Thruster control method and system based on high-order iterative learning of forgetting factor

Abstract

The present invention belongs to the field of trajectory tracking control, and provides a thruster control method and system based on forgetting factor high-order iterative learning. The method constructs a forgetting factor fractional-order high-order iterative learning controller according to the error information between the thruster system output and the expected trajectory, the forgetting factor, and the corresponding fractional-order transformation; the expected trajectory of the thruster system is preset, the operation dynamics model of the thruster system is initialized, the forgetting factor fractional-order high-order iterative learning controller is adjusted according to the convergence condition, the controller acts on the thruster system, and the actual operation trajectory of the thruster system is obtained; it is judged whether the actual operation trajectory of the thruster system meets the expected trajectory, if so, the expected actual motion trajectory is obtained, otherwise, according to the error between the actual operation trajectory and the expected trajectory, the controller is corrected after fractional-order calculus transformation. The convergence speed is improved, the external disturbance is eliminated, and the marine robot can quickly achieve the trajectory tracking task.

Description

Technical Field

[0001] The present invention belongs to the field of trajectory tracking control, and in particular relates to a thruster control method and system based on forgetting factor high-order iterative learning. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] The working environment of marine robots is complex and changeable, and the system is a typical highly nonlinear, strongly coupled kinematic and dynamic system. Its high-precision control problem has always been a hot topic in the field of control research. At present, the precise control methods for marine robot trajectory tracking include sliding mode control, robust control, integer-order learning control, etc. However, both sliding mode control and robust control are based on model control, and it is difficult to accurately model the system in a complex environment during the actual operation of the marine robot; integer-order iterative learning control has few controllable parameters and cannot achieve rapid and accurate results.

[0004] Fractional-order iterative learning control not only has the advantages of integer-order iterative learning control, which is very simple and requires less prior knowledge, but also increases the control of parameters, so it has been widely studied and applied. Existing control methods can achieve the robot's complete tracking of the desired trajectory. However, when the system requires to improve the convergence speed and quickly achieve the accuracy of trajectory tracking control, the existing methods have poor adaptability and cannot meet the requirements; on the other hand, the existing learning control methods are all single-order algorithms, which cannot fully and completely utilize previous information multiple times, making the stability and adaptability of the controller weak.

[0005] The inventors found that the current solution has the following technical problems:

[0006] Although the invention patent with publication number CN106393116A can perform trajectory tracking, it directly obtains the actual motion trajectory based on the motion model and cannot fully consider the external impact of the underwater environment on the system. There will be a large difference between it and the actual motion model, and it cannot accurately describe the motion trajectory of the marine robot thruster.

[0007] In addition, when the system becomes a complex nonlinear system and there are external disturbances, the time-delay trajectory tracking control method of the linear system is still used to obtain the actual motion trajectory, which will result in divergent time effects and make it impossible to effectively track the trajectory. Summary of the invention

[0008] In order to solve at least one technical problem existing in the above-mentioned background technology, the present invention provides a thruster control method and system based on forgetting factor high-order iterative learning, which realizes effective tracking of the trajectory by designing a forgetting factor fractional-order high-order iterative learning controller in order to solve the problem that the system becomes a complex nonlinear system and there are external disturbances.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

[0010] A first aspect of the present invention provides a thruster control method based on high-order iterative learning of forgetting factors, comprising the following steps:

[0011] Taking the propeller as the motion control object, the operation dynamics model of the propeller system is constructed based on the coordinate system and the characteristics of the propeller;

[0012] The desired trajectory of the propulsion system is preset, and a forgetting factor fractional-order high-order iterative learning controller is constructed according to the error information between the output of the propulsion system and the desired trajectory, the forgetting factor, and the corresponding fractional-order transformation;

[0013] Initialize the operation dynamics model of the propulsion system, adjust the forgetting factor fractional high-order iterative learning controller according to the convergence condition, and use the controller to act on the propulsion system to obtain the actual operation trajectory of the propulsion system;

[0014] Determine whether the actual running trajectory of the thruster system meets the expected trajectory. If so, obtain the expected actual motion trajectory. Otherwise, according to the error between the actual running trajectory and the expected trajectory, correct the controller through fractional calculus transformation until the trajectory tracking of the thruster system is completed.

[0015] A second aspect of the present invention provides a thruster control system based on high-order iterative learning of forgetting factors, comprising:

[0016] The dynamic model construction is configured as follows: taking the propeller as the motion control object, and constructing the operation dynamic model of the propeller system based on the coordinate system and the characteristics of the propeller;

[0017] The controller structure is configured to: preset a desired trajectory of the propulsion system, and construct a forgetting factor fractional-order high-order iterative learning controller according to error information between the propulsion system output and the desired trajectory, a forgetting factor, and a corresponding fractional-order transformation;

[0018] The actual operation trajectory acquisition module is configured to: initialize the operation dynamics model of the propulsion system, adjust the forgetting factor fractional high-order iterative learning controller according to the convergence condition, and act on the propulsion system through the controller to obtain the actual operation trajectory of the propulsion system;

[0019] Determine whether the actual running trajectory of the thruster system meets the expected trajectory. If so, obtain the expected actual motion trajectory. Otherwise, according to the error between the actual running trajectory and the expected trajectory, correct the controller through fractional calculus transformation until the trajectory tracking of the thruster system is completed.

[0020] A third aspect of the present invention provides a computer-readable storage medium.

[0021] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the thruster control method based on high-order iterative learning of forgetting factors as described above.

[0022] A fourth aspect of the present invention provides a computer device.

[0023] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the thruster control method based on high-order iterative learning of forgetting factors as described above are implemented.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] In order to solve the problem that the prior art directly obtains the actual motion trajectory based on the motion model and cannot fully consider the external influence of the underwater environment on the system, there will be a large difference between the actual motion model and the motion trajectory of the marine robot propeller, the motion trajectory of the propeller is obtained by constructing a forgetting factor fractional-order high-order iterative learning controller, the current error information is used in the controller, and the previous data information and adjustable parameter variables are added to ensure the convergence of the system, eliminate the influence of the marine environment disturbance on the system, and make the control law of the controller have better stability and adaptability.

[0026] The present invention effectively utilizes the unique advantage of the forgetting factor fractional-order high-order iterative learning law in regulating the monotonic convergence of tracking learning over traditional iterative learning. In addition, it increases the number of error information and adjustable parameters, improves the convergence speed, eliminates external disturbances, and enables the marine robot to quickly achieve trajectory tracking tasks.

[0027] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0029] Figure 1 It is a flow chart of a design method of a forgetting factor fractional-order high-order iterative learning law controller for a marine robot according to the present invention;

[0030] Figure 2 A coordinate system representing the underwater motion of the marine robot;

[0031] Figure 3 This is a flow chart of the forgetting factor fractional-order high-order iterative learning control principle of the present invention;

[0032] Figure 4 It is the curve of the marine robot trajectory tracking error as the number of iterations increases;

[0033] Figure 5(a) and Figure 5(b) are the trajectory tracking results of the marine robot after 15 iterations. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0035] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0036] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0037] As mentioned in the background technology, when the system becomes a complex nonlinear system and there are external disturbances, the time-delay trajectory tracking control method of the linear system is still used to obtain the actual motion trajectory, which will lead to divergence time and thus the inability to complete effective trajectory tracking. The present invention provides a marine robot thruster control method and system based on forgetting factor fractional-order high-order iterative learning, which uses all current and previous error information and the forgetting factor to adjust the control of the marine robot thruster to achieve precise tracking and enhance adaptive capabilities.

[0038] Embodiment 1

[0039] like Figure 1 As shown, this embodiment provides a thruster control method based on high-order iterative learning of forgetting factors, comprising the following steps:

[0040] Step 1: Taking the propeller as the motion control object, the operation dynamics model of the propeller system is constructed based on the coordinate system and the characteristics of the propeller;

[0041] Step 2: preset the desired trajectory of the propulsion system, and construct a forgetting factor fractional-order high-order iterative learning controller based on the error information between the output of the propulsion system and the desired trajectory, the forgetting factor, and the corresponding fractional-order transformation;

[0042] Step 3: Initialize the input of the operation dynamics model of the propulsion system, adjust the control law of the forgetting factor fractional high-order iterative learning controller according to the convergence condition, apply the control law to the propulsion system, and obtain the actual operation trajectory of the propulsion system;

[0043] Step 4: Determine whether the actual running trajectory of the propulsion system meets the expected trajectory. If so, obtain the expected actual motion trajectory. Otherwise, according to the error between the actual running trajectory and the expected trajectory, correct the forgetting factor fractional-order high-order iterative learning controller through fractional-order calculus transformation until the trajectory tracking of the propulsion system is completed.

[0044] In order to more clearly understand the technical solution of the present invention, this embodiment is explained by taking a marine robot as an example. The marine robot moves through water. Compared with ground movement, it also needs to consider the influence of external environmental factors such as buoyancy, gravity and resistance. A suitable thruster can be selected based on the constructed coordinate system and the dynamic equation of the thruster. Therefore, the marine robot thruster can be selected as the motion analysis object under the coordinates of the system.

[0045] Step 1: The coordinate system includes a fixed coordinate system and a moving coordinate system. The coast fixed point is used as the fixed coordinate system, and the propeller mass point is used as the moving coordinate system to construct the operation dynamics model of the propeller system;

[0046] The dynamic model of a 6-DOF rigid-body marine robot is constructed, with 3 directions of axial motion and 3 degrees of freedom of axis rotation. The dynamic model of the 6-DOF marine robot is obtained by the Lagrange-Euler method as follows:

[0047]

[0048] In the formula, represents the position and posture vector of the marine robot in a fixed coordinate system; ν = [uv ω pqr] T represents the linear velocity and angular velocity vector of the robot in the motion coordinate system; J(η) represents the transformation matrix; M represents the inertia matrix; C(ν) represents the Coriolis centripetal moment; D(ν) represents the fluid resistance torque; g(η) represents the force matrix under the combined action of gravity and buoyancy; τ represents the torque vector generated by the propeller of the marine robot, Represents the position velocity vector of the marine robot in a fixed coordinate system.

[0049] The marine robot moves with 6 degrees of freedom underwater, and its movement mode can be regarded as simple free movement, and the coupling between the degrees of freedom is small. The corresponding dynamic motion characteristics are obtained by using the Jacobian matrix and Lagrange formula in the frame coordinate system. The kinematic and dynamic characteristics of the marine robot can be accurately obtained in the constructed coordinate system, which provides a guarantee for the design of the propulsion controller.

[0050] like Figure 3 As shown, step 2: preset the desired trajectory y of the propulsion system d (t), a forgetting factor fractional-order high-order iterative learning controller is constructed based on the error information between the propulsion system output and the expected trajectory, the forgetting factor and the corresponding fractional-order transformation. Specifically, the current input of the propulsion system is equal to γ ​​times the initial input, (1-γ) times the input at the previous moment and the sum of all the learning terms after the fractional-order transformation of the previous tracking error; where the tracking error is the difference between the current position of the propulsion system and the expected motion trajectory of the preset marine robot propulsion system, and the tracking error learning term is equal to the sum of the α-order fractional differentials of the tracking error K d times;

[0051] Therefore, the expression of the constructed controller is:

[0052]

[0053] Among them, u k (t) is the current input of the marine robot propeller; u0(t) is the initial input of the marine robot propeller; u k-1 (t) is the input of the marine robot propulsion system at the previous moment; e k (t) = y d (t)-y k (t) is the tracking error, which is the difference between the current position of the marine robot propeller and the expected motion trajectory of the marine robot propeller, and the tracking error learning term is equal to the sum of the α-order fractional differentials of the tracking error K d times; α and K d are all parameters of the fractional-order high-order iterative learning control law, α∈(0,1), K d is any positive number, γ is the forgetting factor, satisfying γ∈[0,1];

[0054] In order to achieve precise control of the marine robot and eliminate the impact of marine environmental disturbances on the system, a forgetting factor fractional-order high-order iterative learning controller was constructed based on the error information of the thruster control output, the forgetting factor and the corresponding fractional-order transformation.

[0055] Step 3: Initialize the input u0(t) of the propulsion system's operating dynamics model, the initialization state vector η0(t), v0(t) and the parameters of the forgetting factor fractional high-order iterative learning controller;

[0056] In the specific implementation process, the data acquisition device can be used to obtain the actual motion trajectory of the marine robot. k (t) and then transferred to the robot thruster.

[0057] The feasibility of the control law of the forgetting factor fractional-order high-order iterative learning controller is verified, and the system convergence of the proposed method is verified.

[0058] If the system satisfies the condition ||(1-γ)IK d ∑ρ k ||<1, where I is the identity matrix, sup represents the upper limit of the value, g(η) represents the force matrix under the combined action of gravity and buoyancy, ξ is the coefficient of [0,1], λ is the (0,+∞) parameter, and T is the iteration cycle. The designed controller is effective. ξ=||(1-γ)IK d ∑ρ k ||<1, the smaller ξ is, the faster the control convergence speed is and the better the effect is.

[0059] In step 4, the error between the actual motion trajectory and the expected motion trajectory of the marine robot propeller is collected and calculated, and the controller control input is corrected through fractional calculus transformation to obtain a new output. After repeated learning iterations, the influence of the marine environment on the system is gradually eliminated, and finally the trajectory of the marine robot is accurately controlled.

[0060] Simulation verification:

[0061] like Figure 2 As shown, two coordinate systems are established according to the right-hand rule: the static coordinate system (E-XYZ) and the dynamic coordinate system (OX'Y'Z'). Taking the motion of the ROV underwater robot as an example, the hydrodynamic loss term D(v) = 0 and the external interference force are not considered. The center of gravity is the same as the origin of the dynamic coordinate system, there is no heel or pitch, and the center of buoyancy coincides with the center of gravity. The coefficient matrices corresponding to the underwater robot motion system (1) are:

[0062]

[0063]

[0064]

[0065] M=diag{m+m u m+m v m+mω I x +m p I y +m q I z +m r};

[0066]

[0067]

[0068] τ=τ1+τ2

[0069]

[0070] Among them, m = 4kg is the mass of the robot, m u 、m v 、m w are the additional masses generated in the direction of the moving coordinate axis; m p 、m q 、m r are the additional masses generated along the rotation direction of the moving coordinate axis, which can be regarded as 0 for the convenience of calculation; I * is the unit matrix, B is the buoyancy of the marine robot, G is the gravity, which can be set as B = G; x b ,y b 、z b is the buoyancy center coordinate of the underwater robot, which coincides with the center coordinate as the coordinate origin [0 0 0]; ρ is the water density; Cd is the dimensionless resistance coefficient set to 1; S X' , S Y '、S Z' are the cross-sectional areas of the underwater robot perpendicular to the X', Y', and Z' axes respectively; (u r 、v r 、w r ) is the velocity of the water flow relative to the robot, 0.1 m / s; (K X' , K Y' , K Z' ) is the resistance torque coefficient 0.1. Ti is the thrust generated by the ith thruster, R Ti is the vertical distance between the ith thruster and the coordinate axis parallel to it.

[0071] In the time interval [0, 1], the ROV marine robot runs from point (0 0 0) in the xoy plane, the parameters in the z-axis direction are all 0, the expected trajectories in the x and y directions are x(t) = 2sin(4πt)cos(2πt) and y(t) = 2sin(4πt)cos(πt), and the initial error of the system is 0; the environmental disturbance is based on the convergence condition of the designed controller, and the learning gain in the learning control algorithm is selected as γ = 0.1; α = 0.6; K d =1.

[0072] from Figure 4 It can be seen that as the number of iterations increases, the outputs in both directions tend to the expected trajectory. Figure 4 is the position tracking error in the x (error 1) and y (error 2) directions, and tends to 0; FIG5(a) and FIG5(b) are the tracking effect diagrams of the 15th iteration in the x and y directions, respectively. It can be seen from FIG5(a) and FIG5(b) that the controller designed by the present invention has better control performance.

[0073] Embodiment 2

[0074] This embodiment provides a thruster control system based on high-order iterative learning of forgetting factors, including:

[0075] The dynamic model building module is configured to: take the propeller as the motion control object and build an operation dynamic model of the propeller system based on the coordinate system and the characteristics of the propeller;

[0076] The controller construction module is configured to: preset a desired trajectory of the propulsion system, and construct a forgetting factor fractional-order high-order iterative learning controller according to error information between the propulsion system output and the desired trajectory, a forgetting factor, and a corresponding fractional-order transformation;

[0077] The actual operation trajectory acquisition module is configured to: initialize the operation dynamics model of the propulsion system, adjust the forgetting factor fractional high-order iterative learning controller according to the convergence condition, and act on the propulsion system through the controller to obtain the actual operation trajectory of the propulsion system;

[0078] It is determined whether the actual running trajectory of the thruster system meets the expected trajectory. If so, the expected actual motion trajectory is obtained. Otherwise, the controller is corrected after fractional calculus transformation according to the error between the actual running trajectory and the expected trajectory.

[0079] Embodiment 3

[0080] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps in the thruster control method based on high-order iterative learning of forgetting factors as described above are implemented.

[0081] Embodiment 4

[0082] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the thruster control method based on high-order iterative learning of forgetting factors as described above are implemented.

[0083] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.

[0084] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0085] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0086] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0087] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A propeller control method based on high-order iterative learning of forgetting factors, characterized in that: The steps include: Taking the propeller as the motion control object, the operation dynamics model of the propeller system is constructed based on the coordinate system and the characteristics of the propeller; The desired trajectory of the propulsion system is preset, and a forgetting factor fractional-order high-order iterative learning controller is constructed according to the error information between the output of the propulsion system and the desired trajectory, the forgetting factor, and the corresponding fractional-order transformation; Initialize the operation dynamics model of the propulsion system, adjust the forgetting factor fractional high-order iterative learning controller according to the convergence condition, and use the controller to act on the propulsion system to obtain the actual operation trajectory of the propulsion system; Determine whether the actual running trajectory of the propulsion system meets the expected trajectory. If so, obtain the expected actual motion trajectory. Otherwise, according to the error between the actual running trajectory and the expected trajectory, correct the controller through fractional calculus transformation until the trajectory tracking of the propulsion system is completed. The forgetting factor fractional high-order iterative learning controller includes three parts: The current input of the error information booster is equal to γ ​​times the initial input, (1-γ) times the input at the previous moment, and the sum of all previous tracking error fractional order transformation learning terms, where the tracking error learning term is equal to the sum of the α-fold fractional order differentials of the tracking error K d times.

2. The thruster control method based on forgetting factor high-order iterative learning as claimed in claim 1, characterized in that: The expression of the operation dynamics model of the thruster system is: Wherein, η represents the robot position posture vector in the fixed coordinate system; ν represents the linear velocity and angular velocity vector of the robot in the moving coordinate system; J(η) represents the transformation matrix; M represents the inertia matrix; C(ν) represents the Coriolis centripetal moment; D(ν) represents the fluid resistance moment; g(η) represents the force matrix under the combined action of gravity and buoyancy; τ represents the torque vector generated by the robot thruster.

3. The thruster control method based on forgetting factor high-order iterative learning as claimed in claim 1, characterized in that: The convergence condition is specifically: If the system satisfies the condition ||(1-γ)IK d ∑ρ k ||<1, where I is the identity matrix, sup represents the upper limit of the value, g(η) represents the force matrix under the combined action of gravity and buoyancy, ξ is the coefficient of [0,1], λ is the (0,+∞) parameter, and T is the iteration period. The designed controller is effective.

4. The thruster control method based on forgetting factor high-order iterative learning as claimed in claim 1, characterized in that: The coordinate system includes a fixed coordinate system and a moving coordinate system, with the coast fixed point as the fixed coordinate system and the propeller particle as the moving coordinate system.

5. The thruster control method based on forgetting factor high-order iterative learning as claimed in claim 1, characterized in that: The propulsion system is a marine robot propulsion system.

6. The thruster control method based on forgetting factor high-order iterative learning as claimed in claim 1, characterized in that: The corresponding dynamic motion characteristics of the thruster are obtained by using the Jacobian matrix and Lagrange formula.

7. A propeller control system based on high-order iterative learning of forgetting factors, adopting the propeller control method based on high-order iterative learning of forgetting factors according to any one of claims 1 to 6, characterized in that: include: The dynamic model construction is configured as follows: taking the propeller as the motion control object, and constructing the operation dynamic model of the propeller system based on the coordinate system and the characteristics of the propeller; The controller structure is configured to: preset a desired trajectory of the propulsion system, and construct a forgetting factor fractional-order high-order iterative learning controller according to error information between the propulsion system output and the desired trajectory, a forgetting factor, and a corresponding fractional-order transformation; The actual operation trajectory acquisition module is configured to: initialize the operation dynamics model of the propulsion system, adjust the forgetting factor fractional high-order iterative learning controller according to the convergence condition, and act on the propulsion system through the controller to obtain the actual operation trajectory of the propulsion system; Determine whether the actual running trajectory of the thruster system meets the expected trajectory. If so, obtain the expected actual motion trajectory. Otherwise, according to the error between the actual running trajectory and the expected trajectory, correct the controller through fractional calculus transformation until the trajectory tracking of the thruster system is completed.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the thruster control method based on high-order iterative learning of forgetting factors as described in any one of claims 1 to 6 are implemented.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the thruster control method based on forgetting factor high-order iterative learning as described in any one of claims 1 to 6 are implemented.

Images