be calculated to eliminate randomness and obtain a definite expectation expression. This expression integrates the system state derivative, the upper and lower limits of the time-varying delays, and the statistical characteristics of the random disturbances.

[0027] It should be noted that in this embodiment, the rate of change of the functional over time is obtained by differentiation, reflecting the trend of energy change in the system; the expectation operation is used to handle random factors in the system, transforming the stability analysis of the stochastic system into a deterministic analysis, so that the stability trend of the system can be determined through the expectation expression. Benefits: Unifying the dynamic changes, time delay effects, and random disturbances of the system into a single expression helps to more comprehensively consider the impact of various factors on system stability.

[0028] Step S104: Extract intermediate judgment conditions for system synchronization and stability from the result after taking the expectation through mathematical transformation. The intermediate judgment conditions consist of multiple inequalities including time-varying time delay upper and lower limits, state variables and control parameters.

[0029] In this embodiment, when extracting intermediate criteria for system synchronization and stability from the result of differentiation and expectation through mathematical transformations, mathematical methods such as rearranging terms, combining like terms, and factorization are used to organize and simplify the expectation expression, transforming the complex expression into a series of inequalities that clearly reflect the conditions required for system stability. These inequalities contain key factors such as the upper and lower limits of time-varying time delays, system state variables, and control parameters. Each inequality constrains the system's behavior from different perspectives, collectively constituting the intermediate criteria for system synchronization and stability.

[0030] This embodiment uses mathematical transformations to extract the key parts of the expression directly related to system stability, converting them into inequalities that are easy to analyze and process, thus clarifying the constraints that the system must satisfy to maintain stability. This allows the selection of controller parameters to revolve around satisfying these conditions, improving the relevance and effectiveness of controller design.

[0031] In some specific embodiments, step S104 further includes the following implementation: S1041: Summarize the physical meaning and mathematical relationship of each element (system state derivative, time-varying time delay, random disturbance, etc.) in the result after taking the derivative and expectation, and clarify the coupling relationship of state transmission, time delay effect and disturbance effect in multi-UAV formation network.

[0032] The elements involve system state derivatives, time-varying delays, random disturbances, etc.

[0033] S1042: Based on the characteristics of multi-UAV inspection scenarios, such as formation constraints and state limitations associated with inspection paths, targeted mathematical transformations are performed on the derivative to obtain the expected result, highlighting key terms related to formation stability.

[0034] This embodiment uses mathematical techniques such as inequality transformation and variable substitution, combined with the formation constraints and path constraints of multi-UAV inspection scenarios, to modify the derivative to obtain the expected result, so that the mathematical expression can more directly reflect the scenario's need for stability.

[0035] S1043: Extract the core constraints related to the system's synchronization and stability from the deformed results, and combine them with the actual physical boundaries of time-varying time delay limits, state variables, and control parameters, such as the range of control input amplitude and the reasonable range of state variables, to construct a preliminary set of inequalities.

[0036] This embodiment can be based on the logic of system energy negative definite stability in Lyapunov stability. From the transformed mathematical results, key mathematical terms that can reflect the energy change trend and determine whether the system is stable can be selected. These terms can be combined with quadratic related terms of state variables and attenuation terms of time delay effects. In combination with the control parameters of multiple UAVs and the actual possible value range of state variables, a system of inequalities can be constructed. These inequalities must meet the requirement that the energy trend of the system is conducive to stability.

[0037] S1044: Verify the completeness of the preliminary set of inequalities for determining the synchronous stability of multi-UAV cooperative formation networks, supplement the constraints added due to scenario characteristics, and form the final intermediate determination conditions.

[0038] This embodiment uses proof by contradiction, assuming system instability when conditions are not met, simulating a formation scenario, and verifying whether the initial set of inequalities can accurately determine the stable state. Addressing the non-uniform time delays and environmental disturbances caused by complex terrain in multi-UAV inspections, it analyzes whether any constraints are missing in the initial conditions, supplements the corresponding mathematical terms, and ensures that the conditions fully cover the stability requirements under real inspection scenarios.

[0039] It should be noted that multi-UAV cooperative formation networks exhibit complexities such as time-varying delays and random interference. Their state changes are influenced by their own dynamics, mutual interactions, and external factors. By differentiating the Lyapunov–Krasovskii generalized function and obtaining its expectation, the energy change trend of the system can be captured. Based on the correlation between energy change and system stability, constraints can be extracted from the trend to determine whether the system is synchronously stable. By considering the formation and path characteristics of multi-UAV inspection scenarios, the extracted conditions are made more closely aligned with practical application requirements, ensuring that the controller design can cope with real-world inspection interference.

[0040] Step S105: Under the premise of synchronous asymptotic stability, define parameters related to the upper and lower limits of time delay and state variables, construct a diagonal matrix and multiply it by the intermediate decision conditions before and after, and adjust the expression form.

[0041] Under the premise of synchronous asymptotic stability, this embodiment defines parameters related to the upper and lower limits of time delay and state variables. These parameters need to accurately reflect the range of time delay and the characteristics of state variables. For example, parameters such as the rate of change of time delay and the magnitude of state variables can be defined. When constructing the diagonal matrix, the diagonal elements of the matrix correspond to the defined parameters. By multiplying the diagonal matrix by the intermediate decision conditions before and after, the expression form of the intermediate decision conditions is adjusted, making the coefficients and structure of the expression more regular and facilitating subsequent processing.

[0042] This embodiment can mathematically transform and optimize intermediate decision conditions by defining appropriate parameters and constructing a specific diagonal matrix, adjusting the structure of the expression to better meet the requirements of converting nonlinear inequalities into linear matrix inequalities.

[0043] In some specific embodiments, step S105 specifically includes the following steps: Step S1051: Combining the dynamic change characteristics of state variables during multi-UAV formation flight, and based on the actual fluctuation range of the upper and lower limits of time delay, determine the specific physical meaning and value boundaries of the parameters to ensure the correlation between the parameters and the actual operating state of the system.

[0044] Specifically, this step can employ a linear or nonlinear relationship formula between the parameter and the upper and lower limits of the time delay, such as parameter k = ατ. max +βτ minWhere α and β are coefficients, and τ max τ min The upper and lower limits of the time delay are defined by this formula, which allows the parameters to reflect the impact of the time delay range on the system.

[0045] Step S1052: Based on the weight ratio and mutual influence of each item in the intermediate decision conditions, define the element value rules of the diagonal matrix so that the matrix elements can reflect the importance of different state variables in the system stability.

[0046] Step S1053: Based on the inequality structure of the intermediate judgment condition, select the specific order of multiplication of the diagonal matrix before and after multiplication, and determine the optimal multiplication order through multiple trials to simplify the difficulty of subsequent expression transformation.

[0047] Step S1054: Perform formal normalization on the expression after multiplying the matrix before and after, remove redundant terms and adjust the order of terms to make it conform to the basic format requirements for subsequent conversion into linear matrix inequalities.

[0048] It should be noted that step S105 involves defining parameters related to the key characteristics of the system, constructing a diagonal matrix with specific physical meaning, and adjusting the expression form of the intermediate decision conditions using matrix multiplication and back-multiplication operations. The aim is to eliminate structural factors in the expression that hinder subsequent conversion to linear matrix inequalities, enhance the adaptability of the expression to the actual stability requirements of the system, and lay the foundation for converting the nonlinear inequality system into a solvable linear matrix inequality. Implementation: When defining parameters, the variation law of time delay and the dynamic range of state variables under different flight scenarios of multi-UAV formations are comprehensively considered, ensuring that the parameters not only contain basic characteristic information but also incorporate scenario adaptability factors. When constructing the diagonal matrix, differentiated weight values ​​are assigned to matrix elements based on the priority of the control target. The matrix element configuration is optimized by simulating the matrix effect under different flight states multiple times. When performing matrix multiplication operations, the multiplication order is dynamically adjusted according to the coupling relationship of each item in the intermediate decision conditions. Finally, the expression structure is fine-tuned through iterative steps to ensure that the adjusted form retains key stability information while facilitating subsequent numerical calculations.

[0049] Step S106: The system of inequalities that still contain nonlinear terms after adjustment is equivalently converted into linear matrix inequalities, solved using standard numerical calculation software, and the specific expression of the feedback control law is derived based on the transformed stability judgment conditions to complete the design of the stability controller for the multi-UAV autonomous cooperative formation network.

[0050] Step S106 of this embodiment: When converting the adjusted system of inequalities that still contains nonlinear terms into equivalent linear matrix inequalities, auxiliary variables are introduced, and the properties of matrices and equivalence transformation techniques of inequalities are used to transform the nonlinear terms into linear forms, ensuring that the system of inequalities before and after the transformation is mathematically equivalent. The linear matrix inequalities are solved using the LMI toolbox of MATLAB to obtain the matrix parameters that satisfy the conditions. Based on these parameters, the specific expression of the feedback control law is derived, and the structure and parameters of the controller are determined, thereby completing the stability controller design for the multi-UAV autonomous cooperative formation network. The feedback control law is determined by the solved parameters to ensure that the system meets the stability requirements. This guarantees the stability and cooperative performance of the multi-UAV formation system under various conditions and reduces the difficulty of controller design.

[0051] In some specific embodiments, step S106 further includes the following specific steps: Step S1061: For the nonlinear features such as the time-varying time delay upper and lower limit product terms and the cross product terms of state variables contained in the adjusted inequalities, the nonlinear terms are linearized by introducing auxiliary variables. For example, the product term of the time-varying time delay upper limit τ̄ and the state variable x is expressed as a linear combination of τ̄·x to ensure the feasibility of subsequent matrix operations.

[0052] Step S1062: Define a diagonal matrix with a hierarchical structure based on the dimension of the system state variables, the number of upper and lower limits of time-varying delays, and the dimension of the control input; wherein the main diagonal elements are positive definite matrices related to the norm of the state variables, and the secondary diagonal elements are relaxation variable matrices to compensate for the effects of time-varying delays and signal packet loss, ensuring that the original nonlinear inequalities can be converted into linear forms after matrix multiplication.

[0053] Step S1063: The constructed layered diagonal matrix is ​​divided into blocks using Schur's complement theorem. The inequality containing nonlinear terms is decomposed into multiple submatrix inequalities. By adjusting the position and sign of the submatrixes, the nonlinear cross terms in the original inequality are eliminated, and finally the standard linear matrix inequality (LMI) form is obtained, whose variables only include the controller gain matrix to be designed.

[0054] Step S1064: Verify the feasibility of LMI and solve for the controller parameters. By introducing slack variables to expand the variable set of LMI, and under the premise of ensuring the equivalence of the original stability conditions, the high-dimensional non-convex LMI is transformed into a convex optimization problem. The minimum value of the slack variables is solved using standard numerical calculation software (such as the LMI toolbox of MATLAB), thereby obtaining the controller gain matrix that satisfies the stability conditions.

[0055] As can be seen, step S106 transforms the stability criterion containing nonlinear terms into a numerically solvable linear matrix inequality (LMI), based on the equivalent transformation theory of matrix inequalities and convex optimization theory. By substituting variables, the product of time-varying delays and state variables is transformed into a linear combination, reducing the nonlinear complexity of the problem. A layered diagonal matrix is ​​constructed, and its diagonal dominance property is used to separate the multivariate coupling terms in the original inequality. Cross-terms are eliminated through matrix partitioning and Schur's complement theorem, making the inequality present the standard form of an LMI. Relaxation variables are introduced to transform the non-convex LMI into a convex optimization problem. The optimal values ​​of the relaxation variables are solved using numerical computation software, thus obtaining the controller parameters that satisfy the conditions. This process, through the clever selection of mathematical tools and the optimized design of the matrix structure, solves the problem that the original nonlinear inequality could not be directly solved, ensuring the feasibility and effectiveness of the controller design.

[0056] Furthermore, as a refinement and extension of the specific implementation method of the above-mentioned multi-UAV cooperative formation network stability controller design method, in order to fully illustrate the specific implementation process in this embodiment, the multi-UAV cooperative formation network stability controller design method, considering the existence of communication time-varying delay and synchronization control signal packet loss, establishes and reconstructs the mathematical model of the control system of the multi-UAV autonomous cooperative formation network; selects the controller design method for restoring synchronization stability of the multi-UAV autonomous cooperative formation network derived from the Lyapunov–Krasovskii generalized function; and executes specific steps based on the algorithm for restoring synchronization stability of the multi-UAV autonomous cooperative formation network. Specifically, the steps include the following: For complex networks with multi-UAV formations exhibiting time-varying communication delays and packet loss in synchronization control signals, mathematical modeling is employed. Using functional analysis and probabilistic methods, and by selecting the Lyapunov–Krasovskii functional and Schur's complement theorem, the synchronization stability conditions for restoring a synchronously stable controller in a network containing autonomous cooperative formations of multiple UAVs are derived. By solving a system of inequalities, the controller design method is further deduced.

[0057] Due to the Lurie nonlinear characteristics of rotary-wing UAVs, considering the existence of time-varying communication delays and packet loss of synchronization control signals among multiple UAVs, the multi-UAV cooperative formation network is established as follows:

[0058]

[0059]

[0060] in, , , , and These are the monitored UAV flight state variables, the input variables of the UAV cooperative control algorithm, the external disturbance, and the system output variables, respectively. Based on this, the relationship between the control of the multi-UAV formation system and the formation network can be described as follows: Figure 2 As shown.

[0061] It should be noted that, It is the first derivative of the state vector of the multi-UAV formation system at time t, which describes the rate of change of the UAV state over time. It is the core object for analyzing the dynamic behavior and stability of the system and is used to characterize the evolution trend of the UAV state in the formation. x(t) is the state vector of the multi-UAV formation system at time t, which contains key state information such as UAV position, speed, and attitude. It is the basic data for modeling and analysis and reflects the current overall operating status of the formation. A It describes the coupling relationship of the internal states of a multi-UAV formation system under zero-delay conditions; Ai It reflects the impact of time-varying communication delays on the current system state, and is used to accurately model the formation dynamics affected by delay interference.

[0062] Time-varying communication delay reflects the time lag in information interaction between multiple UAVs. It is a key interference factor affecting the coordination and stability of formation and needs to be carefully considered in modeling and controller design to compensate for the negative impact of delay on formation synchronization and stability. U(t) is the control input applied at time t, used to adjust the state of the multi-UAV formation. It is the operational variable to achieve formation stability and flight along the desired trajectory. One of the design goals of the controller is to determine a suitable u(t) to counteract interference and maintain formation stability. These are external disturbances or nonlinear correlation terms, representing external factors that affect the stability of multi-UAV formations, such as airflow disturbances and environmental interference. They need to be reflected in the model and their effects suppressed by the controller. D correlates the influence of ω(t) on the system state, and D1 correlates another type of disturbance term ω1(t) to quantify the strength of the effect of external disturbance on the state of multi-UAV formation, and to assist in the design of a robust controller.

[0063] B is the control input matrix, with dimensions adapted to the system state vector x(t) and the control input vector u(t). For example, if the system state is n-dimensional and the control input is m-dimensional, B is typically an n×m matrix used to characterize how the control input u(t) affects the state evolution of a multi-UAV formation. In multi-UAV cooperative formation, u(t) represents the formation control command, and B determines the manner and intensity of the control command's influence on the UAV's state (position, attitude, velocity, etc.). When designing a stable controller, it is necessary to optimize u(t) to counteract interference.

[0064] M is the current state output matrix, with dimensions adapted to the system state vector x(t) and output vector z(t). If the state is n-dimensional and the output is p-dimensional, M is a p×n matrix that describes how the current system state x(t) is mapped to the output z(t).

[0065] In formation stability analysis, z(t) is often used as a key feature to extract outputs, such as formation synchronization error and formation deviation, which are key indicators that need to be monitored. M determines which states are used and with what weights to constitute the output, which is the basis for subsequent controller design based on output feedback and system stability analysis, and directly affects the controller's handling of key formation states.

[0066] Ni is the time-delay state output matrix. In multi-UAV formations, communication time-varying delays can occur, and these delays can interfere with the current formation's coordination. For example, UAVs may receive delayed information, affecting formation synchronization. Ni incorporates the impact of time-delay states into the output, allowing stability analysis to cover the correlation between time-delay interference, output characteristics, and system state. This is a crucial step in designing robust controllers. By accurately modeling the effect of time delays on the output using Ni, control strategies can be designed to counteract time delays and ensure formation stability.

[0067] z(t) is the output vector used to extract key state features of a multi-UAV formation system. It can be associated with indicators that need to be monitored and controlled, such as formation synchronization error and formation deviation. It serves as the basis for designing feedback controllers and analyzing system stability.

[0068] It is a nonlinear function, reflecting the Lurie-type nonlinear characteristics present in multi-UAV formation systems, such as UAV dynamic nonlinearity and cooperative interaction nonlinearity. Describing the nonlinear mapping relationship between the output z(t) and the disturbance term ω(t) is crucial for accurately modeling real-world complex formation systems. Controller design must consider its impact on stability and employ adaptation methods to address the challenges posed by nonlinearity.

[0069] , , , and These are the monitored UAV flight state variables, UAV cooperative control algorithm input variables, input variables, external disturbances, and system output variables; Nonlinear connectivity It is a time-varying quantization function with memory rows, and it is piecewise continuous with respect to time t.

[0070] Nonlinear connectivity It is a time-varying quantization function with memory rows, and it is piecewise continuous with respect to time t; its characteristics are globally Lipchitz, and it satisfies the following conditions. , , in, and It is a constant real matrix and satisfies .

[0071] Using appropriate mathematical techniques, the above system can be described as follows:

[0072]

[0073]

[0074] in , These are the upper and lower limits of time-varying delays, used for algorithmic discrimination.

[0075] Therefore, the latency of the formation network can be expressed as: ,

[0076] ,

[0077] in, , These are its upper and lower bounds, respectively; It is time-varying delay fall into The probability of; Is when The probability is The boundary of network latency.

[0078] Therefore, random variables It can be considered as a Bernoulli-distributed white noise, whose mathematical definition is , Therefore, we can obtain , ,in yes The expectation.

[0079] To standardize the above model, we can rewrite the control variables as follows:

[0080] in, , .

[0081] Therefore, considering the existence of time-varying communication delays and packet loss of synchronization control signals, the mathematical model of multi-UAV autonomous cooperative formation network can be reconstructed as follows:

[0082]

[0083]

[0084] , in

[0085]

[0086]

[0087] In this method, the following Lyapunov–Krasovskii functionals are selected:

[0088] in,

[0089]

[0090]

[0091]

[0092]

[0093] V(t) is a Lyapunov–Krasovskii generalized function used to analyze the stability of multi-UAV formation systems. By constructing a suitable energy function, the sign of its derivative is used to determine whether the formation system can remain stable under disturbances such as time-varying delay, nonlinearity, and control signal packet loss. It is the core tool for stability analysis and supports the subsequent derivation of the design conditions for the stable controller.

[0094] In the formula, k=1, 2, 3, 4, 5 are the sub-terms of the generalized function. They characterize the energy of the multi-UAV formation system from the current state energy, the energy accumulation of the time-delay state, and the compensation of the integral term for delay or nonlinearity. Combined, they comprehensively cover the system state, time-delay characteristics, and nonlinear effects, ensuring that Lyapunov analysis can accurately capture the system stability trend under complex disturbances, and provide a basis for deriving stability conditions and controller design.

[0095] It is the first term of the Lyapunov–Krasovskii generalized function. It is the energy fundamental term describing the current state x(t) of the multi-UAV formation system. It is a regular core term in Lyapunov analysis. The positive definiteness of P ensures that the energy of the state itself is measurable and can be used to determine stability. If the derivative of the energy function is negative definite, the state tends to be stable, laying the foundation for subsequent sub-term collaborative analysis of system stability.

[0096] P is a positive definite weighting matrix used to adjust the weight of the current state x(t) in the energy function, so that Lyapunov analysis can accurately reflect the stability trend of a multi-UAV formation system after being disturbed, and assist in deriving the conditions for a stable controller.

[0097] It is the integral term in the Lyapunov–Krasovskii functional that is associated with communication time-varying delay. By integrating the state within different time delay intervals, it compensates for the shortcomings of simply analyzing the current state, more comprehensively characterizes the dynamic characteristics of multi-UAV formation systems under communication delay interference, improves the adaptability of Lyapunov analysis to time delay scenarios, and supports the derivation of stability conditions.

[0098] Q i1 Q i2 Q i3 It is a positive definite weighted matrix used to adjust the weight of the state integral term in different time delay intervals, adapting to the complex characteristics of communication delay in multi-UAV formations, enabling the integral term to accurately capture the interference of time delay on system energy and stability, assisting in the design of robust controllers to offset the negative impact of communication delay and ensure formation stability.

[0099] It is the integral term in the Lyapunov–Krasovskii functional that is associated with control time-varying delay. It addresses the time delay of control command transmission and execution, supplementing the shortcomings of current state and communication delay analysis. It comprehensively covers scenarios where multi-UAV formations are affected by control signal packet loss and delay interference, improves the adaptability of Lyapunov analysis to complex control delays, and provides a more accurate analytical basis for stable controller design.

[0100] R i1 Ri2 R i3 It is a positive definite weighted matrix that adjusts the weights of the state integral terms in different intervals of control delay, adapts to the interference characteristics of control delay on the stability of multi-UAV formation, enables the integral terms to effectively characterize the impact of control delay, assists in the design of controllers to compensate for control delay, and ensures the stability of the formation in scenarios where control signal transmission lags.

[0101] It is a double integral term in the Lyapunov–Krasovskii functional that handles the derivative of time-varying communication delays. By integrating the time delay interval and the state derivative, it makes up for the shortcomings of conventional integral terms in characterizing the rate of change of time delay, improves the adaptability of Lyapunov analysis to the complex time-varying characteristics of communication delays, and ensures that the stability of the formation system can still be accurately analyzed in scenarios with dynamic changes in communication delays, supporting the design of stable controllers.

[0102] Z i1 Z i2 It is a positive definite weighted matrix that adjusts the weights of integral terms related to the derivative of communication time delay, adapts to the interference of the rate of change of communication delay on the stability of multi-UAV formation, and enables the dual integral terms to accurately reflect the impact of dynamic changes in time delay. This assists in the design of the controller to actively compensate for the unstable factors caused by changes in time delay and ensures the stability of the formation.

[0103] It is a double integral term in the Lyapunov–Krasovskii functional that handles the time-varying delay derivative of the control. It integrates the control delay interval and the state derivative, making up for the shortcomings of conventional integral terms in analyzing the rate of change of control delay. It is adapted to complex scenarios such as control signal packet loss and dynamic changes in delay, improves the accuracy of Lyapunov analysis, and provides support for designing stable controllers that can cope with dynamic disturbances in control delay.

[0104] Z i3 Z i4 It is a positive definite weighted matrix that adjusts the weights of the integral terms related to the derivative of the control delay, adapts to the interference of the rate of change of control delay on the stability of multi-UAV formation, and enables the dual integral terms to effectively capture the impact of dynamic changes in control delay, assisting the controller design in compensating for such interference and ensuring the stability of the formation under dynamic changes in control delay.

[0105] Taking the derivative of the whole and taking the expectation, we get

[0106] (28)

[0107] (29)

[0108] (30)

[0109] (31)

[0110]

[0111] Through the corresponding mathematical transformations, we can obtain...

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] in, The expectation is obtained by taking the derivative of the first term V1(t) of the Lyapunov-Krasovskii functional and using it to analyze the changing trend of the current state energy of a multi-UAV formation system. It is the basis for stability determination. If the expectation is negative, it indicates that the system energy has a decaying trend, which is conducive to stability.

[0118] x(t) and x˙(t) are the state vectors and their first derivatives of the multi-UAV formation system at time t, respectively. They reflect the state and rate of change of the UAVs in the formation, such as position, velocity, and attitude. They are the core objects for modeling and analyzing stability, and the trend of state change is directly related to whether the formation is stable and cooperative.

[0119] P: Positive definite weighting matrix, used to construct the Lyapunov functional V1(t)=xT(t)Px(t), adjust the weight of the current state in energy analysis, and affect the sensitivity of stability determination. It needs to be selected reasonably during design so that the analysis can accurately reflect the stability trend of the formation after being disturbed.

[0120] φ(t): A vector associated with the system state or output. Combined with the formulas mentioned earlier, it may be related to nonlinear characteristics and disturbances, reflecting the effect of nonlinearity or disturbances on the state in multi-UAV formations. In the differentiation process, it correlates state changes with the influence of disturbances / nonlinearity, and is a key factor in analyzing formation stability under complex scenarios. By taking the expectation of the derivative of V1(t), the energy change of the current state is quantified. Combined with P and φ(t), the stability trend of the formation system under no-delay / basic state is initially captured, laying the foundation for subsequent analysis of complex factors such as time delays and disturbances.

[0121] The expected value of the integral term V2(t) in the Lyapunov-Krasovskii functional related to the time-varying delay of communication is used to analyze the impact of the state lag introduced by the communication delay on the energy change of the formation system. It is a key analytical term for compensating for communication delay interference and ensuring formation stability.

[0122] τ i τ i1 τ i2 The time parameters related to the time-varying delay of communication characterize the lag characteristics of information interaction between multiple UAVs. They are the core interference factors affecting the coordination and stability of formation. During the differentiation process, the state influence of different time delay intervals is associated through these parameters.

[0123] Q i1 Q i2 Q i3 : Positive definite weighting matrix, used to adjust the weights of the state integral terms in different time delay intervals of V2(t), adapting to the time-varying and segmented effects of communication delay, so that the expected calculation can accurately capture the interference of time delay on system energy and stability, and assist in the design of robust controllers to offset the negative impact of communication delay.

[0124] μ τi These parameters, related to the rate of change of communication time-varying delay, reflect the dynamic characteristics of time delay changes. When taking the expected value after differentiation, they are used to quantify the additional interference of time delay changes on system energy, improving the adaptability of the analysis to time-varying communication delay scenarios. Focusing on the impact of communication time-varying delay on the energy changes of the formation system, this study accurately models the system dynamics under communication delay interference through time delay parameters, weighting matrices, and time-varying rate parameters. This provides a stability analysis basis for designing controllers to compensate for communication delay, ensuring that the formation can still coordinate stably in scenarios with delayed information interaction.

[0125] : is the expectation of the integral term V3(t) in the Lyapunov-Krasovskii functional that is related to the time-varying delay of the control. It is used to analyze the impact of the transmission and execution lag of control commands on the energy changes of the formation system. It is a key analytical term for compensating for control signal packet loss / delay and ensuring the effectiveness of control.

[0126] h i h i1 h i2 The time parameter related to the time-varying delay of the control describes the lag characteristics from the sending to the execution of the control command. It directly affects the adjustment effect of the control input on the formation state and is the core manifestation of control interference.

[0127] R i1 R i2 R i3 : is a positive definite weighted matrix used to adjust the weights of the state integral terms in different control delay intervals in V3(t), adapting to the complex characteristics of control delay, so that the expected calculation can accurately capture the interference of control delay on system energy and stability, assist in the design of controller to compensate for control delay, and ensure that control commands effectively adjust the formation state.

[0128] μ hi Parameters related to the rate of change of control time-varying delay reflect the dynamic characteristics of control delay, such as the rate at which control command lag increases / decreases. When taking the expected value after differentiation, these parameters quantify the additional disturbance of control delay changes to system energy, improving the adaptability of the analysis to time-varying control delay scenarios. Focusing on the impact of control time-varying delay on the energy changes of the formation system, this study accurately models the system dynamics under control command lag disturbances through control delay parameters, weighting matrices, and time-varying rate parameters. This provides a stability analysis basis for designing controllers that compensate for control delay and ensure control effectiveness, ensuring stable coordination of the formation even in scenarios with control signal transmission lag.

[0129] The expected value of the double integral term V4(t) in the Lyapunov-Krasovskii functional, which deals with the derivative of the time-varying delay in communication, is used to analyze the impact of the dynamic changes in the time-varying delay in communication on the energy changes of the formation system in a more refined manner, thus making up for the inadequacy of the conventional integral term in characterizing the rate of change of the time delay.

[0130] , : Related time parameters of time-varying delay in communication are further correlated with the dynamic change range of time delay, supporting the capture of the rate of change of time delay by the dual integral term.

[0131] Zi1 and Zi2 are positive definite weighted matrices used to adjust the weights of the double integral terms related to the communication delay derivative. This adapts to the impact of the communication delay rate of change on system energy and stability, ensuring that the expected value calculation accurately reflects the impact of dynamic delay changes. This assists in designing a controller to proactively compensate for instability caused by delay variations. Addressing the dynamic characteristics of time-varying communication delays, the expected value is obtained by differentiating the double integral terms, allowing for a more refined capture of the impact of the delay rate of change on the formation system's energy. This improves the adaptability of stability analysis to complex communication delay scenarios, providing a basis for designing more robust formation controllers and ensuring stable operation of the formation even with dynamic changes in communication delays.

[0132] The expected value of the double integral term V5(t) in the Lyapunov-Krasovskii functional, which deals with the time-varying delay derivative of the control, is used to analyze the impact of the dynamic changes in the time-varying delay of the control on the energy changes of the formation system in a more refined manner, thus making up for the inadequacy of the conventional integral term in characterizing the rate of change of the control delay.

[0133] h i1 h i2 : It controls the time-varying delay related time parameters, further correlates the dynamic change range of the control delay, and supports the capture of the control delay change rate by the dual integral term.

[0134] Z i3 Z i4 A positive definite weighted matrix is ​​used to adjust the weights of the double integral terms related to the control delay derivative, adapting to the disturbances of the control delay rate of change on system energy and stability. This ensures that the expected value calculation accurately reflects the impact of dynamic changes in control delay, assisting in the design of controllers to actively compensate for instability factors caused by control delay variations. For the dynamic characteristics of time-varying control delays, the expected value is obtained by differentiating the double integral terms, allowing for a more refined capture of the impact of the control delay rate of change on the formation system energy. This improves the adaptability of stability analysis to complex control delay scenarios, providing a basis for designing formation controllers capable of handling dynamic disturbances caused by control delays, and ensuring the effectiveness and stability of formation control.

[0135] The expected value of the derivative of the complete Lyapunov-Krasovskii functional V(t) = ∑k=15Vk(t) is taken. The energy change trend of the multi-UAV formation system under complex interference is comprehensively characterized by taking into account the influence of the current state, communication time-varying delay, control time-varying delay and their dynamic changes. This is the core basis for determining whether the system is stable. If E{V˙(t)} < 0, the system is asymptotically stable.

[0136] ω(t) and K: ω(t) is the external disturbance or nonlinear correlation term, and K is the possible correlation gain matrix. In the comprehensive expectation calculation, it reflects the effect of external disturbance and control strategy on system energy and is a key factor in analyzing robust stability and designing anti-disturbance controller.

[0137] ζ(t), φ(t), ψ(t): Vectors associated with system state, disturbance, and control input. After mathematical transformation, they comprehensively reflect the state deviation, disturbance effects, and control effects of the multi-UAV formation system. They are transformed into stability judgment conditions through tools such as linear matrix inequalities to support the design of stable controllers.

[0138] α and β: Coefficients related to time delay interval segmentation and interference compensation, used to adjust the weights of different interference / time delay compensation terms, adapting to the stability requirements of complex scenarios in multi-UAV formations, enabling the comprehensive expected value calculation to more accurately reflect the actual stability trend of the system, and assisting in controller parameter optimization. Integrating the expected derivatives of each component functional, and transforming them mathematically into a form convenient for stability determination and controller design, comprehensively considering multi-dimensional interference, provides the final judgment basis for system energy changes. This is the core analytical step in designing a stable controller for multi-UAV cooperative formations. By allowing E{V˙(t)}<0, the controller parameter conditions are derived to ensure stable cooperative operation of the formation under complex interference.

[0139] Therefore, when the following n inequalities hold, considering the existence of time-varying communication delays and packet loss of synchronization control signals, the multi-UAV autonomous cooperative formation network is stable:

[0140] in , , , , , , , ,

[0141] , , , , , , ,

[0142] , , , , , , , , ,

[0143] Based on the stability criteria for drone formation networks derived above, and under the premise of synchronous asymptotic stability, define... , , ; , , , Furthermore, by constructing the following diagonal matrix and multiplying it by the aforementioned stability criterion before and after, we can obtain...

[0144] in, And the stability conditions mentioned above Having the same structure, and , The remaining symbols are defined in the same way as those in the stability criterion.

[0145] Because the above system of inequalities exists , Since there are two items, the above system of inequalities is not a linear matrix inequality and cannot be calculated using standard numerical calculation software.

[0146] because The following inequalities Equivalent to Thus, the stability criterion for the control system design method described above can be obtained, therefore the feedback control law is: .

[0147] This application addresses the problem of restoring synchronization stability in a multi-UAV formation network under conditions of time-varying communication delays and packet loss of synchronization control signals. It utilizes mathematical analysis to analyze the corresponding digital time-delay system, deriving a method for calculating the control gain for restoring synchronization stability in a multi-UAV formation network under these conditions. This invention can comprehensively describe a controller design method for restoring synchronization stability in an autonomous cooperative formation network composed of multiple UAVs under conditions of time-varying communication delays and packet loss of synchronization control signals during inspection operations at new energy power plants.

[0148] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0149] The following are embodiments of the multi-UAV cooperative formation network stability controller design system provided in this disclosure. This system and the multi-UAV cooperative formation network stability controller design method of the above embodiments belong to the same inventive concept. For details not described in detail in the embodiments of the multi-UAV cooperative formation network stability controller design system, please refer to the embodiments of the multi-UAV cooperative formation network stability controller design method described above.

[0150] like Figure 3 As shown, the system includes: a model building module 201, used to establish a mathematical model of a multi-UAV cooperative formation network; Frame analysis module 202 uses Lyapunov–Krasovskii generalized functions as a stability analysis tool; The expectation derivation module 203 is used to differentiate the Lyapunov–Krasovskii functional and take the expectation to obtain the expectation expression containing the system state derivative, time-varying time delay upper and lower limits and random disturbance terms. The condition extraction module 204 is used to extract intermediate judgment conditions for system synchronization and stability from the result of taking the expectation after mathematical transformation. The intermediate judgment conditions consist of multiple inequalities including time-varying time delay upper and lower limits, state variables and control parameters. The parameter adjustment module 205 is used to define parameters related to the upper and lower limits of time delay and state variables under the premise of synchronous asymptotic stability, construct a diagonal matrix and multiply it by the intermediate judgment conditions before and after, and adjust the expression form. The formation design module 206 is used to convert the system of inequalities that still contain nonlinear terms after adjustment into equivalent linear matrix inequalities, solve them using standard numerical calculation software, and derive the specific expression of the feedback control law based on the transformed stability judgment conditions, thus completing the design of the stability controller for the multi-UAV autonomous cooperative formation network.

[0151] like Figure 4 As shown, this application also provides an electronic device, including a display module 103, a memory 102, a processor 101, and a computer program stored in the memory and executable on the processor 101. When the processor 101 executes the program, it implements the steps of a multi-UAV cooperative formation network stability controller design method.

[0152] In embodiments of the present invention, electronic devices include, but are not limited to, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments described and / or claimed herein.

[0153] In this embodiment, processor 101 may be implemented using at least one of an application-specific integrated circuit, a programmable logic device, a field-programmable gate array, a processor, a controller, a microcontroller, a microprocessor, or an electronic unit designed to perform the functions described herein. In some cases, such an implementation may be implemented within a controller. For software implementation, implementations such as processes or functions may be implemented with separate software modules that allow the performance of at least one function or operation. Software code may be implemented by a software application (or program) written in any suitable programming language, and the software code may be stored in memory and executed by the controller.

[0154] The display module 103 is used to display information input by the user or information provided to the user. The display module 103 may include a display panel, which may be configured in the form of a liquid crystal display, an organic light-emitting diode, or the like.

[0155] The memory 102 can be used to store software programs and various data. The memory 102 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0156] This application also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of a design method for a multi-UAV cooperative formation network stability controller.

[0157] The storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0158] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for a stable controller for a multi-UAV cooperative formation network, characterized in that the method... Comprise: S101: Establish a mathematical model of multi-UAV cooperative formation network; S102: Based on Lyapunov-Krasovskii function as a stability analysis tool; S103: Derivation of Lyapunov-Krasovskii function and taking the expected operation to get the expected expression containing system state derivative, time-varying time delay upper and lower limit and random disturbance term; S104: Through mathematical transformation, the intermediate judgment condition of system synchronization stability is extracted from the result of derivation and expectation, which is composed of a plurality of inequalities containing time-varying time delay upper and lower limit, state variable and control parameter; S105: Under the premise of synchronization asymptotic stability, define the parameters related to time delay upper and lower limit and state variable, construct diagonal matrix and pre-multiply and post-multiply the intermediate judgment condition, and adjust the expression form; S106: Convert the inequality group still containing nonlinear terms after adjustment into linear matrix inequality form, solve by standard numerical calculation software, and deduce the specific expression of feedback control law based on the converted stability judgment condition, complete the stability controller design of multi-UAV autonomous cooperative formation network.

2. The multi-UAV cooperative formation network stability controller design method according to claim 1, wherein in step S101, a mathematical model is established as follows: x(t) is the state vector of the multi-UAV formation system at time t, reflecting the current overall operation state of the formation; Equation (1) Equation (2) Equation (3) wherein, is the first derivative of the multi-UAV formation system state vector at time t, describing the rate of change of the UAV state over time; Ai A is to describe the coupling relationship of the internal state of the multi-UAV formation system in the case of no delay; 3. The multi-UAV cooperative formation network stability controller design method according to claim 1, wherein the Lyapunov-Krasovskii function in step S102 is: embodies the influence of the delay state on the current system state when there is a time-varying delay in communication. is time-varying communication delay, is the control input applied at time t, which is used to adjust the multi-UAV formation state; is the external disturbance or nonlinear coupling term; D associates the influence of ω(t) on the system state, and D1 associates another type of disturbance term ω1(t), which is used to quantify the strength of the external disturbance on the multi-UAV formation state; B is a control input matrix; M is a current state output matrix; Ni is a time-delay state output matrix; z(t) is an output vector; is a nonlinear function; , , , and are respectively a monitored unmanned aerial vehicle flight state variable, an unmanned aerial vehicle cooperative control algorithm input variable, an input variable, an external disturbance and a system output variable; Nonlinearly linked quantities are memoryless, positive time-varying quantization functions and are piecewise continuous in time t. wherein V(t) is the Lyapunov-Krasovskii function, used to analyze the stability of the multi-UAV formation system; P is a positive definite weighting matrix, used to adjust the weight of the current state x(t) in the energy function; Formula (7) wherein Equation (8) Formula (9) Formula (10) Equation (11) Formula (12) 4. The multi-UAV cooperative formation network stability controller design method according to claim 3, wherein the derivation of Lyapunov-Krasovskii function and the taking of expected operation in step S103 are as follows: k = 1, 2, 3, 4, 5, are partial items of the universal function; is the first term of the Lyapunov-Krasovskii function, is the base term describing the state of the multi-UAV formation system at the current time instant x(t). Through corresponding mathematical transformation is the integral term associated with the time-varying communication delay in the Lyapunov-Krasovskii function; Q i1 , Q i2 , Q i3 is a positive definite weighting matrix used to adjust the weight of the state integral term in different time lag intervals; is the integral term associated with the control time-varying delay in the Lyapunov-Krasovskii function; R i1 , R i2 , R i3 is a positive definite weighting matrix, which adjusts the weights of the state integral terms in different intervals of control delay. is the double integral term related to the derivative of the communication time-varying delay in the Lyapunov-Krasovskii function; Z i1 , Z i2 is a positive definite weighting matrix that adjusts the weights of the communication time delay derivative related integral terms; is a double integral term related to the derivative of the control time-varying delay in the Lyapunov-Krasovskii function; Z i3 , Z i4 is a positive definite weighting matrix that adjusts the weight of the derivative-related integral term of the control time delay. P: positive definite weighting matrix, used to construct Lyapunov function; φ(t): vector associated with system state or output; 5. The multi-UAV cooperative formation network stability controller design method according to claim 3, wherein step S105 specifically comprises: Equation (13) Equation (14) Equation (15) Official (16) Equation (17) According to the dynamic change characteristics of the state variables of the multi-UAV formation flight and the actual fluctuation range of the time delay upper and lower limit, the specific physical meaning and value boundary of the parameters are determined; Equation (18) Equation (19) In formula (13), : the derivative of the first term of Lyapunov-Krasovskii function V1(t) is taken and then the expectation is taken; x(t), : the state vector and its first derivative of the multi-UAV formation system at time t, reflecting the position, speed, attitude state and change rate of the UAVs in the formation According to the weight proportion and mutual influence relationship of each term in the intermediate judgment condition, the element value rule of the diagonal matrix is defined, so that the matrix elements can reflect the importance of different state variables in system stability; In formula (14), τ is the expectation of the integral term in the Lyapunov-Krasovskii functional that relates to the time-varying delay of communication; i τ i1 τ i2 : Time parameters related to communication time-varying delay; Q i1 Q i2 Q i3 : Positive definite weighting matrix, used to adjust the weights of the state integral terms in different time delay intervals of V2(t); μ τi Parameters related to the rate of change of time-varying delay in communication; In equation (15), : derivative of the integral term V3(t) associated with the control time-varying delay in the Lyapunov-Krasovskii function; h i , i1 , i2 : time parameter associated with the control time-varying delay; R i1 , i2 , i3 : positive definite weighting matrix used to adjust the weight of the state integral terms in V3(t) for different control delay intervals; μ hi : parameter associated with the rate of change of the control time-varying delay In equation (16), : The derivative of the double integral term V4(t) related to the derivative of the communication time-varying delay in the Lyapunov-Krasovskii function is taken and expected; τ i1 , τ i2 : The time parameter related to the communication time-varying delay in equation (14); Z i1 , Z i2 : A positive definite weighting matrix used to adjust the weight of the double integral term related to the derivative of the communication time delay. In equation (17), : derivative of the double integral term V5(t) related to the derivative of the control time-varying delay in the Lyapunov-Krasovskii function after taking expectation; h i1 , i2 : same as h in equation (15); Z i3 , i4 : positive definite weighting matrix for adjusting the weight of the double integral term related to the derivative of the control time delay. Equation (18), Equation (19) in, : Take expectation after derivation of complete Lyapunov-Krasovskii function V(t)=∑k=15Vk(t); ω(t), K: ω(t) is external disturbance or nonlinear correlation term, K is correlation gain matrix; ζ(t), φ(t), ψ(t): vectors associated with system state, disturbance, control input; α, β: coefficients related to time delay interval segmentation and disturbance compensation. According to the inequality structure characteristics of the intermediate judgment condition, the specific order of pre-multiplication and post-multiplication of the diagonal matrix is selected, and the optimal multiplication order is determined through multiple trials. ​ ​ ​ ​ The expressions after the front multiplication and the post-multiplication matrix are formally regularized, redundant terms are removed, and the arrangement of each term is adjusted to meet the format requirements for subsequent conversion to linear matrix inequalities.

6. The multi-UAV cooperative formation network stability controller design method of claim 1, wherein, Step S104 specifically includes: S1041: Sort out the physical meaning and mathematical correlation of each element in the derivative expectation result, and clarify the coupling relationship of state transmission, time delay influence, and disturbance effect in the multi-UAV formation network; S1042: According to the characteristics of the multi-UAV inspection scene, perform targeted mathematical transformation on the derivative expectation result to highlight the key items related to formation stability; S1043: From the transformed result, extract the core constraints related to system synchronization stability, combine the actual physical boundaries of the upper and lower limits of the time-varying time delay, state variables, and control parameters, and construct a preliminary inequality set; S1044: Verify the completeness of the preliminary inequality set for multi-UAV cooperative formation network synchronization stability judgment, supplement the newly added constraint items due to scene characteristics, and form the final intermediate judgment condition.

7. The multi-UAV cooperative formation network stability controller design method of claim 1, wherein, Step S106 specifically includes: For the nonlinear characteristics such as the product of the upper and lower limits of the time-varying time delay and the cross product of the state variables included in the adjusted inequality, linearize the nonlinear terms by introducing auxiliary variables; According to the dimensions of the system state variables, the number of upper and lower limits of the time-varying time delay, and the dimensions of the control input, define a diagonal matrix with a hierarchical structure; Use the Schur complement theorem to block process the constructed hierarchical diagonal matrix, decompose the inequality containing nonlinear terms into multiple submatrix inequalities, adjust the position and sign of the submatrix to eliminate the nonlinear cross terms in the original inequality, and finally obtain the standard linear matrix inequality form; By introducing relaxation variables to expand the variable set of LMI, convert the high-dimensional non-convex LMI into a convex optimization problem, solve the minimum value of the relaxation variable, and thus obtain the controller gain matrix that satisfies the stability condition. 8.A system for designing a multi-UAV cooperative formation network stability controller, characterized in that, The system is used to implement the multi-UAV cooperative formation network stability controller design method of any one of claims 1 to 7; The system includes: A model construction module for establishing a mathematical model of a multi-UAV cooperative formation network; A framework analysis module based on Lyapunov-Krasovskii functional as a stability analysis tool; An expectation derivation module for deriving and taking expectation of the Lyapunov-Krasovskii functional to obtain an expectation expression containing system state derivatives, time-varying time delay upper and lower limits, and random disturbance terms; A condition extraction module for extracting an intermediate judgment condition for system synchronization stability from the derivative expectation result through mathematical transformation, the intermediate judgment condition consisting of multiple inequalities containing time-varying time delay upper and lower limits, state variables, and control parameters; A parameter adjustment module is configured to define parameters related to upper and lower limits of time delay and state variables under the premise of synchronization asymptotic stability, construct diagonal matrices and intermediate decision conditions for pre-multiplication and post-multiplication, and adjust expression forms. A formation design module is configured to equivalently convert the inequality group still containing nonlinear terms after adjustment into a linear matrix inequality form, solve through standard numerical calculation software, and derive specific expressions of a feedback control law based on the converted stability decision condition to complete stability controller design of a multi-unmanned aerial vehicle autonomous cooperative formation network.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the multi-unmanned aerial vehicle cooperative formation network stability controller design method according to any one of claims 1 to 7 when executing the program.

10. A storage medium having stored thereon a computer program, characterized in that The computer program implements the steps of the multi-unmanned aerial vehicle cooperative formation network stability controller design method according to any one of claims 1 to 7 when executed by the processor.

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