A cooperative string stability prediction control method based on unmanned aerial vehicles

Abstract

The application particularly relates to a cooperative string stability model predictive control method based on unmanned aerial vehicles, and belongs to the field of unmanned aerial vehicle control, and comprises the following steps: establishing a discrete time state space model of a following unmanned aerial vehicle; introducing a step factor beta, and establishing a determination relationship between control increments at each step in a future prediction time domain and a current time control increment; based on the state space model and the determination relationship, establishing a local optimization problem of a distributed model predictive controller for the following unmanned aerial vehicle; in a control period, the following unmanned aerial vehicle solves the local optimization problem, obtains an optimal current control increment, updates a current control quantity and outputs the current control quantity to an executing mechanism, and cooperative control of the unmanned aerial vehicle is realized. The application also relates to a cooperative string stability model predictive control system based on unmanned aerial vehicles, an electronic device and a computer readable storage medium. The application adopts a distributed efficient model predictive control strategy, and ensures that different types of unmanned aerial vehicles can maintain the stability and string stability of a queue when flying in formation.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, specifically to a cooperative string-stability predictive control method for multi-UAV formation flight scenarios, employing a distributed parameterized model predictive queue control algorithm. Background Technology

[0002] The rapid development of unmanned aerial vehicle (UAV) technology has yielded remarkable achievements in military, commercial, and scientific research fields. With the widespread application of UAVs, the requirements for their flight performance are becoming increasingly stringent. During UAV flight, string stability, as an important dynamic characteristic, plays a crucial role in flight control and navigation.

[0003] String stability refers to whether a drone's flight trajectory can be maintained within a stable plane or three-dimensional space during flight. The string stability of a drone directly affects its maneuverability, stability, and safety, thus becoming a focus of research. In traditional aircraft, string stability has long been a widely studied topic, with a primary focus on stability and control. However, with the rise of drones, their unique structure and application requirements have made the string stability problem more complex and diverse.

[0004] Unmanned aerial vehicles (UAVs) come in many varieties, including fixed-wing UAVs, multi-rotor UAVs, and vertical takeoff and landing (VTOL) UAVs. They differ significantly in design, and their string stability requirements vary accordingly. The structural design of the UAV, the performance of its power system, the control algorithm, and weather conditions are all important factors affecting string stability. For example, fixed-wing UAVs typically have a larger wingspan and wing area, making it relatively easier to maintain string stability, while multi-rotor UAVs, due to their unique rotor structure, require more complex control systems to maintain stable flight. Traditional PID control algorithms have achieved some success in maintaining UAV string stability; however, their ability to handle complex disturbances and nonlinear systems is limited.

[0005] In existing technologies, ensuring the stability and chordal stability of different types of UAVs in formation flight, especially under conditions of communication delays and external interference, remains a critical technical challenge. While traditional model predictive control can handle constrained problems, its computational complexity is too high over long prediction time domains, making it difficult to meet the real-time requirements of UAV flight control systems. Furthermore, it cannot effectively utilize historical mission data for self-optimization, limiting its large-scale application in complex dynamic environments. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of traditional model predictive control in handling nonlinear UAV platoon control problems with communication delays and interference, such as high computational load, poor real-time performance, inability to guarantee string stability, and lack of self-learning and optimization capabilities. This invention provides a cooperative string-stability predictive control method based on UAVs. For UAV platoon systems with forward and backward communication topologies and constrained linear dynamic models, a distributed and efficient model predictive control strategy is adopted to ensure that different types of UAVs can maintain platoon stability and string stability during formation flight.

[0007] To achieve the above objectives, on the one hand, the present invention provides a cooperative string-stability predictive control method based on unmanned aerial vehicles (UAVs), applied to a convoy system including one lead UAV and multiple follower UAVs, characterized by comprising the following steps: Step 1: Establish a discrete-time state-space model for each following drone, defining state variables including position, velocity, and acceleration, as well as control inputs including throttle commands; Step 2: Introduce the step factor β to establish a deterministic relationship between the control increments at each step in the future prediction time domain and the control increment at the current time. This simplifies the optimization problem of the multi-step control increment sequence into a univariate optimization problem with the control increment at the current time as the decision variable. The deterministic relationship is as follows: , Let be the predictive control increment for the i-th following drone at time k for the m-th future step. Let be the current control increment to be solved at time k; m is the prediction step number; β is an adjustable parameter that satisfies 0 < β; Step 3: Based on the state space model and the deterministic relationship, construct a local optimization problem for a distributed model predictive controller for each following UAV. The objective function of the optimization problem is used to minimize the deviation between the UAV's own state and the desired state determined by the preceding UAV's state. The constraints of the optimization problem include at least system dynamic constraints and actuator physical constraints, as well as spacing error propagation constraints to ensure the chordal stability of the queuing system. Step 4: In each control cycle, each following UAV solves the local optimization problem to obtain the optimal current control increment Δu. i (k), and according to Δu i (k) Update the current control variable u i (k) = u i (k-1)+ Δu i (k) and output to the actuator to achieve coordinated control of the drone.

[0008] Furthermore, in step 1, the discrete-time state-space model is in incremental form to control the increment Δu. i(k)=u i (k)-u i (k-1) is used as the system input.

[0009] Furthermore, the spacing error propagation constraint in step 3 is specifically as follows: The maximum spacing error of any UAV behind in the queue should be less than a fixed proportional coefficient γ of the maximum spacing error of the UAV directly communicating with it in front. i γ i Between 0 and 1.

[0010] Furthermore, in step 4, solving the local optimization problem involves transforming the constraints into matrix operations and then explicitly solving them using the Moore-Penrose generalized inverse matrix.

[0011] Furthermore, the UAV-based cooperative string-stabilized predictive control method also includes an iterative learning control step for repetitive flight missions: after each mission batch is completed, the initial value or reference trajectory of the controller for the next batch is updated according to a preset learning law using the inter-batch error information generated during the current flight, so as to improve the control accuracy in subsequent batches.

[0012] Furthermore, the iterative learning control step adopts a phased learning strategy, dividing the entire task process into multiple consecutive flight phases, designing an independent iterative learning law for each phase, and using a transition function near the phase switching point to weight and fuse the learning laws of adjacent phases in order to suppress control command jumps.

[0013] Furthermore, the step factor β is scheduled according to different flight phases: When a fast dynamic response is required, select 0 < β < 1; when a stable operating state is required, select β > 1.

[0014] To achieve the above objectives, in a second aspect, the present invention also provides a cooperative string stability predictive control system based on unmanned aerial vehicles (UAVs), for implementing the aforementioned UAV-based cooperative string stability predictive control method, comprising: The model building module is used to perform step 1 and build a discrete-time state-space model for each following UAV. The control simplification module is used to execute step 2, introducing a step factor β to simplify the optimization problem of the multi-step control increment sequence into a single-variable optimization problem. The optimization and solution module is used to execute steps 3 and 4, construct and solve the local optimization problem for each following UAV, and obtain the optimal control increment; An execution module, deployed on each follower drone, is used to receive control commands output by the optimization solution module and convert them into drive signals to control the flight status of the drone.

[0015] To achieve the above objectives, in a third aspect, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the above-described cooperative string stability predictive control method based on unmanned aerial vehicles.

[0016] To achieve the above objectives, in a fourth aspect, the present invention also provides a computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the above-described cooperative string-stabilized predictive control method based on unmanned aerial vehicles.

[0017] Compared with the prior art, the present invention has the following beneficial technical effects: Significantly improves computational efficiency and meets real-time requirements: By introducing a step factor β, the solution for future multi-step control increments is simplified to the solution for single-step control increments, transforming the complex high-dimensional sequence optimization problem into simple low-dimensional matrix operations, and even yielding analytical solutions. This results in an order-of-magnitude reduction in online computation, fundamentally solving the problem of high computational complexity in traditional model predictive control. This enables the algorithm to run in real-time on resource-constrained embedded flight control systems, meeting the real-time requirements of large-scale formation distributed control.

[0018] Superior control performance, balancing responsiveness and smoothness: By flexibly designing the value of the step factor β, the control strategy can be adjusted according to mission requirements, achieving an optimal balance between rapid response and smooth operation, enabling dynamic adjustment of the control strategy. When 0 < β < 1, the system responds quickly and has strong dynamic adjustment capabilities, suitable for agile scenarios such as formation formation and speed change tracking; when β > 1, the control output is smooth, effectively reducing actuator wear and saving energy, suitable for stable operation modes such as long-endurance cruise. This flexibility allows the controller to achieve the optimal balance between rapid response and smooth operation.

[0019] Possessing continuous self-learning and optimization capabilities, control accuracy improves over time: It combines iterative learning control with stepped model predictive control. For cyclically executed UAV missions, the system can utilize historical batch flight data and automatically correct control commands through a dynamic model of inter-batch state errors. As the number of mission batches increases, the system effectively overcomes repetitive interferences such as model uncertainty and constant wind disturbances, achieving progressively higher control accuracy and surpassing the model's inherent precision in tracking performance.

[0020] The invention boasts strong engineering practicality, fully guaranteeing system reliability and safety: It rigorously considers the physical constraints of the actuators in the optimization problem, limiting the control variables and their rate of change within a feasible range, fundamentally avoiding the generation of infeasible commands and ensuring flight safety. Simultaneously, through a phased iterative learning strategy and transition processing between phases, it effectively suppresses control command jumps that may occur during the switching between different flight phases, ensuring the continuity and stability of the entire mission. Furthermore, the distributed architecture based on a forward-following communication topology allows each UAV to require only information from the preceding UAV, reducing the communication burden and enhancing system scalability. Attached Figure Description

[0021] Figure 1 The flowchart of the cooperative string-stability predictive control method based on UAV provided in the embodiment of the present invention is shown. The method adopts a step-by-step model predictive control algorithm. The step-by-step model predictive control algorithm estimates the state through a Kalman filter, minimizes the estimation error of the UAV state through a recursive method, and achieves short-term prediction through iterative calculation of the state-space model. Detailed Implementation

[0022] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments.

[0025] This invention provides a cooperative string-stability predictive control method based on unmanned aerial vehicles (UAVs). For the cooperative control problem of a following heterogeneous UAV swarm system, a distributed MPC strategy is proposed to guarantee the string stability of the swarm system. This strategy transforms the constrained optimization problem into matrix operations by staggering the control sequence and using iterative computation, significantly reducing online computation time and ensuring that all feasible solutions satisfy the system constraints and string stability conditions. Sufficient conditions for asymptotic stability of the system are established using Lyapunov's stability theorem and Moore-Penrose's generalized inverse matrix, and the tracking performance of the system is analyzed.

[0026] The present invention discloses a cooperative string-stabilized predictive control method based on unmanned aerial vehicles (UAVs), comprising the following steps: Step 1: Establish the longitudinal dynamics model of the UAV A formation of n+1 drones flying on the same horizontal plane is established, in which one drone acts as the lead drone, numbered 0; the remaining n drones are follower drones, numbered from 1 to n. Flight status of the pilot drone = ,in, The location of the lead drone. To guide the speed of the drone, Acceleration for the lead drone; the flight status of the lead drone provides a reference benchmark for the platoon; The following drones adopt a forward-following communication topology, that is: the first following drone receives flight status information from the lead drone; the i-th following drone only receives flight status information from the (i-1)-th following drone directly in front of it (i≥2). Assuming an ideal communication network between drones, with no latency or packet loss; the control objective of each following drone is to maintain a fixed, desired safe distance from the drone it is directly communicating with. ; Each follower drone's flight follows Newton's second law, and its dynamic model considers the following types of forces: the driving force provided by the engine, air resistance proportional to the square of the velocity, constant mechanical friction resistance, and gravity. The engine's dynamic response is modeled as a time constant τ with inertia. i The first-order function; the dynamic model of the following UAV is a nonlinear dynamic model. By linearizing the nonlinear dynamic model of the following UAV at typical operating points and compensating for gravity and constant mechanical friction resistance, the u of the i-th following UAV is obtained. i (k) is a simplified first-order dynamic model with input and acceleration as output; where u i (k) represents the control input of the i-th following UAV at sampling time k, which is the power adjustment command. This model is a continuous-time model, indicating that the acceleration response of the UAV can be regarded as a first-order inertial process, and its time constant is determined by the engine characteristics. To facilitate digital controller design, the above continuous-time model is discretized with a fixed sampling period h, resulting in a discrete-time state-space model suitable for computer control: (k+1) = (k)+ (k) (1) in, The discrete-time state matrix, = ; For the input matrix, = ;τ i Let be the inertial time constant of the i-th follower drone engine; (k) represents the control input of the i-th following UAV at sampling time k, which is the power adjustment command; (k) is the flight state vector of the i-th following UAV at sampling time k. = ,in, Let i represent the position, velocity, and acceleration of the i-th following UAV at sampling time k, respectively; k represents the sampling time; and i is the UAV number, i∈[1,n]; The discrete-time state-space model establishes the mathematical relationship between the current flight state, the next flight state, and the current control input; To improve control smoothness, this invention uses control increment as the optimization variable. By solving for and gradually accumulating the control increment, the actual control command applied to the actuator is obtained. Based on the discrete-time state-space model, the queue state prediction relationship at multiple future sampling times can be recursively obtained. Specifically, at the current time k, based on the current flight state of the following UAV and combined with the control increment sequence for the next N steps in the prediction time domain, the flight state evolution trajectory within the next N steps is recursively predicted; the state prediction vector and control increment vector of the i-th following UAV in the prediction time domain are defined as follows: (k) ≜ (2) Δ (k) ≜ (3) in, (k) represents the prediction vector of the i-th following UAV at the current time k for the next N steps of flight state. It is used to stack the state variables of each future step in a unified form so as to construct the state prediction model and optimize the objective function later; Δ (k) represents the prediction vector of the i-th following UAV at the current time k for the control increment of the next N steps. It is used to write the control increment of each future step in a unified vector form so as to solve it together with the state prediction model. The above prediction relationship is given by a constant matrix determined by system parameters; N is the prediction time domain length, which is an adjustable parameter; the larger the value of N, the stronger the controller's ability to predict future states, but the corresponding computational complexity will also increase. The control objectives of following a drone involve three levels, which must be met simultaneously: Speed ​​consistency: During platooning, the speed of all following drones should eventually match the speed of the lead drone; Spacing Maintenance: The actual distance between each follower drone and its lead drone should eventually stabilize at the desired fixed spacing. ; String stability: The queue must have the ability to suppress and attenuate the backward propagation of spacing errors. Specifically, the maximum spacing error of any UAV behind the queue (i≥2) should be less than a fixed proportionality coefficient γ of the maximum spacing error of the UAV directly communicating with it (i-1). i γ i Between 0 and 1, this ensures that local disturbances are not amplified step by step as they propagate along the queue, but rather gradually decay; The above control objective can be further expressed as: (4) Among them, e i (k) represents the distance error of the i-th following UAV relative to its predecessor at sampling time k, used to measure the deviation between the actual distance and the expected safe distance; γ i This represents the string stability attenuation coefficient corresponding to the i-th following drone, used to limit the maximum amplification of the error during the queuing propagation process; If the above conditions still hold when the reference speed of the lead drone changes, it indicates that the entire platoon can still converge to a new balanced operating state with consistent speed and constant spacing after undergoing transient adjustments. Step 2, Basic Algorithm of Stepped Model Predictive Control To address the issues of excessive computational complexity and insufficient real-time performance of traditional model predictive control over long prediction time domains, this invention proposes a stepped model predictive control algorithm. The core of this algorithm lies in parameterizing the multi-step control increment sequence that originally needed to be optimized separately within the prediction time domain into a sequence uniquely determined by the current control increment through a preset stepped structure, thereby reducing the dimensionality and computational burden of the optimization problem while ensuring control performance. In traditional model predictive control, it is usually necessary to solve the control increment sequence for multiple future times at each sampling time. This invention introduces an adjustable step factor β to establish a definite proportional relationship between the control increment at each future time and the current control increment. Specifically, the control increment of the i-th following UAV at sampling time k is defined as Δu. i (k)=u i (k)-u i (k-1); Starting from the current time k, the predictive control increment Δu at the m-th step in the future. i (k+m|k) is determined by the current control increment Δui (k) is determined together with the m-th power of the step factor β: (5) Formula (5) is used to construct the stepwise change law of the control increment in the prediction time domain, so that the control increments in each future step are no longer independent optimization variables, but are obtained by recursion from the current control increment according to a preset ratio. The value of the step factor β is a key parameter of the algorithm, which directly affects the distribution characteristics of the predicted control sequence in the time domain. When 0 < β < 1, the future control increment gradually decreases with the increase of the prediction step, indicating that the algorithm assigns higher weight to the current control action while reducing the amplitude of the long-term control action. This setting helps to improve the smoothness of the control input and enhance the stability and feasibility of the control strategy. When β=1, the control increments at each step in the prediction time domain maintain the same amplitude, and the control increment sequence is of equal amplitude distribution. When β>1, the future control increment gradually increases with the increase of the prediction step, indicating that the algorithm relatively enhances the weight of the long-term control action. This setting may increase the system's adjustment strength to long-term state changes, but it will also increase the control input amplitude and the risk of system oscillation. Therefore, it usually needs to be carefully selected in combination with system stability and actuator constraints. Through the above construction, the control increment vector ΔU throughout the entire prediction time domain i (k) can be represented as the current control increment Δu i The product of (k) and the fixed structure coefficient vector, i.e. the future control increment sequence, is compressed into a parameterized form determined by a single variable; thus, the original multidimensional optimization variable can be reduced to one dimension, fundamentally reducing the complexity of the optimization problem and improving the efficiency of online solution. Step 3, Stepped model prediction iterative learning control algorithm To further improve the control accuracy and adaptability of UAV platoons in repetitive flight missions such as periodic cruises and formation keeping, this invention innovatively incorporates the idea of ​​iterative learning control into the stepped model predictive control framework, forming a stepped model predictive iterative learning control algorithm. When a drone performs the same or similar flight missions multiple times, referred to as batch missions, its dynamic characteristics and environmental disturbances are often repetitive. Iterative learning control aims to use the control experience and error information of historical batch missions to continuously correct the control law of the current batch mission, thereby achieving successive performance improvements.

[0027] Considering that UAV missions may include multiple flight phases with different characteristics, such as acceleration, constant speed, and deceleration, this invention adopts a phased iterative learning strategy to divide the entire mission process into several consecutive phases, for example, by flight state or route segmentation; within each phase, the dynamic characteristics of the system are considered to be repeated; the algorithm allows for the design of independent iterative learning laws for each phase, but special attention should be paid to the control smoothness near the phase switching point to avoid system oscillation or performance degradation caused by abrupt changes in the control law. In the j-th flight phase, let u j (s,r) represents the control command at the s-th sampling time within flight phase j of the r-th mission batch, and its iterative update follows the formula: (6) That is, by utilizing the control experience from the previous batch at the same stage and time, and adding the correction terms from the current batch, the control instructions for the current batch are formed; where the update quantity r j (s,r) is a modification term to be designed; This formula makes full use of historical control information, making the learning process inheritable; To facilitate the description of the changes in system variables across both time and batch dimensions, two difference operators are introduced: Time difference operator δT: used to describe the change of a signal, such as flight state x, control vector u, or output y, between adjacent sampling times within the same batch; Batch differential operator δr: used to describe the change of a certain signal quantity at the same relative sampling time within the same flight phase between adjacent batches. This signal quantity includes flight state x, control vector u, or output y. Update volume r j The design of (s,r) is the core of this algorithm. This invention uses the idea of ​​model predictive control to construct r. j (s,r), specifically, a dynamic model of the state error between batches is established: the change in state between adjacent batches within the same stage is determined by the system dynamic matrix C of that stage (stage j). j Control matrix D j And the amount of updates to be updated, r j (s,r) are jointly determined; this model reveals the mechanism by which current batch control corrections eliminate inter-batch state deviations: = (7) Based on this, an optimization objective oriented towards inter-batch performance is designed, such as minimizing the deviation between the current batch and the desired trajectory, while simultaneously limiting the size of the update quantity. By combining this objective with the dynamic model of inter-batch state error, the optimal update quantity sequence r can be solved online. j(s,r), this process is essentially a small-scale predictive control problem with low computational burden; The algorithm strictly considers the physical limits of the actuator and imposes a hard constraint on the rate of change δT(u) of the control command u, limiting the maximum change of the control command between adjacent time points, and ensuring that the generation of the control command is feasible and safe.

[0028] To achieve a smooth transition between different flight phases, the algorithm introduces an overlapping region or transition function near the phase switching moment and performs weighted fusion of the learning laws of adjacent phases, thereby effectively suppressing the control command jump caused by phase switching and ensuring the continuity and stability of control throughout the entire flight. Step 4, Iterative steps of the ladder model predictive queue controller Step 1, Design Parameters: Select the prediction time domain length N and the string stability attenuation coefficient γ i and step factor β; Step 2: Based on the batch-to-batch error dynamic model and constraints, construct the corresponding model predictive control solution process; Step 3: At each sampling time k, perform the following operations sequentially for each local optimization problem: ① Measure the current flight status of the UAV and the information of the preceding aircraft, and calculate the current control increment Δu of the UAV based on the local optimization problem. i (k); ② Determine whether the desired control increment satisfies the chord stability constraint and actuator constraint of formula (4); ③ If satisfied, proceed to step ④; if not satisfied, adjust the relevant parameters according to the constraint contraction strategy and solve again until the constraint conditions are met. ④ According to = + Update the control quantity and apply the updated control command to the control system; ⑤ Set k=k+1 and enter the next sampling period.

[0029] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and all such modifications and improvements fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A cooperative string-stability predictive control method based on unmanned aerial vehicles (UAVs), applied to a platoon system comprising one lead UAV and multiple follower UAVs, characterized in that, Includes the following steps: Step 1: Establish a discrete-time state-space model for each following drone, defining state variables including position, velocity, and acceleration, as well as control inputs including throttle commands; Step 2: Introduce the step factor β to establish a deterministic relationship between the control increments at each step in the future prediction time domain and the control increment at the current time. This simplifies the optimization problem of the multi-step control increment sequence into a univariate optimization problem with the control increment at the current time as the decision variable. The deterministic relationship is as follows: , Let be the predictive control increment for the i-th following drone at time k for the m-th future step. Let be the current control increment to be solved at time k; m is the prediction step number; β is an adjustable parameter that satisfies 0 < β; Step 3: Based on the state space model and the deterministic relationship, construct a local optimization problem for a distributed model predictive controller for each following UAV. The objective function of the optimization problem is used to minimize the deviation between the UAV's own state and the desired state determined by the preceding UAV's state. The constraints of the optimization problem include at least system dynamic constraints and actuator physical constraints, as well as spacing error propagation constraints to ensure the chordal stability of the queuing system. Step 4: In each control cycle, each following UAV solves the local optimization problem to obtain the optimal current control increment Δu. i (k), and according to Δu i (k) Update the current control variable u i (k) = u i (k-1)+ Δu i (k) and output to the actuator to achieve coordinated control of the drone.

2. The cooperative string-stability predictive control method based on unmanned aerial vehicles according to claim 1, characterized in that, The discrete-time state-space model is in incremental form to control the increment Δu. i (k)=u i (k)-u i (k-1) is used as the system input.

3. The cooperative string-stability predictive control method based on unmanned aerial vehicles according to claim 1, characterized in that, The spacing error propagation constraint in step 3 is specifically as follows: The maximum spacing error of any UAV behind in the queue should be less than a fixed proportional coefficient γ of the maximum spacing error of the UAV directly communicating with it in front. i γ i Between 0 and 1.

4. The cooperative string-stability predictive control method based on unmanned aerial vehicles according to claim 1, characterized in that, In step 4, solving the local optimization problem involves transforming the constraints into matrix operations and then explicitly solving them using the Moore-Penrose generalized inverse matrix.

5. The cooperative string-stability predictive control method based on unmanned aerial vehicles according to claim 1, characterized in that, It also includes an iterative learning control step for repetitive flight missions: after each mission batch is completed, the initial value or reference trajectory of the controller for the next batch is updated according to a preset learning law using the inter-batch error information generated in this flight, so as to improve the control accuracy in subsequent batches.

6. The cooperative string-stability predictive control method based on unmanned aerial vehicles according to claim 5, characterized in that, The iterative learning control step adopts a phased learning strategy, dividing the entire mission process into multiple consecutive flight phases, designing an independent iterative learning law for each phase, and using a transition function near the phase switching point to weight and fuse the learning laws of adjacent phases in order to suppress control command jumps.

7. The cooperative string-stability predictive control method based on unmanned aerial vehicles according to claim 1, characterized in that, The step factor β is scheduled according to different flight phases: When a fast dynamic response is required, select 0 < β < 1; when a stable operating state is required, select β > 1.

8. A cooperative string stability predictive control system based on unmanned aerial vehicles (UAVs), used to implement the cooperative string stability predictive control method based on UAVs as described in any one of claims 1 to 7, characterized in that, include: The model building module is used to perform step 1 and build a discrete-time state-space model for each following UAV. The control simplification module is used to execute step 2, introducing a step factor β to simplify the optimization problem of the multi-step control increment sequence into a single-variable optimization problem. The optimization and solution module is used to execute steps 3 and 4, construct and solve the local optimization problem for each following UAV, and obtain the optimal control increment; An execution module, deployed on each follower drone, is used to receive control commands output by the optimization solution module and convert them into drive signals to control the flight status of the drone.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the cooperative string-stabilized predictive control method based on unmanned aerial vehicles as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the UAV-based cooperative string-stabilized predictive control method as described in any one of claims 1 to 7.

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