Online optimal guidance method, device and electronic equipment based on secondary rectification

Abstract

The present invention provides an online optimal guidance method, device and electronic equipment based on secondary rectification. In this method, a first optimal control problem containing process constraints is converted into a second optimal control problem without process constraints, and the second optimal control problem is solved by a model prediction static programming method to obtain a control quantity update formula in an analytical iterative form. Based on the above control quantity update formula, the control quantity guess value is iteratively corrected to obtain the optimal guidance instruction, that is, a universal solution algorithm with an analytical iterative form is realized, which has a simple form, extremely short single iteration time, and less total time, greatly improving the solution efficiency. In addition, the first optimal control problem containing process constraints is converted into a second optimal control problem without process constraints, and then the second optimal control problem is solved by a model prediction static programming method, which improves the accuracy of the solution and has good versatility.

Description

Technical Field

[0001] The present invention relates to the technical field of online guidance of aircraft, and in particular to an online optimal guidance method, device and electronic equipment based on secondary rectification. Background Art

[0002] In many cases, the online guidance problem of an aircraft can be reduced to an optimal control problem with process constraints that requires an online solution. Examples include online trajectory planning for a reusable rocket recovery stage and online optimal guidance of air-to-air missiles under field-of-view constraints. Researching methods to solve optimal control problems with process constraints is of great engineering significance.

[0003] A similar class of problems to those with process constraints is those with terminal constraints. Online solutions for these problems are relatively mature, forming the well-known model predictive control (MPC) approach. These methods typically employ analytical iterative algorithms and are computationally efficient.

[0004] Currently, there are no analytical iterative algorithms for optimal control problems with process constraints. Existing solutions can be roughly divided into three categories: the first is suboptimal methods. These methods start with the optimal solution without process constraints and iteratively modify it using a specific strategy until the constraints are satisfied. The disadvantage of these methods is that the solutions do not meet optimality and may even differ significantly from the optimal solution. The second category is discrete optimization methods. These methods discretize the dynamic equations, transforming the optimal control problem into a nonlinear programming problem and solving it using various optimization techniques. The disadvantages of these methods are that their convergence depends on the optimization algorithm used after discretization (if the optimization algorithm is poorly chosen, the solution will not converge well), and online solving of nonlinear programming problems is time-consuming. The third category is convex optimization methods. These methods transform the original problem into a convex optimization problem through specialized convexification techniques and then solve it using mature toolkits. The disadvantage of these methods is that the convexification process requires individual analysis of each problem, so only some problems meet the convexification conditions, while those that do not meet the convexification conditions cannot be solved.

[0005] In summary, the current solution methods for optimal control problems with process constraints have technical problems such as poor accuracy, low efficiency and poor versatility. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide an online optimal guidance method, device and electronic equipment based on secondary rectification to alleviate the technical problems of poor accuracy, low efficiency and poor versatility of existing solutions to optimal control problems with process constraints.

[0007] In a first aspect, an embodiment of the present invention provides an online optimal guidance method based on secondary rectification, comprising:

[0008] Build an aircraft dynamics model to obtain the first optimal control problem that includes process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance;

[0009] The first optimal control problem is converted into a second optimal control problem without process constraints and including augmented terminal constraints, the performance index and augmented nonlinear dynamic equations by state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented by a quadratic rectification function;

[0010] discretizing the second optimal control problem using the Euler method to obtain a discrete form of the second optimal control problem;

[0011] Obtaining a control quantity guess value corresponding to the control quantity in the second optimal control problem in the discrete form, and calculating a discrete state quantity and a final terminal output value based on the control quantity guess value and the second optimal control problem in the discrete form;

[0012] Calculating a deviation between the final terminal output value and the expected terminal output value, and determining whether the deviation is less than a preset threshold;

[0013] If it is not less than the preset threshold, updating the control quantity guess value based on the discrete state quantity, the deviation, and an analytical iterative form of a control quantity update formula to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem through a model prediction static programming method;

[0014] The updated control quantity guess value is used as the control quantity guess value, and the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem is returned to execute until the deviation is less than the preset threshold, and the control quantity guess value corresponding to the deviation being less than the preset threshold is used as the optimal guidance instruction.

[0015] Furthermore, the method further comprises:

[0016] If the deviation is smaller than the preset threshold, the control amount guess value is used as the optimal guidance instruction.

[0017] Furthermore, the first optimal control problem is transformed into a second optimal control problem without process constraints and including augmented terminal constraints, the performance index and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, including:

[0018] If the process constraint of the first optimal control problem is C(x(t), u(t))≤0, the state quantity x(t) has n dimensions, the process constraint C(x(t), u(t)) has m dimensions, and the terminal constraint ψ(x(t f ), t f ) has l dimensions, then delete the process constraints and add a new m-dimensional state quantity x n+i (t), i = 1, 2, ..., m, and x n+i (t0) = 0, and at the same time, a new m-dimensional terminal constraint ψ is added i (x(t f ), t f ), i=1, 2,...,m, and ψ i (x(t f ), t f )=x n+1 (t f )=0, where ReQU(x) represents the quadratic rectification function, Indicates the control quantity;

[0019] The m-dimensional process constraint in the first optimal control problem is replaced by the newly added m-dimensional state quantity and the newly added m-dimensional terminal constraint to obtain the second optimal control problem, wherein the second optimal control problem is:

[0020] ψ * (x * (t f ), t f )=0, where the augmented state quantity x * (t) has n+m dimensions, the augmented terminal constraint ψ * (x * (t f ), t f ) has l+m dimensions, is the performance index, is the augmented nonlinear dynamic equation.

[0021] Furthermore, the control quantity guess value is updated based on the discrete state quantity, the deviation and the control quantity update formula in an analytical iterative form, including:

[0022] Update the formula according to the control quantity

[0023] The control amount guess value is updated to obtain the updated control amount guess value, wherein U k represents the updated control quantity guess value, Q k Represents the weight matrix of the control amount, B kDenotes the sensitivity matrix calculated based on the discrete state quantity, dY N represents the deviation, represents the estimated value of the control amount.

[0024] Furthermore, the process of solving the control quantity update formula includes:

[0025] discretizing the second optimal control problem using the Euler method to obtain a discrete form of the second optimal control problem;

[0026] linearizing the final terminal output in the second optimal control problem in the discrete form to obtain a linearized terminal output error;

[0027] linearizing the state equation in the second optimal control problem in the discrete form to obtain a linearized state error;

[0028] Obtaining a new linear terminal output error according to the linear terminal output error and the linear state quantity error;

[0029] Determining an augmented performance index based on the new linearized terminal output error and the performance index;

[0030] The augmented performance index is deduced according to the first-order necessary conditions to obtain the control quantity deviation formula;

[0031] The control quantity update formula is derived according to the control quantity deviation formula and the new linear terminal output error.

[0032] Furthermore, calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem includes:

[0033] Substituting the control quantity guess value into the second optimal control problem in discrete form for iterative calculation, the discrete state quantity and the final terminal output value are obtained.

[0034] In a second aspect, an embodiment of the present invention further provides an online optimal guidance device based on secondary rectification, comprising:

[0035] A construction unit is used to construct an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance;

[0036] a conversion unit, configured to convert the first optimal control problem into a second optimal control problem without process constraints and including augmented terminal constraints, the performance index, and an augmented nonlinear dynamic equation through state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented using a quadratic rectifier function;

[0037] a discrete unit, configured to discretize the second optimal control problem using the Euler method to obtain a discrete form of the second optimal control problem;

[0038] an acquisition and calculation unit, configured to acquire a control quantity guess value corresponding to the control quantity in the second optimal control problem in the discrete form, and calculate a discrete state quantity and a final terminal output value based on the control quantity guess value and the second optimal control problem in the discrete form;

[0039] a calculation and judgment unit, configured to calculate a deviation between the final terminal output value and the expected terminal output value, and to judge whether the deviation is less than a preset threshold;

[0040] an updating unit, configured to update the control quantity guess value based on the discrete state quantity, the deviation, and an analytical iterative control quantity update formula to obtain an updated control quantity guess value if the control quantity is not less than the preset threshold, wherein the control quantity update formula is obtained by solving the second optimal control problem using a model predictive static programming method;

[0041] A return execution unit is used to use the updated control quantity guess value as the control quantity guess value, return to execute the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem, until the deviation is less than the preset threshold, and use the control quantity guess value corresponding to the deviation being less than the preset threshold as the optimal guidance instruction.

[0042] Furthermore, the device is also used for:

[0043] If the deviation is smaller than the preset threshold, the control amount guess value is used as the optimal guidance instruction.

[0044] In a third aspect, an embodiment of the present invention further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods described in the first aspect when executing the computer program.

[0045] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to execute any method described in the first aspect above.

[0046] In an embodiment of the present invention, an online optimal guidance method based on quadratic rectification is provided, comprising: constructing an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance; converting the first optimal control problem into a second optimal control problem that does not contain process constraints and includes augmented terminal constraints, performance indicators and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented using a quadratic rectification function; discretizing the second optimal control problem using the Euler method to obtain a second optimal control problem in discrete form; obtaining a control quantity guess value corresponding to the control quantity in the discrete form of the second optimal control problem, and calculating the control quantity guess value according to the control quantity guess value and the second optimal control problem in discrete form. Calculate the discrete state quantity and the final terminal output value; calculate the deviation between the final terminal output value and the expected terminal output value, and determine whether the deviation is less than a preset threshold; if it is not less than the preset threshold, update the control quantity guess value based on the discrete state quantity, the deviation and the control quantity update formula in analytical iterative form to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem through the model prediction static programming method; use the updated control quantity guess value as the control quantity guess value, return to execute the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem, until the deviation is less than the preset threshold, and use the control quantity guess value corresponding to the deviation less than the preset threshold as the optimal guidance instruction. From the above description, it can be seen that in the online optimal guidance method based on secondary rectification of the present invention, the first optimal control problem containing process constraints can be converted into a second optimal control problem without process constraints, and then the second optimal control problem is solved by the model prediction static programming method to obtain an analytical iterative form of control quantity update formula, and the control quantity guess value is iteratively corrected based on the above control quantity update formula to obtain the optimal guidance instruction, that is, a universal solution algorithm with an analytical iterative form is realized, which is concise in form. Since it is an analytical iterative form of control quantity update formula, a single iteration takes very little time and the total time is less, which greatly improves the solution efficiency. In addition, the above-mentioned method of converting the first optimal control problem containing process constraints into a second optimal control problem without process constraints and then solving the second optimal control problem by the model prediction static programming method improves the accuracy of the solution and has good versatility, alleviating the technical problems of poor accuracy, low efficiency and poor versatility of the existing solution methods for optimal control problems with process constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 A flowchart of an online optimal guidance method based on secondary rectification provided by an embodiment of the present invention;

[0049] Figure 2 A schematic diagram of the lift coefficient of an electromagnetic booster rocket provided in an embodiment of the present invention;

[0050] Figure 3 A schematic diagram of the drag coefficient of an electromagnetic booster rocket provided in an embodiment of the present invention;

[0051] Figure 4 A schematic diagram of a trajectory curve provided by an embodiment of the present invention;

[0052] Figure 5 A schematic diagram of a trajectory inclination angle-time curve provided by an embodiment of the present invention;

[0053] Figure 6 A schematic diagram of a speed-time curve provided by an embodiment of the present invention;

[0054] Figure 7 A schematic diagram of a control variable-time curve provided by an embodiment of the present invention;

[0055] Figure 8 A schematic diagram of an angle of attack-time curve provided by an embodiment of the present invention;

[0056] Figure 9 A schematic diagram of a dynamic pressure-time curve provided by an embodiment of the present invention;

[0057] Figure 10 A schematic diagram of an angle of attack-time curve under different simulation conditions provided by an embodiment of the present invention;

[0058] Figure 11 A schematic diagram comparing control variable-time curves with and without process constraints provided in an embodiment of the present invention;

[0059] Figure 12 A schematic diagram of a control variable-time curve under different numbers of iterations provided by an embodiment of the present invention;

[0060] Figure 13 A schematic diagram of terminal errors under different numbers of iterations provided by an embodiment of the present invention;

[0061] Figure 14 A schematic diagram of an online optimal guidance device based on secondary rectification provided by an embodiment of the present invention;

[0062] Figure 15 A schematic diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the embodiments. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0064] The current solution methods for optimal control problems with process constraints have poor accuracy, low efficiency and poor versatility.

[0065] Based on this, in the online optimal guidance method based on secondary rectification of the present invention, the first optimal control problem containing process constraints can be converted into a second optimal control problem without process constraints, and then the second optimal control problem is solved by the model prediction static programming method to obtain a control quantity update formula in an analytical iterative form, and the control quantity guess value is iteratively corrected based on the above control quantity update formula to obtain the optimal guidance instruction, that is, a general solution algorithm with an analytical iterative form is realized, the form is simple, and since it is a control quantity update formula in an analytical iterative form, a single iteration takes very little time, and the total time is less, which greatly improves the solution efficiency. In addition, the above-mentioned method of converting the first optimal control problem containing process constraints into a second optimal control problem without process constraints and then solving the second optimal control problem by the model prediction static programming method improves the accuracy of the solution and has good versatility.

[0066] To facilitate understanding of this embodiment, an online optimal guidance method based on secondary rectification disclosed in an embodiment of the present invention is first introduced in detail.

[0067] Example 1:

[0068] According to an embodiment of the present invention, an embodiment of an online optimal guidance method based on secondary rectification is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0069] Figure 1 is a flow chart of an online optimal guidance method based on secondary rectification according to an embodiment of the present invention, such as Figure 1As shown, the method includes the following steps:

[0070] Step S102: constructing an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators, and nonlinear dynamic equations required for online guidance;

[0071] Specifically, the aircraft dynamics model can be expressed as: Among them, x(t) represents the state quantity, u(t) represents the control quantity, and t represents time.

[0072] The first optimal control problem to be solved for online guidance is expressed as:

[0073] C(x(t),(t))≤0

[0074] ψ(x(t f ), t f )=0

[0075] , where J represents the performance index, u(t) represents the control quantity, and Q represents the control quantity weight matrix. represents the nonlinear dynamics equation, x(t) represents the state quantity, C(x(t), u(t))≤0 represents the process constraint, ψ(x(t f ), t f )=0 indicates terminal constraint.

[0076] Step S104, transforming the first optimal control problem into a second optimal control problem without process constraints and including augmented terminal constraints, performance indicators, and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, wherein state augmentation is implemented using a quadratic rectifier function;

[0077] Specifically, the so-called state augmentation refers to expanding the dimension of the state quantity, and the terminal constraint augmentation refers to expanding the dimension of the terminal constraint. The process will be described in detail below and will not be repeated here.

[0078] Step S106, using the Euler method to discretize the second optimal control problem to obtain a discrete form of the second optimal control problem;

[0079] Step S108, obtaining a control quantity guess value corresponding to the control quantity in the second optimal control problem in a discrete form, and calculating a discrete state quantity and a final terminal output value based on the control quantity guess value and the second optimal control problem in a discrete form;

[0080] Step S110, calculating the deviation between the final terminal output value and the expected terminal output value, and determining whether the deviation is less than a preset threshold;

[0081] Specifically, the final terminal output value is expressed as YN , the expected terminal output value is given, expressed as

[0082] Step S112: If the value is not less than the preset threshold, the control quantity guess value is updated based on the discrete state quantity, the deviation, and the control quantity update formula in an analytical iterative form to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem using a model prediction static programming method;

[0083] In step S114, the updated guessed control value is used as the guessed control value, and the step of calculating the discrete state quantity and the final terminal output value according to the guessed control value and the second optimal control problem in discrete form is returned to execute until the deviation is less than the preset threshold, and the guessed control value corresponding to the deviation less than the preset threshold is used as the optimal guidance instruction.

[0084] In an embodiment of the present invention, an online optimal guidance method based on quadratic rectification is provided, comprising: constructing an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance; converting the first optimal control problem into a second optimal control problem that does not contain process constraints and includes augmented terminal constraints, performance indicators and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented using a quadratic rectification function; discretizing the second optimal control problem using the Euler method to obtain a second optimal control problem in discrete form; obtaining a control quantity guess value corresponding to the control quantity in the discrete form of the second optimal control problem, and calculating the control quantity guess value according to the control quantity guess value and the second optimal control problem in discrete form. Calculate the discrete state quantity and the final terminal output value; calculate the deviation between the final terminal output value and the expected terminal output value, and determine whether the deviation is less than a preset threshold; if it is not less than the preset threshold, update the control quantity guess value based on the discrete state quantity, the deviation and the control quantity update formula in analytical iterative form to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem through the model prediction static programming method; use the updated control quantity guess value as the control quantity guess value, return to execute the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem, until the deviation is less than the preset threshold, and use the control quantity guess value corresponding to the deviation less than the preset threshold as the optimal guidance instruction. From the above description, it can be seen that in the online optimal guidance method based on secondary rectification of the present invention, the first optimal control problem containing process constraints can be converted into a second optimal control problem without process constraints, and then the second optimal control problem is solved by the model prediction static programming method to obtain an analytical iterative form of control quantity update formula, and the control quantity guess value is iteratively corrected based on the above control quantity update formula to obtain the optimal guidance instruction, that is, a universal solution algorithm with an analytical iterative form is realized, which is concise in form. Since it is an analytical iterative form of control quantity update formula, a single iteration takes very little time and the total time is less, which greatly improves the solution efficiency. In addition, the above-mentioned method of converting the first optimal control problem containing process constraints into a second optimal control problem without process constraints and then solving the second optimal control problem by the model prediction static programming method improves the accuracy of the solution and has good versatility, alleviating the technical problems of poor accuracy, low efficiency and poor versatility of the existing solution methods for optimal control problems with process constraints.

[0085] The above content briefly introduces the online optimal guidance method based on secondary rectification of the present invention. The specific contents involved are described in detail below.

[0086] In an optional embodiment of the present invention, the method further comprises the following steps:

[0087] If the deviation is less than the preset threshold, the guessed value of the control amount is used as the optimal guidance instruction.

[0088] In an optional embodiment of the present invention, the first optimal control problem is transformed into a second optimal control problem without process constraints and including augmented terminal constraints, performance indicators, and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, specifically comprising the following steps:

[0089] (1) If the process constraint of the first optimal control problem is C(x(t), u(t))≤0, the state quantity x(t) has n dimensions, the process constraint C(x(t), u(t)) has m dimensions, and the terminal constraint ψ(x(t) f ), t f ) has l dimensions, then delete the process constraints and add a new m-dimensional state quantity x n+i (t), i = 1, 2, ..., m, and x n+i (t0) = 0, and at the same time, a new m-dimensional terminal constraint ψ is added i (x(t f ), t f ), i=1, 2,...,m, and ψ i (x(t f ), t f )=x n+i (t f )=0, where ReQU(x) represents the quadratic rectification function, u(t) represents the control quantity;

[0090] Specifically, the state augmentation process is expressed as follows: if the state quantity x(t) of the first optimal control problem has n dimensions, the process constraint C(x(t), u(t)) has m dimensions, and the terminal constraint ψ(x(t f ), t f ) has l dimensions, then delete the process constraints and add a new m-dimensional state quantity x n+i (t), i = 1, 2, ..., m, we have: x n+i (t0) = 0, where ReQU(x) represents the quadratic rectification function, u(t) represents the control quantity;

[0091] Newly added m-dimensional terminal constraint ψ i (x(t f ), t f ), i=1, 2,...,m, and ψ i (x(t f ), t f )=xn+i (t f )=0.

[0092]

[0093] The above x n+i (t0) = 0 and ψ i (x(t f ), t f )=x n+i (t f )=0 is equivalent to the process constraint C(x(t),u(t))≤0, so the newly added m-dimensional state quantity and the newly added m-dimensional terminal constraint can be used to replace the m-dimensional process constraint in the first optimal control problem.

[0094] (2) The newly added m-dimensional state quantity and the newly added m-dimensional terminal constraint are used to replace the m-dimensional process constraint in the first optimal control problem to obtain the second optimal control problem, where the second optimal control problem is: ψ * (x * (t f ), t f )=0, where the augmented state quantity x * (t) has n+m dimensions, augmented terminal constraint Ψ * (x * (t f ), t f ) has l+m dimensions, is the performance indicator, is the augmented nonlinear dynamics equation.

[0095] Specifically, * indicates augmentation.

[0096] In an optional embodiment of the present invention, updating the control variable guess value based on the discrete state quantity, the deviation and the control variable update formula in an analytical iterative form specifically includes the following steps:

[0097] Update the formula according to the control quantity Update the control quantity guess value to obtain the updated control quantity guess value, where U k Represents the updated control quantity guess value, Q k Represents the weight matrix of the control amount, B k Represents the sensitivity matrix calculated based on discrete state quantities, dY N Indicates deviation, Indicates the guess value of the control amount.

[0098] In an optional embodiment of the present invention, the process of solving the control amount update formula specifically includes the following steps:

[0099] (1) The second optimal control problem is discretized using the Euler method to obtain the second optimal control problem in a discrete form;

[0100] Specifically, the second optimal control problem is ψ * (x * (t f ), t f )=0, the second optimal control problem is discretized by Euler method to obtain the discrete form of the second optimal control problem. Its state equation (derived from the above-mentioned augmented nonlinear dynamic equation), output equation (derived from the above-mentioned augmented terminal constraint) and performance index are as follows:

[0101] X k+1 =F k (X k , U k )

[0102] Y k =h(X k )

[0103] Among them, the state quantity is X∈R n+m (R represents the real number domain), the control quantity is U∈R p , the output variable (i.e. terminal output) is Y∈R l+m , k=1,2,…,N is the time step, Q k Represents the discrete control weight matrix.

[0104] (2) linearizing the final terminal output in the second optimal control problem in discrete form to obtain a linearized terminal output error;

[0105] Specifically, the Taylor series expansion is used to convert the terminal output (i.e., the final terminal output) Y N Expanding and ignoring high-order small quantities, we can obtain the linearized terminal output error as follows:

[0106] Among them, Y N Represents the final terminal output value, Indicates the expected terminal output value, dY N Represents the terminal output error (also known as deviation, terminal output deviation), represents the terminal output error of the linearized representation (i.e., the linearized terminal output error, specifically, the expression of the linearized terminal output error).

[0107] (3) Linearize the state equation in the discrete form of the second optimal control problem to obtain the linearized state error;

[0108] Specifically, according to the state equation X k+1 =F k (X k , U k ), we can get the state error of the k+1th time step, that is, the linearized state error (obtained by Taylor expansion of the state equation):

[0109]

[0110] Let k = N-1, then the linear state error is expressed as:

[0111]

[0112] (4) Obtaining a new linear terminal output error based on the linear terminal output error and the linear state quantity error;

[0113] Specifically, through iteration, the terminal output error can be expressed as a linear combination of the initial state quantity deviation and the control quantity deviation at each step (i.e., the new linearized terminal output error), as shown below:

[0114] dY N =AdX1+B1dU1+B2dU2+…+B N-1 dU N-1

[0115] ,in,

[0116] Since the initial conditions are specified, the initial values ​​of the state quantities have no error, that is, dX1 = 0. The output error of the new linear terminal can be simplified to:

[0117] B k Represents the sensitivity matrix, which can be calculated recursively as shown below, thus greatly saving calculation time.

[0118]

[0119] (5) Determine the augmented performance index based on the output error and performance index of the new linear terminal;

[0120] Specifically, it can be seen that The number of unknowns in is greater than the number of constraints, and the solution of this equation is not unique. Therefore, we can As the constraint condition of the system, the augmented performance index is obtained as shown in the following formula (the original performance index is: ):

[0121] in, Indicates the guess value of the control quantity, dU k represents the control deviation (k represents the time step), represents the updated guess value of the control quantity, and λ represents the Lagrange multiplier.

[0122] (6) Based on the first-order necessary conditions, the augmented performance index is derived to obtain the control quantity deviation formula;

[0123] Specifically, the augmented performance index is derived based on the first-order necessary conditions, and we obtain:

[0124]

[0125] From this, we can obtain the control quantity deviation formula, that is, the expression for the control quantity deviation (where only the Lagrange multiplier λ is unknown), as shown below:

[0126] (7) The control quantity update formula is derived based on the control quantity deviation formula and the new linear terminal output error.

[0127] Specifically, in order to obtain the Lagrange multiplier λ, the control deviation formula is Substitute the new linear terminal output error You can get:

[0128] ,in,

[0129] Assumption A λ is non-singular, then the expression of the Lagrange multiplier can be obtained as:

[0130] Then the expression of Lagrange multiplier is Substitute the control quantity deviation formula into You can get:.

[0131] Then the control quantity update formula is:

[0132] In an optional embodiment of the present invention, calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the second optimal control problem in discrete form specifically includes the following steps:

[0133] Substitute the guessed value of the control quantity into the second optimal control problem in discrete form and perform iterative calculation to obtain the discrete state quantity and the final terminal output value.

[0134] Specifically, the second optimal control problem in discrete form is expressed as: Xk+1 =F k (X k , U k )Y k =h(X k )

[0135] The current control amount guess value U k and the current state X k Known, then we can use X k+1 =F k (X k , U k ) Iterate to get the state quantity X of the next time step k+1 , because k = 1, 2, ..., N, so, we can get multiple discrete state quantities, and at the same time, we can use Y k =h(X k ) to obtain the final terminal output value Y n .

[0136] The online optimal guidance method based on secondary rectification of the present invention realizes a universal solution algorithm with an analytical iterative form, which is simple in form and has significant effect; the algorithm is insensitive to initial values ​​and can be corrected from zero control to optimal control without the need for adjacent standard control; the algorithm has high calculation accuracy and fast convergence speed; the algorithm consumes very little time for a single iteration and the total time consumption is relatively low.

[0137] The present invention is further described in detail below by taking the electromagnetic booster rocket first stage online trajectory planning process as an example:

[0138] Under the assumption of a flat earth, the rotation of the electromagnetic booster rocket around its center of mass is ignored, and it is regarded as a controllable mass point. Only its motion in the longitudinal plane is considered, and its dynamic model is expressed as follows:

[0139]

[0140] Where h is the height, x is the range, V is the speed, θ is the trajectory inclination, α is the angle of attack, u is the control quantity, m is the mass, T is the engine thrust, D and L are the aerodynamic drag and lift respectively, L = qSC L , D=qSC D , m=15000-126.8t,T=325572,where q is the dynamic pressure, S is the reference area of ​​the electromagnetic booster rocket, which is 1.1304m2, and C L and C D are the lift coefficient and drag coefficient of the electromagnetic booster rocket, which can be obtained by polynomial fitting, as shown in the attached figure. Figure 2 and Figure 3As shown, v is the local atmospheric density, which is a function of the height h, as shown in the following formula, where ρ0 is the atmospheric density at sea level, which is taken as 1.225 kg / m 3 , b is a constant, taken as -0.00013889.

[0141] ρ=ρ0e bh .

[0142] The optimal control problem to be solved for online trajectory planning of the first stage of an electromagnetic booster rocket with limited attack angle and dynamic pressure (i.e., process constraints) is expressed as:

[0143]

[0144] |α|≤α max

[0145] q≤q max .

[0146] The simulation parameter settings in this example are described in the table below (the subscript f indicates the end time).

[0147]

[0148]

[0149] All simulation programs are completed in a personal computer with a CPU main frequency of 2.3GHz and a MATLAB 2022b simulation environment. A more efficient compilation environment will improve computing efficiency.

[0150] The method proposed in this invention (i.e., online optimal guidance method based on quadratic rectification, referred to as RQMPC) is used to solve this example. At the same time, the optimal solution is calculated by the optimal control software GPOPSⅡ (an authoritative and accurate toolkit for offline optimal guidance instruction). The simulation results are as follows: Figure 4-Figure 9 As shown in the figure, the solution of the algorithm (RQMPC) is consistent with the calculation results of GPOPSⅡ, and meets the optimality. Among them, the control variable curve is highly nonlinear, the attack angle modulus meets the constraint of less than 10 degrees, and the dynamic pressure meets the constraint of less than 120kPa.

[0151] Set different simulation conditions as shown in the table, the simulation results are as follows Figure 10 As shown in the figure, it can be seen that the algorithm solution results are consistent with the optimal solution results calculated by GPOPSⅡ.

[0152] parameter Case 0 Case 1 Case 2 <![CDATA[θ0]]> 30 degrees 29deg 28deg

[0153] Compared with the optimal solution obtained after removing the process constraints, the simulation results are as follows Figure 11As shown, we can see that there is a big difference between the two, which reflects the necessity of algorithms with process constraints.

[0154] Output the results of different iteration times. The simulation results are as follows: Figure 12 As shown, it can be seen that the algorithm is not sensitive to the initial value and can be corrected from zero control to optimal control without the need for adjacent standard control.

[0155] Output the terminal output error under different iteration times, such as Figure 13 As shown, it can be seen that the algorithm has high calculation accuracy (each parameter can reach the corresponding error value) and fast convergence speed (it can converge after about 20 iterations).

[0156] Because the algorithm is an analytical iterative approach and does not require solving the optimization problem at each iteration, the average single iteration time is extremely short, taking only 2.8 milliseconds in this example. In terms of total solution time, the algorithm takes 0.119 seconds, while GPOPS II takes 15.29 seconds to solve the same example, which is only 0.778% of the time.

[0157] Example 2:

[0158] An embodiment of the present invention also provides an online optimal guidance device based on secondary rectification. The online optimal guidance device based on secondary rectification is mainly used to execute the online optimal guidance method based on secondary rectification provided in Example 1 of the present invention. The online optimal guidance device based on secondary rectification provided in an embodiment of the present invention is specifically introduced below.

[0159] Figure 14 Schematic diagram of an online optimal guidance device based on secondary rectification according to an embodiment of the present invention, Figure 14 As shown, the device mainly includes: a building unit 10, a conversion unit 20, a discrete unit 30, an acquisition and calculation unit 40, a calculation and judgment unit 50, an update unit 60 and a return execution unit 70, wherein:

[0160] A construction unit is used to construct an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance;

[0161] a conversion unit, configured to convert the first optimal control problem into a second optimal control problem without process constraints and including augmented terminal constraints, performance indicators, and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented using a quadratic rectifier function;

[0162] A discrete unit is used to discretize the second optimal control problem using the Euler method to obtain the second optimal control problem in a discrete form;

[0163] an acquisition and calculation unit, configured to acquire a control quantity guess value corresponding to the control quantity in the second optimal control problem in a discrete form, and calculate a discrete state quantity and a final terminal output value based on the control quantity guess value and the second optimal control problem in a discrete form;

[0164] a calculation and judgment unit, configured to calculate the deviation between the final terminal output value and the expected terminal output value, and to judge whether the deviation is less than a preset threshold;

[0165] an updating unit, configured to update the control quantity guess value based on the discrete state quantity, the deviation, and an analytical iterative control quantity update formula if the control quantity is not less than a preset threshold, to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem using a model predictive static programming method;

[0166] The return execution unit is used to use the updated control quantity guess value as the control quantity guess value, return to execute the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem, until the deviation is less than the preset threshold, and use the control quantity guess value corresponding to the deviation less than the preset threshold as the optimal guidance instruction.

[0167] In an embodiment of the present invention, an online optimal guidance method based on quadratic rectification is provided, comprising: constructing an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance; converting the first optimal control problem into a second optimal control problem that does not contain process constraints and includes augmented terminal constraints, performance indicators and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented using a quadratic rectification function; discretizing the second optimal control problem using the Euler method to obtain a second optimal control problem in discrete form; obtaining a control quantity guess value corresponding to the control quantity in the discrete form of the second optimal control problem, and calculating the control quantity guess value according to the control quantity guess value and the second optimal control problem in discrete form. Calculate the discrete state quantity and the final terminal output value; calculate the deviation between the final terminal output value and the expected terminal output value, and determine whether the deviation is less than a preset threshold; if it is not less than the preset threshold, update the control quantity guess value based on the discrete state quantity, the deviation and the control quantity update formula in analytical iterative form to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem through the model prediction static programming method; use the updated control quantity guess value as the control quantity guess value, return to execute the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem, until the deviation is less than the preset threshold, and use the control quantity guess value corresponding to the deviation less than the preset threshold as the optimal guidance instruction. From the above description, it can be seen that in the online optimal guidance method based on secondary rectification of the present invention, the first optimal control problem containing process constraints can be converted into a second optimal control problem without process constraints, and then the second optimal control problem is solved by the model prediction static programming method to obtain an analytical iterative form of control quantity update formula, and the control quantity guess value is iteratively corrected based on the above control quantity update formula to obtain the optimal guidance instruction, that is, a universal solution algorithm with an analytical iterative form is realized, which is concise in form. Since it is an analytical iterative form of control quantity update formula, a single iteration takes very little time and the total time is less, which greatly improves the solution efficiency. In addition, the above-mentioned method of converting the first optimal control problem containing process constraints into a second optimal control problem without process constraints and then solving the second optimal control problem by the model prediction static programming method improves the accuracy of the solution and has good versatility, alleviating the technical problems of poor accuracy, low efficiency and poor versatility of the existing solution methods for optimal control problems with process constraints.

[0168] Optionally, the device is also used to: if the deviation is less than a preset threshold, use the guessed value of the control amount as the optimal guidance instruction.

[0169] Optionally, the conversion unit is further configured to: if the process constraint of the first optimal control problem is C(x(t), u(t))≤0, the state quantity x(t) has n dimensions, the process constraint C(x(t), u(t)) has m dimensions, and the terminal constraint ψ(x(t f ), t f ) has l dimensions, then delete the process constraints and add a new m-dimensional state quantity x n+i (t), i = 1, 2, ..., m, and x n+i (t0) = 0, and at the same time, a new m-dimensional terminal constraint ψ is added i (x(t f ), t f ), i=1, 2,...,m, and ψ i (x(t f ), t f )=x n+i (t f )=0, where ReQU(x) represents the quadratic rectification function, u(t) represents the control quantity; the newly added m-dimensional state quantity and the newly added m-dimensional terminal constraint are used to replace the m-dimensional process constraint in the first optimal control problem to obtain the second optimal control problem, where the second optimal control problem is:

[0170] ψ * (x * (t f ), t f )=0, where the augmented state quantity x * (t) has n+m dimensions, augmented terminal constraint Ψ * (x * (t f ), t f ) has l+m dimensions, is the performance indicator, is the augmented nonlinear dynamics equation.

[0171] Optionally, the updating unit is further configured to: update the formula according to the control amount

[0172] Update the control quantity guess value to obtain the updated control quantity guess value, where U k Represents the updated control quantity guess value, Q k Represents the weight matrix of the control amount, B k Represents the sensitivity matrix calculated based on discrete state quantities, dY N Indicates deviation, Indicates the guess value of the control quantity.

[0173] Optionally, the device is also used to: discretize the second optimal control problem using the Euler method to obtain the second optimal control problem in discrete form; linearize the final terminal output in the discrete form of the second optimal control problem to obtain a linearized terminal output error; linearize the state equation in the discrete form of the second optimal control problem to obtain a linearized state quantity error; obtain a new linearized terminal output error based on the linearized terminal output error and the linearized state quantity error; determine an augmented performance indicator based on the new linearized terminal output error and the performance indicator; derive the augmented performance indicator based on the first-order necessary condition to obtain a control quantity deviation formula; derive a control quantity update formula based on the control quantity deviation formula and the new linearized terminal output error.

[0174] Optionally, the acquisition and calculation unit is further configured to: substitute the guessed value of the control quantity into a second optimal control problem in a discrete form for iterative calculation to obtain a discrete state quantity and a final terminal output value.

[0175] The device provided in the embodiment of the present invention has the same implementation principle and technical effects as those in the aforementioned method embodiment. For the sake of brief description, for matters not mentioned in the device embodiment, reference can be made to the corresponding content in the aforementioned method embodiment.

[0176] like Figure 15 As shown, an electronic device 600 provided in an embodiment of the present application includes: a processor 601, a memory 602 and a bus, wherein the memory 602 stores machine-readable instructions executable by the processor 601. When the electronic device is running, the processor 601 communicates with the memory 602 through the bus, and the processor 601 executes the machine-readable instructions to perform the steps of the online optimal guidance method based on secondary rectification as described above.

[0177] Specifically, the memory 602 and the processor 601 can be general-purpose memories and processors, which are not specifically limited here. When the processor 601 runs the computer program stored in the memory 602, the online optimal guidance method based on secondary rectification can be executed.

[0178] The processor 601 may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method can be completed by an integrated logic circuit of hardware in the processor 601 or by instructions in the form of software. The above-mentioned processor 601 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The various methods, steps, and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in conjunction with the embodiments of the present application can be directly embodied as being executed by a hardware decoding processor, or can be executed by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium well-known in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, etc. The storage medium is located in memory 602, and processor 601 reads the information in memory 602 and performs the steps of the above method in conjunction with its hardware.

[0179] Corresponding to the above-mentioned online optimal guidance method based on secondary rectification, an embodiment of the present application also provides a computer-readable storage medium, which stores machine-executable instructions. When the computer-executable instructions are called and executed by a processor, the computer-executable instructions prompt the processor to execute the steps of the above-mentioned online optimal guidance method based on secondary rectification.

[0180] The online optimal guidance device based on secondary rectification provided in the embodiment of the present application can be specific hardware on the device or software or firmware installed on the device. The device provided in the embodiment of the present application, its implementation principle and the technical effect produced are the same as those in the aforementioned method embodiment. For the sake of brief description, where the device embodiment is not mentioned, reference can be made to the corresponding content in the aforementioned method embodiment. Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can all refer to the corresponding processes in the aforementioned method embodiment, and will not be repeated here.

[0181] In the embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interface, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0182] For another example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions and operations of the devices, methods and computer program products according to multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of code, and the module, program segment or a part of code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of the boxes in the block diagram and / or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0183] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0184] In addition, each functional unit in the embodiments provided in the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0185] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the online optimal guidance method based on secondary rectification described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, and other media that can store program codes.

[0186] It should be noted that similar numbers and letters represent similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description and are not to be understood as indicating or implying relative importance.

[0187] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present application, which are used to illustrate the technical solutions of the present application, rather than to limit them. The scope of protection of the present application is not limited thereto. Although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-mentioned embodiments within the technical scope disclosed in the present application, or perform equivalent replacements for some of the technical features thereof. However, these modifications, changes, or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application. They should all be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. An online optimal guidance method based on secondary rectification, characterized in that: include: Build an aircraft dynamics model to obtain the first optimal control problem that includes process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance; The first optimal control problem is converted into a second optimal control problem without process constraints and including augmented terminal constraints, the performance index and augmented nonlinear dynamic equations by state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented by a quadratic rectification function; discretizing the second optimal control problem using the Euler method to obtain a discrete form of the second optimal control problem; Obtaining a control quantity guess value corresponding to the control quantity in the second optimal control problem in the discrete form, and calculating a discrete state quantity and a final terminal output value based on the control quantity guess value and the second optimal control problem in the discrete form; Calculating a deviation between the final terminal output value and the expected terminal output value, and determining whether the deviation is less than a preset threshold; If it is not less than the preset threshold, updating the control quantity guess value based on the discrete state quantity, the deviation, and an analytical iterative form of a control quantity update formula to obtain an updated control quantity guess value, wherein the control quantity update formula is obtained by solving the second optimal control problem through a model prediction static programming method; The updated control quantity guess value is used as the control quantity guess value, and the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem is returned to execute until the deviation is less than the preset threshold, and the control quantity guess value corresponding to the deviation being less than the preset threshold is used as the optimal guidance instruction.

2. The method according to claim 1, characterized in that The method further comprises: If the deviation is smaller than the preset threshold, the control amount guess value is used as the optimal guidance instruction.

3. The method according to claim 1, characterized in that The first optimal control problem is transformed into a second optimal control problem without process constraints and including augmented terminal constraints, the performance index and augmented nonlinear dynamic equations through state augmentation and terminal constraint augmentation, including: If the process constraint of the first optimal control problem is C(x(t), u(t))≤0, the state quantity x(t) has n dimensions, the process constraint C(x(t), u(t)) has m dimensions, and the terminal constraint ψ(x(t f ), t f ) has l dimensions, then delete the process constraints and add a new m-dimensional state quantity x n+i (t), i = 1, 2, ..., m, and x n+i (t0) = 0, and at the same time, a new m-dimensional terminal constraint ψ is added i (x(t f ), t f ), i=1, 2,...,m, and ψ i (x(t f ), t f )=x n+i (t f )=0, where ReQU(x) represents the quadratic rectification function, u(t) represents the control quantity; The m-dimensional process constraint in the first optimal control problem is replaced by the newly added m-dimensional state quantity and the newly added m-dimensional terminal constraint to obtain the second optimal control problem, wherein the second optimal control problem is: ψ * (x * (t f ), t f )=0, where the augmented state quantity x * (t) has n+m dimensions, the augmented terminal constraint ψ * (x * (t f ), t f ) has l+m dimensions, is the performance index, is the augmented nonlinear dynamic equation.

4. The method according to claim 1, wherein Updating the control quantity guess value based on the discrete state quantity, the deviation, and an analytical iterative control quantity update formula includes: Update the formula according to the control quantity The control amount guess value is updated to obtain the updated control amount guess value, wherein U k represents the updated control quantity guess value, Q k Represents the weight matrix of the control amount, B k Denotes the sensitivity matrix calculated based on the discrete state quantity, dY N represents the deviation, represents the estimated value of the control amount.

5. The method according to claim 1, wherein The process of solving the control quantity update formula includes: discretizing the second optimal control problem using the Euler method to obtain a discrete form of the second optimal control problem; linearizing the final terminal output in the second optimal control problem in the discrete form to obtain a linearized terminal output error; linearizing the state equation in the second optimal control problem in the discrete form to obtain a linearized state error; Obtaining a new linear terminal output error according to the linear terminal output error and the linear state quantity error; Determining an augmented performance index based on the new linearized terminal output error and the performance index; The augmented performance index is deduced according to the first-order necessary conditions to obtain the control quantity deviation formula; The control quantity update formula is derived according to the control quantity deviation formula and the new linear terminal output error.

6. The method according to claim 1, characterized in that Calculating a discrete state quantity and a final terminal output value according to the control quantity guess value and the second optimal control problem in discrete form includes: Substituting the control quantity guess value into the second optimal control problem in discrete form for iterative calculation, the discrete state quantity and the final terminal output value are obtained.

7. An online optimal guidance device based on secondary rectification, characterized in that: include: A construction unit is used to construct an aircraft dynamics model to obtain a first optimal control problem including process constraints, terminal constraints, performance indicators and nonlinear dynamic equations required for online guidance; a conversion unit, configured to convert the first optimal control problem into a second optimal control problem without process constraints and including augmented terminal constraints, the performance index, and an augmented nonlinear dynamic equation through state augmentation and terminal constraint augmentation, wherein the state augmentation is implemented using a quadratic rectifier function; a discrete unit, configured to discretize the second optimal control problem using the Euler method to obtain a discrete form of the second optimal control problem; an acquisition and calculation unit, configured to acquire a control quantity guess value corresponding to the control quantity in the second optimal control problem in the discrete form, and calculate a discrete state quantity and a final terminal output value based on the control quantity guess value and the second optimal control problem in the discrete form; a calculation and judgment unit, configured to calculate a deviation between the final terminal output value and the expected terminal output value, and to judge whether the deviation is less than a preset threshold; an updating unit, configured to update the control quantity guess value based on the discrete state quantity, the deviation, and an analytical iterative control quantity update formula to obtain an updated control quantity guess value if the control quantity is not less than the preset threshold, wherein the control quantity update formula is obtained by solving the second optimal control problem using a model predictive static programming method; A return execution unit is used to use the updated control quantity guess value as the control quantity guess value, return to execute the step of calculating the discrete state quantity and the final terminal output value according to the control quantity guess value and the discrete form of the second optimal control problem, until the deviation is less than the preset threshold, and use the control quantity guess value corresponding to the deviation being less than the preset threshold as the optimal guidance instruction.

8. The device according to claim 7, characterized in that The device is also used for: If the deviation is smaller than the preset threshold, the control amount guess value is used as the optimal guidance instruction.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to execute the method according to any one of claims 1 to 6.

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