CN114020018B - Determination method and device of missile control strategy, storage medium and electronic equipment - Google Patents
Determination method and device of missile control strategy, storage medium and electronic equipment Download PDFInfo
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Abstract
The application provides a determination method and device of missile control strategy, storage medium and electronic equipment, wherein the determination method comprises the following steps: determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed; performing iterative solution based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy; updating the first control strategy by using the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and obtaining an optimal control strategy and an optimal value function; and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining the control strategy of the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed. In this way, the unknown parameters are determined by utilizing missile state data in combination with an optimal control algorithm, so that optimal control on missile track tracking is realized.
Description
Technical Field
The present disclosure relates to the field of control algorithms, and in particular, to a method and apparatus for determining a missile control policy, a storage medium, and an electronic device.
Background
In the field of automatic control, there are a variety of control methods. For example: robust control techniques, sliding mode control techniques, backstepping control techniques, predictive control techniques, and the like. These control schemes combine their own control advantages to achieve better control performance by adjusting the controller parameters. However, these control methods are more capable of ensuring system stability and do not combine performance metrics with controller design. Whether the final control result meets the performance index is more than artificial judgment, and the design of the controller and the required performance index cannot be combined through theoretical analysis. Therefore, the optimal control theory has received a lot of attention, and it can design an optimal controller under a given performance index. There are various methods of solving the optimal controller, for example: maximum and minimum principle, linear quadratic optimal control, optimal robust control and dynamic planning method.
In the existing stage, under the condition of considering parameter uncertainty, a nonlinear control algorithm, such as a robust compensation algorithm, an H infinite control method, a synovial membrane control method and the like, is designed, so that the influence of the parameter uncertainty and the like on missile performance is solved. However, such methods require suppression of the effects of missile parameter uncertainty based on controlled object model information. And uncertainty (such as uncertainty of a tracking target and uncertainty of pneumatic parameters) exists in an actual missile dynamic model. It is not applicable to the case where the parameters are completely unknown and the controlled object model information is unknown. Therefore, a determination method for a missile control strategy is urgently needed to be realized, and accurate control of a missile system is realized.
Disclosure of Invention
In view of this, the present application aims to provide a method, an apparatus, a storage medium and an electronic device for determining a missile control policy, where when determining the control policy of a missile system to be analyzed, nonlinearity and uncertain system parameters in the missile system are considered, and an unknown parameter matrix including nonlinearity and uncertain system parameters is determined through an optimal control policy, so as to determine the control policy for implementing the missile system to be analyzed, thereby improving the accuracy of the missile system control to be analyzed.
The embodiment of the application provides a determination method of a missile control strategy, which comprises the following steps:
determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed;
performing iterative solution based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy;
updating the first control strategy by using the reference control strategy until the updated control strategy meets the preset control strategy updating conditions, and obtaining an optimal control strategy and an optimal value function;
And determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining the control strategy of the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed.
Further, a parameter equation of the missile system to be analyzed is established by the following method:
acquiring position information of the missile under a three-dimensional inertial coordinate, running state parameter information of the missile and parameter information of air to determine a movement linear equation of the missile;
acquiring a position vector and a speed vector of the missile, and determining an initial model equation of the missile;
determining a first reference target equation, a second reference target equation, a first target equation and a second target equation based on the motion linear equation of the missile;
determining a control force vector equation of the missile based on the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable;
and determining a parameter equation of the missile system to be analyzed based on the control force vector equation of the missile and the initial model equation of the missile.
Further, before the control strategy updating is performed based on the control strategy and the reference control strategy until the updated control strategy meets the preset control strategy updating condition and the optimal control strategy and the optimal value function method are obtained, the determining method comprises the following steps:
Acquiring a reference signal in a missile system to be analyzed, and determining an augmentation function based on a parameter equation of the missile system to be analyzed and the reference signal;
determining a value function based on the position tracking error parameter, the control quantity data, the discount factor parameter, the system parameter and the matrix parameter of the augmentation function;
and carrying out derivative operation on the value function based on the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation, so as to determine the parallel update condition of the value function and the first control strategy based on the second value function parameter equation.
Further, the determining method includes:
the optimal control strategy is determined based on the position tracking error parameter, the discount factor parameter, the system parameter, the control quantity data, and the augmentation function.
Further, the determining method further includes:
and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal value function, the optimal controller in the optimal control strategy and the system parameters.
The embodiment of the application also provides a determining device of the missile control strategy, which comprises the following steps:
The output determining module is used for determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed;
the iteration solving module is used for carrying out iteration solving based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy;
the updating module is used for updating the first control strategy by utilizing the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and then an optimal control strategy and an optimal value function are obtained;
and the control module is used for determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy so as to carry out tracking control on the missile based on the optimal control strategy, the unknown parameter matrix and a parameter equation of the missile system to be analyzed.
Further, the determining device further includes a system establishment module, where the system establishment module is configured to:
acquiring position information of the missile under a three-dimensional inertial coordinate, running state parameter information of the missile and parameter information of air to determine a movement linear equation of the missile;
Acquiring a position vector and a speed vector of the missile, and determining an initial model equation of the missile;
determining a first reference target equation, a second reference target equation, a first target equation and a second target equation based on the motion linear equation of the missile;
determining a control force vector equation of the missile based on the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable;
and determining a parameter equation of the missile system to be analyzed based on the control force vector equation of the missile and the initial model equation of the missile.
Further, the determining device includes a function determining module, where the function determining module is configured to:
acquiring a reference signal in a missile system to be analyzed, and determining an augmentation function based on a parameter equation of the missile system to be analyzed and the reference signal;
determining a value function based on the position tracking error parameter, the control quantity data, the discount factor parameter, the system parameter and the matrix parameter of the augmentation function;
and carrying out derivative operation on the value function based on the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation, so as to determine the parallel update condition of the value function and the first control strategy based on the second value function parameter equation.
The embodiment of the application also provides electronic equipment, which comprises: the system comprises a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, the processor and the memory are communicated through the bus when the electronic device runs, and the machine-readable instructions are executed by the processor to execute the steps of the method for determining the missile control strategy.
Embodiments of the present application also provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of a method of determining a missile control strategy as described above.
The application provides a determination method of missile control strategy, which comprises the following steps: determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed; performing iterative solution based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy; updating the first control strategy by using the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and obtaining an optimal control strategy and an optimal value function; and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining the control strategy of the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed.
In this way, when the control strategy of the missile system to be analyzed is determined, the nonlinearity and uncertain system parameters in the missile system are considered, and an unknown parameter matrix containing the nonlinearity and uncertain system parameters is determined through the optimal control strategy, so that the control strategy of the missile system to be analyzed is determined, and the accuracy of the missile system control to be analyzed is improved.
In order to make the above objects, features and advantages of the present application more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that other related drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for determining a missile control strategy according to an embodiment of the present application;
FIG. 2 is a diagram of missile trace tracking provided in an embodiment of the present application;
Fig. 3 is a schematic structural diagram of a missile control strategy determining device according to an embodiment of the present application;
FIG. 4 is a second schematic structural diagram of a missile control strategy determination device according to the second embodiment of the present disclosure;
fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it should be understood that the accompanying drawings in the present application are only for the purpose of illustration and description, and are not intended to limit the protection scope of the present application. In addition, it should be understood that the schematic drawings are not drawn to scale. A flowchart, as used in this application, illustrates operations implemented according to some embodiments of the present application. It should be appreciated that the operations of the flow diagrams may be implemented out of order and that steps without logical context may be performed in reverse order or concurrently. Moreover, one or more other operations may be added to the flow diagrams and one or more operations may be removed from the flow diagrams as directed by those skilled in the art.
In addition, the described embodiments are only some, but not all, of the embodiments of the present application. The components of the embodiments of the present application, which are generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, as provided in the accompanying drawings, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, are intended to be within the scope of the present application.
In order to enable those skilled in the art to make and use the present disclosure, the following embodiments are provided in connection with a particular application scenario "control algorithm technology," and it is within the purview of those skilled in the art to apply the general principles defined herein to other embodiments and applications scenario without departing from the spirit and scope of the present disclosure.
The method, apparatus, electronic device or computer readable storage medium described below in the embodiments of the present application may be applied to any scenario requiring control algorithm technology, and the embodiments of the present application do not limit specific application scenarios, and any scheme using the method and apparatus for determining a missile control policy provided in the embodiments of the present application is within the scope of protection of the present application.
According to research, in the current stage, a missile model is simplified into a linear model, and an optimal control strategy is obtained based on a plurality of optimization methods (such as a Riccati differential method and a theta-D method) and a traditional optimal control method. Since such methods simplify the system into a linear model, and the conventional optimal control method requires complete model parameter information. However, the dynamics of the missile in actual flight are strongly nonlinear, so that the method does not reach a truly optimal control strategy due to inaccuracy of a research model. Or aiming at a nonlinear model, a nonlinear control algorithm, such as a robust compensation algorithm, an H infinite control method, a synovial membrane control method and the like, is designed under the condition of considering parameter uncertainty, so that the influence of the parameter uncertainty and the like on the performance of the missile is solved. However, such methods require suppression of the effects of missile parameter uncertainty based on controlled object model information. And uncertainty (such as uncertainty of a tracking target and uncertainty of pneumatic parameters) exists in an actual missile dynamic model. It is not applicable to the case where the parameters are completely unknown and the controlled object model information is unknown.
Based on the above, the purpose of the application is to provide a determination method of a missile control strategy, when determining the control strategy of a missile system to be analyzed, nonlinear and uncertain system parameters in the missile system are considered, an unknown parameter matrix containing the nonlinear and uncertain system parameters is determined through an optimal control strategy, and the control strategy for realizing the missile system to be analyzed is determined, so that the accuracy rate of the missile system control to be analyzed is improved.
Referring to fig. 1, fig. 1 is a flowchart of a method for determining a missile control policy according to an embodiment of the present application. As shown in fig. 1, an embodiment of the present application provides a method for determining a control policy, including:
s101: and determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed.
In the step, an initial control strategy is set for the missile system to be analyzed, so that the initial control strategy performs strategy control on an initial controller, and flight error data and control quantity data of the missile system under the initial control strategy are determined.
Here, by setting upSetting an initial controller, wherein +_>Is a steady-state control quantity, u ve To explore the noise.
Here, the initial control strategy may be a strategy for controlling tracking control of the missile, and this part is not limited.
The initial controller is used for being applied to missile track tracking tasks.
S102: and carrying out iterative solution based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy.
In the step, the obtained control quantity data is subjected to iterative solution to obtain a first control strategy, and the first control strategy utilizes a Belman equation to obtain a reference value function and a reference control strategy.
Here, the first control strategy is that the control quantity data is obtained by performing iterative solution, e.g.For the control strategy updated at the nth iteration.
Here, for any oneV can be obtained by the following Belman equation n And->The bellman equation is as follows:
wherein eβt is a defined parameter, Δt is a time interval, V n For the reference value function, ep is the position tracking error parameter, Q is one of the system parameters, R is one of the system parameters,for reference control strategy->Is a steady-state control quantity, u ve To explore noise, x is the reference signal dynamics, +.>Is the first control strategy.
Here, since the reference value function is unknown, it may result in that the optimal controller cannot be directly obtained, and thus the above iterative algorithm is introduced to approach the optimal performance index and the optimal controller.
S103: and updating the first control strategy by using the reference control strategy until the updated control strategy meets the preset control strategy updating conditions, and obtaining an optimal control strategy and an optimal value function.
In the step, after the reference control strategy is obtained, the first control strategy is updated according to the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and then the optimal control strategy and the optimal value function are obtained.
Here, the update policy isSo that the reference strategy is->The value of (2) is assigned to the first control strategy +.>
Here, the preset control policy update condition is thatFirst control strategy->With reference controlIf the difference value of (2) is smaller than epsilon, stopping updating the control strategy.
Where ε > 0 is one acceptable calculation accuracy for the settings.
When the preset control updating condition is met, continuously learning and updating the optimal control parameters by using a reinforcement learning algorithm to finally obtain an optimal control strategyHere, V * As a function of the optimum value +.>And R is a system parameter, B is an unknown matrix, and an optimal control strategy is determined by using the system parameter, the unknown matrix, the optimal value function and the optimal control tracker together, so that the missile is tracked and controlled by using the optimal control strategy.
S104: and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining the control strategy of the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed.
In the step, an unknown parameter matrix in the missile system to be analyzed is determined according to the acquired optimal control strategy, then the missile is tracked and controlled according to the optimal control strategy, the unknown parameter matrix and a parameter equation of the missile system to be analyzed, so that a tracker of the optimal control strategy is learned by utilizing missile state data in combination with an optimal control algorithm, and the optimal control method for missile track tracking is realized.
Here, the unknown parameter matrix is some unknown parameters of the missile during the flight, such as dynamic unknown parameters of the missile.
Here, the parameter equation of the missile system to be analyzed is established by the following method:
a: and acquiring the position information of the missile under the three-dimensional inertial coordinates, the running state parameter information of the missile and the parameter information of air to determine a movement linear equation of the missile.
Wherein the movement of the missile in space is described by the following linear equation of movement, by treating the missile as a particle:
wherein x represents the transverse position information of the missile under the three-dimensional inertial coordinate system, y represents the longitudinal position information of the missile under the three-dimensional inertial coordinate system, z represents the position information of the missile under the three-dimensional inertial coordinate system in the direction perpendicular to the transverse coordinate and the longitudinal coordinate, V is the speed information of the missile, theta is the ballistic inclination angle of the missile, phi is the ballistic deflection angle, and m is the mass of the missile; x represents the resistance of the missile in the flying process, F X For controlling force of missile in transverse coordinate, F y For controlling force of missile in transverse coordinate, F z Is the control force of the missile in the direction perpendicular to the transverse coordinate and the longitudinal coordinate.
B: and acquiring a position vector and a speed vector of the missile, and determining an initial model equation of the missile.
Wherein F= [ F ] x F y F z ] T Representing missile control force vector, F X For controlling force of missile in transverse coordinate, F y For controlling force of missile in transverse coordinate, F z Is the control force of the missile in the direction perpendicular to the transverse coordinate and the longitudinal coordinate. In the actual flight process of the missile, the missile is launched from the ground to rise into the high altitude, and the resistance coefficient c of the missile x And the air density ρ are constantly changing and thus have a gradual change and uncertainty. The motion model of the missile has the characteristic of affine nonlinearity, and all channels are mutually coupled, so that the model is difficult to directly solve the optimal control problem, and the affine nonlinearity system feedback linearization method based on the differential geometry theory is needed to solve the problem.
In order to apply the feedback linearization method to the missile system, let p= [ x y z ]] T A position vector representing the missile,representing a missile velocity vector, wherein x represents transverse position information of the missile in a three-dimensional inertial coordinate system, y represents longitudinal position information of the missile in the three-dimensional inertial coordinate system, and z represents the transverse coordinate and longitudinal sitting of the missile in the three-dimensional inertial coordinate system Positional information in a direction perpendicular to the target.
Based on the position vector and the velocity vector of the missile, determining an initial model equation of the missile as Wherein c 3,2 ＝[0 1 0] T α (P, v) is a first reference target equation, β (P, v) is a second target reference equation, P is a position vector of the missile, and v is a velocity vector of the missile. Here, an initial model of the missile is determined using the position vector of the missile and the velocity vector of the missile.
C: and determining a first reference target equation, a second reference target equation, a first target equation and a second target equation based on the movement linear equation of the missile.
Here, the first reference target equation is:
wherein V is the speed information of the missile, θ is the ballistic inclination angle of the missile, and ψ is the ballistic deflection angle. And wherein m is the mass of the missile, ρ is the air density parameter, c x Is the drag coefficient. Here, the first reference target equation is determined using the velocity information of the missile, the ballistic tilt angle of the missile, the ballistic deflection angle, the mass of the missile, the air density parameter, and the drag coefficient.
Here, the second reference target equation is:
wherein V is the speed information of the missile, θ is the ballistic inclination angle of the missile, ψ is the ballistic deflection angle, and m is the mass of the missile, and herein, the second reference target equation is determined by using the speed information of the missile, the ballistic inclination angle of the missile, the ballistic deflection angle and the mass of the missile.
Considering that the ballistic inclination angle theta and the ballistic deflection angle phi are both measurable in the actual flight of the missile, and the drag coefficient c x The air density ρ and the mass m are uncertainty, and the uncertainty parameters are set as follows:
here, the first objective equation is:
wherein V is the speed information of the missile, θ is the ballistic inclination angle of the missile, and ψ is the ballistic deflection angle. Here, the first target equation is determined using the velocity information of the missile, the ballistic tilt angle of the missile, and the ballistic deflection angle.
Here, the second objective equation is:
wherein V is the speed information of the missile, θ is the ballistic inclination angle of the missile, and ψ is the ballistic deflection angle. Here, the second target equation is determined using the velocity information of the missile, the ballistic tilt angle of the missile, and the ballistic deflection angle.
D: and determining a control force vector equation of the missile based on the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable.
Here, the control force vector equation of the missile is determined according to the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable.
The step-by-step calculation is performed first, and the first reference target equation, the second reference target equation, the first target equation and the second target equation can be obtained according to the first reference target equation, the second reference target equation and the second target equation:
α (p, v) =σ·α' (p, v) and
then, the feedback variable is set to u v Satisfies, and then determines the control force vector equation of guided missile to be:
F＝σ·β(p，v) -1 (u y -α′(p，v))；
beta (p, v) is the second target reference equation, alpha' (p, v) is the first target equation, and sigma is the uncertainty parameter.
E: and determining a parameter equation of the missile system to be analyzed based on the control force vector equation of the missile and the initial model equation of the missile.
Substituting the obtained control force vector equation of the missile into an initial model equation of the missile, and further determining that a parameter equation of the missile system to be analyzed isWherein P is the position vector of the missile, V is the speed parameter of the missile, sigma is an indefinite parameter, u v G is a gravity constant for control amount data.
Further, the tracking control determining method includes:
a: and acquiring a reference signal in the missile system to be analyzed, and determining an augmentation function based on a parameter equation of the missile system to be analyzed and the reference signal.
Wherein, x= [ p v ] is set] T Determining according to a parameter equation of the missile system to be analyzed:
v＝Cx；
wherein A= [0 ] 6×3 c 6，1 c 6，2 c 6，3 ]，B＝[0 3×3 σI 3 ] T Y is the system state output, c= [ I 3×3 0 3×3 ]And outputting a matrix for the missile system to be analyzed.
The set reference signal dynamics are as follows:
y 0 ＝C 0 x 0 ；
Wherein x is 0 ∈R 6×1 Representing the reference signal state, A 0 ∈R 6×1 Representing the reference signal dynamic matrix. Due to determination of the missile system to be analyzedy=cx and the reference signal can be an augmentation function:
wherein, e p ∈R 6×1 representing position tracking error, +.>
b: a value function is determined based on the position tracking error parameter, the control quantity data, the discount factor parameter, the system parameter, and the matrix parameter of the augmentation function.
Wherein, the design value function is:
wherein,beta is a discount factor, P is a matrix, Q>0，R>0, Q, R are set system parameters, e p U is a position tracking error parameter v Is control quantity data.
Further, deriving the above-mentioned value function obtains equation 1:
here, β is the discount factor, P is the matrix, Q>0，R>0, Q, R are set system parameters, e p U is a position tracking error parameter v Is control quantity data.
Wherein the method comprises the steps ofSet V * As a function of the optimum value. Based on classical optimal control theory, an optimal control strategy can be obtained:
here, V * As a function of the optimum value of the function,for optimal control of the tracker, R is a system parameter, and B is an unknown matrix.
Further, it willSubstituting into equation 1 yields the hamilton equation as follows:
here, V * As a function of the optimum value of the function,for optimal control of the tracker, R is a system parameter, B is an unknown matrix, e p A=diag (a, a 0 )，Beta is the discount factor.
In practical application, the parameters of the missile part are unknownThe matrix is unknown and thus it is difficult to obtain an accurate hamiltonian equation. This makes the optimal solution obtained based on the conventional optimal control algorithm unable to maintain optimality in practice. An reinforcement learning algorithm is described below, which obtains an optimal solution according to the actual situation by using missile status information and identifies a system parameter matrix B in practice.
In order to accurately determine the optimal value of Hamiltonian, an explored steady-state control amount is added to the missile system.
c: and carrying out derivative operation on the value function based on the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation, so as to determine the parallel update condition of the value function and the first control strategy based on the second value function parameter equation.
After an explored steady-state control quantity is added into the missile system to be analyzed, the amplification system at the moment is as follows:
wherein, is a steady-state control quantity, u ve To explore noise->For the control strategy updated at the nth iteration.
And carrying out derivative operation on the value function by utilizing the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation:
Wherein V is n As a function of the reference value, e p For the position tracking error parameter, Q is one of the system parameters, R is one of the system parameters,is a steady-state control quantity, u ve To explore noise-> For the control strategy updated at the nth iteration.
Further, multiplying e at the same time at both ends of the second value function parameter equation βt And integrating to obtain a second value function parameter equation:
wherein V is n As a function of the reference value, e p For the position tracking error parameter, Q is one of the system parameters, R is one of the system parameters,is a steady-state control quantity, u ve To explore noise->For the control strategy updated at the nth iteration.
Further, the value function V can be determined according to the second value function parameter equation n And a first control strategyAnd updating simultaneously.
Further, the optimal control strategy is determined based on the position tracking error parameter, the discount factor parameter, the system parameter, the control amount data, and the augmentation function.
Here, the optimal tracking control strategy is solved using iterative learning and neural network techniques, and the optimal value function and the optimal controller can be approximated by multiple iterations of the above iterative algorithm.
Further, based on the optimal value function, an optimal controller in the optimal control strategy and system parameters, an unknown parameter matrix in the missile system to be analyzed is determined.
Here, after determining the optimal control strategy, use is made ofDetermining unknown parameter matrix->
In a specific embodiment, a missile flight simulation system is built, wherein parameters are set as follows: missile mass is m=158 kg, pneumatic parameter c x Air density ρ=0.868, missile characteristic area s=0.0324, =0.74. The value of the obtainable unknown parameter σ is σ= 6.5858 ×10 -5 . The initial position of the missile is set as follows: p= [ 250-240-250] T m. The time interval Δt=0.05s in the reinforcement learning algorithm, the matrix is set to q=50, r=i 3 . The discount factor is set to β=0.01. The optimal controller is learned through a reinforcement learning algorithm and applied to a track tracking task, and unknown parameters sigma= 6.5835 ×10 are identified by utilizing the learned optimal strategy -5 . Referring to fig. 2, fig. 2 is a missile trace tracking diagram according to an embodiment of the present application. As shown in fig. 2, it can be seen that in this embodiment, the missile position at the longitudinal position can determine that the optimal controller has good trajectory tracking performance.
The application provides a determination method of missile control strategy, which comprises the following steps: determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed; performing iterative solution based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy; updating the first control strategy by using the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and obtaining an optimal control strategy and an optimal value function; and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, so that the missile is tracked and controlled based on the optimal control strategy, the unknown parameter matrix and a parameter equation of the missile system to be analyzed.
In this way, when the control strategy of the missile system to be analyzed is determined, the nonlinearity and uncertain system parameters in the missile system are considered, and an unknown parameter matrix containing the nonlinearity and uncertain system parameters is determined through the optimal control strategy, so that the control strategy of the missile system to be analyzed is determined, and the accuracy of the missile system control to be analyzed is improved.
Referring to fig. 3 and fig. 4, fig. 3 is a schematic structural diagram of a determining device for missile control strategy according to an embodiment of the present application; FIG. 4 is a second schematic structural diagram of a missile control strategy determination device according to the second embodiment of the present disclosure; as shown in fig. 3, the determining apparatus 300 includes:
the output determining module 310 is configured to determine control quantity data of the missile system to be analyzed based on an initial control policy set by the missile system to be analyzed;
the iteration solving module 320 is configured to obtain a first control strategy by performing iteration solving based on the control quantity data, and obtain a reference value function and a reference control strategy based on the first control strategy;
the update solving module 330 is configured to update the first control policy by using the reference control policy until the updated control policy meets a preset control policy update condition, and obtain an optimal control policy and an optimal value function;
The control module 340 is configured to determine an unknown parameter matrix in the missile system to be analyzed based on the optimal control policy, and determine a control policy for the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed.
Further, as shown in fig. 4, the determining apparatus 300 further includes a system establishment module 350, where the system establishment module 350 is configured to:
acquiring position information of the missile under a three-dimensional inertial coordinate, running state parameter information of the missile and parameter information of air to determine a movement linear equation of the missile;
acquiring a position vector and a speed vector of the missile, and determining an initial model equation of the missile;
determining a first reference target equation, a second reference target equation, a first target equation and a second target equation based on the motion linear equation of the missile;
determining a control force vector equation of the missile based on the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable;
and determining a parameter equation of the missile system to be analyzed based on the control force vector equation of the missile and the initial model equation of the missile.
Further, as shown in fig. 4, the determining apparatus 300 includes a function determining module 360, where the function determining module 360 is configured to:
acquiring a reference signal in a missile system to be analyzed, and determining an augmentation function based on a parameter equation of the missile system to be analyzed and the reference signal;
determining a value function based on the position tracking error parameter, the control quantity data, the discount factor parameter, the system parameter and the matrix parameter of the augmentation function;
and carrying out derivative operation on the value function based on the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation, so as to determine the parallel update condition of the value function and the first control strategy based on the second value function parameter equation.
Further, as shown in fig. 4, the control module 340 is configured to:
the optimal control strategy is determined based on the position tracking error parameter, the discount factor parameter, the system parameter, the control quantity data, and the augmentation function.
Further, as shown in fig. 4, the update solution module 330 is configured to:
and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal value function, the optimal controller in the optimal control strategy and the system parameters.
The embodiment of the application provides a missile control strategy determining device, which comprises: the output determining module is used for determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed; the iteration solving module is used for carrying out iteration solving based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy; the updating solving module is used for updating the first control strategy by utilizing the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and then an optimal control strategy and an optimal value function are obtained; the control module is used for determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining the control strategy of the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed.
In this way, when the control strategy of the missile system to be analyzed is determined, the nonlinearity and uncertain system parameters in the missile system are considered, and an unknown parameter matrix containing the nonlinearity and uncertain system parameters is determined through the optimal control strategy, so that the control strategy of the missile system to be analyzed is determined, and the accuracy of the missile system control to be analyzed is improved.
Referring to fig. 5, fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present application. As shown in fig. 5, the electronic device 500 includes a processor 510, a memory 520, and a bus 530.
The memory 520 stores machine-readable instructions executable by the processor 510, when the electronic device 500 is running, the processor 510 communicates with the memory 520 through the bus 530, and when the machine-readable instructions are executed by the processor 510, the steps of the method for determining the missile control policy in the method embodiment shown in fig. 1 may be executed, and the specific implementation manner may refer to the method embodiment and will not be described herein.
The embodiment of the present application further provides a computer readable storage medium, where a computer program is stored on the computer readable storage medium, and when the computer program is executed by a processor, the steps of the method for determining a missile control policy in the method embodiment shown in fig. 1 may be executed, and a specific implementation manner may refer to the method embodiment and will not be described herein.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, and are not repeated herein.
In the several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods may be implemented in other manners. The above-described apparatus embodiments are merely illustrative, for example, the division of the units is merely a logical function division, and there may be other manners of division in actual implementation, and for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be through some communication interface, device or unit indirect coupling or communication connection, which may be in electrical, mechanical or other form.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in each embodiment of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer readable storage medium executable by a processor. Based on such understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Finally, it should be noted that: the foregoing examples are merely specific embodiments of the present application, and are not intended to limit the scope of the present application, but the present application is not limited thereto, and those skilled in the art will appreciate that while the foregoing examples are described in detail, the present application is not limited thereto. Any person skilled in the art may modify or easily conceive of the technical solution described in the foregoing embodiments, or make equivalent substitutions for some of the technical features within the technical scope of the disclosure of the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (6)
1. The method for determining the missile control strategy is characterized by comprising the following steps:
determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed;
performing iterative solution based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy;
updating the first control strategy by using the reference control strategy until the updated control strategy meets the preset control strategy updating conditions, and obtaining an optimal control strategy and an optimal value function;
determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining a control strategy for the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed;
and before the control strategy is updated based on the control strategy and the reference control strategy until the updated control strategy meets the preset control strategy updating conditions and the optimal control strategy and optimal value function method are obtained, the determining method comprises the following steps:
acquiring a reference signal in a missile system to be analyzed, and determining an augmentation function based on a parameter equation of the missile system to be analyzed and the reference signal;
Determining a value function based on the position tracking error parameter, the control quantity data, the discount factor parameter, the system parameter and the matrix parameter of the augmentation function;
performing derivative operation on the value function based on the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation, so as to determine the parallel update condition of the value function and the first control strategy based on the second value function parameter equation;
the determining method comprises the following steps:
determining the optimal control strategy based on the position tracking error parameter, the discount factor parameter, the system parameter, the control quantity data and the augmentation function;
the determining method further comprises the following steps:
and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal value function, the optimal controller in the optimal control strategy and the system parameters.
2. A method of determining according to claim 1, wherein the parameter equation of the missile system to be analyzed is established by:
acquiring position information of the missile under a three-dimensional inertial coordinate, running state parameter information of the missile and parameter information of air to determine a movement linear equation of the missile;
Acquiring a position vector and a speed vector of the missile, and determining an initial model equation of the missile;
determining a first reference target equation, a second reference target equation, a first target equation and a second target equation based on the motion linear equation of the missile;
determining a control force vector equation of the missile based on the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable;
and determining a parameter equation of the missile system to be analyzed based on the control force vector equation of the missile and the initial model equation of the missile.
3. A missile control strategy determination device, characterized in that the determination device comprises:
the output determining module is used for determining control quantity data of the missile system to be analyzed based on an initial control strategy set by the missile system to be analyzed;
the iteration solving module is used for carrying out iteration solving based on the control quantity data to obtain a first control strategy, and obtaining a reference value function and a reference control strategy based on the first control strategy;
the updating solving module is used for updating the first control strategy by utilizing the reference control strategy until the updated control strategy meets the preset control strategy updating condition, and then an optimal control strategy and an optimal value function are obtained;
The control module is used for determining an unknown parameter matrix in the missile system to be analyzed based on the optimal control strategy, and determining a control strategy for the missile system to be analyzed by combining a parameter equation of the missile system to be analyzed;
the determining device comprises a function determining module for:
acquiring a reference signal in a missile system to be analyzed, and determining an augmentation function based on a parameter equation of the missile system to be analyzed and the reference signal;
determining a value function based on the position tracking error parameter, the control quantity data, the discount factor parameter, the system parameter and the matrix parameter of the augmentation function;
performing derivative operation on the value function based on the exploration steady-state control quantity in the missile system to be analyzed to determine a second value function parameter equation, so as to determine the parallel update condition of the value function and the first control strategy based on the second value function parameter equation;
the control module is used for:
determining the optimal control strategy based on the position tracking error parameter, the discount factor parameter, the system parameter, the control quantity data and the augmentation function;
The update solving module is used for:
and determining an unknown parameter matrix in the missile system to be analyzed based on the optimal value function, the optimal controller in the optimal control strategy and the system parameters.
4. A determining device according to claim 3, further comprising a system set-up module for:
acquiring position information of the missile under a three-dimensional inertial coordinate, running state parameter information of the missile and parameter information of air to determine a movement linear equation of the missile;
acquiring a position vector and a speed vector of the missile, and determining an initial model equation of the missile;
determining a first reference target equation, a second reference target equation, a first target equation and a second target equation based on the motion linear equation of the missile;
determining a control force vector equation of the missile based on the first reference target equation, the second reference target equation, the first target equation, the second target equation and the state feedback variable;
and determining a parameter equation of the missile system to be analyzed based on the control force vector equation of the missile and the initial model equation of the missile.
5. An electronic device, comprising: a processor, a memory and a bus, said memory storing machine readable instructions executable by said processor, said processor and said memory communicating via said bus when the electronic device is running, said machine readable instructions when executed by said processor performing the steps of a method of determining a missile control strategy according to either of claims 1 and 2.
6. A computer-readable storage medium, on which a computer program is stored, which computer program, when being executed by a processor, performs the steps of a method of determining a missile control strategy according to any one of claims 1 and 2.
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Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5435503A (en) * | 1993-08-27 | 1995-07-25 | Loral Vought Systems Corp. | Real time missile guidance system |
| WO2008039226A2 (en) * | 2006-03-29 | 2008-04-03 | Raytheon Company | Onboard guidance method for ballistic missiles |
| CN105202972A (en) * | 2015-09-16 | 2015-12-30 | 北京理工大学 | Multi-missile cooperative engagement guidance method based on model predictive control technique |
| CN105867399A (en) * | 2016-04-18 | 2016-08-17 | 北京航天自动控制研究所 | Method for determining multi-state tracking guidance parameters |
| CN106647287A (en) * | 2017-02-20 | 2017-05-10 | 南京航空航天大学 | Method for guiding input constraining differential game based on self-adaptive dynamic planning |
| CN110456821A (en) * | 2019-08-22 | 2019-11-15 | 安徽大学 | Aerial vehicle trajectory method for optimally controlling and system based on Dynamic trigger mechanism |
| CN111442697A (en) * | 2020-02-07 | 2020-07-24 | 北京航空航天大学 | Over-emphasis guidance method and trajectory shaping guidance method based on pseudo-spectrum correction |
| CN112925203A (en) * | 2021-01-21 | 2021-06-08 | 深圳翱诺科技有限公司 | Optimal tracking control algorithm based on reinforcement learning |
| CN113325866A (en) * | 2021-05-20 | 2021-08-31 | 南京航空航天大学 | Differential game cooperative guidance method based on event triggering |
-
2021
- 2021-11-03 CN CN202111292421.2A patent/CN114020018B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5435503A (en) * | 1993-08-27 | 1995-07-25 | Loral Vought Systems Corp. | Real time missile guidance system |
| WO2008039226A2 (en) * | 2006-03-29 | 2008-04-03 | Raytheon Company | Onboard guidance method for ballistic missiles |
| CN105202972A (en) * | 2015-09-16 | 2015-12-30 | 北京理工大学 | Multi-missile cooperative engagement guidance method based on model predictive control technique |
| CN105867399A (en) * | 2016-04-18 | 2016-08-17 | 北京航天自动控制研究所 | Method for determining multi-state tracking guidance parameters |
| CN106647287A (en) * | 2017-02-20 | 2017-05-10 | 南京航空航天大学 | Method for guiding input constraining differential game based on self-adaptive dynamic planning |
| CN110456821A (en) * | 2019-08-22 | 2019-11-15 | 安徽大学 | Aerial vehicle trajectory method for optimally controlling and system based on Dynamic trigger mechanism |
| CN111442697A (en) * | 2020-02-07 | 2020-07-24 | 北京航空航天大学 | Over-emphasis guidance method and trajectory shaping guidance method based on pseudo-spectrum correction |
| CN112925203A (en) * | 2021-01-21 | 2021-06-08 | 深圳翱诺科技有限公司 | Optimal tracking control algorithm based on reinforcement learning |
| CN113325866A (en) * | 2021-05-20 | 2021-08-31 | 南京航空航天大学 | Differential game cooperative guidance method based on event triggering |
Non-Patent Citations (3)
| Title |
|---|
| Distributed Fuzzy Adaptive Backstepping Optimal Control for Nonlinear Multimissile Guidance Systems With Input Saturation;Jingliang Sun;IEEE Transactions on Fuzzy Systems;第27卷(第3期);第447-461页 * |
| 基于动态逆的复合控制导弹H∞最优输出跟踪控制;王青;兵工学报;第35卷(第4期);第552-558页 * |
| 基于推力矢量的超空泡导弹最优控制研究;杨献文;控制工程;第17卷(第S2期);第116-119页 * |
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