A morphing aircraft control method and system based on reachable set solution

Abstract

This application provides a control method and system for deformable aircraft based on reachability set calculation. The method includes: acquiring the real-time flight state and current mission command of the deformable aircraft; generating a state target set based on the current mission command; calculating and generating a reachable set of the state target set in the state space based on the level set method according to the real-time flight state, a preset aircraft dynamics model, and preset constraints, wherein the aircraft dynamics model is constructed based on the design parameters of the deformable aircraft; determining the current safety state boundary of the deformable aircraft based on the boundary of the reachable set; determining the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space; and performing real-time control of the deformable aircraft according to the control method corresponding to the flight safety level to improve the safety of the deformable aircraft during flight.

Description

Technical Field

[0001] This application relates to the field of aircraft control technology, and in particular to a deformable aircraft control method and system based on reachability set solution. Background Technology

[0002] Deformable aircraft can change their shape in real time according to the flight environment and mission requirements to optimize aerodynamic performance and extend their flight envelope. However, this capability makes their dynamic models exhibit complex characteristics of strong nonlinearity, rapid time-varying, and multi-modal switching. These characteristics make it difficult to accurately and quickly describe and calculate the safety boundary of the flight state—that is, the set of states that can guarantee the stability and controllability of the aircraft under permissible control inputs. If the flight state accidentally exceeds this boundary, it can easily lead to a runaway accident. Therefore, how to solve this dynamically changing "maximum controllable boundary" online and efficiently is the core challenge to ensure the flight safety of deformable aircraft and fully unleash their performance potential. Reachability set theory provides a powerful mathematical framework for solving this problem. By systematically describing the set of all initial states that can reach the target state under given control constraints, it lays the theoretical foundation for the quantitative analysis of dynamic safety boundaries.

[0003] To ensure flight safety, existing technologies have proposed various methods for determining and protecting safety boundaries. These mainly include: stability domain analysis methods based on Lyapunov energy functions to construct the system's attraction domain; methods based on bifurcation and catastrophe theory to analyze equilibrium point bifurcation behavior; and methods based on specific fluid kinematics theories to establish stall boundary models. However, these methods all have significant limitations when applied to deformable aircraft. For example, the Lyapunov method often results in overly conservative safety boundaries due to the lack of a universal standard for energy function selection; while bifurcation and catastrophe theory is applicable to high-order nonlinear systems, its computational complexity is too high, making it difficult to meet real-time requirements; and methods based on specific fluid models fail to fully consider the effects of the control system and external disturbances, resulting in insufficient engineering applicability. A more common problem is that traditional methods are mostly based on offline, global calculations. When faced with rapidly changing time-space models and high-dimensional state spaces in deformable aircraft, they generally suffer from poor dynamic adaptability and difficulty in balancing computational efficiency and accuracy, failing to meet the safety control requirements during flight. Summary of the Invention

[0004] To address the aforementioned technical problems, this application provides a control method and system for deformable aircraft based on reachability set calculation, thereby improving the safety of deformable aircraft during flight.

[0005] In a first aspect, embodiments of this application provide a deformable aircraft control method based on reachability set solution, including: Acquire the real-time flight status and current mission commands of the transforming aircraft; Generate a state target set based on the current task instructions; Based on the real-time flight state, the preset aircraft dynamics model, and the preset constraints, the reachable set of the state target set is calculated and generated in the state space using the level set method. The aircraft dynamics model is constructed based on the design parameters of the deformable aircraft, and the state space is the set of all reachable flight states of the deformable aircraft. The current safety state boundary of the deformable aircraft is determined based on the boundary of the reachable set; The flight safety level of the deformable aircraft is determined based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space. The deformable aircraft is controlled in real time according to the control method corresponding to the flight safety level.

[0006] This application provides a control method for deformable aircraft based on reachability set calculation. By calculating the safety state boundary in real time, the flight safety level is dynamically evaluated, and real-time control is performed accordingly, thereby improving the safety of the deformable aircraft during flight. Specifically, this embodiment first generates a state target set by acquiring real-time flight status and mission commands, and then calculates the reachability set based on the level set method to determine the safety state boundary. This process not only considers the real-time state of the aircraft but also incorporates preset dynamic models and constraints, ensuring the dynamics and accuracy of the safety boundary. By understanding the relative positional relationship between the real-time flight status and the safety boundary, the system can accurately determine the flight safety level and adopt corresponding control strategies, effectively avoiding the risk of loss of control due to the flight status exceeding the safety boundary. Furthermore, this embodiment supports online real-time calculation, adapting to the rapid time-varying characteristics of the deformable aircraft model, significantly improving flight safety and control efficiency.

[0007] In one possible implementation, the step of generating a reachable set of the state target set in the state space based on the level set method, according to the real-time flight state, a preset aircraft dynamics model, and preset constraints, includes: Centered on the real-time flight state, and based on the state variable constraints and control duration constraints in the constraints, a reachable set solution space containing the state target set is generated in the state space. The reachable set solution space is divided into grids according to the preset grid spacing to generate a corresponding discrete network, wherein each grid point in the discrete network corresponds to a flight state. Based on the relative positional relationship between each grid point and the state target set, the initial level set function value of each grid point is generated; Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, and then the initial level set function value of each grid point is iteratively updated until the level set function value of each grid point converges, thus obtaining the final level set function value of each grid point. The reachability set of the state target set is determined based on the final level set function value of each of the grid points.

[0008] This embodiment provides a method for generating reachable sets. First, a reachable set solution space is generated based on state variable constraints and control duration constraints. Mesh partitioning discretizes the continuous state space, ensuring that the reachable set solution is not performed in the entire state space, but rather in a finite, engineering-relevant local state space within the prediction time domain. This significantly reduces computational complexity while maintaining computational precision. Then, initial level set function values ​​are set based on the relative positions of grid points and the state target set, providing reasonable initial conditions for subsequent iterative calculations. Finally, the Hamilton-Jacobi equation is solved iteratively through time-progression, dynamically updating the level set function values ​​until convergence, thereby accurately describing the boundary of the reachable set. Through these methods, this embodiment not only improves computational efficiency but also adapts to the complexity and time-varying nature of deformable aircraft during flight, providing a reliable data foundation for real-time safety control and ensuring the safety of deformable aircraft during flight.

[0009] Furthermore, generating the initial level set function value for each grid point based on the relative positional relationship between each grid point and the state target set includes: Determine whether each of the grid points is located inside, outside, or on the boundary of the state target set; Wherein, if any of the grid points is located inside the state target set, the initial level set function value of the grid point is determined to be 1; If any of the grid points is located outside the state target set, then the initial level set function value of the grid point is determined to be -1; If any of the grid points is located on the boundary of the state target set, then the initial level set function value of the grid point is determined to be 0.

[0010] This application provides a method for generating initial level set function values. Different initial values ​​are assigned based on the relative position (inside, outside, or boundary) of grid points and the state target set, thereby accurately reflecting the relationship between grid points and the target set. By setting internal points to 1, external points to -1, and boundary points to 0, clear initial conditions are provided for subsequent iterative calculations, which helps to accelerate convergence and improve computational accuracy. This ensures the reliability and stability of reachability set solutions and improves the safety of deformable aircraft during flight.

[0011] Furthermore, based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, thereby iteratively updating the initial level set function values ​​of each grid point until the level set function values ​​converge, obtaining the final level set function values ​​of each grid point. Each iterative update process includes: Calculate the approximate left and right spatial gradient values ​​of the current level set function value for each of the grid points; Based on the approximate values ​​of the left and right spatial gradients, the aircraft dynamics model, and the control input constraints, a numerical Hamiltonian function is constructed. The numerical Hamiltonian function is solved by time-progression, and the current level set function value of each grid point is updated according to the calculation result to obtain the updated level set function value of each grid point. Determine whether each of the updated level set function values ​​has converged. If so, use each of the updated level set function values ​​as the corresponding final level set function values; otherwise, perform the next iteration update based on each of the updated level set function values.

[0012] This embodiment details the iterative update process of the level set function value, including steps such as calculating the spatial gradient approximation, constructing the numerical Hamiltonian function, time-progressive solution, and convergence determination. This process effectively solves the Hamilton-Jacobi equation using numerical methods, dynamically updating the level set function value until convergence is achieved. Through iterative updates, the system can gradually approximate the true reachability set boundary, improving the accuracy of subsequent flight safety level assessments. While ensuring computational efficiency, it achieves a precise description of the safety boundary, thereby enhancing the safety of the deformable aircraft during flight.

[0013] Furthermore, determining the reachability set of the state target set based on the final level set function value of each of the grid points includes: Extract several target grid points from each of the aforementioned grid points, where the final level set function value is 0; Construct zero isosurfaces based on each of the target grid points; The interior region of the zero isosurface is defined as the reachable set of the state target set.

[0014] This application clarifies how to determine the reachable set of a state target set from the final level set function values ​​of grid points, specifically including extracting zero-value grid points, constructing zero isosurfaces, and determining the interior region as the reachable set. This embodiment visualizes the boundary of the reachable set using mathematical methods, providing a clear and reliable way to determine the reachable set. The construction of zero isosurfaces accurately describes the geometry of the reachable set, while the determination of the interior region provides an intuitive basis for the safety assessment of the flight state, improving the safety of morphing aircraft during flight. Furthermore, this embodiment has good versatility, is applicable to state spaces of different dimensions, and can adapt to the complexity and diversity of morphing aircraft models.

[0015] In one possible implementation, generating the state target set according to the current task instruction includes: Determine the desired flight state based on the current mission instructions; Centered on the desired flight state, a closed region is generated in the state space according to a preset state change range as the state target set. The state change range is determined comprehensively based on the sensor accuracy, control accuracy, and simulation accuracy of the aircraft dynamics model.

[0016] This application embodiment defines the method for generating the state target set. The desired flight state is determined based on mission instructions, and a closed region is generated centered on this state as the target set. The setting of the state change range comprehensively considers sensor accuracy, control accuracy, and model simulation accuracy, ensuring the rationality and practicality of the target set. By generating a closed region, the system can cover a reasonable range of flight state changes, avoiding deviations in safety boundary calculations caused by improper target set settings, ensuring the real-time generation of safety boundaries, and thus improving the safety of the deformable aircraft during flight. Furthermore, this embodiment can dynamically adjust the target set according to different mission requirements, providing a flexible and reliable basis for real-time control.

[0017] In one possible implementation, determining the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space includes: In the state space, if the real-time flight state is located within the safety state boundary and the distance from the safety state boundary is greater than a preset threshold, then the flight safety level is the first safety level. If the real-time flight status is within the safety status boundary and the distance to the safety status boundary is less than or equal to a preset threshold, then the flight safety level is the second safety level. If the real-time flight status is outside the safety status boundary, then the flight safety level is the third safety level.

[0018] This application's embodiments categorize flight safety levels into three levels based on the distance relationship between real-time flight status and safety boundaries, achieving refined assessment of flight status. The first safety level indicates that the flight status is within and far from the safety boundary, constituting a safe state. The second safety level indicates that the flight status is close to the safety boundary, requiring attention to potential risks. The third safety level indicates that the flight status has exceeded the safety boundary, constituting a dangerous state. This grading mechanism accurately reflects the aircraft's safety status, providing a scientific basis for the formulation of subsequent control strategies. By assessing safety levels in real time, the system can promptly issue warnings and take corresponding measures when abnormalities occur in the flight status, effectively improving flight safety and reliability.

[0019] Furthermore, the real-time control of the deformable aircraft based on the control method corresponding to the flight safety level includes: If the flight safety level is the first safety level, then the deformable aircraft is controlled to continue executing the preset mission tracking control law; If the flight safety level is the second safety level, then a corresponding correction amount is generated based on the distance and relative orientation between the real-time flight state and the safety state boundary; the correction amount is superimposed on the mission tracking control law to generate a modified mission tracking control law; the deformable aircraft is controlled to execute the modified mission tracking control law. If the flight safety level is the third safety level, then an emergency control law is generated with the center point of the state target set as the target; the deformable aircraft is controlled to execute the emergency control law.

[0020] This application's embodiments formulate corresponding control strategies for different flight safety levels, achieving hierarchical control. When the aircraft is in the first safety level, the system continues to execute the preset mission tracking control law to ensure the smooth completion of the flight mission. When in the second safety level, the system generates correction values ​​based on the distance and orientation between the real-time state and the safety boundary, which are then superimposed on the mission tracking control law to fine-tune the flight state and prevent it from approaching the safety boundary further. When in the third safety level, the system generates an emergency control law with the center point of the state target set as the target, ensuring that the aircraft quickly returns to a safe state. This hierarchical control strategy can flexibly adjust the control method according to the real-time safety status of the aircraft and prioritize ensuring flight safety, enabling the aircraft to perform flight missions while ensuring flight safety, thus improving the safety of the morphing aircraft during flight.

[0021] Secondly, embodiments of this application provide a deformable aircraft control system based on reachable set calculation, including an acquisition module, a target set generation module, a reachable set generation module, a boundary determination module, a safety assessment module, and a control module; The acquisition module is used to acquire the real-time flight status and current mission instructions of the deformable aircraft. The target set generation module is used to generate a state target set according to the current task instruction; The reachable set generation module is used to calculate and generate the reachable set of the state target set in the state space based on the level set method according to the real-time flight state, the preset aircraft dynamics model and the preset constraints. The aircraft dynamics model is constructed based on the design parameters of the deformable aircraft, and the state space is the set of all reachable flight states of the deformable aircraft. The boundary determination module is used to determine the current safety state boundary of the deformable aircraft based on the boundary of the reachable set; The safety assessment module is used to determine the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space; The control module is used to control the deformable aircraft in real time according to the control method corresponding to the flight safety level.

[0022] Furthermore, the reachability set generation module, based on the real-time flight state, a preset aircraft dynamics model, and preset constraints, calculates and generates the reachability set of the state target set in the state space using the level set method, including: Centered on the real-time flight state, and based on the state variable constraints and control duration constraints in the constraints, a reachable set solution space containing the state target set is generated in the state space. The reachable set solution space is divided into grids according to the preset grid spacing to generate a corresponding discrete network, wherein each grid point in the discrete network corresponds to a flight state. Based on the relative positional relationship between each grid point and the state target set, the initial level set function value of each grid point is generated; Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, and then the initial level set function value of each grid point is iteratively updated until the level set function value of each grid point converges, thus obtaining the final level set function value of each grid point. The reachability set of the state target set is determined based on the final level set function value of each of the grid points. Attached Figure Description

[0023] Figure 1 A flowchart illustrating a deformable aircraft control method based on reachability set solution provided in this application embodiment; Figure 2 A schematic diagram of the backward reachable set in a deformable aircraft control method based on reachable set solution provided in an embodiment of this application; Figure 3 A schematic diagram of the controllable invariant set and optimization index in a deformable aircraft control method based on reachability set solution provided in this application embodiment; Figure 4 This is a schematic diagram of the reachable set solution process in a deformable aircraft control method based on reachable set solution provided in an embodiment of this application.

[0024] Figure 5 A schematic diagram of the two-dimensional safety boundary of a deformable aircraft at a speed of Mach 9 in a deformable aircraft control method based on reachability set solution provided in an embodiment of this application; Figure 6 A schematic diagram of the three-dimensional safety boundary of a deformable aircraft at a speed of Mach 9 in a deformable aircraft control method based on reachability set solution provided in this application embodiment; Figure 7 This is a schematic diagram of a deformable aircraft control system based on reachability set solution, provided as an embodiment of this application. Detailed Implementation

[0025] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0026] It should be noted that the step numbers in this document are only for the convenience of explaining the specific embodiments and are not intended to limit the order in which the steps are performed. In the description of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of that feature.

[0027] Example 1: like Figure 1 As shown, Embodiment 1 provides a deformable aircraft control method based on reachability set solution, including steps S1-S6: Step S1: Obtain the real-time flight status and current mission instructions of the transforming aircraft; Step S2: Generate a state target set according to the current task instruction; Step S3: Based on the real-time flight state, the preset aircraft dynamics model, and the preset constraints, calculate and generate the reachable set of the state target set in the state space using the level set method. The aircraft dynamics model is constructed based on the design parameters of the deformable aircraft, and the state space is the set of all reachable flight states of the deformable aircraft. Step S4: Determine the current safety state boundary of the deformable aircraft based on the boundary of the reachable set; Step S5: Determine the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space; Step S6: Perform real-time control on the deformable aircraft according to the control method corresponding to the flight safety level.

[0028] This application provides a control method for deformable aircraft based on reachability set calculation. By calculating the safety state boundary in real time, the flight safety level is dynamically evaluated, and real-time control is performed accordingly, thereby improving the safety of the deformable aircraft during flight. Specifically, this embodiment first generates a state target set by acquiring real-time flight status and mission commands, and then calculates the reachability set based on the level set method to determine the safety state boundary. This process not only considers the real-time state of the aircraft but also incorporates preset dynamic models and constraints, ensuring the dynamics and accuracy of the safety boundary. By understanding the relative positional relationship between the real-time flight status and the safety boundary, the system can accurately determine the flight safety level and adopt corresponding control strategies, effectively avoiding the risk of loss of control due to the flight status exceeding the safety boundary. Furthermore, this embodiment supports online real-time calculation, adapting to the rapid time-varying characteristics of the deformable aircraft model, significantly improving flight safety and control efficiency.

[0029] In a preferred embodiment, in step S1, the real-time flight state of the deformable aircraft is determined by data collected in real time by sensors, including but not limited to speed, angle of attack, pitch rate, and pitch angle, with the data coming from sensors such as pitot tubes, inertial navigation systems, and angular rate gyroscopes. The current mission command includes, but is not limited to, the current target deformable configuration and desired flight state of the deformable aircraft.

[0030] In a preferred embodiment, the process of constructing the aircraft dynamics model is as follows: Since deformable aircraft are only affected by Earth's gravity, aerodynamics, and aerodynamic torque, the following assumptions can be made: (1) Without considering the Earth's rotational angular velocity and the influence of the Earth's oblateness, the Earth is a homogeneous sphere; (2) The deformable aircraft has a surface-symmetrical aerodynamic shape; (3) The influence of elastic motion is not considered in the derivation of the aircraft, and it is regarded as a rigid body; Since modeling of hypersonic vehicles has relatively mature results, and the main difference between morphing vehicles and traditional vehicles lies in the rapid time-varying nature of aerodynamic parameters caused by deformation, the dynamic model of unpowered flight of morphing vehicles is given by the equations of motion around the center of mass and the equations of motion around the center of mass, described as follows: (1) (2) In the formula, For speed, It is the acceleration due to gravity. For rotational inertia, , , These are roll rate, yaw rate, and pitch rate, respectively. , , These are lift, drag, and lateral force, respectively. , , These are the rolling moment, yaw moment, and pitch moment, respectively. Atmospheric density, For the characteristic area, For characteristic length, , , These are the lift coefficient, drag coefficient, and lateral force coefficient, respectively. , , These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively.

[0031] These two equations constitute the established dynamic model of the deformable aircraft, providing the physical foundation for the reachability set solution throughout the paper. Their core functions are: defining the system's state space and control input, clarifying the descriptive dimensions of the safety boundary, and providing ordinary differential equations describing the system's dynamic evolution. Specifically, given a state point x, control input u, and current aerodynamic parameters, the model outputs the state derivative dx / dt. This derivative is used to calculate the evolution direction of the reachability set and the gradient information of the level set function.

[0032] Specific required parameters: (1) State variable x, which comes from the grid points in the state space, such as (Velocity, angle of attack, pitch rate, pitch angle) are traversed by the algorithm during the solution process.

[0033] (2) Control input u, such as (Rudder deflection and deformation).

[0034] (3) Aerodynamic parameters, such as lift coefficient, drag coefficient, and side force coefficient , , Roll moment coefficient, yaw moment coefficient, pitch moment coefficient , , .

[0035] (4) Constant parameters. Such as mass m, moment of inertia I_yy, reference area (These parameters may vary with deformation), reference length, atmospheric density, etc., are determined by the aircraft design and flight conditions.

[0036] Output results: (1) State derivative dx / dt. That is, [dV / dt, dα / dt, dq / dt, dθ / dt]^T calculated by the equation. (2) Jacobian matrix, which is obtained by linearizing the nonlinear equation at the equilibrium point and is used for controllability analysis.

[0037] In one possible implementation, step S2, generating the state target set according to the current task instruction, includes: Determine the desired flight state based on the current mission instructions; Centered on the desired flight state, a closed region is generated in the state space according to a preset state change range as the state target set. The state change range is determined comprehensively based on the sensor accuracy, control accuracy, and simulation accuracy of the aircraft dynamics model.

[0038] This application embodiment defines the method for generating the state target set. The desired flight state is determined based on mission instructions, and a closed region is generated centered on this state as the target set. The setting of the state change range comprehensively considers sensor accuracy, control accuracy, and model simulation accuracy, ensuring the rationality and practicality of the target set. By generating a closed region, the system can cover a reasonable range of flight state changes, avoiding deviations in safety boundary calculations caused by improper target set settings, ensuring the real-time generation of safety boundaries, and thus improving the safety of the deformable aircraft during flight. Furthermore, this embodiment can dynamically adjust the target set according to different mission requirements, providing a flexible and reliable basis for real-time control.

[0039] In one possible implementation, step S3, which involves calculating and generating a reachable set of the state target set in the state space based on the level set method, according to the real-time flight state, a preset aircraft dynamics model, and preset constraints, includes: Centered on the real-time flight state, and based on the state variable constraints and control duration constraints in the constraints, a reachable set solution space containing the state target set is generated in the state space. The reachable set solution space is divided into grids according to the preset grid spacing to generate a corresponding discrete network, wherein each grid point in the discrete network corresponds to a flight state. Based on the relative positional relationship between each grid point and the state target set, the initial level set function value of each grid point is generated; Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, and then the initial level set function value of each grid point is iteratively updated until the level set function value of each grid point converges, thus obtaining the final level set function value of each grid point. The reachability set of the state target set is determined based on the final level set function value of each of the grid points.

[0040] This embodiment provides a method for generating reachable sets. First, a reachable set solution space is generated based on state variable constraints and control duration constraints. Mesh partitioning discretizes the continuous state space, ensuring that the reachable set solution is not performed in the entire state space, but rather in a finite, engineering-relevant local state space within the prediction time domain. This significantly reduces computational complexity while maintaining computational precision. Then, initial level set function values ​​are set based on the relative positions of grid points and the state target set, providing reasonable initial conditions for subsequent iterative calculations. Finally, the Hamilton-Jacobi equation is solved iteratively through time-progression, dynamically updating the level set function values ​​until convergence, thereby accurately describing the boundary of the reachable set. Through these methods, this embodiment not only improves computational efficiency but also adapts to the complexity and time-varying nature of deformable aircraft during flight, providing a reliable data foundation for real-time safety control and ensuring the safety of deformable aircraft during flight.

[0041] Furthermore, generating the initial level set function value for each grid point based on the relative positional relationship between each grid point and the state target set includes: Determine whether each of the grid points is located inside, outside, or on the boundary of the state target set; Wherein, if any of the grid points is located inside the state target set, the initial level set function value of the grid point is determined to be 1; If any of the grid points is located outside the state target set, then the initial level set function value of the grid point is determined to be -1; If any of the grid points is located on the boundary of the state target set, then the initial level set function value of the grid point is determined to be 0.

[0042] This application provides a method for generating initial level set function values. Different initial values ​​are assigned based on the relative position (inside, outside, or boundary) of grid points and the state target set, thereby accurately reflecting the relationship between grid points and the target set. By setting internal points to 1, external points to -1, and boundary points to 0, clear initial conditions are provided for subsequent iterative calculations, which helps to accelerate convergence and improve computational accuracy. This ensures the reliability and stability of reachability set solutions and improves the safety of deformable aircraft during flight.

[0043] Furthermore, based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, thereby iteratively updating the initial level set function values ​​of each grid point until the level set function values ​​converge, obtaining the final level set function values ​​of each grid point. Each iterative update process includes: Calculate the approximate left and right spatial gradient values ​​of the current level set function value for each of the grid points; Based on the approximate values ​​of the left and right spatial gradients, the aircraft dynamics model, and the control input constraints, a numerical Hamiltonian function is constructed. The numerical Hamiltonian function is solved by time-progression, and the current level set function value of each grid point is updated according to the calculation result to obtain the updated level set function value of each grid point. Determine whether each of the updated level set function values ​​has converged. If so, use each of the updated level set function values ​​as the corresponding final level set function values; otherwise, perform the next iteration update based on each of the updated level set function values.

[0044] This embodiment details the iterative update process of the level set function value, including steps such as calculating the spatial gradient approximation, constructing the numerical Hamiltonian function, time-progressive solution, and convergence determination. This process effectively solves the Hamilton-Jacobi equation using numerical methods, dynamically updating the level set function value until convergence is achieved. Through iterative updates, the system can gradually approximate the true reachability set boundary, improving the accuracy of subsequent flight safety level assessments. While ensuring computational efficiency, it achieves a precise description of the safety boundary, thereby enhancing the safety of the deformable aircraft during flight.

[0045] Furthermore, determining the reachability set of the state target set based on the final level set function value of each of the grid points includes: Extract several target grid points from each of the aforementioned grid points, where the final level set function value is 0; Construct zero isosurfaces based on each of the target grid points; The interior region of the zero isosurface is defined as the reachable set of the state target set.

[0046] This application clarifies how to determine the reachable set of a state target set from the final level set function values ​​of grid points, specifically including extracting zero-value grid points, constructing zero isosurfaces, and determining the interior region as the reachable set. This embodiment visualizes the boundary of the reachable set using mathematical methods, providing a clear and reliable way to determine the reachable set. The construction of zero isosurfaces accurately describes the geometry of the reachable set, while the determination of the interior region provides an intuitive basis for the safety assessment of the flight state, improving the safety of morphing aircraft during flight. Furthermore, this embodiment has good versatility, is applicable to state spaces of different dimensions, and can adapt to the complexity and diversity of morphing aircraft models.

[0047] Specifically, reachability sets can provide a complete description of the set of all possible trajectories in a system. They can be divided into two categories based on the direction of computation: forward reachability sets and backward reachability sets. Forward reachability sets are defined as: given an initial state, the set of all states that the system can reach within a specific time range under arbitrary control input; backward reachability sets, as the inverse process, are all initial states that can reach the target under control, determined by analyzing the target state. The safety boundary problem of a deformable aircraft is to solve for a set of state boundaries given the initial state space, such that the deformable aircraft remains stable and controllable regardless of any set of state variables taken from this set. This embodiment uses the backward reachability set method to solve for the safety boundary of the deformable aircraft. For the longitudinal system of the deformable aircraft, the initial state parameters include: state variables x, which come from the grid points in the state space, such as... The parameters (velocity, angle of attack, pitch rate, pitch angle) are traversed by the algorithm during the solution process. The dynamic characteristics of the deformable aircraft can be described by the following ordinary differential equations: (3) In the formula, for A 3D flight state vector, containing information such as altitude ,speed Angle of attack wait, Represents a time variable. Represents the control input vector, including things like rudder deflection. and deformation amount Vector field It satisfies the boundedness and Lipschitz continuity conditions.

[0048] The backward reachable set, according to the dynamic system analysis, is defined as: given a control input (i.e., control input constraints), the set of all initial states to which the system state can converge to the target state set in a finite time. Its complement is called the unreachable set, representing the set of states to which the system state can never reach the target state set. The control input is a given range, not a fixed value; more precisely, it is described as the allowed range or policy set of the given control input, under the presence of at least one allowed time-varying control signal, allowing the system to converge to the target set. Specific control input parameters are... (Rudder deflection and deformation).

[0049] like Figure 2 The diagram illustrates the geometry of the backward reachable set. The blue area represents the safe state target set, determined by the aerodynamic model and deformable aircraft design parameters; the specific range of this area can be adjusted according to the needs of the flight mission. The green area circled in the diagram represents the safe backward reachable set. Studies show that different initial states, under different control inputs, can converge to different target states within the same time conditions. Specifically, under appropriate control, the initial states circled in the diagram... and This ensures that the system's trajectory converges to the safe target set; while the initial state outside the circle... Under any control input, the safe target set cannot be entered; therefore, it is defined as the set of unsafe states that must be avoided during flight. When there is a set... Any one of these states after time Subsequently, when all safe target sets can be reached under permissible control measures, this set... The reachable set of the target set is called the maximum controllable safety boundary. If the deformable aircraft's state exceeds this boundary due to operational errors or external interference, it cannot be returned to a safe state through control inputs, potentially leading to a safety accident. Using the maximum controllable boundary to define the safety boundary set has a dual advantage: on the one hand, it can fully explore the performance potential of the deformable aircraft; on the other hand, by covering all critical state variables, it ensures the reliability of the protection mechanism.

[0050] The solution for the safety set can be achieved using the level set method. The level set method is a numerical technique for describing the evolution of dynamic implicit surfaces. Its key lies in using the zero level set of a high-dimensional level set function to represent a low-dimensional deformation curve. The dynamic changes of the curve are described through the evolution of the closed hypersurface. Compared with other methods, this method utilizes basic set operations to represent complex geometries and has the advantage of computational simplicity. Specifically, performance indices are first established. : , (4) This indicator uses the level set method. Defined as state vector to allowable boundary The positive distance function. The optimization objective is to minimize The index, whose optimal solution corresponds to the maximum controllable invariant set. The boundary of the (reachable set). u is the set of allowed control inputs, such as rudder deflection and deformation as mentioned above. t is the integration time variable. For example... Figure 3 As shown, the maximum controllable safety set S is the largest set of states that the system can maintain within under the action of permissible control u. The permissible boundary C is a statically given constraint boundary. The relationship between the two is one of inclusion; that is, the safety set S lies entirely within the permissible region enclosed by the permissible boundary C. In other words, C is the outer boundary or constraint boundary of S.

[0051] In the process of solving S, the following assumptions are made. It is compact and and It is bounded and the Lipschitz continuity condition is satisfied. Let the Hamiltonian function be: (5) (6) In the formula, H is the Hamiltonian function, x is the state vector, p is the gradient vector (i.e., the gradient of the level set function at the current state x), and u is the control input. This formula represents selecting the value that minimizes p^T f(x,u) among all instantaneously permissible controls u. This corresponds to finding an optimal instantaneous control that makes the system state move in the direction that most quickly reduces the value of the level set function Φ (i.e., tends towards safety).

[0052] Therefore, the solution to the above optimization problem can be reduced to Hamilton-Jacobi partial differential equations, namely: (7) In the equation, V is the value function, i.e., the positive distance function mentioned above, x is the state variable, t is the time variable, and H is the Hamiltonian function. This equation describes the partial differential equation that the value function V must satisfy. Solving this equation yields V over the entire state space, and thus the safety boundary.

[0053] Boundary conditions are , Distance from the boundary at the terminal time The distance function. The assumptions guarantee the continuity of the optimal solution method for the value function, and that the system has a unique continuous solution at all times. This simplifies the solution process. Since optimal control theory can only guarantee that... The system maintains its final state, but during state transitions, the system state trajectory may deviate from the expected state. In addition, since the positive definiteness of the index must be guaranteed, equation (7) is modified to obtain: (8) Level set theory and its viscous finite element method provide an effective means of solving equation (7). This theory utilizes implicit surface description and a computational framework based on level set gradients, and ensures stable convergence of the algorithm by re-initializing the level set as a key step. As an important tool in fields such as interface evolution, solving the Hamilton-Jacobi-Bellman equation, and multiphase flow analysis, the level set method is applied to the accurate calculation of the safety boundary of deformable aircraft in this study.

[0054] In a preferred embodiment, based on the foregoing modeling, the longitudinal state equation of the deformable aircraft during flight can be expressed as: (9) System state variables This refers to the flight speed, angle of attack, pitch rate, and pitch angle of the transforming aircraft, as well as the control inputs. This refers to the deformation and rudder deflection of the deformable aircraft.

[0055] Rectangular area for control input Transforming equation (10) into the form of a level set function, we obtain equation (11): (10) (11) In the formula, φ is a scalar function of the constraint level set function, whose value represents the "safety margin" between the current state x and a violation of any constraint. A larger positive value indicates greater safety; a value of 0 indicates that a constraint boundary has just been touched; a negative value indicates that at least one constraint has been violated. V, α, q, and φ are the system's state variables. Other values ​​with min and max subscripts represent the allowable upper and lower limits of the state variables, generally the initial range of values ​​for the state variables, determined by the aircraft itself or its aerodynamic characteristics.

[0056] The required Hamiltonian function can be expressed as follows: (12) In the formula, , , , yes For state parameters , , , It is obtained by taking a partial derivative.

[0057] In the specific calculation, based on formulas (10), (11) and state equation (9), equation (8) is solved, and the invariant set obtained is the longitudinal maximum controllable boundary set of the deformable aircraft.

[0058] Based on the reachability set theory of the Hamilton-Jacobi equations, the solution process for the longitudinal safety set of deformable aircraft can be summarized as follows: Step 1: State Space Discretization. Based on the flight envelope and physical constraints, determine the initial value range of each state variable, i.e., the state space. Discretize the state space... Within their respective allowable ranges, the area is uniformly divided using a grid. Let the first... The sequence of grid points in each state dimension is as follows: .set up This represents the number of grid points in this dimension. This represents the grid spacing.

[0059] Step 2: Initialize the level set function. At the initial moment... Define the level set function ,in This is expressed by equation (4). For each grid point... Calculate the initial level set function value, which takes a positive value in the safe region and a negative value in the unsafe region.

[0060] Step 3: Calculate the gradient approximation (left and right derivatives). For each grid point, along the... In the dimensional direction, the left and right derivatives are approximated using a first-order upwind difference scheme: (13) Record the minimum and maximum values ​​of the left and right derivatives for subsequent calculations of numerical viscosity: (14) Step 4: Construct an approximate scheme for the Hamiltonian function. The Hamiltonian function is discretized using the Lax-Friedrichs numerical flux scheme: (15) The first term in the formula This is the value of the Hamiltonian function under the average gradient; the second term It is a numerical viscosity term that ensures the stability of the format.

[0061] Local wave velocity The value of Hamilton's function is the first... The maximum absolute value of the gradient of each component within the local interval: (16) The Hamilton function itself can be given by equation (12).

[0062] Step 5: Solve the Hamilton-Jacobi equation using time-progression. The Hamilton-Jacobi equation is solved using the following time-progression scheme: (17) Then use the Euler display format: (18) This formula indicates that, under optimal control Under the influence of , the directional derivative of the level set function value along the system trajectory decays at a rate determined by the Hamiltonian function.

[0063] Step Six: CFL Conditions Guarantee Numerical Stability. To ensure numerical stability, the time step ∆t must satisfy the CFL conditions: (19) In the formula, It is the first The maximum absolute value of the dimensional dynamic equations over the entire state space can usually be obtained from the previously calculated values. It is estimated by the global maximum value. It is the CFL number, and to ensure stability, it is usually taken as... At the beginning of each time step, calculate based on the current state. The upper limit, and choose the appropriate To meet the above conditions.

[0064] Step 7: Determine convergence and safe set. Set a small positive number as the convergence tolerance, or set a maximum simulation time. Repeat steps 3 to 6 until the level set function converges. The converged sub-zero level set: (20) This is the desired longitudinal safety set (i.e., the reachable set of the state target set), which indicates that there exists a control strategy within this set that ensures the system state always satisfies the constraints.

[0065] The flowchart of the algorithm for solving reachable sets is shown below. Figure 4 As shown, the steps can be summarized as follows: 1. Dynamics Modeling and Constraint Definition. Based on the structural parameters and aerodynamic characteristics of the deformable aircraft, a nonlinear dynamics model is established, and the physical constraints of state variables and control inputs (including rudder deflection and deformation) are determined.

[0066] 2. State space discretization and level set function initialization. The continuous state space is divided into grids within the constraints, and a level set function value is initialized at each grid point. This function value is positive within a preset initial safety target set and negative outside of it.

[0067] 3. Iteratively solve the Hamilton-Jacobi equation. This is the core step of this invention. Based on the dynamic model in step 1, the Hamilton-Jacobi equation is constructed and discretized using the Lax-Friedrichs numerical scheme. The equation is then solved iteratively on a discrete grid using time-progression. This process continues until the level set function value converges. The system iteratively executes the following steps on the discrete grid until the level set function converges: 3.1 Calculate the approximate left and right spatial gradients of the level set function at each grid point; 3.2 Based on the gradient approximation and dynamic model, a numerical Hamiltonian function in the Lax-Friedrichs scheme is constructed; 3.3 Using the explicit Euler scheme, according to Update the level set function values ​​at the grid points; 3.4 The time step is adaptively adjusted according to the CFL condition to ensure numerical stability.

[0068] The specific formulas and parameters involved have been listed in steps two through six above.

[0069] 4. Reachability Set Extraction. The zero isosurface of the converged level set function is extracted. The internal region enclosed by this isosurface is the reachable set of the state target set of the deformable aircraft under the current configuration and conditions. Specifically, the system performs post-processing on the converged final level set function field Φ_final. By detecting the sign change of the function values ​​within the grid cells and performing linear interpolation, the set of state points satisfying Φ_final(x) = 0 is extracted. The hypersurface formed by these points is the safety boundary, and the closed region {x |Φ_final(x)≥0} inside it is the maximum controllable safety boundary set (reachable set). The system can store and output this boundary set for subsequent control modules to call.

[0070] In one possible implementation, step S5, determining the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space, includes: In the state space, if the real-time flight state is located within the safety state boundary and the distance from the safety state boundary is greater than a preset threshold, then the flight safety level is the first safety level. If the real-time flight status is within the safety status boundary and the distance to the safety status boundary is less than or equal to a preset threshold, then the flight safety level is the second safety level. If the real-time flight status is outside the safety status boundary, then the flight safety level is the third safety level.

[0071] This application's embodiments categorize flight safety levels into three levels based on the distance relationship between real-time flight status and safety boundaries, achieving refined assessment of flight status. The first safety level indicates that the flight status is within and far from the safety boundary, constituting a safe state. The second safety level indicates that the flight status is close to the safety boundary, requiring attention to potential risks. The third safety level indicates that the flight status has exceeded the safety boundary, constituting a dangerous state. This grading mechanism accurately reflects the aircraft's safety status, providing a scientific basis for the formulation of subsequent control strategies. By assessing safety levels in real time, the system can promptly issue warnings and take corresponding measures when abnormalities occur in the flight status, effectively improving flight safety and reliability.

[0072] Furthermore, the real-time control of the deformable aircraft based on the control method corresponding to the flight safety level includes: If the flight safety level is the first safety level, then the deformable aircraft is controlled to continue executing the preset mission tracking control law; If the flight safety level is the second safety level, then a corresponding correction amount is generated based on the distance and relative orientation between the real-time flight state and the safety state boundary; the correction amount is superimposed on the mission tracking control law to generate a modified mission tracking control law; the deformable aircraft is controlled to execute the modified mission tracking control law. If the flight safety level is the third safety level, then an emergency control law is generated with the center point of the state target set as the target; the deformable aircraft is controlled to execute the emergency control law.

[0073] This application's embodiments formulate corresponding control strategies for different flight safety levels, achieving hierarchical control. When the aircraft is in the first safety level, the system continues to execute the preset mission tracking control law to ensure the smooth completion of the flight mission. When in the second safety level, the system generates correction values ​​based on the distance and orientation between the real-time state and the safety boundary, which are then superimposed on the mission tracking control law to fine-tune the flight state and prevent it from approaching the safety boundary further. When in the third safety level, the system generates an emergency control law with the center point of the state target set as the target, ensuring that the aircraft quickly returns to a safe state. This hierarchical control strategy can flexibly adjust the control method according to the real-time safety status of the aircraft and prioritize ensuring flight safety, enabling the aircraft to perform flight missions while ensuring flight safety, thus improving the safety of the morphing aircraft during flight.

[0074] In a preferred embodiment, numerical simulation experiments were conducted to verify the effectiveness of the provided deformable aircraft control method. Assuming that the conditions are naturally satisfied, without loss of generality, the allowable state space range is defined. It is defined as a closed hypercube region. Based on the aerodynamic characteristic analysis of deformable aircraft and actual control simulation experience, the allowable range of flight state variables is: (twenty one) The solution is obtained through programming in MATLAB, with grid numbers set to 15, 10, 15, and 10 respectively. While the grid number is relatively small due to computational efficiency and capability considerations, the convergence is guaranteed by the level set algorithm, resulting in relatively accurate results. The initial result is a four-dimensional hyperspace solid, which is not conducive to research and analysis. Next, it is quantized by block segmentation and Gaussian smoothing of the boundaries. With a fixed velocity and pitch rate of change, the two-dimensional safety boundary composed of the angle of attack and pitch angle provides the most intuitive display of the flight envelope, suitable for control system design. The two-dimensional attitude safety boundary of the morphing aircraft at a steady-state speed of Mach 9 at high altitude is then determined. like Figure 5 As shown in the figure, the green area represents the obtained reachable set, which is the safe state space, and the corresponding three-dimensional safety boundary. like Figure 6 As shown.

[0075] like Figure 5 As shown, this is a schematic diagram of the two-dimensional safety boundary of the deformable aircraft on the angle of attack-pitch plane when the aircraft is flying at a speed of Mach 9. The green area in the figure is the set of safe states (i.e., the reachable set) calculated by the method of this invention. The boundary line of this area (i.e., the edge of the green area) is the safety boundary. The figure shows two key features: (1) Irregularity of the safety area: The boundary is not a simple geometric shape, but a complex curve determined by the nonlinear dynamics and constraints of the system, which reflects the ability of the method of this invention to handle nonlinear problems. (2) Verification of the controllability of the state points: The state point x_in located in the green area has a full-rank controllability matrix, indicating that there is a control strategy to keep it in the safe domain or return to the safe target set; while the state point x_out located outside the area has a non-rank controllability matrix, which belongs to the unreachable dangerous state. The figure intuitively proves the correctness and physical meaning of the solution results of this invention, and provides a direct safety boundary for the design of flight control laws.

[0076] like Figure 6As shown, this is a schematic diagram of the safety boundary slice of the deformable aircraft in the three-dimensional state space of velocity-angle of attack-pitch rate obtained by the embodiment of this application. The figure shows the surface formed by the safety boundary in the three dimensions of pitch angle, angle of attack and pitch rate under the condition of fixed Mach 9. The three-dimensional surface clearly reveals: (1) Multivariable coupled safety envelope: The safety boundary changes in complexity with the pitch angle, angle of attack and pitch rate, and the traditional two-dimensional envelope cannot describe this coupling relationship. (2) High-dimensional processing capability of the method of this invention: Through the level set method, this invention can naturally calculate and express such complex boundary surfaces on high-dimensional grids, breaking through the limitation of traditional methods in performing high-dimensional visualization analysis. This figure provides richer state safety information for pilots or autonomous control systems.

[0077] Furthermore, to ensure the safety and validity of the calculated results, this embodiment selects flight states within and outside the safety boundary and performs controllability analysis respectively to verify the effectiveness of the deformable aircraft control method based on reachability set solution proposed in this application. First, by linearizing the nonlinear equations of the system at the equilibrium point, the Jacobian matrix of the system at that equilibrium point is calculated to obtain the linearized system: (twenty two) Then construct the controllability matrix. (twenty three) Calculate matrix And determine the rank C, if If the equilibrium point is such that the system is locally controllable, then the system is locally controllable in the vicinity of that equilibrium point. This paper selects the equilibrium point... As a typical example, among them These are the points closest to the calculated safety boundary. Substituting them into the state equation and neglecting minor effects, we obtain... (twenty four) Substituting the above formula into the formula for the controllability matrix, we can calculate that its rank is 4.

[0078] Then select points outside the boundary again. ,in Substituting the values ​​into the state equations and then into the controllability matrix formula, we find that its rank is 3, which is less than 4. Therefore, points outside the boundary are uncontrollable. This theoretically proves that the two selected control inputs (rudder deflection and deformation) are capable of completely manipulating the four state variables.

[0079] Example 2: like Figure 7As shown, Embodiment 2 provides a deformable aircraft control system based on reachability set calculation, including an acquisition module 10, a target set generation module 20, a reachability set generation module 30, a boundary determination module 40, a safety assessment module 50, and a control module 60. The acquisition module 10 is used to acquire the real-time flight status and current mission instructions of the deformable aircraft. The target set generation module 20 is used to generate a state target set according to the current task instruction; The reachable set generation module 30 is used to calculate and generate the reachable set of the state target set in the state space based on the level set method according to the real-time flight state, the preset aircraft dynamics model and the preset constraints. The aircraft dynamics model is constructed based on the design parameters of the deformable aircraft, and the state space is the set of all reachable flight states of the deformable aircraft. The boundary determination module 40 is used to determine the current safety state boundary of the deformable aircraft based on the boundary of the reachable set; The safety assessment module 50 is used to determine the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space; The control module 60 is used to control the deformable aircraft in real time according to the control method corresponding to the flight safety level.

[0080] In one possible implementation, the reachability set generation module 30, based on the real-time flight state, a preset aircraft dynamics model, and preset constraints, calculates and generates a reachability set of the state target set in the state space using the level set method, including: Centered on the real-time flight state, and based on the state variable constraints and control duration constraints in the constraints, a reachable set solution space containing the state target set is generated in the state space. The reachable set solution space is divided into grids according to the preset grid spacing to generate a corresponding discrete network, wherein each grid point in the discrete network corresponds to a flight state. Based on the relative positional relationship between each grid point and the state target set, the initial level set function value of each grid point is generated; Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, and then the initial level set function value of each grid point is iteratively updated until the level set function value of each grid point converges, thus obtaining the final level set function value of each grid point. The reachability set of the state target set is determined based on the final level set function value of each of the grid points.

[0081] Furthermore, generating the initial level set function value for each grid point based on the relative positional relationship between each grid point and the state target set includes: Determine whether each of the grid points is located inside, outside, or on the boundary of the state target set; Wherein, if any of the grid points is located inside the state target set, the initial level set function value of the grid point is determined to be 1; If any of the grid points is located outside the state target set, then the initial level set function value of the grid point is determined to be -1; If any of the grid points is located on the boundary of the state target set, then the initial level set function value of the grid point is determined to be 0.

[0082] Furthermore, based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, thereby iteratively updating the initial level set function values ​​of each grid point until the level set function values ​​converge, obtaining the final level set function values ​​of each grid point. Each iterative update process includes: Calculate the approximate left and right spatial gradient values ​​of the current level set function value for each of the grid points; Based on the approximate values ​​of the left and right spatial gradients, the aircraft dynamics model, and the control input constraints, a numerical Hamiltonian function is constructed. The numerical Hamiltonian function is solved by time-progression, and the current level set function value of each grid point is updated according to the calculation result to obtain the updated level set function value of each grid point. Determine whether each of the updated level set function values ​​has converged. If so, use each of the updated level set function values ​​as the corresponding final level set function values; otherwise, perform the next iteration update based on each of the updated level set function values.

[0083] Furthermore, determining the reachability set of the state target set based on the final level set function value of each of the grid points includes: Extract several target grid points from each of the aforementioned grid points, where the final level set function value is 0; Construct zero isosurfaces based on each of the target grid points; The interior region of the zero isosurface is defined as the reachable set of the state target set.

[0084] In one possible implementation, the target set generation module 20 generates a state target set based on the current task instruction, including: Determine the desired flight state based on the current mission instructions; Centered on the desired flight state, a closed region is generated in the state space according to a preset state change range as the state target set. The state change range is determined comprehensively based on the sensor accuracy, control accuracy, and simulation accuracy of the aircraft dynamics model.

[0085] In one possible implementation, the safety assessment module 50 determines the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space, including: In the state space, if the real-time flight state is located within the safety state boundary and the distance from the safety state boundary is greater than a preset threshold, then the flight safety level is the first safety level. If the real-time flight status is within the safety status boundary and the distance to the safety status boundary is less than or equal to a preset threshold, then the flight safety level is the second safety level. If the real-time flight status is outside the safety status boundary, then the flight safety level is the third safety level.

[0086] Furthermore, the control module 60 performs real-time control of the deformable aircraft according to the control method corresponding to the flight safety level, including: If the flight safety level is the first safety level, then the deformable aircraft is controlled to continue executing the preset mission tracking control law; If the flight safety level is the second safety level, then a corresponding correction amount is generated based on the distance and relative orientation between the real-time flight state and the safety state boundary; the correction amount is superimposed on the mission tracking control law to generate a modified mission tracking control law; the deformable aircraft is controlled to execute the modified mission tracking control law. If the flight safety level is the third safety level, then an emergency control law is generated with the center point of the state target set as the target; the deformable aircraft is controlled to execute the emergency control law.

[0087] This application provides a morphing aircraft control system based on reachability set calculation. By calculating the safety state boundary in real time, it dynamically assesses the flight safety level and performs real-time control accordingly, thereby improving the safety of the morphing aircraft during flight. Specifically, this embodiment first generates a state target set by acquiring real-time flight status and mission commands, and then calculates the reachability set based on the level set method to determine the safety state boundary. This process not only considers the real-time state of the aircraft but also incorporates preset dynamic models and constraints, ensuring the dynamic nature and accuracy of the safety boundary. By understanding the relative positional relationship between the real-time flight status and the safety boundary, the system can accurately determine the flight safety level and adopt corresponding control strategies, effectively avoiding the risk of loss of control due to the flight status exceeding the safety boundary. Furthermore, this embodiment supports online real-time calculation, adapting to the rapid time-varying characteristics of the morphing aircraft model, significantly improving flight safety and control efficiency.

[0088] For a more detailed explanation of the working principle and procedures of this embodiment, please refer to the relevant description in Embodiment 1.

[0089] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application for those skilled in the art.

Claims

1. A control method for deformable aircraft based on reachable set solution, characterized in that, include: Acquire the real-time flight status and current mission commands of the transforming aircraft; Generate a state target set based on the current task instructions; Based on the real-time flight state, the preset aircraft dynamics model, and the preset constraints, the reachable set of the state target set is calculated and generated in the state space using the level set method. The aircraft dynamics model is constructed based on the design parameters of the deformable aircraft, and the state space is the set of all reachable flight states of the deformable aircraft. The current safety state boundary of the deformable aircraft is determined based on the boundary of the reachable set; The flight safety level of the deformable aircraft is determined based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space. The deformable aircraft is controlled in real time according to the control method corresponding to the flight safety level.

2. The deformable aircraft control method based on reachability set solution as described in claim 1, characterized in that, The step of generating a reachable set of the state target set in the state space based on the level set method, according to the real-time flight state, the preset aircraft dynamics model, and the preset constraints, includes: Centered on the real-time flight state, and based on the state variable constraints and control duration constraints in the constraints, a reachable set solution space containing the state target set is generated in the state space. The reachable set solution space is divided into grids according to the preset grid spacing to generate a corresponding discrete network, wherein each grid point in the discrete network corresponds to a flight state. Based on the relative positional relationship between each grid point and the state target set, the initial level set function value of each grid point is generated; Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, and then the initial level set function value of each grid point is iteratively updated until the level set function value of each grid point converges, thus obtaining the final level set function value of each grid point. The reachability set of the state target set is determined based on the final level set function value of each of the grid points.

3. The deformable aircraft control method based on reachability set solution as described in claim 2, characterized in that, The step of generating the initial level set function value for each grid point based on the relative positional relationship between each grid point and the state target set includes: Determine whether each of the grid points is located inside, outside, or on the boundary of the state target set; Wherein, if any of the grid points is located inside the state target set, the initial level set function value of the grid point is determined to be 1; If any of the grid points is located outside the state target set, then the initial level set function value of the grid point is determined to be -1; If any of the grid points is located on the boundary of the state target set, then the initial level set function value of the grid point is determined to be 0.

4. The deformable aircraft control method based on reachability set solution as described in claim 2, characterized in that, Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, thereby iteratively updating the initial level set function values ​​of each grid point until the level set function values ​​converge, obtaining the final level set function values ​​of each grid point. Each iterative update process includes: Calculate the approximate left and right spatial gradient values ​​of the current level set function value for each of the grid points; Based on the approximate values ​​of the left and right spatial gradients, the aircraft dynamics model, and the control input constraints, a numerical Hamiltonian function is constructed. The numerical Hamiltonian function is solved by time-progression, and the current level set function value of each grid point is updated according to the calculation result to obtain the updated level set function value of each grid point. Determine whether each of the updated level set function values ​​has converged. If so, use each of the updated level set function values ​​as the corresponding final level set function values; otherwise, perform the next iteration update based on each of the updated level set function values.

5. The deformable aircraft control method based on reachability set solution as described in claim 3, characterized in that, Determining the reachability set of the state target set based on the final level set function value of each of the grid points includes: Extract several target grid points from each of the aforementioned grid points, where the final level set function value is 0; Construct zero isosurfaces based on each of the target grid points; The interior region of the zero isosurface is defined as the reachable set of the state target set.

6. The deformable aircraft control method based on reachability set solution as described in claim 1, characterized in that, The step of generating a state target set based on the current task instruction includes: Determine the desired flight state based on the current mission instructions; Centered on the desired flight state, a closed region is generated in the state space according to a preset state change range as the state target set. The state change range is determined comprehensively based on the sensor accuracy, control accuracy, and simulation accuracy of the aircraft dynamics model.

7. The deformable aircraft control method based on reachability set solution as described in claim 1, characterized in that, Determining the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space includes: In the state space, if the real-time flight state is located within the safety state boundary and the distance from the safety state boundary is greater than a preset threshold, then the flight safety level is the first safety level. If the real-time flight status is within the safety status boundary and the distance to the safety status boundary is less than or equal to a preset threshold, then the flight safety level is the second safety level. If the real-time flight status is outside the safety status boundary, then the flight safety level is the third safety level.

8. The deformable aircraft control method based on reachability set solution as described in claim 7, characterized in that, The real-time control of the deformable aircraft based on the control method corresponding to the flight safety level includes: If the flight safety level is the first safety level, then the deformable aircraft is controlled to continue executing the preset mission tracking control law; If the flight safety level is the second safety level, then a corresponding correction amount is generated based on the distance and relative orientation between the real-time flight state and the safety state boundary; the correction amount is superimposed on the mission tracking control law to generate a modified mission tracking control law; the deformable aircraft is controlled to execute the modified mission tracking control law. If the flight safety level is the third safety level, then an emergency control law is generated with the center point of the state target set as the target; the deformable aircraft is controlled to execute the emergency control law.

9. A deformable aircraft control system based on reachable set solution, characterized in that, It includes an acquisition module, a target set generation module, a reachable set generation module, a boundary determination module, a security assessment module, and a control module; The acquisition module is used to acquire the real-time flight status and current mission instructions of the deformable aircraft. The target set generation module is used to generate a state target set according to the current task instruction; The reachable set generation module is used to calculate and generate the reachable set of the state target set in the state space based on the level set method according to the real-time flight state, the preset aircraft dynamics model and the preset constraints. The aircraft dynamics model is constructed based on the design parameters of the deformable aircraft, and the state space is the set of all reachable flight states of the deformable aircraft. The boundary determination module is used to determine the current safety state boundary of the deformable aircraft based on the boundary of the reachable set; The safety assessment module is used to determine the flight safety level of the deformable aircraft based on the relative positional relationship between the real-time flight state and the safety state boundary in the state space; The control module is used to control the deformable aircraft in real time according to the control method corresponding to the flight safety level.

10. A deformable aircraft control system based on reachability set solution as described in claim 9, characterized in that, The reachability set generation module, based on the real-time flight state, a preset aircraft dynamics model, and preset constraints, calculates and generates the reachability set of the state target set in the state space using the level set method, including: Centered on the real-time flight state, and based on the state variable constraints and control duration constraints in the constraints, a reachable set solution space containing the state target set is generated in the state space. The reachable set solution space is divided into grids according to the preset grid spacing to generate a corresponding discrete network, wherein each grid point in the discrete network corresponds to a flight state. Based on the relative positional relationship between each grid point and the state target set, the initial level set function value of each grid point is generated; Based on the aircraft dynamics model and the control input constraints in the constraints, the Hamilton-Jacobi equation is solved iteratively in the discrete network through time-progression, and then the initial level set function value of each grid point is iteratively updated until the level set function value of each grid point converges, thus obtaining the final level set function value of each grid point. The reachability set of the state target set is determined based on the final level set function value of each of the grid points.

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