Multi-segment multi-constraint pseudo-spectrum online optimal guidance method

Abstract

The invention provides a multi-section multi-constraint pseudo-spectrum online optimal guidance method. The method comprises the steps that 1, a combined power aircraft model is established; step 2, establishing a multi-section multi-constraint optimal control problem model with undetermined end time of each section; 3, solving a first-order necessary condition and a cross-section condition; 4, linearizing the kinetic model and first-order necessary conditions; 5, carrying out pseudo-spectrum discretization to obtain an optimal instruction updating strategy; and step 6, applying the optimal instruction updating strategy to form an online guidance law. Through the method, rapid and accurate guidance can be carried out, the characteristics of combined power in different speed domains and airspaces are utilized to the maximum extent, and the transport load of the aircraft is improved. Compared with the optimal trajectory calculated by a GPOPS-II tool under different examples, the method provided by the invention is verified to be capable of adapting to single-stage orbit injection in different scenes, the convergence speed is high, the precision is high, and the obtained trajectory has optimality.

Description

Technical Field

[0001] The present invention provides a multi-constraint pseudo-spectral online optimal guidance method applied to a single-stage orbital combined-power aircraft, and belongs to the fields of aerospace technology, weapon technology, and guidance control. Background Art

[0002] Single-stage orbital vehicles (SOTOs) can achieve direct entry from the ground to low-Earth orbit (LEO) via a single launch, offering significant advantages in reducing launch costs and increasing spacecraft reusability, thus possessing high application potential. One of their core technologies is the combined propulsion system. Single-stage orbital vehicles often utilize a rocket-based combined cycle (RBCC) propulsion system, which combines the advantages of ramjets and rocket engines, capable of maintaining high efficiency over a wide range of airspace and speeds.

[0003] However, the ascent phase guidance of single-stage orbital vehicles presents a major challenge in their development. Due to the multimodal dynamic characteristics and strong nonlinearity of hybrid-powered vehicles, the guidance law design process involves multiple segments, strong interior and terminal constraints, and uncertain terminal times for each segment, all of which pose significant challenges. In addition to requiring the vehicle to smoothly enter orbit, suborbital space missions also require maximizing payload capacity and achieving maximum economic benefits. Ascent phase guidance commands designed using optimal control theory can fully utilize the capabilities of hybrid-powered vehicles and maximize payload capacity along the optimal path. Existing optimal guidance methods often suffer from high computational complexity and poor real-time performance when dealing with multiple constraints. Especially in changing flight environments and uncertain dynamic characteristics, the effectiveness and robustness of guidance methods still have significant room for improvement.

[0004] As an efficient numerical optimization method, pseudospectral methods have been widely used in the field of control and guidance in recent years. Pseudospectral methods can transform complex nonlinear optimal control problems into nonlinear programming problems, thereby significantly reducing computational complexity. However, traditional pseudospectral methods still have some limitations when dealing with multi-segment, multi-constraint, and real-time guidance problems. Therefore, for the multi-segment, multi-constraint pseudospectral online optimal guidance problem of a single-stage integrated propulsion vehicle, a new improved method is needed to solve the multi-segment, multi-constraint optimal control problem with uncertain terminal times of each segment, thereby improving the computational efficiency and robustness of the guidance system. Summary of the Invention

[0005] Traditional guidance methods are difficult to use in complex models with multiple segments and uncertain end times. This results in an inability to effectively utilize the capabilities of combined-propulsion aircraft in different airspaces and speed ranges, increases unnecessary energy consumption, and reduces payload capacity. To address this issue, the present invention incorporates a correction term for the end times of each segment within the framework of a linear Gaussian pseudo-spectral model predictive control method. This allows it to adapt to optimal control problems with multiple segments, multiple constraints, and uncertain end times, maximizing the aircraft's payload capacity.

[0006] like Figure 1 As shown, the steps for implementing the present invention are as follows:

[0007] Step 1. Build a combined propulsion aircraft model

[0008] Combined-powered vehicles primarily move in the longitudinal plane, with movement in the transverse plane being relatively minor and negligible compared to the longitudinal plane. Therefore, when studying the multi-stage optimal control of a vehicle during its ascent phase, only the longitudinal plane motion can be considered. Based on the characteristics of rocket-based combined-cycle RBCC engines, the entire ascent phase is divided into four stages: First, the ejector mode stage, in which the vehicle takes off horizontally from the ground in ejector mode. When accelerating to Mach numbers of 2.5-3, a mode transition occurs, switching to the scramjet and scramjet modes. The scramjet mode activates at Mach numbers of 5-6, and the two modes share a unified mathematical model. At Mach numbers of 9-10, the vehicle switches to the rocket mode for the final ascent and orbit insertion.

[0009] In this step, the basic parameters of the aircraft and the parameter calculation model are obtained. This calculation model is a nonlinear model. The parameters include: the current state vector, the current nominal control vector, the current nominal end time of each segment, the parameters of the spherical earth model, and the aircraft aerodynamic and power parameters.

[0010] Step 2. Establish an optimal control problem model with multiple segments and multiple constraints and uncertain end time of each segment

[0011] According to the thrust characteristics, the ascent section of the aircraft is divided into sections for overall optimization. The interior point constraints and terminal constraints between the sections of the aircraft are considered to form a weighted combination performance index of maximum terminal mass and smooth control quantity. The state variable connection conditions between the sections are supplemented, and the aircraft model is supplemented to form a nonlinear optimal control problem model.

[0012] Step 3. Solve the first-order necessary conditions and transversality conditions

[0013] The Hamiltonian function is defined based on the weighted performance index from the previous step, and the nonlinear first-order necessary conditions are obtained using the Hamiltonian function. Transversality conditions are obtained based on the Hamiltonian function and the weighted performance index. Transversality conditions can be divided into different types depending on whether they contain interior point constraints and terminal constraints.

[0014] Step 4. Linearized dynamics model and first-order necessary conditions

[0015] The nonlinear optimal control problem and nonlinear first-order necessary conditions are obtained from steps 2 and 3. These are linearized according to the small perturbation linearization principle to obtain linear differential equations for state vector-related quantities and the control vector. The state vector-related quantities include the state deviation and the co-state vector corresponding to the state vector.

[0016] Step 5. Pseudo-spectral discretization to obtain the optimal instruction update strategy

[0017] This section applies Gaussian pseudospectral discretization to the linearized optimal control problem and the necessary first-order linearization conditions obtained in the previous section. The idea behind Gaussian pseudospectral discretization is to use Lagrange interpolation polynomials to interpolate at the zeros (LG points) of Legendre orthogonal polynomials to approximate the state and control variables. The differential equations are then replaced by differential approximation matrices, transforming the differential equations into algebraic equations. Solving the differential equations algebraically reduces the computational complexity of the differential equations and improves real-time computing capabilities.

[0018] The linearized first-order necessary conditions and the linearized optimal control problem model are combined, supplemented by the Gaussian quadrature formula to obtain boundary conditions, which include correction terms for the end times of each segment. Gaussian pseudospectral discretization at the LG point yields the optimal control problem equation for multiple segments, multiple constraints, and variable end times. Solving this equation yields the optimal command update. The optimal command includes the optimal control command and the optimal end time command for each segment.

[0019] Step 6. Apply the optimal instruction update strategy to form the online guidance law

[0020] This step describes how to apply the optimal instruction update strategy. First, the optimal control model in step 2 is ballistically predicted and integrated using the current nominal control vector and the current nominal end time of each segment in step 1 to calculate whether the preset terminal constraint accuracy threshold is met, such as a position error of less than 1m and a velocity error of less than 1m / s. If so, the current nominal control vector and the current nominal end time of each segment are the optimal instructions. If not, the optimal instruction update strategy obtained in step 5 is applied to update the optimal instructions. The updated instructions are used as the current nominal control vector and the current nominal end time of each segment for ballistic integration, and the above process is repeated until the terminal constraint accuracy requirements are met.

[0021] So far, the control law proposed in the present invention has been able to be applied in simulation.

[0022] In summary, the above process demonstrates that the proposed method, a multi-segment, multi-constraint pseudo-spectral online optimal guidance method, can be used for rapid and precise guidance, maximizing the characteristics of the combined propulsion system in different speed and airspace domains, thereby increasing the payload capacity of the vehicle. Comparisons with the optimal trajectory calculated using the GPOPS-II tool under various calculation examples demonstrate the proposed method's adaptability to single-stage orbit insertion in various scenarios, with rapid convergence and high accuracy, resulting in an optimal trajectory.

[0023] The advantages of the present invention are:

[0024] (1) A multi-segment multi-constraint pseudo-spectral online optimal guidance method is proposed, which can be applied to complex combined propulsion aircraft models to solve problems with hard internal constraints and terminal constraints.

[0025] (2) It can adapt to the situation where the terminal time of each segment is unknown under complex aircraft models, greatly enhancing the authenticity of the model.

[0026] (3) It can be guided with high convergence speed and calculation accuracy, and the obtained trajectory is the optimal trajectory, which greatly gives play to the advantages of the combined power aircraft in different airspace and speed domains, reduces unnecessary energy consumption of the aircraft, and maximizes the transport load. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flow chart of a multi-segment, multi-constraint pseudo-spectral online optimal guidance method applied to a single-stage orbital combined-power vehicle.

[0028] Figure 2 It is a schematic diagram of the force analysis of a single-stage orbital combined-power aircraft in the longitudinal plane.

[0029] Figure 3 This is the application process of the present invention.

[0030] In the above figure, the symbols and codes involved are explained as follows:

[0031] Figure 2 In the equation, L is lift, D is drag, G is gravity, P is thrust, v is the vehicle velocity vector, α is the angle of attack, and γ is the trajectory inclination. DETAILED DESCRIPTION

[0032] The purpose of the embodiments of the present application is to provide a method for calculating the guidance law of a single-machine combined-power aircraft during the orbital insertion process, thereby obtaining an optimal online pseudo-spectral guidance law that is more accurate, has more practical application value, and has smaller error with actual missile control.

[0033] Step 1. Build a combined power aircraft model, such as Figure 2 As shown;

[0034] The vertical dynamics model of the RBCC combined power aircraft is established as follows:

[0035]

[0036] Where: λ is longitude; is latitude; v is velocity; h is speed; Re is the radius of the earth; γ is the ballistic inclination; ψ is the ballistic deviation; r is the distance from the center of the earth; h is the flight altitude; m is the mass of the aircraft; α is the angle of attack (AOA); P is the thrust of the aircraft; I sp is the specific impulse; g is the local acceleration due to gravity; L is the lift; and D is the drag. Re is 6378.245 km.

[0037] Given the current nominal control vector and the current nominal end time of each segment.

[0038] There are four different modes of aircraft thrust. The mathematical models for the subramjet and scramjet modes are the same. The thrust and ramjet modes are expressed as follows:

[0039]

[0040] Among them, P1 and I sp1 are the thrust and specific impulse of the ejection mode, P2 and I sp2 are the thrust and specific impulse of the subramjet and scramjet modes, P3 and I sp3 are the thrust and specific impulse of the rocket mode, respectively. T1 represents the segmentation time between the ejection mode and the scramjet mode, T2 represents the segmentation time between the scramjet mode and the rocket mode, and T3 represents the time required for the spacecraft to enter orbit and meet terminal constraints.

[0041] The aircraft model is equipped with five engines in total. The ejection mode power of a single engine is:

[0042] P1=427568.12N,I sp1 =p1Ma 2 +p2Ma+p3 (3)

[0043] The modal dynamics of subramjet and scramjet are:

[0044] C t =p Ct1 Ma+p Ct2 ,I sp2 =p Isp1 Ma 2 +p Isp2 Ma+p Isp3 (4)

[0045] P2=C t qA1 (5)

[0046] Among them, C t is the thrust coefficient, A1 is the engine inlet area, and q is the dynamic pressure. m (m=1,2,3), and (k=1, 2, 3) are the ejection mode ramjet fitting curve coefficient, the subramjet and scramjet mode thrust coefficient fitting curve coefficient, and the subramjet and scramjet mode ramjet fitting curve coefficient, respectively.

[0047] The rocket power mode is:

[0048] P3=518776.72N,I sp3 =445s (6)

[0049] The takeoff mass of the aircraft is set to 350,000 kg and the reference area is 240.15 m 2 The engine inlet area is 4.27m 2 , equipped with five RBCC engines. The initial moment is the moment when the aircraft takes off. The given initial conditions are as follows:

[0050]

[0051] Set the suborbital entry scenario, and the corresponding terminal conditions are as follows:

[0052]

[0053] Step 2. Establish an optimal control problem model with multiple segments and multiple constraints and uncertain end time of each segment

[0054] Based on the thrust characteristics, the ascent phase of the vehicle is divided into four sections for overall optimization: the ejection mode section, the subramjet section, the scramjet section, and the rocket mode section. The subscript '(i)' in the process indicates the i-th stage. Considering a multi-stage nonlinear continuous dynamic system with interior point constraints and terminal constraints, the differential equation for each section can be written as:

[0055]

[0056] Among them, x (i) ∈R n is the state variable of the i-th segment, u (i) ∈R m is the control variable for the i-th segment.

[0057] According to the aircraft model in the first step, the state quantity of the aircraft model in the i-th segment is given as follows:

[0058] x (i) =[λ (i) φ (i) h (i) v(i) θ (i) ψ (i) α (i) m (i) ] T ,i=1,2,3,4 (8)

[0059] The control quantity is the first-order derivative of the angle of attack, which can be written as:

[0060]

[0061] In summary, the optimal control problem of the combined power single-stage orbital entry vehicle model is given:

[0062]

[0063] Since the optimal control problem model divides the flight segment into four segments, the terminal state of the previous segment should be guaranteed to be consistent with the initial state of the next segment, that is:

[0064]

[0065] Among them, x (i) (t0 (i) ) is the state variable at the initial moment of segment i, x (i-1) (t0 (i-1) ) is the state variable at the end of the i-1 segment. (i) and t f (i) The initial moment of segment i is the final moment. The aircraft's mission is to minimize fuel loss and ensure it can carry a larger payload. At the same time, flight control changes must be minimized to ensure a smoother flight. Therefore, the performance index includes the optimal terminal mass term and the control integral term. The performance index is shown below:

[0066]

[0067] Among them, m f is the terminal mass of the aircraft, t i (i=1,2,3,4) represents the time separation points of different stages, t4 and t f equivalence.

[0068] The expected values of interior point constraints and terminal constraints are:

[0069]

[0070] The extended performance indicators are:

[0071]

[0072] Among them, μ is the covariate variable, υ is the Lagrange multiplier vector corresponding to the terminal constraint, I(x(t n ),t n ) and φ(x(t f ),t f ) are interior point constraints and terminal constraints respectively, is the derivative of the state quantity, f is the nonlinear equation of the dynamic system, and π is the Lagrange multiplier vector corresponding to the interior point constraint.

[0073] Step 3. Solve the first-order necessary conditions and transversality conditions

[0074] Define the Hamiltonian function:

[0075]

[0076] f (i) is the nonlinear equation of the i-th segment dynamic system. The first-order necessary condition is obtained through the Hamiltonian function and the extended performance index:

[0077]

[0078] Where H is the Hamiltonian function. The transversality condition is solved using the Hamiltonian function and the extended performance index. Transversality conditions can be divided into different types depending on whether they contain interior point constraints and terminal constraints. For equations containing interior point constraints, the transversality condition is:

[0079]

[0080] Otherwise the transversality condition is:

[0081]

[0082] In equations containing terminal constraints, the transversality condition is:

[0083]

[0084] Otherwise the transversality condition is:

[0085]

[0086] in, and Represent the terminal co-state variables of the 1st, 2nd and 3rd segments respectively, and Represent the initial co-state variables of the 2nd, 3rd and 4th segments respectively. I(x(t1), t1), I(x(t2), t2) and I(x(t3), t3) represent the interior point constraints of the 1st, 2nd and 3rd segments, μ is the co-state variable, is the terminal costate variable, π is the Lagrange multiplier vector corresponding to the interior point constraint, and υ is the Lagrange multiplier vector corresponding to the terminal constraint.

[0087] Step 4. Linearized dynamics model and first-order necessary conditions

[0088] The differential equations of each segment of the multi-segment nonlinear continuous dynamic system are shown in formula (7). Performing a first-order Taylor expansion at yields:

[0089]

[0090] Among them, A (i) for point The derivative matrix of the equation with respect to the state variables, B (i) for point The equation at is the derivative matrix of the control variables:

[0091]

[0092] We obtain some first-order necessary conditions for linearization:

[0093]

[0094] The control update expression of the linear system can be obtained as:

[0095]

[0096] The approximate linearized expression of the kinetic equation is obtained as follows:

[0097]

[0098] Step 5. Pseudo-spectral discretization to obtain the optimal instruction update strategy

[0099] The linearized first-order necessary conditions and the linearized optimal control problem model are combined, supplemented by the Gaussian quadrature formula to obtain boundary conditions, which include correction terms for the end times of each segment. Gaussian pseudospectral discretization at the LG point yields the optimal control problem equation for multiple segments, multiple constraints, and variable end times. Solving this equation yields the optimal command update. The optimal command includes the optimal control command and the optimal end time command for each segment.

[0100] The optimal control problem equation for multiple segments and multiple constraints with uncertain terminal time of each segment is as follows:

[0101]

[0102] Among them, the subscript k indicates that this is the kth LG point, Ni indicates the number of LG points in the i-th segment, is an N i×N i +1 matrix, yes The adjoint matrix, ω is the quadrature coefficient of the Gaussian quadrature formula, δx (i) represents the state deviation of the i-th segment, represents the initial state deviation of the i-th segment, represents the terminal state variable of segment i, u pk (i) represents the nominal control quantity at the kth LG point in the i-th segment, δt f (i) Indicates the time correction at the end of the i-th segment.

[0103] Since the Hamiltonian function in this problem does not explicitly contain time, the equation supplemented by the release of each terminal time can be written as:

[0104]

[0105] By adding the connection conditions of each state quantity, the connection conditions of each co-state variable and the cross-sectional conditions, and adding the interior point constraints and terminal constraints, a set of closed equations can be obtained. Solving the closed equations can obtain the first-order time correction term δt f (i) , then the time update term is:

[0106]

[0107] Where s is the number of iterations.

[0108] The interior point and terminal accuracy conditions are:

[0109]

[0110] where dh, dv, and dγ are the absolute values of the differences between the interior point and terminal heights, velocities, and trajectory inclinations predicted by the trajectory integral and the expected interior point and terminal heights, velocities, and trajectory inclinations, respectively.

[0111] Step 6. Pseudo-spectral discretization to obtain the optimal instruction update strategy

[0112] according to Figure 3 In the steps shown, the optimal control model from step 2 is first subjected to trajectory prediction integration using the current nominal control vector and the current nominal end times of each segment from step 1 to determine whether the terminal constraint accuracy requirements are met. If so, the current nominal control vector and the current nominal end times are the optimal instructions. If not, the optimal instruction update strategy obtained in step 5 is applied to update the optimal instructions. The updated instructions are used as the current nominal control vector and the current nominal end times for trajectory integration, and the above process is repeated until the terminal constraint accuracy requirements are met.

Claims

1. A multi-segment multi-constraint pseudo-spectral online optimal guidance method, characterized in that: The steps include: Step 1. Build a combined propulsion aircraft model The multi-stage optimal control problem for the vehicle during the ascent phase only considers motion in the longitudinal plane. Based on the characteristics of rocket-based combined cycle RBCC engine vehicles, the entire ascent phase is divided into four sections: First, the ejection mode section, in which the vehicle takes off horizontally from the ground in ejection mode. When accelerating to Mach numbers of 2.5 to 3, a mode transition is performed, switching to the subramjet and scramjet modes. The scramjet mode is activated at Mach numbers of 5 to 6, and the two modes have a unified mathematical model. When accelerating to Mach numbers of 9 to 10, the vehicle switches to the rocket mode for the final climb and orbit insertion. Step 2. Establish an optimal control problem model with multiple segments and multiple constraints and uncertain end time of each segment The ascent section of the aircraft is divided into segments for overall optimization. The interior point constraints and terminal constraints between the segments are considered to form a weighted combination performance index of maximum terminal mass and smooth control quantity. The state variable connection conditions between the segments are supplemented, and the aircraft model is supplemented to form a nonlinear optimal control problem model. Step 3. Solve the first-order necessary conditions and transversality conditions The Hamiltonian function is defined based on the weighted performance index, and the nonlinear first-order necessary conditions are obtained through the Hamiltonian function. The transversality conditions are obtained based on the Hamiltonian function and the weighted performance index. The transversality conditions are divided into different types according to whether they contain interior point constraints and terminal constraints. Step 4. Linearized dynamics model and first-order necessary conditions The nonlinear optimal control problem and the nonlinear first-order necessary conditions are obtained from steps 2 and 3, and are linearized according to the small perturbation linearization principle to obtain linear differential equations of state vector-related quantities and control vectors; wherein the state vector-related quantities include: a state deviation quantity and a co-state vector corresponding to the state vector; Step 5. Pseudo-spectral discretization to obtain the optimal instruction update strategy Gaussian pseudospectral discretization is performed on the linearized optimal control problem and the linearized first-order necessary conditions. The idea of Gaussian pseudospectral discretization is to use Lagrange interpolation polynomials to interpolate at the zero points of Legendre orthogonal polynomials, i.e., LG points, to approximate the state variables and control variables. Then, the differential equations are replaced by differential approximation matrices, thereby converting the differential equations into algebraic equations, which are then solved using algebraic equations. The first-order necessary conditions and the optimal control problem model are linearized simultaneously, and the boundary conditions are obtained by using the Gaussian quadrature formula. The boundary conditions include correction terms for the terminal time of each segment. Gaussian pseudo-spectral discretization is performed at the LG point to obtain the optimal control problem equation with multiple segments and multiple constraints and uncertain terminal time of each segment. This equation is solved to obtain the optimal instruction update; the optimal instruction includes the optimal control instruction and the optimal terminal time instruction of each segment. Step 6. Apply the optimal instruction update strategy to form the online guidance law The optimal control model in step 2 is subjected to trajectory prediction integration using the current nominal control vector and the current nominal end time of each segment in step 1 to calculate whether the preset terminal constraint accuracy threshold is met. If so, the current nominal control vector and the current nominal end time of each segment are the optimal instructions. If not, the optimal instruction update strategy obtained in step 5 is applied to update the optimal instructions; the updated instructions are used as the current nominal control vector and the current nominal end time of each segment for trajectory integration, and the above process is repeated until the terminal constraint accuracy requirements are met.

2. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1, characterized in that: In step 1, the vertical dynamics model of the RBCC combined power aircraft is established as follows: Where: λ is longitude; is latitude; v is velocity; h is speed; Re is the radius of the earth; γ is the ballistic inclination; ψ is the ballistic deviation; r is the distance from the center of the earth; h is the flight altitude; m is the mass of the aircraft; α is the angle of attack AOA; P is the thrust of the aircraft; I sp is the specific impulse; g is the local acceleration of gravity; L is the lift; D is the drag; Re is 6378.245 km.

3. A multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1 or 2, characterized in that: There are four different modes of aircraft thrust. The mathematical models for the subramjet and scramjet modes are the same. The thrust and ramjet are expressed as follows: Among them, P1 and I sp1 are the thrust and specific impulse of the ejection mode, P2 and I sp2 are the thrust and specific impulse of the subramjet and scramjet modes, P3 and I sp3 are the thrust and specific impulse of the rocket mode respectively; T1 represents the segmentation time between the ejection mode and the scramjet mode, T2 represents the segmentation time between the scramjet mode and the rocket mode, and T3 represents the time for the spacecraft to enter orbit and meet the terminal constraints.

4. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 3, characterized in that: The aircraft model is equipped with five engines in total. The ejection mode power of a single engine is: P1=427568.12N,I sp1 =p1Ma 2 +p2Ma+p3 (3) The modal dynamics of subramjet and scramjet are: C t =p Ct1 Ma+p Ct2 ,I sp2 =p Isp1 Ma 2 + p Isp2 Ma+p Isp3 (4) P2=C t qA1 (5) Among them, C t is the thrust coefficient, A1 is the engine inlet area, q is the dynamic pressure; p m (m=1,2,3),p Ctj (j=1,2) and p Ispk (k=1,2,3) are the ejection mode ramjet fitting curve coefficient, the subramjet and scramjet mode thrust coefficient fitting curve coefficient, and the subramjet and scramjet mode ramjet fitting curve coefficient respectively; The rocket power mode is: P3=518776.72N,I sp3 =445s (6) The takeoff mass of the aircraft is set to 350,000 kg and the reference area is 240.15 m 2 The engine inlet area is 4.27m 2 , equipped with 5 RBCC engines; the initial moment is the moment when the aircraft takes off.

5. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1, characterized in that: In step 2, the subscript (i) indicates the i-th stage; consider a multi-stage nonlinear continuous dynamic system with interior point constraints and terminal constraints. The differential equation of each stage system is written as: Among them, x (i) ∈R n is the state variable of the i-th segment, u (i) ∈R m is the control variable for the i-th segment; The state of the aircraft model in the i-th segment is given as follows: x (i) =[λ (i) f (i) h (i) v (i) i (i) ψ (i) a (i) m (i) ] T ,i=1,2,3,4 (8) The control quantity is the first-order derivative of the angle of attack and is written as: In summary, the optimal control problem of the combined power single-stage orbital entry vehicle model is given:

6. A multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1 or 5, characterized in that: Since the optimal control problem model divides the flight segment into four segments, the terminal state of the previous segment should be guaranteed to be consistent with the initial state of the next segment, that is: Among them, x (i) (t0 (i) ) is the state variable at the initial moment of segment i, x (i-1) (t0 (i-1) ) is the state variable at the end of the i-1 segment; t0 (i) and The initial moment of the i-th segment is the terminal moment; the flight mission of the aircraft is to minimize fuel loss as much as possible to ensure that the aircraft can carry a larger payload; at the same time, ensure that the flight control changes are as small as possible to make the flight process relatively stable, so the performance index includes the terminal mass optimal term and the control integral term; the performance index is shown in the following formula: Among them, m f is the terminal mass of the aircraft, t i (i=1,2,3,4) represents the time separation points of different stages, t4 and t f equivalence; The extended performance indicators are: Among them, μ is the covariate variable, υ is the Lagrange multiplier vector corresponding to the terminal constraint, I(x(t n ),t n ) and φ(x(t f ),t f ) are interior point constraints and terminal constraints respectively, is the derivative of the state quantity, f is the nonlinear equation of the dynamic system, and π is the Lagrange multiplier vector corresponding to the interior point constraint.

7. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1, characterized in that: In step 3, define the Hamiltonian function: f (i) is the nonlinear equation of the i-th segment dynamic system; the first-order necessary condition is obtained through the Hamiltonian function and the extended performance index: Where H is the Hamiltonian function. The transversality condition is solved by the Hamiltonian function and the extended performance index. The transversality condition is divided into different types according to whether it contains interior point constraints and terminal constraints. For equations containing interior point constraints, the transversality condition is: Otherwise the transversality condition is: In equations containing terminal constraints, the transversality condition is: Otherwise the transversality condition is: in, and Represent the terminal co-state variables of the 1st, 2nd and 3rd segments respectively, and Represent the initial co-state variables of the 2nd, 3rd and 4th segments respectively; I(x(t1), t1), I(x(t2), t2) and I(x(t3), t3) represent the interior point constraints of the 1st, 2nd and 3rd segments, μ is the co-state variable, is the terminal costate variable, π is the Lagrange multiplier vector corresponding to the interior point constraint, and υ is the Lagrange multiplier vector corresponding to the terminal constraint.

8. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1, characterized in that: In step 4, the differential equations of each segment of the multi-segment nonlinear continuous dynamic system are At its point Performing a first-order Taylor expansion at yields: Among them, A (i) for point The derivative matrix of the equation with respect to the state variables, B (i) for point The equation at is the derivative matrix of the control variables: We obtain some first-order necessary conditions for linearization: The control update expression of the linear system is obtained as: The approximate linearized expression of the kinetic equation is obtained as follows:

9. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 1, characterized in that: In step 5, the optimal control problem equation for multiple segments and multiple constraints with uncertain terminal time of each segment is as follows: Among them, the subscript k indicates that this is the kth LG point, Ni indicates the number of LG points in the i-th segment, is an N i ×N i +1 matrix, yes The adjoint matrix, ω is the quadrature coefficient of the Gaussian quadrature formula, δx (i) represents the state deviation of the i-th segment, represents the initial state deviation of the i-th segment, represents the terminal state variable of segment i, u pk (i) represents the nominal control quantity at the kth LG point in the i-th segment, Indicates the time correction at the end of the i-th segment.

10. The multi-segment multi-constraint pseudo-spectrum online optimal guidance method according to claim 9, characterized in that: Since this Hamiltonian function does not explicitly contain time, the equation supplemented by the release of each terminal time is written as: Supplement the connection conditions of each state quantity, each co-state variable connection conditions and cross-sectional conditions, supplement the interior point constraints and terminal constraints, and obtain a set of closed equations. Solve the closed equations to obtain the first-order time correction term. Then the time update term is: Where s is the number of iterations.

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