CN117784619B - Under-actuated unmanned ship fault-tolerant control method based on zero and differential game - Google Patents
Under-actuated unmanned ship fault-tolerant control method based on zero and differential game Download PDFInfo
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Abstract
The invention discloses an underactuated unmanned ship fault-tolerant control method based on zero and differential games, which belongs to the technical field of fault-tolerant control and comprises the following steps: s1, constructing a kinematic equation and a kinetic equation of an underactuated unmanned ship; s2, determining a first price model; s3, determining the virtual control rate of the under-actuated unmanned ship; s4, constructing a first-order filter model; s5, determining a first input signal and a second input signal; s6, generating a second cost model for both game parties of the underactuated unmanned ship; s7, determining the actual control rate of the underactuated unmanned ship by utilizing a zero and differential game algorithm, designing a virtual optimal control law by using an optimal control method based on reinforcement learning, and obtaining the minimum error and the minimum energy consumption by taking the error variable and the system state quantity of the system as cost functions through iteration.
Description
Technical Field
The invention belongs to the technical field of fault-tolerant control, and particularly relates to an underactuated unmanned ship fault-tolerant control method based on zero and differential games.
Background
Ocean occupies about 71% of the earth's surface area with abundant resources. Nowadays, with the development of technologies such as automation and artificial intelligence, unmanned systems have become a social hotspot. In the marine field, including under-actuated unmanned boats, unmanned underwater vehicles, autonomous underwater vehicles, and the like. In recent years, these systems have been widely studied in theory and practice. The under-actuated unmanned ship is widely applied and reliably operated, and has excellent capability of executing various tasks, such as monitoring marine environment, completing military tasks and the like. Therefore, the underactuated unmanned ship has extremely high research value. Aiming at the practical problem of the under-actuated unmanned ship, the under-actuated unmanned ship has the advantages of low energy consumption and simple structure by only providing control force of surge and yaw movement, so that the under-actuated unmanned ship has important practical significance in research.
The control of the existing under-actuated unmanned ship faces great challenges, and the stability of the control system is greatly influenced due to strong nonlinearity and coupling of the control method, uncertainty of model parameters, external disturbance and other uncertain factors, so that the control method applied to the under-actuated unmanned ship has the capabilities of resisting disturbance and reducing uncertain factors, and the stability and control precision of the under-actuated unmanned ship in the actual operation process are ensured. Researchers have also used many methods to address this difficulty, such as methods using neural network approximations, adaptive blurring methods, and various observers to address unknown dynamic and complex input nonlinearity issues. At present, a plurality of control theories and methods are presented for track tracking control and fault-tolerant control of the under-actuated unmanned ship. Based on the concept of convergence time and stability of the control system, the original system is converted into a new system through time-varying transformation (including state scaling, time scaling and other technologies), the uncertainty of matching/mismatching and unknown control coefficients are processed, an appropriate Liapunov inequality is constructed, and appropriate control gain is selected to prove the limitation of all closed-loop signals, particularly the limitation of control input. Whereby limited time control, fixed time control, predefined time control and prescribed time control occur. The development of under-actuated unmanned ship track tracking control is performed through the development of PID control, sliding mode control, fuzzy control and self-adaptive control, most of the control methods are based on a Liapunov function to construct a controller design, the PID control method is simple, and aiming at the adjustment of proportional, differential and integral terms in a system, the stability and convergence of the system can be realized by setting gain parameters of the three terms, but the parameter adjusting process is complex. The sliding mode control is realized by introducing errors into a designed sliding mode surface, so that the method can enable systematic errors to be converged, has strong robustness, and can be used for solving the problems of parameter uncertainty, external interference, nonlinear characteristics and the like of a system; but other methods need to be designed to address the buffeting phenomenon due to its own characteristics. The fuzzy control is a control method based on the fuzzy logic principle, and the uncertainty and the ambiguity of the system are processed by establishing a fuzzy rule, so that the control of the complex system is realized. But its fuzzy rule base design is subjective and requires a lot of expert knowledge and experience in the design of fuzzy rules.
Control methods based on reinforcement learning are currently receiving extensive attention from researchers. Optimal control is an optimization problem aimed at finding a control strategy that allows the system to achieve optimal performance under given constraints. It involves controlling the system over a period of time to achieve a particular goal. However, due to the difficulty in the solution process, numerical methods, approximation and optimization techniques are generally used, so that not only is the calculation complex but also the calculation amount is large. The reinforcement learning is combined with the optimal control method to obtain optimal control output, and the unknown complex continuous function in the process is solved through the actor-criticizer neural network structure based on the self-adaptive dynamic programming method, so that the computational complexity is greatly reduced, and the robustness is high. The unmanned ship may have a problem of equipment failure or equipment failure in actual operation, so that the fault-tolerant control problem should be considered.
Disclosure of Invention
The invention provides an under-actuated unmanned aerial vehicle fault-tolerant control method based on zero and differential games, which aims to solve the problems of low unmanned aerial vehicle robustness, poor control effect, slow response of a control system and faults and bias of an unmanned aerial vehicle actuator in the existing control algorithm in the track tracking problem of the under-actuated unmanned aerial vehicle.
The technical scheme of the invention is as follows: the fault-tolerant control method of the underactuated unmanned ship based on zero and differential game comprises the following steps:
s1, constructing a kinematic equation and a kinetic equation of an underactuated unmanned ship;
s2, determining a first price model according to a kinematic equation and a dynamics equation of the under-actuated unmanned ship;
s3, determining the virtual control rate of the underactuated unmanned ship according to the first price model;
s4, constructing a first-order filter model;
S5, determining a first input signal and a second input signal according to the failure of an actuator and the bias of the actuator of the underactuated unmanned ship based on the first-order filter model;
S6, generating a second cost model for both game parties of the underactuated unmanned ship according to the first input signal and the second input signal;
And S7, determining the actual control rate of the underactuated unmanned ship by utilizing a zero and differential game algorithm according to the second cost model.
Further, in S1, the expression of the kinematic equation of the under-actuated unmanned ship is:
；
In the method, in the process of the invention, Representing the velocity in the abscissa direction of an under-actuated unmanned ship in a fixed coordinate system of the earth,/>Representing the velocity in the ordinate direction of an underactuated unmanned ship in a fixed coordinate system of the earth,/>Representing yaw rate of under-actuated unmanned ship in earth fixed coordinate system,/>Representing the yaw angle of an underactuated unmanned ship in a fixed coordinate system of the earth,/>Representing the speed of an unmanned ship in the direction of heave,/>Representing the speed of the unmanned ship in the lateral drift direction,/>Representing the speed of the unmanned ship in the bow-swing direction;
in S1, the expression of the kinetic equation of the under-actuated unmanned ship is as follows:
；
；
In the method, in the process of the invention, Representing acceleration of unmanned ship in heave direction,/>Representing acceleration of unmanned ship in transverse floating direction,/>Representing acceleration of unmanned ship in bow-swing direction,/>The mass and the rotational inertia coefficients in the pitching direction of the unmanned ship are represented,Representing the coefficients of mass and moment of inertia in the direction of unmanned ship cross-drift,/>Representing mass and moment of inertia coefficients in the yaw direction of an unmanned ship,/>Infinite hydrodynamic damping term representing heave direction,/>Infinite hydrodynamic damping term representing lateral float direction,/>Infinite hydrodynamic damping term representing yaw direction,/>Representing control input in the direction of unmanned ship heave,/>Representing control input in the yaw direction of an unmanned boat,/>Representing external disturbance in the direction of heave experienced by unmanned vessels,/>Represents external disturbance in the direction of the lateral drift suffered by the unmanned ship,/>Representing external disturbance in the yaw direction to which the unmanned ship is subjected,/>Representing first model parameters in the direction of unmanned ship heave,/>Representing second model parameters in the direction of unmanned ship heave,/>Representing third model parameters in the direction of unmanned ship heave,/>Representing first model parameters in the direction of unmanned ship drift,/>Representing second model parameters in the direction of unmanned ship drift,/>Representing third model parameters in the unmanned ship lateral drift direction,/>Representing first model parameters in the yaw direction of an unmanned ship,/>Representing second model parameters in the yaw direction of the unmanned ship,/>Representing third model parameters in the yaw direction of the unmanned ship,/>Representing the ith model parameter in the direction of unmanned ship heave,/>Representing the ith model parameter in the unmanned ship's lateral drift direction,/>The i-th model parameter in the bow direction of the unmanned ship is represented, i represents a model parameter number, and t represents a time variable.
Further, S2 comprises the following sub-steps:
s21, determining a first error variable function, a second error variable function, a third error variable function and a fourth error variable function according to a kinematic equation and a dynamics equation of the under-actuated unmanned ship;
S22, determining a first price model according to the first error variable function, the second error variable function, the third error variable function and the fourth error variable function.
Further, in S21, the expression of the first error variable function is:
；
In the method, in the process of the invention, Error value representing the actual abscissa of the unmanned ship in the earth fixed coordinate system and the abscissa of the desired trajectory,/>Error representing the actual ordinate of the unmanned ship in the earth fixed coordinate system and the ordinate of the desired trajectory,/>Representing a desired heading angle of an unmanned ship in an earth fixed coordinate system,/>Representing the abscissa of an under-actuated unmanned ship in a fixed coordinate system of the earth,/>Representing the ordinate of the underactuated unmanned ship in the earth fixed coordinate system,/>An abscissa representing a desired trajectory in a fixed coordinate system of the earth,/>An ordinate representing a desired trajectory in the earth's fixed coordinate system;
in S21, the expression of the second error variable function is:
；
In the method, in the process of the invention, Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing the yaw angle of the under-actuated unmanned ship in the earth fixed coordinate system;
in S21, the expression of the third error variable function is:
；
In the method, in the process of the invention, Error representing actual course angular velocity and filtering course angular velocity of unmanned ship in yaw direction,/>Error representing actual speed and filtering speed of unmanned ship,/>Representing the speed of the unmanned ship in the yaw direction,/>Representing the speed of an unmanned ship in the direction of heave,/>Representing the filtered angular velocity of the unmanned ship in the yaw direction,/>Representing the unmanned ship filtering speed;
In S21, the expression of the fourth error variable function is:
；
In the method, in the process of the invention, Representing unmanned ship heading angular velocity filtering error,/>Represents the speed filtering error of the unmanned ship,Estimated value representing actual heading angular velocity of unmanned ship in yaw direction,/>An estimated value representing the actual speed of the unmanned ship;
in S22, the expression of the first price model is:
；
In the method, in the process of the invention, Representing a first cost function,/>Representing a third tariff function,/>Representing the actual course angular velocity of the unmanned ship in the yaw direction,/>Indicating the actual speed of the unmanned ship.
Further, S3 comprises the following sub-steps:
S31, determining an optimal value model according to the first price model, and determining a virtual optimal control rate function of the unmanned ship according to the optimal value model;
And S32, performing reinforcement learning on the virtual optimal control rate function of the under-actuated unmanned ship by utilizing the critic neural network and the actor neural network in sequence to obtain the virtual control rate of the under-actuated unmanned ship.
Further, in S31, the expression of the best value model is:
；
；
In the method, in the process of the invention, Representing a first optimal cost function,/>Representing a third optimal cost function,/>Representing a first cost function,/>Representing a third tariff function,/>Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing the actual course angular velocity of the unmanned ship in the yaw direction,/>Representing the optimal actual course angular velocity of the unmanned ship in the yaw direction,/>Representing the actual speed of the unmanned ship,/>The optimal actual speed of the unmanned ship is represented,Representing a first intermediate cost function,/>Third intermediate cost function,/>Representing a first positive constant,/>Representing a third positive constant,/>Representing the first bellman residual variable,/>Representing a third bellman residual variable, t representing a time variable;
in S31, the expression of the virtual optimal control rate function of the unmanned ship is:
；
In the method, in the process of the invention, Representing virtual optimal control rate of unmanned ship in bow-swing direction,/>And the virtual optimal control rate of the unmanned ship in the pitching direction is represented.
Further, in S32, the update law expression of critic neural network is:
；
In the method, in the process of the invention, Update rate of weight vector representing first critic neural network,/>Update rate of weight vector representing third critic neural network,/>Represent the learning rate of the first critic neural network,/>Represent the learning rate of the third critic neural network,/>Representing a first intermediate variable related to the angle error variable,/>Representing a first intermediate variable related to a position error variable,/>Weight vector estimator representing a first actor neural network,/>Weight vector estimator representing third actor neural network,/>Weight vector estimator representing a first critic neural network,/>Weight vector estimator representing third critic neural network,/>Representing a first positive constant,/>Representing a third positive constant,/>Derivative representing the desired heading angle of an unmanned ship in a fixed-earth coordinate system,/>Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing a bounded function,/>Representing a radial basis function of a first neural network,/>Representing a radial basis function of a third neural network, t representing a time variable;
In S32, the update law expression of actor neural network is:
；
In the method, in the process of the invention, Update rate of weight vector representing first actor neural network,/>Update rate of weight vector representing third actor neural network,/>Represent the learning rate of the first actor neural network,/>Represent the learning rate of the third actor neural network,/>Indicating the angle of the unmanned boat.
Further, in S4, the expression of the first order filter model is:
；
In the method, in the process of the invention, Representing the first parameter of the filter,/>Representing the second parameter of the filter,/>First derivative representing filtered angular velocity of unmanned ship in yaw direction,/>First derivative representing unmanned ship filtering speed,/>Representing the filtered angular velocity of the unmanned ship in the yaw direction,/>Representing unmanned ship filtering speed,/>Estimated value representing actual heading angular velocity of unmanned ship in yaw direction,/>And representing an estimate of the actual speed of the unmanned aerial vehicle.
Further, in S5, the first input signalThe expression of (2) is:
；
In the method, in the process of the invention, Representing a first failure rate in fault tolerant control,/>Representing a first intermediate variable of the system input,/>Representing a first actuator bias in fault tolerant control;
in the S5, the second input signal The expression of (2) is:
；
In the method, in the process of the invention, Representing a second failure rate in fault tolerant control,/>Representing a second intermediate variable of the system input,/>Representing a second actuator bias in fault tolerant control.
Further, in S6, the expression of the second cost model is:
；
In the method, in the process of the invention, Representing a second cost function,/>Representing a fourth cost function,/>Representing fault tolerant control first parameter,/>Representing fault tolerant control second parameter,/>Error representing actual course angular velocity and filtering course angular velocity of unmanned ship in yaw direction,/>Error representing actual speed and filtering speed of unmanned ship,/>Representing a first intermediate variable of the system input,/>Representing first actuator bias in fault tolerant control,/>Representing a second intermediate variable of the system input,/>Representing a second actuator bias in fault tolerant control.
The beneficial effects of the invention are as follows:
(1) According to the invention, a virtual optimal control law is designed by using an optimal control method based on reinforcement learning, and the minimum error and the minimum energy consumption are obtained by taking the error variable and the system state quantity of the system as cost functions through iteration;
(2) The invention uses actor-critic neural network structure based on reinforcement learning, and solves the complex nonlinear equation through strategy learning and optimal value learning;
(3) The invention uses the zero and differential game method in the game theory, takes the control signal and the actuator fault signal as the two game parties, and takes the two game parties and the system error as the components of the cost function according to the characteristics of zero sum of the total value of the two game parties, thereby further obtaining the optimal result.
Drawings
FIG. 1 is a flow chart of an under-actuated unmanned boat fault tolerance control method based on zero and differential gaming;
FIG. 2 is a trace plot of an under-actuated unmanned boat;
FIG. 3 is an under-actuated unmanned boat angle error plot;
FIG. 4 is a graph of under-actuated unmanned boat position error;
FIG. 5 is an under-actuated unmanned boat angle control input diagram;
FIG. 6 is a diagram of an under-actuated unmanned boat position control input;
FIG. 7 is an under-actuated unmanned boat angle virtual control input diagram;
FIG. 8 is a virtual control input diagram for the position of an under-actuated unmanned boat;
FIG. 9 is a graph of an under-actuated unmanned boat cost function.
Detailed Description
Embodiments of the present invention are further described below with reference to the accompanying drawings.
As shown in fig. 1, the invention provides an underactuated unmanned ship fault-tolerant control method based on zero and differential game, which comprises the following steps:
s1, constructing a kinematic equation and a kinetic equation of an underactuated unmanned ship;
s2, determining a first price model according to a kinematic equation and a dynamics equation of the under-actuated unmanned ship;
s3, determining the virtual control rate of the underactuated unmanned ship according to the first price model;
s4, constructing a first-order filter model;
S5, determining a first input signal and a second input signal according to the failure of an actuator and the bias of the actuator of the underactuated unmanned ship based on the first-order filter model;
S6, generating a second cost model for both game parties of the underactuated unmanned ship according to the first input signal and the second input signal;
And S7, determining the actual control rate of the underactuated unmanned ship by utilizing a zero and differential game algorithm according to the second cost model.
In the embodiment of the present invention, in S1, the expression of the kinematic equation of the under-actuated unmanned ship is:
；
In the method, in the process of the invention, Representing the velocity in the abscissa direction of an under-actuated unmanned ship in a fixed coordinate system of the earth,/>Representing the velocity in the ordinate direction of an underactuated unmanned ship in a fixed coordinate system of the earth,/>Representing yaw rate of under-actuated unmanned ship in earth fixed coordinate system,/>Representing the yaw angle of an underactuated unmanned ship in a fixed coordinate system of the earth,/>Representing the speed of an unmanned ship in the direction of heave,/>Representing the speed of the unmanned ship in the lateral drift direction,/>Representing the speed of the unmanned ship in the bow-swing direction;
in S1, the expression of the kinetic equation of the under-actuated unmanned ship is as follows:
；
；
In the method, in the process of the invention, Representing acceleration of unmanned ship in heave direction,/>Representing acceleration of unmanned ship in transverse floating direction,/>Representing acceleration of unmanned ship in bow-swing direction,/>The mass and the rotational inertia coefficients in the pitching direction of the unmanned ship are represented,Representing the coefficients of mass and moment of inertia in the direction of unmanned ship cross-drift,/>Representing mass and moment of inertia coefficients in the yaw direction of an unmanned ship,/>Infinite hydrodynamic damping term representing heave direction,/>Infinite hydrodynamic damping term representing lateral float direction,/>Infinite hydrodynamic damping term representing yaw direction,/>Representing control input in the direction of unmanned ship heave,/>Representing control input in the yaw direction of an unmanned boat,/>Representing external disturbance in the direction of heave experienced by unmanned vessels,/>Represents external disturbance in the direction of the lateral drift suffered by the unmanned ship,/>Representing external disturbance in the yaw direction to which the unmanned ship is subjected,/>Representing first model parameters in the direction of unmanned ship heave,/>Representing second model parameters in the direction of unmanned ship heave,/>Representing third model parameters in the direction of unmanned ship heave,/>Representing first model parameters in the direction of unmanned ship drift,/>Representing second model parameters in the direction of unmanned ship drift,/>Representing third model parameters in the unmanned ship lateral drift direction,/>Representing first model parameters in the yaw direction of an unmanned ship,/>Representing second model parameters in the yaw direction of the unmanned ship,/>Representing third model parameters in the yaw direction of the unmanned ship,/>Representing the ith model parameter in the direction of unmanned ship heave,/>Representing the ith model parameter in the unmanned ship's lateral drift direction,/>The i-th model parameter in the bow direction of the unmanned ship is represented, i represents a model parameter number, and t represents a time variable.
In an embodiment of the present invention, S2 comprises the following sub-steps:
s21, determining a first error variable function, a second error variable function, a third error variable function and a fourth error variable function according to a kinematic equation and a dynamics equation of the under-actuated unmanned ship;
S22, determining a first price model according to the first error variable function, the second error variable function, the third error variable function and the fourth error variable function.
In the embodiment of the present invention, in S21, the expression of the first error variable function is:
；
In the method, in the process of the invention, Error value representing the actual abscissa of the unmanned ship in the earth fixed coordinate system and the abscissa of the desired trajectory,/>Error representing the actual ordinate of the unmanned ship in the earth fixed coordinate system and the ordinate of the desired trajectory,/>Representing a desired heading angle of an unmanned ship in an earth fixed coordinate system,/>Representing the abscissa of an under-actuated unmanned ship in a fixed coordinate system of the earth,/>Representing the ordinate of the underactuated unmanned ship in the earth fixed coordinate system,/>An abscissa representing a desired trajectory in a fixed coordinate system of the earth,/>An ordinate representing a desired trajectory in the earth's fixed coordinate system;
in S21, the expression of the second error variable function is:
；
In the method, in the process of the invention, Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing the yaw angle of the under-actuated unmanned ship in the earth fixed coordinate system;
in S21, the expression of the third error variable function is:
；
In the method, in the process of the invention, Error representing actual course angular velocity and filtering course angular velocity of unmanned ship in yaw direction,/>Error representing actual speed and filtering speed of unmanned ship,/>Representing the speed of the unmanned ship in the yaw direction,/>Representing the speed of an unmanned ship in the direction of heave,/>Representing the filtered angular velocity of the unmanned ship in the yaw direction,/>Representing the unmanned ship filtering speed;
In S21, the expression of the fourth error variable function is:
；
In the method, in the process of the invention, Representing unmanned ship heading angular velocity filtering error,/>Represents the speed filtering error of the unmanned ship,Estimated value representing actual heading angular velocity of unmanned ship in yaw direction,/>An estimated value representing the actual speed of the unmanned ship;
in S22, the expression of the first price model is:
；
In the method, in the process of the invention, Representing a first cost function,/>Representing a third tariff function,/>Representing the actual course angular velocity of the unmanned ship in the yaw direction,/>Indicating the actual speed of the unmanned ship.
In an embodiment of the present invention, S3 comprises the following sub-steps:
S31, determining an optimal value model according to the first price model, and determining a virtual optimal control rate function of the unmanned ship according to the optimal value model;
And S32, performing reinforcement learning on the virtual optimal control rate function of the under-actuated unmanned ship by utilizing the critic neural network and the actor neural network in sequence to obtain the virtual control rate of the under-actuated unmanned ship.
In the embodiment of the present invention, in S31, the expression of the optimal value model is:
；
；
In the method, in the process of the invention, Representing a first optimal cost function,/>Representing a third optimal cost function,/>Representing a first cost function,/>Representing a third tariff function,/>Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing the actual course angular velocity of the unmanned ship in the yaw direction,/>Representing the optimal actual course angular velocity of the unmanned ship in the yaw direction,/>Representing the actual speed of the unmanned ship,/>The optimal actual speed of the unmanned ship is represented,Representing a first intermediate cost function,/>Third intermediate cost function,/>Representing a first positive constant,/>Representing a third positive constant,/>Representing the first bellman residual variable,/>Representing a third bellman residual variable, t representing a time variable;
in S31, the expression of the virtual optimal control rate function of the unmanned ship is:
；
In the method, in the process of the invention, Representing virtual optimal control rate of unmanned ship in bow-swing direction,/>And the virtual optimal control rate of the unmanned ship in the pitching direction is represented.
In the embodiment of the present invention, in S32, the update law expression of critic neural networks is:
；
In the method, in the process of the invention, Update rate of weight vector representing first critic neural network,/>Update rate of weight vector representing third critic neural network,/>Represent the learning rate of the first critic neural network,/>Represent the learning rate of the third critic neural network,/>Representing a first intermediate variable related to the angle error variable,/>Representing a first intermediate variable related to a position error variable,/>Weight vector estimator representing a first actor neural network,/>Weight vector estimator representing third actor neural network,/>Weight vector estimator representing a first critic neural network,/>Weight vector estimator representing third critic neural network,/>Representing a first positive constant,/>Representing a third positive constant,/>Derivative representing the desired heading angle of an unmanned ship in a fixed-earth coordinate system,/>Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing a bounded function,/>Representing a radial basis function of a first neural network,/>Representing a radial basis function of a third neural network, t representing a time variable;
In S32, the update law expression of actor neural network is:
；
In the method, in the process of the invention, Update rate of weight vector representing first actor neural network,/>Update rate of weight vector representing third actor neural network,/>Represent the learning rate of the first actor neural network,/>Represent the learning rate of the third actor neural network,/>Indicating the angle of the unmanned boat.
In the embodiment of the present invention, in S4, the expression of the first order filter model is:
；
In the method, in the process of the invention, Representing the first parameter of the filter,/>Representing the second parameter of the filter,/>First derivative representing filtered angular velocity of unmanned ship in yaw direction,/>First derivative representing unmanned ship filtering speed,/>Representing the filtered angular velocity of the unmanned ship in the yaw direction,/>Representing unmanned ship filtering speed,/>Estimated value representing actual heading angular velocity of unmanned ship in yaw direction,/>And representing an estimate of the actual speed of the unmanned aerial vehicle.
In the embodiment of the present invention, in S5, the first input signalThe expression of (2) is:
；
In the method, in the process of the invention, Representing a first failure rate in fault tolerant control,/>Representing a first intermediate variable of the system input,/>Representing a first actuator bias in fault tolerant control;
s5, a second input signal The expression of (2) is:
；
In the method, in the process of the invention, Representing a second failure rate in fault tolerant control,/>Representing a second intermediate variable of the system input,/>Representing a second actuator bias in fault tolerant control.
In the embodiment of the present invention, in S6, the expression of the second cost model is:
；
In the method, in the process of the invention, Representing a second cost function,/>Representing a fourth cost function,/>Representing fault tolerant control first parameter,/>Representing fault tolerant control second parameter,/>Error representing actual course angular velocity and filtering course angular velocity of unmanned ship in yaw direction,/>Error representing actual speed and filtering speed of unmanned ship,/>Representing a first intermediate variable of the system input,/>Representing first actuator bias in fault tolerant control,/>Representing a second intermediate variable of the system input,/>Representing a second actuator bias in fault tolerant control.
In order to verify the effectiveness of the present invention, numerical simulation experiments were performed using the following models, as follows.
And carrying out a numerical simulation experiment on the under-actuated unmanned ship through the selected model parameters, and verifying the effectiveness of the provided under-actuated unmanned ship fault-tolerant control method based on reinforcement learning and zero and differential game. Model parameters are shown in table 1, controller design parameters are shown in table 2, and neural network design parameters are shown in table 3.
TABLE 1
In the table 1, the contents of the components,Representing the mass and moment of inertia coefficients in the direction of unmanned ship heave,/>Representing the coefficients of mass and moment of inertia in the direction of unmanned ship cross-drift,/>Representing mass and moment of inertia coefficients in the yaw direction of an unmanned ship,/>Representing first model parameters in the direction of unmanned ship heave,/>Representing second model parameters in the direction of unmanned ship heave,/>Representing third model parameters in the direction of unmanned ship heave,/>Representing first model parameters in the direction of unmanned ship drift,/>Representing second model parameters in the direction of unmanned ship drift,/>Representing third model parameters in the unmanned ship lateral drift direction,/>Representing first model parameters in the yaw direction of an unmanned ship,/>Representing second model parameters in the yaw direction of the unmanned ship,/>Representing third model parameters in the yaw direction of the unmanned ship,/>Representing the desired speed of the unmanned ship in the direction of heave,/>Indicating the desired speed of the unmanned boat in the yaw direction.
TABLE 2
In the table 2 of the description of the present invention,Represent the learning rate of the first actor neural network,/>Represent the learning rate of the third actor neural network,/>Represent the learning rate of the first critic neural network,/>Represent the learning rate of the third critic neural network,/>Representing a first positive constant,/>Representing a second positive constant,/>Representing a third positive constant,/>Representing a fourth positive constant,/>Represent the learning rate of the second critic neural network,/>Represent the learning rate of the fourth critic neural network,/>Represent learning rate of fifth actor neural network,/>Represent learning rate of sixth actor neural network,/>Representing the first parameter of the filter,/>Representing the second parameter of the filter,/>Representing fault tolerant control first parameter,/>Representing fault tolerant control of the second parameter.
TABLE 3 Table 3
In the table 3, the contents of the components,Representing the central value of the first neural network basis function,/>Representing the central value of the basis function of the second neural network,/>Representing the central value of the basis function of the third neural network,/>Representing the central value of the basis function of the fourth neural network,/>Representing the width of the central point of the first neural network basis function,/>Representing the center point width of the second neural network basis function,/>Representing the center point width of the third neural network basis function,/>Center point width representing basis function of fourth neural network,/>Representing the neural network node distribution.
The initial position of the underactuated unmanned ship is selected as in the simulation experimentAnd the initial speeds are all 0. The desired trajectory of the under-actuated unmanned boat is set to/>And/>And the initial conditions were all 0. In Table 3/>Representing a neural network with 72 nodes, ranging from/>Similarly/>All initial weights of the neural network are 0. Wherein/>Representing initial/>, of unmanned boat in simulationCoordinate value/>Representing the initiation of an unmanned boat in a simulationCoordinate value/>Representing the initial angle of the unmanned ship in the simulation,/>Representing unmanned boat/>First derivative of coordinates,/>Representing the desired speed in the direction of unmanned ship heave,/>Representing the desired speed in the direction of unmanned ship heave,/>Representing simulation time,/>Representing unmanned boat/>First derivative of coordinates,/>Representing the desired speed in the yaw direction of an unmanned boat,/>And (3) representing equipartition calculation, and B representing node distribution of the neural network.
Simulation of actuator failure in simulation experiments is as follows:
Case 1: ，/>，/>，/>，/>；
case 2: ，/>，/>，/>，/>；
case 3: ，/>，/>，/>，/>；
Case 4: ，/>，/>，/>，/>。
wherein, Representing a first failure rate in fault tolerant control,/>Representing a second failure rate in the fault tolerant control,Representing first actuator bias in fault tolerant control,/>Representing a second actuator bias in fault tolerant control.
The simulation results are shown in fig. 2-9. FIG. 2 is a trace diagram of the control method according to the present invention, which can be seen inThe position can track the expected track well, the unmanned ship position is basically overlapped with the expected track position in the subsequent control process, and the tracking effect is good. FIG. 3 is an error value of the actual course angle of the unmanned aerial vehicle and the course angle in the desired trajectory during control, the error being at/>Convergence is accomplished and the error stabilizes around 0 and the curve has no significant jitter. Fig. 4 shows the error values of the actual position of the unmanned ship and the position in the desired track during the control process, and the error values finally converge to about 0.5m during the simulation process. Fig. 5 shows the variation of the controller 1 under the fault experienced in the simulation, and it can be seen that the controller 1 is dithered at both 80s and 85s, and the controller 1 adjusts and recovers to a stable value with time 0.2s and 2s, respectively, due to the influence of the actuator fault and the compensation function in the control method. Fig. 6 shows the variation of the control 2 in the case of a partial failure of the actuator, which is set at 60s, it being possible to see in fig. 6 that there is a significant fluctuation at 60s, but that it is very fast and stable. Fig. 7 and 8 are graphs of the change in virtual control rate during simulation, where both the simulation process is substantially converged and there is no apparent jitter. FIG. 9 is a graph of the total cost function during the simulation process, where the cost function eventually converges around 35, and the convergence can be completed for about 3s, and the value of the total cost function is small. The experimental result well shows that the proposed under-actuated unmanned ship fault tolerance method based on reinforcement learning and zero and differential game optimal control has good robustness and accuracy, high convergence speed, good neural network fitting effect and good effect of coping with actuator faults. /(I)
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (4)
1. The fault-tolerant control method of the underactuated unmanned ship based on zero and differential game is characterized by comprising the following steps of:
s1, constructing a kinematic equation and a kinetic equation of an underactuated unmanned ship;
s2, determining a first price model according to a kinematic equation and a dynamics equation of the under-actuated unmanned ship;
s3, determining the virtual control rate of the underactuated unmanned ship according to the first price model;
s4, constructing a first-order filter model;
S5, determining a first input signal and a second input signal according to the failure of an actuator and the bias of the actuator of the underactuated unmanned ship based on the first-order filter model;
S6, generating a second cost model for both game parties of the underactuated unmanned ship according to the first input signal and the second input signal;
s7, determining the actual control rate of the underactuated unmanned ship by utilizing a zero and differential game algorithm according to the second cost model;
in the step S1, the expression of the kinematic equation of the under-actuated unmanned ship is as follows:
；
In the method, in the process of the invention, Representing the velocity in the abscissa direction of an under-actuated unmanned ship in a fixed coordinate system of the earth,/>Representing the velocity in the ordinate direction of an underactuated unmanned ship in a fixed coordinate system of the earth,/>Representing yaw rate of under-actuated unmanned ship in earth fixed coordinate system,/>Representing the yaw angle of an underactuated unmanned ship in a fixed coordinate system of the earth,/>Representing the speed of an unmanned ship in the direction of heave,/>Representing the speed of the unmanned ship in the lateral drift direction,/>Representing the speed of the unmanned ship in the bow-swing direction;
In the step S1, the expression of the kinetic equation of the under-actuated unmanned ship is as follows:
；
；
In the method, in the process of the invention, Representing acceleration of unmanned ship in heave direction,/>Representing acceleration of unmanned ship in transverse floating direction,/>Representing acceleration of unmanned ship in bow-swing direction,/>Representing the mass and moment of inertia coefficients in the direction of unmanned ship heave,/>Representing the coefficients of mass and moment of inertia in the direction of unmanned ship cross-drift,/>The mass and the rotational inertia coefficients in the bow direction of the unmanned ship are represented,Infinite hydrodynamic damping term representing heave direction,/>Infinite hydrodynamic damping term representing lateral float direction,/>Infinite hydrodynamic damping term representing yaw direction,/>Representing control input in the direction of unmanned ship heave,/>Representing control input in the yaw direction of an unmanned boat,/>Representing external disturbance in the direction of heave experienced by unmanned vessels,/>Represents external disturbance in the direction of the lateral drift suffered by the unmanned ship,/>Representing external disturbance in the yaw direction to which the unmanned ship is subjected,/>Representing first model parameters in the direction of unmanned ship heave,/>Representing second model parameters in the direction of unmanned ship heave,/>Representing third model parameters in the direction of unmanned ship heave,/>Representing first model parameters in the direction of unmanned ship drift,/>Representing second model parameters in the direction of unmanned ship drift,/>Representing third model parameters in the unmanned ship lateral drift direction,/>Representing first model parameters in the yaw direction of an unmanned ship,/>Representing second model parameters in the yaw direction of the unmanned ship,/>Representing third model parameters in the yaw direction of the unmanned ship,/>Representing the ith model parameter in the direction of unmanned ship heave,/>Representing the ith model parameter in the unmanned ship's lateral drift direction,/>The method comprises the steps of representing an ith model parameter in the bow direction of the unmanned ship, wherein i represents a model parameter number, and t represents a time variable;
The step S2 comprises the following substeps:
s21, determining a first error variable function, a second error variable function, a third error variable function and a fourth error variable function according to a kinematic equation and a dynamics equation of the under-actuated unmanned ship;
S22, determining a first price model according to the first error variable function, the second error variable function, the third error variable function and the fourth error variable function;
the step S3 comprises the following substeps:
S31, determining an optimal value model according to the first price model, and determining a virtual optimal control rate function of the unmanned ship according to the optimal value model;
S32, performing reinforcement learning on the virtual optimal control rate function of the under-actuated unmanned ship by utilizing the critic neural network and the actor neural network in sequence to obtain the virtual control rate of the under-actuated unmanned ship;
In the S4, the expression of the first-order filter model is:
；
In the method, in the process of the invention, Representing the first parameter of the filter,/>Representing the second parameter of the filter,/>First derivative representing filtered angular velocity of unmanned ship in yaw direction,/>First derivative representing unmanned ship filtering speed,/>Representing the filtered angular velocity of the unmanned ship in the yaw direction,/>Representing unmanned ship filtering speed,/>Estimated value representing actual heading angular velocity of unmanned ship in yaw direction,/>An estimated value representing the actual speed of the unmanned ship;
In the S5, a first input signal The expression of (2) is:
；
In the method, in the process of the invention, Representing a first failure rate in fault tolerant control,/>Representing a first intermediate variable of the system input,/>Representing a first actuator bias in fault tolerant control;
in the S5, the second input signal The expression of (2) is:
；
In the method, in the process of the invention, Representing a second failure rate in fault tolerant control,/>Representing a second intermediate variable of the system input,/>Representing a second actuator bias in fault tolerant control;
In the step S6, the expression of the second cost model is:
；
In the method, in the process of the invention, Representing a second cost function,/>Representing a fourth cost function,/>Representing fault tolerant control first parameter,/>Representing fault tolerant control second parameter,/>Error representing actual course angular velocity and filtering course angular velocity of unmanned ship in yaw direction,/>Error representing actual speed and filtering speed of unmanned ship,/>Representing a first intermediate variable of the system input,/>Representing first actuator bias in fault tolerant control,/>Representing a second intermediate variable of the system input,/>Representing a second actuator bias in fault tolerant control.
2. The fault-tolerant control method for an under-actuated unmanned ship based on zero and differential gaming according to claim 1, wherein in S21, the expression of the first error variable function is:
；
In the method, in the process of the invention, Error values representing the actual abscissa of the unmanned aerial vehicle in the earth's fixed coordinate system and the abscissa of the desired trajectory,Error representing the actual ordinate of the unmanned ship in the earth fixed coordinate system and the ordinate of the desired trajectory,/>Representing a desired heading angle of an unmanned ship in an earth fixed coordinate system,/>Representing the abscissa of the under-actuated unmanned ship in the earth's fixed coordinate system,Representing the ordinate of the underactuated unmanned ship in the earth fixed coordinate system,/>An abscissa representing a desired trajectory in a fixed coordinate system of the earth,/>An ordinate representing a desired trajectory in the earth's fixed coordinate system;
In S21, the expression of the second error variable function is:
；
In the method, in the process of the invention, Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing the yaw angle of the under-actuated unmanned ship in the earth fixed coordinate system;
In S21, the expression of the third error variable function is:
；
In the method, in the process of the invention, Error representing actual course angular velocity and filtering course angular velocity of unmanned ship in yaw direction,/>Error representing actual speed and filtering speed of unmanned ship,/>Representing the speed of the unmanned ship in the yaw direction,/>Representing the speed of an unmanned ship in the direction of heave,/>Representing the filtered angular velocity of the unmanned ship in the yaw direction,/>Representing the unmanned ship filtering speed;
In S21, the expression of the fourth error variable function is:
；
In the method, in the process of the invention, Representing unmanned ship heading angular velocity filtering error,/>Representing unmanned ship speed filtering error,/>Estimated value representing actual heading angular velocity of unmanned ship in yaw direction,/>An estimated value representing the actual speed of the unmanned ship;
In S22, the expression of the first price model is:
；
In the method, in the process of the invention, Representing a first cost function,/>Representing a third tariff function,/>Representing the actual course angular velocity of the unmanned ship in the yaw direction,/>Indicating the actual speed of the unmanned ship.
3. The fault-tolerant control method for an under-actuated unmanned ship based on zero and differential gaming according to claim 1, wherein in S31, the expression of the optimal value model is:
；
；
In the method, in the process of the invention, Representing a first optimal cost function,/>Representing a third optimal cost function,/>The first cost function is represented by a first cost function,Representing a third tariff function,/>Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing the actual course angular velocity of the unmanned ship in the yaw direction,/>Representing the optimal actual course angular velocity of the unmanned ship in the yaw direction,/>Representing the actual speed of the unmanned ship,/>Representing the optimal actual speed of the unmanned ship,/>Representing a first intermediate cost function,/>Third intermediate cost function,/>Representing a first positive constant,/>A third positive constant is indicated and is used to indicate,Representing the first bellman residual variable,/>Representing a third bellman residual variable, t representing a time variable;
in S31, the expression of the virtual optimal control rate function of the unmanned ship is:
；
In the method, in the process of the invention, Representing virtual optimal control rate of unmanned ship in bow-swing direction,/>And the virtual optimal control rate of the unmanned ship in the pitching direction is represented.
4. The fault-tolerant control method for an under-actuated unmanned ship based on zero and differential gaming according to claim 1, wherein in S32, the update law expression of critic neural network is:
；
In the method, in the process of the invention, Update rate of weight vector representing first critic neural network,/>Update rate of weight vector representing third critic neural network,/>Represent the learning rate of the first critic neural network,/>Represent the learning rate of the third critic neural network,/>Representing a first intermediate variable related to the angle error variable,/>Representing a first intermediate variable related to a position error variable,/>Weight vector estimator representing a first actor neural network,/>Weight vector estimator representing third actor neural network,/>Weight vector estimator representing a first critic neural network,/>Weight vector estimator representing third critic neural network,/>Representing a first positive constant,/>Representing a third positive constant,/>Derivative representing the desired heading angle of an unmanned ship in a fixed-earth coordinate system,/>Error representing actual course angle and expected course angle of unmanned ship in yaw direction,/>Error representing actual position and expected position of unmanned ship,/>Representing a bounded function,/>Representing a radial basis function of a first neural network,/>Representing a radial basis function of a third neural network, t representing a time variable;
in S32, the update law expression of actor neural network is:
；
In the method, in the process of the invention, Update rate of weight vector representing first actor neural network,/>Update rate of weight vector representing third actor neural network,/>Represent the learning rate of the first actor neural network,/>Represent the learning rate of the third actor neural network,/>Indicating the angle of the unmanned boat.
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