Satellite-borne SAR scene matching curve imaging electromechanical cooperation wave control optimization method based on dynamic programming

Abstract

The invention discloses a spaceborne SAR scene matching curve imaging electromechanical cooperative wave control optimization method based on dynamic programming, and belongs to the technical field of spaceborne SAR. The method comprises the following steps: firstly, acquiring a beam pointing attitude angle time sequence before decomposition by using a satellite-borne SAR non-along-track multi-target imaging satellite-ground configuration joint design and optimization method, and solving a phased array electric scanning angle; secondly, establishing an electromechanical collaborative dynamic planning model comprising a platform mechanical scanning state transition equation, a cost function and a constraint function; initializing parameters such as a mechanical scanning state track, a control input sequence and the like to obtain an initial track and cost; optimal control solution is executed through dynamic planning, and convergence is achieved through inner and outer layer iteration (backward transfer calculation of a control law, forward transfer updating of a track and outer layer correction constraint violation); and finally, outputting a mechanical scanning attitude angle time sequence and a phased array electric scanning angle time sequence, and completing electromechanical cooperative wave control optimization.

Description

Technical Field

[0001] This invention relates to a dynamic programming-based electromechanical co-controlled beam control optimization method for spaceborne SAR scene matching curve imaging, belonging to the field of spaceborne synthetic aperture radar (SAR) technology. Background Technology

[0002] Spaceborne SAR scene matching curve imaging achieves high-resolution, complete imaging of curved scenes by continuously scanning the beam in two dimensions and matching the geographical orientation of the scene. Beam scanning can be achieved through two methods: satellite platform mechanical scanning and phased array antenna electronic scanning. Satellite platform mechanical scanning changes the beam pointing by adjusting the satellite attitude, while phased array antenna electronic scanning changes the beam pointing by weighted phase alignment of the transceiver channels. Mechanical scanning is limited by angular velocity and angular acceleration constraints, and its attitude cannot change drastically, making it unsuitable for curved scenes with steep terrain changes. Electronic scanning is limited by phased array antenna scanning loss and pattern distortion, resulting in a limited beam scanning range that cannot meet the imaging requirements of long curved scenes. By simultaneously controlling phased array antenna electronic scanning and satellite platform mechanical scanning, the shortcomings of both can be effectively compensated for, achieving wide-range, agile beam scanning.

[0003] Existing electromechanical co-beam control methods for spaceborne SAR scene matching curve imaging are mostly based on heuristic algorithms for optimization. These methods optimize the electromechanical / electronic co-beam control by minimizing the objective function (such as the temporal variation range of the mechanical scanning angle) through searching the control parameters of both mechanical and electronic scanning. However, due to the complex variations in scene matching curve imaging configurations, heuristic optimization algorithms cannot simultaneously achieve global optimum and fast convergence, requiring extensive debugging to obtain a feasible solution, resulting in low efficiency.

[0004] Dynamic programming is an optimal trajectory solution method. Under the conditions of well-defined system dynamics and nonlinear cost, augmented Lagrangian-differential dynamic programming can quickly converge to the optimal solution while satisfying the constraints. Therefore, it is of great significance to study an electromechanical co-operated wave control optimization method that can have fast convergence characteristics and approximate the global optimum while satisfying the platform attitude and phased array antenna electronic scanning constraints. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a dynamic programming-based electromechanical co-controlled beam control optimization method for spaceborne SAR scene matching curve imaging. The aim is to achieve efficient convergence and globally optimal electromechanical co-controlled beam control optimization in complex curve scenes, taking into account both platform attitude constraints and phased array antenna electronic scanning constraints.

[0006] A dynamic programming-based electromechanical co-controlled beam control optimization method for spaceborne SAR scene matching curve imaging includes: Step 1: Using the joint design and optimization method of satellite-ground configuration for non-track multi-target imaging of spaceborne SAR, the timing sequence of beam pointing attitude angle before decomposition is obtained; using the machine / electronic co-controlled beam control optimization method of scene matching curve imaging of spaceborne SAR, the phased array electronic scanning angle is solved under the given platform mechanical scanning attitude angle and the attitude angle before decomposition. Step 2: Modeling of electromechanical co-operation dynamic programming for spaceborne SAR scene matching curve imaging, including platform mechanical scanning state transition equations, cost functions, and constraint functions; Step 3: Initialize the mechanical scanning state trajectory, control input sequence, Lagrange multipliers and penalty factors to obtain the initial mechanical scanning trajectory and initial cost; Step 4: Solving the optimal control based on dynamic programming: In each iteration, backpropagation is first performed based on the current trajectory to calculate the gradient of the value function and the Hessian matrix, obtaining the optimal feedback and feedforward control law; then forward propagation is performed to correct the trajectory according to the control law, and the trajectory is updated using the line search criterion to ensure that the cost function decreases monotonically; in the outer iteration, the Lagrange multipliers and penalty factors are updated, and constraint violations are corrected until the convergence condition is met or the iteration limit is reached; Step 5: Output the final mechanical scan attitude angle timing sequence and phased array electronic scan angle timing sequence to achieve electromechanical co-controlled beam control optimization for spaceborne SAR scene matching curve imaging.

[0007] Beneficial effects: This invention provides a dynamic programming-based electromechanical co-operational beam pointing optimization method for spaceborne SAR scene matching curve imaging. By combining augmented Lagrangian concepts with differential dynamic programming, it achieves electromechanical co-operational optimization control of spaceborne SAR beam pointing, and has the following beneficial effects: 1. It can simultaneously satisfy the platform's attitude angle, angular velocity, angular acceleration constraints, and phased array antenna electrical scanning range constraints, ensuring the physical feasibility of the optimization results; 2. Compared with optimization methods based on heuristic search, this invention does not rely on a large number of random searches, significantly reducing the number of iterations and computational complexity, and improving the convergence speed; 3. It has strong adaptability and robustness. By adjusting the cost weight, it can be applied to spaceborne SAR under different configurations and capability conditions. Attached Figure Description

[0008] Figure 1 Flowchart of an electromechanical co-controlled beam control optimization method for spaceborne SAR scene matching curve imaging based on dynamic programming; Figure 2 A schematic diagram defining the platform mechanical scanning attitude angle and the phased array electronic scanning angle; Figure 3Timing diagrams of platform mechanical scanning attitude angles obtained by electromechanical decomposition methods based on global PSO optimization and dynamic programming optimization before electromechanical decomposition. Figure 4 Timing diagrams of platform mechanical scanning attitude angular velocity obtained by electromechanical decomposition methods based on global PSO optimization and dynamic programming optimization; Figure 5 Timing diagrams of platform mechanical scanning attitude angle acceleration obtained by electromechanical decomposition methods based on global PSO optimization and dynamic programming optimization; Figure 6 The time series diagram of the range-direction electronic scanning angle obtained by the electromechanical decomposition method based on global PSO optimization and dynamic programming optimization; Figure 7 The azimuth electrical scanning angle timing diagram obtained by the electromechanical decomposition method based on global PSO optimization and dynamic programming optimization. Detailed Implementation

[0009] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0010] This invention provides a dynamic programming-based electromechanical co-controlled beam control optimization method for spaceborne SAR scene matching curve imaging, the process of which is as follows: Figure 1 As shown, it includes: Step 1: Using the joint design and optimization method of satellite-ground configuration for non-track multi-target imaging of spaceborne SAR, obtain the timing sequence of beam pointing attitude angle before decomposition; using the machine / electronic co-controlled beam control optimization method of spaceborne SAR scene matching curve imaging, solve the phased array electronic scanning angle given the platform mechanical scanning attitude angle and the attitude angle before decomposition.

[0011] The aforementioned pre-decomposition beam pointing attitude angle timing refers to the design of a spaceborne SAR scene matching curve imaging system based on input scene information and spaceborne SAR system parameters. Utilizing a joint design and optimization method for spaceborne SAR non-track multi-target imaging satellite-ground configuration, without constraints on beam control angular velocity and angular acceleration, the system outputs the three-axis rotation angle timing from the satellite orbit coordinate system to the spaceborne SAR system itself, which are the yaw angles. ψ p ( t ), pitch angle θ p ( t Roll angle φ p ( t ).

[0012] The given platform mechanically scanned attitude angles refer to the changes in the satellite platform's attitude around the three axes of yaw, pitch, and roll, which are respectively the mechanically scanned yaw angles. ψ ( t ), mechanical sweeping pitch angle θ ( t ), mechanical sweeping roll angle φ ( t ), used to describe the mechanical scanning trajectory of the platform attitude control system over time.

[0013] The phased array electronic scanning angle is the beam deflection angle achieved by the planar phased array antenna in the range and azimuth directions through phase coordination. Range electronic scanning angle α Defined as the angle between the beam azimuth profile and the antenna normal, the azimuth scanning angle. β Defined as the angle between the beam distance profile and the antenna normal.

[0014] The schematic diagram defining the attitude angle of the mechanical scanning and the phased array scanning angle is shown below. Figure 2 As shown.

[0015] By utilizing the spaceborne SAR scene matching curve imaging machine / electrical co-controlled beam control optimization method, the phased array electronic scanning angle timing can be solved given the pre-decomposition beam pointing attitude angle timing and the platform mechanical scanning angle timing. α ( t )and β ( t As shown in equation (1): (1) Step 2: Modeling of electromechanical co-operation dynamic programming for spaceborne SAR scene matching curve imaging, including platform mechanical scanning state transition equations, cost functions, and constraint functions; The platform mechanical scanning state transition equation refers to the change process of the platform mechanical scanning angle and angular velocity under the action of angular acceleration. The time series is discretized, and the time interval is denoted as... dt Then at a certain moment k The platform's scanning angle and angular velocity are recorded as the state. x k The angular acceleration at that moment is recorded as the control. u k As shown in equation (2): (2) The state transition equation for platform mechanical scanning is shown in equation (3): (3) The cost function refers to the performance index function used in the optimization process of electromechanical co-control of spaceborne SAR to measure the degree of deviation of the beam pointing of the mechanical scanning control from the target beam pointing and the cost of the required phased array electronic scanning angle. At the same time, it constrains the magnitude of the control input and considers the violation penalty of system constraints (such as angle, angular velocity, angular acceleration, electronic scanning angle range, etc.) based on augmented Lagrangian. The single-step cost function is shown in Equation (4).

[0016] (4) in l track,k It is the trajectory tracking cost, which represents the error between the beam pointing of the platform machine scan and the pointing before decomposition, as shown in Equation (5); l elec,k It is the electro-scanning angle cost, which represents the electro-scanning angle cost obtained by electromechanical decomposition based on the current platform electro-scanning angle, as shown in Equation (7); l ctrl,k It is the control cost, which represents the constraint on the mechanical sweep control input (angular acceleration), as shown in equation (8); l AL,k It is the augmented Lagrange cost, which penalizes constraint violations during the optimization process and ensures the physical feasibility of the optimization result, as shown in Equation (9).

[0017] (5) in,(·) T Indicates transpose (the same applies below); Q k Indicates pose weights; h vec This represents the beam pointing function of the current platform machine scan; p k The ideal beam pointing is calculated based on the angles of the three axes before decomposition, as shown in equation (6).

[0018] (6) (7) in, , representing the scanning angle vector; W k This represents the cost weight matrix for electroscanning.

[0019] (8) in, R k This represents the control cost weight matrix.

[0020] (9) in, λk Represents the Lagrange multiplier. I μ,k Let the penalty coefficients be represented as a diagonal matrix, as shown in equation (10); Represents the constraint function.

[0021] (10) in, Indicates the number of constraints.

[0022] The constraint function refers to the system constraint conditions set to ensure that the platform attitude and phased array antenna work within the physically permissible range, including the platform mechanical scanning angle, angular velocity, angular acceleration range and phased array electronic scanning angle range, as shown in equation (11): (11) in,(·) min Indicates the lower limit of the parameter, (·) max Indicates the upper limit of the parameter.

[0023] Terminal cost ( k = N Since there is no input cost (at that time), the electromechanical co-processing dynamic programming model for spaceborne SAR scene matching curve imaging can be modeled as follows: (12) Where x and u represent the planned state and input sequence, and a set of x and u is denoted as a set of trajectories.

[0024] Step 3: Initialize the initial state of the mechanical scan, the control input sequence, the Lagrange coefficients and the penalty coefficients to obtain the initial trajectory and initial cost of the mechanical scan; Since dynamic programming solves the problem by generating a state sequence based on the selected initial state and control input sequence according to the state transition equation, the mechanically scanned state trajectory and control input sequence need to be properly initialized to ensure that the initial state satisfies the physical constraints.

[0025] One alternative implementation is to use a constrained L∞ norm quadratic polynomial for fitting, which models the angular trajectory before decomposition using a quadratic polynomial form, where the coefficients of the quadratic term correspond to the initial angular acceleration, the coefficients of the linear term correspond to the initial angular velocity, and the constant term corresponds to the initial angle.

[0026] The L∞ norm is defined as the maximum fitting error, and the optimization objective is to minimize the maximum fitting error. Physical constraints include angular velocity and angular acceleration constraints. This optimization problem is a linear programming problem, and the optimal solution can be quickly obtained using a conventional linear programming solver.

[0027] By using the constant and linear terms of the obtained quadratic polynomial as the initial state and the quadratic term as the value of the control input sequence, and by selecting the initial Lagrange coefficients and penalty coefficients, the initial trajectory and initial cost of the mechanical scan can be obtained.

[0028] Step 4: Solving the optimal control based on dynamic programming: In the inner iteration, backpropagation is first performed based on the current trajectory to calculate the gradient of the value function and the Hessian matrix, obtaining the optimal feedback and feedforward control law; then forward propagation is performed to correct the trajectory according to the control law, and the trajectory is updated using the line search criterion to ensure that the cost function decreases monotonically until the inner convergence condition is met or the inner iteration upper limit is reached; in the outer iteration, the Lagrange multipliers and penalty factors are updated, and constraint violations are corrected until the outer convergence condition is met or the outer iteration upper limit is reached. Step 41: In the inner iteration, backpropagation is first performed based on the current trajectory to calculate the gradient of the value function and the Hessian matrix, and the optimal feedback and feedforward control law are obtained.

[0029] The value function refers to the function at a given time. k The system starts from the state at that moment. x k Starting from this point, execute the optimal control input sequence u under the condition that the constraints are satisfied. * The minimum cost that can be achieved is shown in equation (13): (13) According to the Bellman optimality principle, the first gradient and second Hessian matrix of the value function at the terminal time are calculated by recursively calculating from the terminal time backward, as shown in equation (14): (14) For any given moment k Define the Q function as the function in the current state. x k And take control u k The immediate cost of each step. l k and subsequent optimal cost V k+1 Sum of these, find the first and second derivatives of the Q-function with respect to the state and control: (15) in,(·) x,k express ,(·) xx,k express subscript u Similarly.

[0030] The calculation method for its optimal feedback and feedforward control law is shown in Equation (16): (16) The update method for the first-order gradient and second-order Hessian matrix of the value function is shown in Equation (17): (17) Step 42: Perform forward propagation, correct the trajectory according to the control law, update the trajectory using the line search criterion, and ensure that the cost function decreases monotonically until the inner convergence condition is met or the inner iteration upper limit is reached.

[0031] Specifically, the method for modifying the control input according to the control law is as follows: (18) in, The search step size is the line search step size. It is the corrected state, derived from the state at the previous moment. and control input Calculated.

[0032] The trajectory update method refers to, given an initial state The new trajectory x is obtained by recursion according to formulas (3) and (18). new and u new .

[0033] The line search criterion refers to the Armijo condition judgment. α Whether the value is appropriate, i.e., calculating the actual cost reduction obtained from the new trajectory. and compared it with the predicted cost reduction amount The comparison and calculation method are as follows: (19) when Greater than or equal to When a certain proportion is considered, it is believed that α If the conditions are met, accept the update; if the conditions are not met, gradually narrow down. α Until the conditions are met or the preset minimum is reached. α This ensures that the cost function remains monotonically decreasing in each iteration.

[0034] The phrase "until the inner layer convergence condition or the inner layer iteration upper limit is reached" means that: when... The inner loop terminates when the number of inner iterations reaches the maximum number of iterations. ε in This represents the inner convergence threshold.

[0035] Step 43: Update the Lagrange coefficients and penalty coefficients in the outer iteration and correct the constraint violations until the convergence condition is met or the iteration limit is reached.

[0036] Specifically, for each time step k, the constraint violation amount is calculated based on formula (11), and the Lagrange coefficients and penalty coefficients are updated. The update method is as follows: (20) Where ⊙ denotes the Hadamard product of vectors, and max(0,·) denotes the non-negative projection onto each dimension component. Φ μ >1 indicates that the penalty coefficient update scaling factor is 1.

[0037] Use the updated λ k and μ k In the next iteration, substitute formulas (4)(9)(10) to calculate the cost function, thereby guiding the system state and control input to correct the violation input.

[0038] The phrase "until the outer layer convergence condition is met or the inner layer iteration upper limit is reached" means that: when... The outer loop terminates when the number of iterations reaches the maximum number of iterations. ε out This represents the inner convergence threshold.

[0039] Step 5: Output the final mechanical scan attitude angle timing sequence and phased array electronic scan angle timing sequence to achieve electromechanical co-controlled beam control optimization for spaceborne SAR scene matching curve imaging.

[0040] Specifically, based on the optimal trajectory obtained in step four, the computer scan attitude angle timing and the phased array electronic scan angle timing are used to achieve electromechanical coordinated wave control optimization for spaceborne SAR scene matching curve imaging.

[0041] Simulation Experiment: The simulation parameters of the electromechanical co-controlled beam control optimization method for spaceborne SAR scene matching curve imaging based on dynamic programming are shown in Table 1.

[0042] Table 1 Simulation parameters of the dynamic programming-based spaceborne SAR scene matching curve imaging electromechanical co-controlled beam control optimization method

[0043] Based on the parameters in the table above, the decomposed beam pointing attitude angle timing sequence can be obtained using the joint design and optimization method for spaceborne SAR non-track multi-target imaging space-ground configuration. To verify the effectiveness of the dynamic programming-based spaceborne SAR scene-matching curve imaging electromechanical co-controlled beam control optimization method, we compared the optimization results of our method with those of electromechanical decomposition using the global PSO algorithm (hereinafter referred to as the comparison method). The decomposed beam pointing attitude angle timing sequence, the platform mechanical scanning attitude angle timing sequence obtained by the comparison method, and the platform mechanical scanning attitude angle timing sequence obtained by our method are shown below. Figure 3As shown. The sweeping speed of the platform machine in the comparison method and the method presented in this paper is as follows. Figure 4 As shown, the sweep angle acceleration of the platform machine in the comparison method and the method described in this paper is as follows: Figure 5 As shown, the timing of the range-direction electronic scanning angle between the comparison method and this method is as follows: Figure 6 As shown, the timing sequence of the azimuth scanning angle of the comparison method and this method is as follows: Figure 7 As shown in the figure, the convergence time of the comparative method is 627s, while the convergence time of this method is 73s. It can be seen from the examples that this method converges faster than the global PSO algorithm. Figures 4-6 It can be seen that, compared with the comparative methods, this method offers greater flexibility in attitude adjustment within the constraints of platform mechanical scanning, fully leveraging the platform's mechanical scanning capabilities; from Figures 6-7 As can be seen, compared with the comparative methods, the two-dimensional phased array electronic scanning angles are all within the constraints, significantly reducing the pressure on phased array electronic scanning under the condition of sparse array antennas. The embodiments demonstrate that this method can simultaneously satisfy the constraints of platform attitude angle, angular velocity, angular acceleration, and phased array antenna electronic scanning range, ensuring the physical feasibility of the optimization results; compared with heuristic search-based optimization methods, it significantly reduces the number of iterations and computational complexity, and improves the convergence speed; it is applicable to spaceborne SAR under different configurations and capabilities, and can effectively improve the imaging quality of electromechanical co-beam control scene matching curves.

[0044] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for optimizing the mechanical-electrical collaborative wave control of a spaceborne SAR scene-matching curve imaging based on dynamic programming, characterized in that, Comprising the following steps: Step one, using the spaceborne SAR non-track multi-target imaging space-ground configuration joint design and optimization method, the decomposition before the beam pointing attitude angle time sequence is obtained; using the spaceborne SAR scene matching curve imaging machine / electricity collaborative wave control optimization method, the electric scanning angle is solved under the given platform machine scanning attitude angle and the decomposition before the attitude angle; Step two, spaceborne SAR scene matching curve imaging machine and electricity collaborative dynamic programming modeling, including platform machine scanning state transition equation, cost function and constraint function; Step three, initialize the machine scanning state trajectory, control input sequence, Lagrange multiplier and penalty factor, obtain the initial trajectory and initial cost of machine scanning; Step four, optimal control solution based on dynamic programming: in each iteration, first backward transfer based on the current trajectory, calculate the value function gradient and Hessian matrix, get the optimal feedback and feedforward control law; then forward transfer, correct the trajectory according to the control law, update the trajectory using line search criterion to ensure the monotonicity of the cost function; update the Lagrange multiplier and penalty factor in the outer iteration, and correct the constraint violation until the convergence condition is met or the iteration limit is reached; Step five, output the final machine scanning attitude angle time sequence and phased array electric scanning angle time sequence, realize the machine and electricity collaborative wave control optimization of spaceborne SAR scene matching curve imaging.

2. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method according to claim 1, characterized in that, The decomposition of the beam pointing attitude angle time sequence in step one is the three-axis rotation angle time sequence of the satellite orbit coordinate system to the onboard SAR body system, which is output after the satellite orbit coordinate system to the onboard SAR body system three-axis rotation angle time sequence is designed and optimized by the joint design and optimization method of the onboard SAR non-track multi-target imaging satellite-ground configuration according to the input scene information and the onboard SAR system parameters without wave control angular velocity and angular acceleration constraints, and the three-axis rotation angles are respectively the yaw angle Ψ p ( t ), the pitch angle θ p ( t ), and the roll angle Φ p ( t ).

3. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The given platform machine scanning attitude angle in step one is the three-axis angle change of the satellite platform attitude around the yaw axis, the pitch axis and the roll axis, and the three-axis angles are machine scanning yaw angle Ψ ( t ), machine scanning pitch angle θ ( t ), and machine scanning roll angle Φ ( t ), which are used to describe the machine scanning trajectory of the platform attitude control system in time sequence.

4. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The phased array electric scanning angle in step one is the beam deflection angle of the flat plate phased array antenna in the range direction and the azimuth direction by phase matching, wherein the range direction electric scanning angle α is defined as the angle between the beam azimuth profile and the normal of the antenna, and the azimuth direction electric scanning angle β is defined as the angle between the beam range profile and the normal of the antenna; phased array electric scanning angle timing α ( t ) and β ( t ) are solved by the following formula: 。 5. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The platform scanning state transition equation in step two is a discrete change process of the platform scanning angle and angular velocity under the action of angular acceleration, and is specifically as follows: the time interval after time sequence discretization is denoted as Dt , the platform scanning angle and angular velocity at a moment k are denoted as state x k , the angular acceleration at the moment is denoted as control u k , x k and u k , and the expression is as follows: ； The platform machine scanning state transition equation is: 。 6. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The cost function in step two is a single step cost function l k The expression is: ； wherein: l track,k is a track tracking cost, representing the error between the platform machine scanning beam pointing and the pointing before decomposition, expressed as wherein (·) T denotes the transpose (same below), Q k denotes the attitude weight; h vec denotes the current platform machine scanning beam pointing function; p k denotes the ideal beam pointing calculated according to the three-axis angles before decomposition; h vec and p k the expression of is: , ; l elec,k is the electrical scan angle cost, representing the electrical scan angle cost resulting from the mechanical-electrical decomposition based on the current platform mechanical scan angle, expressed as wherein represents the electrical scan angle vector; W k represents the electrical scan cost weight matrix; l ctrl,k is the control cost, representing the constraint on the machine scan control input (angular acceleration), expressed as where R k is the control cost weight matrix; l AL,k is the augmented Lagrangian cost, which penalizes constraint violations during optimization to guarantee the physical feasibility of the optimization result, expressed as , λ k denotes the Lagrangian coefficients, I μ,k denotes the penalty coefficient diagonal matrix, expressed as: .

7. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The constraint function in step two is a system constraint condition set to ensure that the platform attitude and phased array antenna work within the physical allowable range, including platform machine scanning angle range, platform machine scanning angular velocity range, platform machine scanning angular acceleration range and phased array electric scanning angle range, and the constraint function expression is: 。 8. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The specific way of initialization in step three is: using the L∞ norm quadratic polynomial fitting with constraints, modeling the pre-decomposition angle trajectory in the form of quadratic polynomial, the quadratic term coefficient of the quadratic polynomial corresponds to the initial angular acceleration, the linear term coefficient corresponds to the initial angular velocity, and the constant term corresponds to the initial angle; define the L∞ norm as the maximum fitting error, the optimization goal is to minimize the maximum fitting error, and the optimization process needs to meet the physical constraints of angular velocity and angular acceleration; this optimization problem is a linear programming problem, and the optimal solution is obtained by using a conventional linear programming solver, then the constant term and the linear term of the quadratic polynomial are taken as the initial state, the quadratic term is taken as the value of the control input sequence, and the initial Lagrange coefficient and penalty factor are selected to obtain the initial trajectory and initial cost of machine scanning.

9. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-optimization method of claim 1, wherein, The specific process of backward transfer in step four is:

1. Define the value function V k x k for a given time instant k , the system starting from state x k , the minimum cost achievable by performing an optimal control input sequence u * while satisfying the constraints, is expressed as ;​ 2. According to Bellman's optimality principle, the first order gradient and the second order Hessian matrix of the terminal time value function are calculated by forward recursion from the terminal time: , ; 3. Define Q function as current state x k , control u k Next step is the cost l k And the sum of the subsequent optimal cost V k+1 The first and second order derivatives of Q function with respect to state and control are calculated: Where (·) x,k Indicates , (·) xx,k Indicates , subscript u Similarly; 4. Computing optimal feedback and feedforward control laws based on Q-function derivatives: , ; 5. The first order gradient and second order Hessian matrix of the value function are updated according to the following equations: .

10. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The specific process of forward transfer in step four is:

1. According to the control law, the control input is corrected, and the correction formula is wherein, is a line search step, is the corrected state, which is obtained by the state and the control input at the previous time according to the platform machine state transition equation, and the initial state ; 2. Update the trajectory using a line search criterion based on the Armijo condition: compute the actual cost reduction of the new trajectory and the predicted cost reduction , when is greater than or equal to a certain fraction of , accept the update, otherwise shrink α until the condition is met or a preset minimum α is reached; 3. The inner layer convergence condition is or the inner layer iteration number reaches the maximum iteration number, wherein Epsilon in is the inner layer convergence threshold.

11. The dynamic programming based space-borne SAR scene-matched curve imaging machine-electricity co-timed wave control optimization method of claim 1, wherein, The specific process of outer iteration in step four is: 1、 For each time step k, the constraint violation is calculated based on the constraint function, the Lagrange coefficient and the penalty coefficient are updated, and the updating method is: where ⊙ denotes the vector Hadamard product, and max(0, ·) denotes the non-negative projection to each dimension component, Phi μ >1 denotes the penalty coefficient updating proportion factor; 2. The updated Lambda k and Mu k Substitute into the cost function calculation, guide the system state and control input correction constraint violation; 3. The outer layer converges if or the number of iterations of the outer layer reaches a maximum number of iterations, wherein Epsilon out is an outer layer convergence threshold.

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