Pseudo-spectral method-based stealth shipboard aircraft re-flight trajectory optimization method, equipment, medium and product

Abstract

The invention discloses an invisible shipboard aircraft re-flight trajectory optimization method and device based on a pseudo-spectral method, a medium and a product, and relates to the technical field of automatic control, and the method comprises the steps: constructing a re-flight dynamics model according to dynamics and kinematics equations of an invisible shipboard aircraft, and determining a target function and constraint conditions; determining a plurality of collocation points through a zero point of a Legendre polynomial, respectively converting a state variable and a control variable into discrete variables at each collocation point, and then converting a target function and a constraint condition into algebraic constraints to obtain a nonlinear programming equation set; solving an optimal solution of the nonlinear programming equation set at each collocation point by using a sequential quadratic programming algorithm; and finally, carrying out serialization by utilizing a Lagrange interpolation polynomial to obtain a camouflage shipboard aircraft re-flight trajectory optimization result. According to the method, the capacity of an execution mechanism of the stealth shipboard aircraft is fully considered, the optimal re-flight track of the stealth shipboard aircraft is obtained, and the problem that the flight capacity in a traditional re-flight strategy is not fully utilized is solved.

Description

Technical Field

[0001] The present application relates to the field of automatic control technology, and in particular to a method, device, medium and product for optimizing the go-around trajectory of a stealth carrier-based aircraft based on a pseudo-spectral method. Background Art

[0002] In recent years, research on stealth carrier-based aircraft landing control has intensified. However, stealth carrier-based aircraft face numerous challenges during landing, including low approach speeds, which are susceptible to turbulence onboard the carrier; limited deck length available for landing; and, unlike landing from land, the lateral and longitudinal motion of the aircraft carrier itself due to the influence of waves during navigation. Due to the complexity of landing, stealth carrier-based aircraft may significantly deviate from their landing trajectory, resulting in a crash or collision with the carrier. To ensure the safety of both the aircraft and the carrier, a go-around is required when the aircraft significantly deviates from the ideal glide path. Statistics show that the go-around probability for stealth carrier-based aircraft is approximately 5% during daytime, while it increases to 12% to 15% during nighttime landings. To ensure safety during a go-around, the pilot typically disables the automatic landing system, pushes the throttle to military thrust, and deflects the elevator to maintain the appropriate angle of attack. However, when adopting this go-around strategy, the flight capability of the stealth carrier-based aircraft is not fully mobilized and utilized, which may easily lead to an increase in the risk rate of go-around and a reduction in the go-around safety zone. Summary of the Invention

[0003] The purpose of this application is to provide a method, device, medium and product for optimizing the go-around trajectory of a stealth carrier-based aircraft based on the pseudo-spectral method, which can fully consider the capabilities of the stealth carrier-based aircraft's actuators and obtain the optimal go-around trajectory of the stealth carrier-based aircraft, thereby solving the problem of underutilization of flight capabilities in traditional go-around strategies and significantly improving the safety and stability of the go-around process.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides a method for optimizing a stealth carrier-based aircraft's go-around trajectory based on a pseudospectral method, comprising:

[0006] According to the dynamics and kinematics equations of stealth carrier-based aircraft, a go-around dynamics model is constructed;

[0007] determining an objective function and constraint conditions for go-around trajectory optimization based on the go-around dynamics model;

[0008] After discretizing the time interval of the missed approach, several collocation points are determined through the zero points of Legendre polynomials.

[0009] Converting the state variables and control variables in the objective function and the constraint conditions into discrete variables at each of the collocation points;

[0010] Converting the objective function and the constraint conditions into algebraic constraints according to the discrete variables to obtain a nonlinear programming equation group;

[0011] Using a sequential quadratic programming algorithm, solving the nonlinear programming equations at each of the collocation points for an optimal solution; the optimal solution includes: an optimal state variable, an optimal control variable, and a terminal time;

[0012] The Lagrange interpolation polynomial is used to make the optimal solution at each of the distribution points continuous, and the optimization result of the stealth carrier-based aircraft's go-around trajectory is obtained.

[0013] Optionally, the objective function includes: a boundary objective function and a path integral function; the boundary objective function is to maximize the clear height of the stern of the ship achieved by the missed approach terminal; the path integral function is to minimize the sinking time of the stealth carrier-based aircraft during the missed approach;

[0014] The constraints include: initial state, terminal state, boundary constraints, state quantity constraints and control quantity constraints.

[0015] Optionally, converting the state variables and control variables in the objective function and the constraint conditions into discrete variables at each of the collocation points specifically includes:

[0016] For each allocation point:

[0017] calculating the derivatives of the Lagrange interpolation polynomial at the collocation points;

[0018] Calculating the derivative of the state variable with respect to the collocation point based on the state variable at the collocation point and the derivative at the collocation point; the state variable at the collocation point is the state variable at the collocation point in the objective function and the constraint condition; the derivative at the collocation point is the derivative of the Lagrange interpolation polynomial at the collocation point;

[0019] The go-around dynamics model is converted into an algebraic equation form according to the derivatives of the state variables with respect to the collocation point, and the go-around dynamics algebraic equation is obtained;

[0020] In combination with the go-around dynamics algebraic equation, the state variables and control variables in the objective function and constraint conditions are respectively converted into discrete variables at the collocation points.

[0021] Optionally, converting the objective function and the constraint conditions into algebraic constraints according to the discrete variables to obtain a nonlinear programming equation system specifically includes:

[0022] According to the discrete variables, the initial state and the terminal state of the collocation point are calculated respectively using the Gaussian integral weight matrix to obtain the collocation point initial state and the collocation point terminal state;

[0023] The objective function is expressed by using the state variables and control variables at the collocation points to obtain the collocation point objective function;

[0024] Converting the state quantity constraint and the control quantity constraint into the state quantity constraint and the control quantity constraint at the collocation point respectively, to obtain the collocation point state quantity constraint and the collocation point control quantity constraint;

[0025] Converting the boundary constraint into a boundary constraint at a collocation point in the form of a state variable to obtain a collocation point boundary constraint;

[0026] The initial state of the matching points, the terminal state of the matching points, the matching point objective function, the matching point state quantity constraint, the matching point control quantity constraint and the matching point boundary constraint are combined to obtain a nonlinear programming equation group.

[0027] Optionally, the using a sequential quadratic programming algorithm to solve the optimal solution of the nonlinear programming equations at each of the collocation points specifically includes:

[0028] Calculating the Lagrangian function of the nonlinear programming equations at the collocation points;

[0029] The Lagrangian function is iteratively solved according to a first formula to obtain the optimal solution of the nonlinear programming equations at the collocation point; the first formula is: Among them, H k is the approximate positive definite matrix of the Hessian matrix of the Lagrangian function, δ k =y k+1 -y k =α k d k , α k and d k are the step size factor and the iterative search direction, y k and y k+1 Represent the values ​​of the variables solved in the kth iteration and the k+1th iteration, respectively. is the gradient of the Lagrangian function with respect to y, and λ and μ are the Lagrangian multipliers introduced when calculating the Lagrangian function.

[0030] Optionally, after discretizing the time interval of the missed approach, a plurality of collocation points are determined by using the zero points of the Legendre polynomials, specifically including:

[0031] Discretize the time interval of the missed approach, and the calculation formula is: Among them, t0 represents the starting time, t f represents the terminal time, t represents the time interval of the missed approach, and τ represents the discretized time interval;

[0032] According to the discretized time interval, the zero points of the Legendre polynomial are calculated to obtain several collocation points; the Legendre polynomial is: Among them, P N (τ) represents the Legendre polynomial of order N, and d means to find the differential.

[0033] Optionally, the group of dynamic and kinematic equations specifically includes: translational kinematic equations, rotational kinematic equations, linear motion equations, and angular motion equations.

[0034] In a second aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement any one of the above-mentioned methods for optimizing the trajectory of a stealth carrier-based aircraft based on pseudo-spectral method.

[0035] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned methods for optimizing the trajectory of a stealth carrier-based aircraft based on pseudo-spectral method.

[0036] In a fourth aspect, the present application provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-mentioned methods for optimizing the stealth carrier-based aircraft's go-around trajectory based on the pseudo-spectral method.

[0037] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0038] The present application provides a method, device, medium, and product for optimizing a go-around trajectory of a stealth carrier-based aircraft based on a pseudospectral method. The method comprises: constructing a go-around dynamics model based on the dynamics and kinematics equations of the stealth carrier-based aircraft; determining an objective function and constraints for optimizing the go-around trajectory based on the go-around dynamics model; discretizing a time interval for the go-around and determining a plurality of collocation points using zeros of Legendre polynomials; converting state variables and control variables in the objective function and constraints into discrete variables at each of the collocation points; converting the objective function and constraints into algebraic constraints based on the discrete variables to obtain a nonlinear programming equation system; solving the nonlinear programming equation system at each of the collocation points using a sequential quadratic programming algorithm; the optimal solution comprising an optimal state variable, an optimal control variable, and a terminal time; and continuousizing the optimal solution at each of the collocation points using a Lagrange interpolation polynomial to obtain an optimized result for the stealth carrier-based aircraft's go-around trajectory. The present application constructs a Lagrange interpolation polynomial by discretizing control quantities and state quantities, approximating the control quantities and state quantities at discrete collocation points, transforming the trajectory optimization problem into a parameter optimization problem, and then adopts a sequential quadratic programming algorithm to solve the nonlinear programming problem, thereby fully considering the capabilities of the stealth carrier-based aircraft's actuators and obtaining the optimal go-around trajectory of the stealth carrier-based aircraft. This solves the problem of underutilization of flight capabilities in traditional go-around strategies and significantly improves the safety and stability of the go-around process. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0040] Figure 1 A flowchart of a method for optimizing the go-around trajectory of a stealth carrier-based aircraft based on pseudospectral method is provided in one embodiment of the present application.

[0041] Figure 2 A schematic diagram of a ship model provided in one embodiment of the present application.

[0042] Figure 3 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0044] This application provides a new control method for planning a go-around trajectory with a large safety margin, taking into account multiple factors such as the motion state and attitude of a stealth carrier-based aircraft, its relative position to the aircraft carrier, and its distance from the sea surface. This method belongs to the field of automatic control technology and is primarily used for performance optimization of stealth carrier-based aircraft.

[0045] In recent years, research on stealth carrier-based aircraft landing control has intensified. However, stealth carrier-based aircraft face numerous challenges during landing, including low approach speeds, which are susceptible to turbulence onboard the carrier; limited deck length available for landing; and, unlike landing from land, the lateral and longitudinal motion of the aircraft carrier itself due to the influence of waves during navigation. Due to the complexity of landing, stealth carrier-based aircraft may significantly deviate from their landing trajectory, resulting in a crash or collision with the carrier. To ensure the safety of both the aircraft and the carrier, a go-around is required when the aircraft significantly deviates from the ideal glide path. Statistics show that the go-around probability for stealth carrier-based aircraft is approximately 5% during daytime, while it increases to 12% to 15% during nighttime landings. To ensure safety during a go-around, the pilot typically disables the automatic landing system, pushes the throttle to military thrust, and deflects the elevator to maintain the appropriate angle of attack. However, when adopting this go-around strategy, the flight capability of the stealth carrier-based aircraft is not fully mobilized and utilized, which may easily lead to an increase in the risk rate of go-around and a reduction in the go-around safety zone.

[0046] Therefore, this application addresses the aforementioned issues and proposes a targeted trajectory optimization method for stealth carrier-based aircraft, addressing unsafe go-around trajectories and small safety margins. This method constructs Lagrange interpolation polynomials by discretizing control variables and state variables. These are approximated at discrete collocation points, transforming the trajectory optimization problem into a parameter optimization problem. A sequential quadratic programming algorithm is then employed to solve the nonlinear programming problem. Leveraging optimal control techniques, this method fully considers the capabilities of the stealth carrier-based aircraft's actuators to determine the optimal go-around trajectory for the stealth carrier-based aircraft. This solves the problem of underutilized flight capabilities in traditional go-around strategies and significantly improves the safety and stability of the go-around process. Furthermore, this method dynamically adjusts the go-around trajectory based on the stealth carrier-based aircraft's real-time state and environmental conditions, ensuring a safe go-around in complex and changing landing environments.

[0047] In this application, control engineers can use pseudospectral methods to calculate the optimal go-around trajectory by obtaining information such as the initial state, target position, and control constraints of a stealth carrier-based aircraft. The main content and steps of this application are: first, the initial go-around state, target terminal state, and admissible control constraints are given; then, using the pseudospectral method, the time domain is discretized and transformed, the state variables and control variables are approximated, and the objective function and constraints are converted, transforming the original trajectory optimization problem into a general nonlinear programming problem; the nonlinear programming problem is solved using a sequential quadratic programming algorithm to obtain the optimal state variables, optimal control variables, and terminal time; finally, these control variables are applied to the stealth carrier-based aircraft dynamics model. In practical applications, the trajectory, speed, and other state variables of the stealth carrier-based aircraft are measured by sensors. The optimal go-around trajectory calculated by this method can provide a reference trajectory for future controller design, enabling the stealth carrier-based aircraft to track the optimal go-around trajectory for go-around, improving go-around safety.

[0048] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0049] In an exemplary embodiment, Figure 1 As shown, a method for optimizing the go-around trajectory of a stealth carrier-based aircraft based on the pseudo-spectral method is provided. The method is executed by a computer device, specifically a computer device such as a terminal or a server, or a terminal and a server. In the embodiment of the present application, the method is described by taking the application of the method to the server as an example, and includes the following steps 201 to 208. Among them:

[0050] S1. Construct a go-around dynamics model based on the dynamics and kinematics equations of the stealth carrier-based aircraft. The dynamics and kinematics equations specifically include: translational kinematics equations, rotational kinematics equations, linear motion equations, and angular motion equations.

[0051] S2. Determine the objective function and constraint conditions for the missed approach trajectory optimization according to the missed approach dynamics model.

[0052] Among them, the objective function includes: a boundary objective function and a path integral function; the boundary objective function is to maximize the net height of the stern achieved by the missed approach terminal; the path integral function is to minimize the sinking time of the stealth carrier-based aircraft during the missed approach; the constraint conditions include: initial state, terminal state, boundary constraint, state quantity constraint and control quantity constraint.

[0053] In this embodiment, the initial state and terminal state as well as the state quantity and control quantity constraints are first given: the initial state x0 is given; the terminal state x f ; State and control quantity constraints x min ≤x≤x max ,umin ≤u≤u max .

[0054] The given initial state and terminal state as well as the state and control quantity constraints include: taking the system state variables as x = [α, β, μ, p, q, r, V, γ, χ, x, y, z] T , given the initial state x0, the component representation means: [x, y, z] T is the aircraft position coordinate defined in the inertial system; V is the aircraft ground speed; [γ,χ] T are the climb angle and heading angle in the track coordinate system, [α, β, μ] T Respectively represent the aircraft's angle of attack, sideslip angle, and speed roll angle; [p, q, r] T They represent the roll, pitch, and yaw angular velocities in the aircraft coordinate system, the terminal state limit, and the horizontal relative position x of the aircraft carrier. f =x gf , the control variable is u=[L,M,N,Y,T] T , where [L,M,N] T They represent the roll, pitch, and yaw moments in the body coordinate system; Y represents the lift in the body coordinate system; and T represents the engine thrust. min ≤s≤s max ,u min ≤u≤u max , where s represents the state variable and u represents the control variable. The minimum and maximum constraints represent the range constraints on the state and control variables, and the specific value range is given by the actual situation.

[0055] S3. After discretizing the time interval of the missed approach, several collocation points are determined through the zero points of the Legendre polynomial.

[0056] Specifically:

[0057] Discretize the time interval of the missed approach, and the calculation formula is: Among them, t0 represents the starting time, t f represents the terminal time, t represents the time interval of the missed approach, and τ represents the discretized time interval;

[0058] According to the discretized time interval, the zero points of the Legendre polynomial are calculated to obtain several collocation points; the Legendre polynomial is: Among them, P N (τ) represents the Legendre polynomial of order N.

[0059] In this embodiment, the time interval is first discretized and transformed: the time interval to be solved [t0,t f ] is transformed to the time interval [-1,1].

[0060] Then Legendre polynomials are introduced to select the collocation points, thereby discretizing the state variables and control variables. N The zero point of (τ) obtains the collocation point τ i , thus discretizing the continuous state variable x(τ) and the control variable U(τ) into the state variable x(τ) at the collocation point. i ) and the control variable U(τ i ).

[0061] S4. Convert the state variables and control variables in the objective function and constraint conditions into discrete variables at each of the matching points.

[0062] Specifically, for each distribution point:

[0063] Compute the derivatives of the Lagrange interpolation polynomial at the collocation points.

[0064] The derivative of the state variable with respect to the distribution point is calculated based on the state variable at the distribution point and the derivative at the distribution point; the state variable at the distribution point is the state variable at the distribution point in the objective function and the constraint condition; the derivative at the distribution point is the derivative of the Lagrange interpolation polynomial at the distribution point.

[0065] The go-around dynamics model is transformed into an algebraic equation form according to the derivatives of the state variables with respect to the collocation points, and the go-around dynamics algebraic equation is obtained.

[0066] In combination with the go-around dynamics algebraic equation, the state variables and control variables in the objective function and constraint conditions are respectively converted into discrete variables at the collocation points.

[0067] S5. Convert the objective function and the constraint conditions into algebraic constraints according to the discrete variables to obtain a nonlinear programming equation group.

[0068] Specifically:

[0069] According to the discrete variables, the initial state and the terminal state of the distribution point are calculated respectively by using the Gaussian integral weight matrix to obtain the distribution point initial state and the distribution point terminal state.

[0070] The objective function is expressed by using the state variables and control variables at the collocation points to obtain the collocation point objective function.

[0071] The state quantity constraint and the control quantity constraint are respectively converted into the state quantity constraint and the control quantity constraint at the distribution point to obtain the distribution point state quantity constraint and the distribution point control quantity constraint.

[0072] The boundary constraints are converted into boundary constraints at the collocation points in the form of state variables to obtain the collocation point boundary constraints.

[0073] The initial state of the matching points, the terminal state of the matching points, the matching point objective function, the matching point state quantity constraint, the matching point control quantity constraint and the matching point boundary constraint are combined to obtain a nonlinear programming equation group.

[0074] In this embodiment, the objective function and constraints are converted: the dynamic differential equation and the objective function are converted into algebraic constraints to obtain a nonlinear programming problem (nonlinear programming equation system). The calculation method is as follows:

[0075] Calculate the Lagrange interpolation polynomial L i (τ) at the collocation point τ m The derivative of :

[0076]

[0077] Where i and j represent the i-th and j-th collocation points; l is the summation symbol. i ) and the derivatives of the corresponding Lagrange interpolation polynomials The derivative of the state variable x(τ) with respect to τ can be estimated:

[0078]

[0079] The differential form of the dynamic model can be estimated by estimating the derivative of the state variable x(τ) with respect to τ. Convert to the following algebraic equation:

[0080]

[0081] Among them, x represents the state variable, u represents the control variable; x(τ m ),U(τ m ) represents the point τ m The state variables and control variables of the initial state x0=x(τ0), the terminal state x(τ N+1 ) can be represented by the Gaussian integral weight matrix w M calculate

[0082]

[0083] The objective function J can be expressed by the state variable x(τ i ) and the control variable U(τ i ) is approximately expressed as:

[0084]

[0085] The state and control constraints can be converted into the state variables x(τ i ) and the control variable U(τ i )Constraints satisfied:

[0086] x min ≤x(τ i )≤x max ,u min ≤U(τ i )≤u max ;

[0087] The boundary constraints are discretized into the state variables x(τ i )Constraints satisfied:

[0088] x(τ0)=x0,x(τ N+1 )=x gf ;

[0089] Further arrangement can be transformed into the standard form of nonlinear programming problem:

[0090]

[0091] Where y is the state variable x(τ i ) and the control variable U(τ i ) and terminal time t f The variable to be determined, h i (y) = 0 represents the i-th equality constraint, corresponding to the above boundary constraints and the dynamic model of algebraic equations, g j (y)≤0 represents the jth inequality constraint, corresponding to the above-mentioned state quantity and control quantity constraints, r and s represent the upper limit of the number of corresponding equality constraints and inequality constraints.

[0092] S6. Using a sequential quadratic programming algorithm, find the optimal solution of the nonlinear programming equations at each of the collocation points; the optimal solution includes: optimal state variables, optimal control variables, and terminal time.

[0093] Specifically:

[0094] The Lagrangian function of the nonlinear programming equations at the collocation points is calculated.

[0095] The Lagrangian function is iteratively solved according to a first formula to obtain the optimal solution of the nonlinear programming equations at the collocation point; the first formula is: Among them, H k is the approximate positive definite matrix of the Hessian matrix of the Lagrangian function, δ k =y k+1 -y k =α k d k , α k and d kare the step size factor and the iterative search direction, y k and y k+1 Represent the values ​​of the variables solved in the kth iteration and the k+1th iteration, respectively. is the gradient of the Lagrangian function with respect to y, and λ and μ are the Lagrangian multipliers introduced when calculating the Lagrangian function.

[0096] In this embodiment, the nonlinear programming problem is solved by using a sequential quadratic programming algorithm to obtain the optimal state variables and optimal control variables at the collocation points. The nonlinear programming equations are solved by the following calculation method:

[0097] The Lagrangian function for calculating nonlinear programming problems is:

[0098]

[0099] The nonlinear programming problem is equivalent to solving the following quadratic programming problem:

[0100]

[0101] Where H k is the approximate positive definite matrix of the Hessian matrix of the Lagrangian function, h i (y) represents the i-th equality constraint, g j (y) represents the jth inequality constraint, y k Indicates the value of the variable to be solved in the kth iteration, and H is calculated according to the following formula k To update:

[0102]

[0103] in, δ k =y k+1 -y k =α k d k , α k and d k are the step size factor and the iterative search direction respectively. According to the above steps, the optimal solution y is solved iteratively. * , that is, the optimal state variables, optimal control variables and terminal moments at the matching points.

[0104] S7. Utilize the Lagrange interpolation polynomial to serialize the optimal solution at each of the distribution points to obtain the optimized result of the stealth carrier-based aircraft's go-around trajectory.

[0105] In this embodiment, the discrete state variables and control variables are made continuous: Lagrange interpolation polynomials are introduced from the optimal state variables and optimal control variables at the matching points to make the state variables and control variables continuous.

[0106] The calculation method is as follows:

[0107]

[0108] Where: x(τ i ) is the state variable x(τ) at the collocation point τ i The value of U(τ i ) is the control variable U(τ) at the matching point τ i The value of L i (τ) is the Lagrange interpolation polynomial.

[0109] Compared with the related art, this embodiment has the following advantages and effects:

[0110] 1. It can significantly improve the accuracy and efficiency of stealth carrier-based aircraft go-around trajectory optimization. By discretizing the problem in the continuous time domain through the pseudo-spectral method, the computational effort is greatly reduced, making the solution process faster.

[0111] 2. This method performs well in dealing with nonlinear constraints and complex objective functions, and can find the optimal solution that is closer to the actual situation.

[0112] 3. The algorithm structure is simple and clear, easy to program and debug, and reduces the difficulty of engineering application.

[0113] 4. Since the pseudo-spectral method has global convergence, it is not easy to fall into the local optimal solution during the solution process, which improves the reliability and stability of the solution.

[0114] During the application process, control engineers can give the initial state of the stealth carrier-based aircraft's go-around and the corresponding allowable control constraints according to actual requirements, and input the control quantity and trajectory calculated by this method to the actuator to realize the trajectory tracking control function.

[0115] As a specific implementation method, the present embodiment provides a method for optimizing a stealth carrier-based aircraft's go-around trajectory based on a pseudospectral method, which specifically includes the following steps:

[0116] First, some symbols are explained: x0 is the initialization state of the aircraft's go-around; x f is the terminal state of the aircraft's missed approach; J is the objective function, reflecting the optimization goal; P N (·) is the Nth-order Legendre polynomial; τ is the collocation point in the discretized time domain; L(·) is the Lagrange interpolation basis function; X(τ) is the state variable at the collocation point; U(τ) is the control variable at the collocation point.

[0117] Step 1: Given the initial state and terminal state as well as the state and control quantity constraints:

[0118] Establish differential equations: Figure 2 As shown, with the geometric center of the structure in the aircraft model as the origin, the x-axis is located in the aircraft symmetry plane, parallel to the body axis, and points to the direction of the aircraft nose. The z-axis and the x-axis are both in the aircraft symmetry plane and perpendicular to the x-axis, with downward as the positive direction. The y-axis is perpendicular to the plane formed by the other two axes and points to the right of the nose. The body coordinate system O is established. b -x b y b z b ; Set a point on the ground plane as the origin of the coordinate system O. The z axis is vertically downward and perpendicular to the horizontal plane. The x axis points to the north of the earth in the horizontal plane. The y axis is in the horizontal plane. Establish an inertial coordinate system O-xyz; The center of the hull is the origin of the aircraft carrier coordinate system. s The axis is perpendicular to the longitudinal symmetry plane of the aircraft carrier and points to the right side of the aircraft carrier; s The axis is in the longitudinal symmetry plane of the aircraft carrier and points to the front of the aircraft carrier; s The axis is in the longitudinal symmetry plane and points to the seabed, establishing the aircraft carrier coordinate system O s -x s y s z s ; Establish the aircraft dynamics and kinematics equations, which can be described by the following differential equations:

[0119] Translational kinematic equations:

[0120]

[0121] Rotational kinematic equations:

[0122]

[0123] Linear motion equation:

[0124]

[0125] The equation of angular motion:

[0126]

[0127] Where [x,y,z] T is the aircraft position coordinate defined in the inertial system; V is the aircraft ground speed; [γ,χ] T are the climb angle and heading angle in the track coordinate system, [α, β, μ] T Respectively represent the aircraft's angle of attack, sideslip angle, and speed roll angle; [p, q, r] T Respectively represent the roll, pitch, and yaw angular velocities in the body coordinate system; [L, M, N] T Respectively represent the roll, pitch, and yaw moments in the body coordinate system; [Y, D, C] TThey represent lift, drag, and lateral force in the aircraft coordinate system; T represents engine thrust; m represents aircraft mass; I x ,I y ,I z ,I xz Denotes the moment of inertia and product of inertia. Take the state vector x=[α,β,μ,p,q,r,V k ,γ,χ,x,y,z] T , control input vector u=[L,M,N,Y,T] T , the above four sets of differential equations are used to construct the go-around dynamics model of stealth carrier-based aircraft

[0128] 2) Given state and terminal constraints: the initial state is x0 = [α0, β0, μ0, p0, q0, r0, V0, γ0, χ0, x0, y0, z0] T , the terminal state is only fixed with respect to the horizontal position x of the aircraft carrier f =x gf , the admissible control constraints include u=[L,M,N,Y,T] T Given the state and control constraints x min ≤x≤x max ,u min ≤u≤u max .

[0129] Objective function design: The design boundary objective function Φ(·) is the stern clear height H achieved at the missed approach terminal. f Maximum, as shown below:

[0130] minΦ(x f ,t f )=1 / H f ;

[0131] Among them, H f Indicates the aft clear height achieved at the missed approach terminal.

[0132] The path integral function G(·) along the flight trajectory is designed to minimize the go-around sinking time of the stealth carrier-based aircraft. Considering that the go-around sinking time of the stealth carrier-based aircraft is closely related to the climb angle γ, it can be expressed as follows:

[0133]

[0134] Where sign(·) is the sign function, and the expression is as follows

[0135]

[0136] Combining the above boundary objective function Φ(·) and the path integral function G(·) along the flight trajectory, the final form of the optimization objective function can be obtained.

[0137]

[0138] Where k is the proportional coefficient, which reflects the weight value of the two optimization objectives.

[0139] 4) Boundary constraints: Set the boundary constraints to x(t0) = x0, x(t f )=x gf , indicating that the aircraft starts a go-around at a given initial state and moves to a given horizontal distance from the aircraft carrier at the end of the go-around.

[0140] 5) The trajectory optimization problem to be solved is expressed as:

[0141]

[0142] Step 2: Time domain discretization and transformation: The time interval to be solved for missed approach [t0,t f ] is transformed to the time interval [-1,1] by the following formula:

[0143]

[0144] Among them, τ is the equivalent time variable after transformation.

[0145] Step 3: Discrete state and control quantities

[0146] By solving the N-order Legendre polynomial P N The zero point of (τ) obtains the collocation set τ LG ={τ1,τ2,…,τ N}:

[0147]

[0148] Let τ0 = -1, τ N+1 =1, we get the collocation point set of the closed interval τ∈[-1,1] -1=τ0<τ1<…<τ m <…<τ N <τ N+1 =1.

[0149] Through the above formula, the continuous state variable x(τ) and the control variable U(τ) to be solved can be converted into the state variable x(τ) to be solved at the collocation point. i ) and the control variable U(τ i ).

[0150] Step 4: Objective function and constraint conversion:

[0151] Step 3 has converted the continuous state variable x(τ) and control variable U(τ) to be solved into the state variable x(τ) at the collocation point.i ) and the control variable U(τ i ), the following constraints are also converted into the state variables x(τ i ) and the control variable U(τ i ) to satisfy the constraints, and convert the objective function into the state variable x(τ i ) and the control variable U(τ i ) is approximately the same as the equation expressed by .

[0152] 1) Calculate the Lagrange interpolation polynomial L i (τ) at the collocation point τ m The derivative of :

[0153]

[0154] 2) Calculate the derivative of the state variable x(τ) with respect to τ: The state variable x(τ) at the collocation point i ) and the derivatives of the corresponding Lagrange interpolation polynomials The derivative of the state variable x(τ) with respect to τ can be calculated.

[0155]

[0156] 3) Dynamic model conversion: The differential form of the dynamic model can be converted by the derivative of the state variable x(τ) with respect to τ Convert to the following algebraic equation

[0157]

[0158] 4) Calculate the terminal state: terminal state x(τ N+1 ) can be represented by the Gaussian integral weight matrix w M calculate:

[0159]

[0160] Among them, x(τ0)=x0, Gaussian integral weight matrix w M It can be calculated by the following formula:

[0161]

[0162] 5) Objective function conversion: The objective function J is converted by the state variable x(τ i ) and the control variable U(τ i ) is approximately expressed as:

[0163]

[0164] 6) State and control constraint conversion: The state and control constraint are converted into the state variable x(τ i ) and the control variable U(τ i )Constraints satisfied:

[0165] x min ≤x(τ i )≤x max ,u min ≤U(τ i )≤u max ;

[0166] 7) Boundary constraint conversion: The boundary constraint is discretized into the state variable x(τ i )Constraints satisfied:

[0167] x(τ0)=x0,x(τ N+1 )=x gf ;

[0168] 8) Further organization can be transformed into the standard form of general nonlinear programming problems:

[0169]

[0170] Where y is the state variable x(τ i ) and the control variable U(τ i ) and terminal time t f The variable to be determined. J = F(y) represents the objective function, corresponding to the objective function conversion at 5) above, h i (y) = 0 represents an equality constraint, corresponding to the boundary constraint at 7) above, g j (y)≤0 represents an inequality constraint, corresponding to the state and control quantity constraints in 6) above.

[0171] Through step 4, the state variables, control variables, performance index functions and constraints to be determined can all be converted into the state variables x(τ i ) and the control variable U(τ i ) and terminal time t f The algebraic expression of , thus transforming the original trajectory optimization problem into a general nonlinear programming problem that is easy to solve.

[0172] Step 5: Solving nonlinear programming problems:

[0173] 1) Calculate the Lagrangian function L(y,λ,μ) of the nonlinear programming problem, thereby transforming the constrained optimization problem into an unconstrained optimization problem:

[0174]

[0175] Among them, λ i and μ j is the Lagrange multiplier.

[0176] 2) Initialization: Initialize the variable to be determined y0, Lagrange multipliers λ0 and μ0, allowable error ε, and the initial Hessian matrix H0.

[0177] 3) Solve the search direction d k : At the current iteration point y k At , construct the following quadratic programming subproblem:

[0178]

[0179] Where H k is the approximate positive definite matrix of the Hessian matrix of the Lagrangian function L(y,λ,μ). Solve the quadratic programming subproblem and obtain the search direction d k and the corresponding Lagrange multiplier λ k and μ k .

[0180] 4) Determine the step size factor α k : Along the search direction d k Finding step size α k , so that it satisfies:

[0181]

[0182] Among them, 0<σ<1;

[0183] 5) Calculate the new iteration point y k+1 :

[0184] y k+1 =y k +α k d k ;

[0185] 6) If ||y k+1 -y k ||≤ε, then take the optimal solution y of the nonlinear programming problem * =y k+1 , the solution is completed and the calculation stops, otherwise go to 7).

[0186] 7) Update the Hessian matrix to get H k+1 , and returns 3):

[0187]

[0188] in, δ k =y k+1 -yk =α k d k .

[0189] Step 6: Make discrete state variables and control variables continuous:

[0190] By solving the nonlinear programming problem in step 5, the optimal solution y of the nonlinear programming problem can be obtained. * , that is, the optimal state variable x(τ i ), optimal control quantity U(τ i ) and terminal moment.

[0191] Through the Lagrange interpolation function L i (τ) can be fitted to obtain the continuous optimal state variable x(τ) and the optimal control quantity U(τ):

[0192]

[0193] Where: x(τ i ) is the state variable at the collocation point τ i The value of U(τ i ) is the control variable at the matching point τ i The value of L i (τ) is the Lagrange interpolation polynomial, which is calculated as follows:

[0194]

[0195] Among them, τ j is the jth collocation point. The time interval [-1,1] is inversely transformed into [t0,t f ];

[0196]

[0197] The optimal state variable x(t) and the optimal control variable U(t) are obtained, which provides a reference trajectory for future controller design, enabling stealth carrier-based aircraft to track the optimal go-around trajectory for go-around and improve go-around safety.

[0198] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 3As shown. The computer device includes a processor, a memory, an input / output interface (I / O) and a communication interface. The processor, memory and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The I / O interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a method for optimizing the go-around trajectory of a stealth carrier-based aircraft based on the pseudo-spectral method is implemented.

[0199] Those skilled in the art will understand that Figure 3 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0200] In an exemplary embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0201] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0202] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0203] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0204] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0205] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0206] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0207] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A stealth carrier-based aircraft go-around trajectory optimization method based on pseudo-spectral method, characterized by: include: According to the dynamics and kinematics equations of stealth carrier-based aircraft, a go-around dynamics model is constructed; determining an objective function and constraint conditions for go-around trajectory optimization based on the go-around dynamics model; After discretizing the time interval of the missed approach, several collocation points are determined through the zero points of Legendre polynomials. Converting the state variables and control variables in the objective function and the constraint conditions into discrete variables at each of the collocation points; Converting the objective function and the constraint conditions into algebraic constraints according to the discrete variables to obtain a nonlinear programming equation group; Using a sequential quadratic programming algorithm, solving the nonlinear programming equations at each of the collocation points for an optimal solution; the optimal solution includes: an optimal state variable, an optimal control variable, and a terminal time; The Lagrange interpolation polynomial is used to make the optimal solution at each of the distribution points continuous, and the optimization result of the stealth carrier-based aircraft's go-around trajectory is obtained.

2. The stealth carrier-based aircraft go-around trajectory optimization method based on pseudospectral method according to claim 1, characterized in that: The objective function includes: a boundary objective function and a path integral function; the boundary objective function is to maximize the clear height of the ship's stern achieved by the missed approach terminal; the path integral function is to minimize the sinking time of the stealth carrier-based aircraft during the missed approach; The constraints include: initial state, terminal state, boundary constraints, state quantity constraints and control quantity constraints.

3. The stealth carrier-based aircraft go-around trajectory optimization method based on pseudospectral method according to claim 2, characterized in that: Converting the state variables and control variables in the objective function and the constraint conditions into discrete variables at each of the collocation points specifically includes: For each allocation point: calculating the derivatives of the Lagrange interpolation polynomial at the collocation points; Calculating the derivative of the state variable with respect to the collocation point based on the state variable at the collocation point and the derivative at the collocation point; the state variable at the collocation point is the state variable at the collocation point in the objective function and the constraint condition; the derivative at the collocation point is the derivative of the Lagrange interpolation polynomial at the collocation point; The go-around dynamics model is converted into an algebraic equation form according to the derivatives of the state variables with respect to the collocation point, and the go-around dynamics algebraic equation is obtained; In combination with the go-around dynamics algebraic equation, the state variables and control variables in the objective function and constraint conditions are respectively converted into discrete variables at the collocation points.

4. The method for optimizing the stealth carrier-based aircraft's missed approach trajectory based on pseudospectral method according to claim 3, characterized in that: The objective function and the constraint conditions are converted into algebraic constraints according to the discrete variables to obtain a nonlinear programming equation system, which specifically includes: According to the discrete variables, the initial state and the terminal state of the collocation point are calculated respectively using the Gaussian integral weight matrix to obtain the collocation point initial state and the collocation point terminal state; The objective function is expressed by using the state variables and control variables at the collocation points to obtain the collocation point objective function; Converting the state quantity constraint and the control quantity constraint into the state quantity constraint and the control quantity constraint at the collocation point respectively, to obtain the collocation point state quantity constraint and the collocation point control quantity constraint; Converting the boundary constraint into a boundary constraint at a collocation point in the form of a state variable to obtain a collocation point boundary constraint; The initial state of the matching points, the terminal state of the matching points, the matching point objective function, the matching point state quantity constraint, the matching point control quantity constraint and the matching point boundary constraint are combined to obtain a nonlinear programming equation group.

5. The stealth carrier-based aircraft go-around trajectory optimization method based on pseudospectral method according to claim 1, characterized in that: The method of using a sequential quadratic programming algorithm to solve the nonlinear programming equations at each of the collocation points specifically includes: Calculating the Lagrangian function of the nonlinear programming equations at the collocation points; The Lagrangian function is iteratively solved according to a first formula to obtain the optimal solution of the nonlinear programming equations at the collocation point; the first formula is: Among them, H k is the approximate positive definite matrix of the Hessian matrix of the Lagrangian function, δ k =y k+1 -y k =α k d k , α k and d k are the step size factor and iterative search direction respectively.

6. The stealth carrier-based aircraft go-around trajectory optimization method based on pseudospectral method according to claim 1, characterized in that: After discretizing the time interval of the missed approach, a number of collocation points are determined by using the zero points of the Legendre polynomials, specifically including: Discretize the time interval of the missed approach, and the calculation formula is: Among them, t0 represents the starting time, t f represents the terminal time, t represents the time interval of the missed approach, and τ represents the discretized time interval; According to the discretized time interval, the zero points of the Legendre polynomial are calculated to obtain several collocation points; the Legendre polynomial is: Among them, P N (τ) represents the Legendre polynomial of order N.

7. The method for optimizing the go-around trajectory of a stealth carrier-based aircraft based on pseudospectral method according to claim 1, characterized in that: The group of dynamic and kinematic equations specifically includes: translational kinematic equations, rotational kinematic equations, linear motion equations and angular motion equations.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the pseudospectral method-based missed approach trajectory optimization method for stealth carrier-based aircraft according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the stealth carrier-based aircraft go-around trajectory optimization method based on pseudo-spectral method according to any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the stealth carrier-based aircraft go-around trajectory optimization method based on pseudo-spectral method according to any one of claims 1 to 7 is implemented.

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