A full drive surface ship tracking control method with time-varying control gain

Abstract

The application provides a tracking control method for a full-drive water surface ship with time-varying control gain, comprising: establishing a full-drive water surface ship system model considering external disturbance; designing a tracking controller combined with time-varying control gain and non-time-varying control gain by using vector backstepping method; analyzing asymptotic tracking performance and practical tracking performance of the tracking controller by using Lyapunov stability theory; analyzing boundedness of control items containing time-varying control gain and control items containing non-time-varying control gain in the tracking controller, and realizing tracking control of the full-drive water surface ship. The application designs a tracking control method containing time-varying control gain based on unknown bounded external disturbance, which is used to realize asymptotic tracking performance of the system and stability of the closed loop system; on the other hand, only by adjusting the value of the time-varying control gain, the asymptotic tracking or practical tracking closed loop performance of the system can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent tracking control of full-drive water surface ships, and in particular to a full-drive water surface ship tracking control method with time-varying control gain. BACKGROUND

[0002] Water surface ships, as an important carrier for human exploration, development and utilization of marine resources, have attracted great attention. Water surface ships can generally be divided into full-drive water surface ships and under-actuated water surface ships. Compared with under-actuated water surface ships, full-drive water surface ships have the characteristics of simpler structure, more flexible and accurate maneuverability, and can effectively reduce the risk of accidents. Therefore, the tracking control method of full-drive water surface ships has always been a hot spot in the industry.

[0003] During the process of sailing on the sea or operating on the sea, water surface ships are inevitably disturbed by external environment such as sea wind, sea wave and ocean current. Since the influence of external disturbance on water surface ships is difficult to be accurately evaluated and quantified, it is also difficult to achieve precise control of water surface ships under external disturbance. Therefore, the control problem of water surface ships under external environmental disturbance has always been an important research direction. The existing methods are mostly based on the premise that the external disturbance is known bounded disturbance to study the control problem of water surface ships, while in fact the bound of external disturbance is difficult to accurately obtain. On the other hand, in the current tracking control research of water surface ships, different tracking controllers are designed to achieve the given tracking control performance based on different tracking control objectives (such as asymptotic tracking, practical tracking), and there is a lack of unified control scheme integrating asymptotic tracking and practical tracking performance. Therefore, it is necessary to provide a full-drive water surface ship tracking control method combining time-varying control gain and non-time-varying control gain. SUMMARY

[0004] In view of the above technical problems, a full-drive water surface ship tracking control method with time-varying control gain is provided. The present application proposes a tracking control method with time-varying control gain for full-drive water surface ship systems under unknown external disturbance. The control method in the present application provides a unified tracking controller design method, which can achieve different tracking performance by adjusting the time-varying control gain parameter.

[0005] The technical means adopted by the present application are as follows:

[0006] A full-drive water surface ship tracking control method with time-varying control gain, comprising:

[0007] establishing a full-drive water surface ship system model considering external disturbance;

[0008] designing a tracking controller combining time-varying control gain and non-time-varying control gain by using vector backstepping method;

[0009] The asymptotic tracking performance and practical tracking performance of the tracking controller are analyzed by using the L'Hopital rule;

[0010] The boundedness of the tracking controller is analyzed to realize the tracking control of the full-drive surface ship.

[0011] Further, the full-drive surface ship system model considering external disturbance is represented as:

[0012]

[0013] wherein η = (x, y, ψ) T represents the position and attitude of the surface ship in the earth coordinate system, (x, y) T represents the position of the surface ship, and ψ represents the yaw angle of the surface ship, v = (v1, v2, v3) T represents the speed of the surface ship, (v1, v2) T represents the linear speed of the surface ship, and v3 represents the yaw angular velocity, u = (u1, u2, u3) T represents the driving force and torque provided by the power system of the surface ship, u1, u2, and u3 represent surge force, sway force, and yaw torque, respectively, the inertia matrix M is a positive definite symmetric matrix, M = diag{m 11 , m 22 , m 33}, m ii > 0 (i = 1, 2, 3), R is a rotation matrix, satisfying R T R = RR T = I3, D(v) is a damping matrix, D(v) = diag{d 11 (v), d 22 (v), d 33 (v)}, wherein d 11 (v) = -l 11 -l 12 |v1|-l 13 |v1| 2 , d ii (v) = -l i1 -l i2 |v2|-l i3 |v3| 2 (i = 2, 3); ξ represents the disturbance acceleration of the surface ship caused by unknown bounded disturbance from the external environment in the earth coordinate system, ξ = ξ(t) = (ξ1(t), ξ2(t), ξ3(t)) T , satisfying |ξ(t)| ≤ K0, K0 being a constant.

[0014] Further, the tracking controller designed by using the vector backstepping method combines time-varying control gain and non-time-varying control gain, and specifically comprises:

[0015] A given tracking signal η r = (x r , y r , ψ r ) T , the following coordinate transformation is introduced:

[0016]

[0017] Wherein, α represents a virtual control;

[0018] Selecting Then:

[0019]

[0020] Wherein, V1 represents a first candidate Lyapunov function, is the derivative of V1;

[0021] According to the Young inequality, and combining R T R = I3, we have:

[0022]

[0023] The virtual control α = -R T C0z1 is designed, wherein the controller parameter matrix C0 = C1 + d1I3 / 2λ min (M), I3 = diag{1, 1, 1}, λ min (M) represents the minimum eigenvalue of the inertia matrix M, the controller parameter matrix to be designed C1 = diag{c 11 , c 12 , c 13}, c 1j > 0 (j = 1, 2, 3), and the controller design parameter d1 > 0;

[0024] Rewrite As:

[0025]

[0026] Let V = V1 + V2, Then:

[0027]

[0028] Wherein, V represents a Lyapunov function, V2 represents a second candidate Lyapunov function, and S is a third-order matrix, S = (s ij ) 3×3and s 12 = -s 21 = 1, s ii = 0 (i = 1, 2, 3) and s 13 = s 31 = s 23 = s 32 = 0;

[0029] According to Young inequality, it is known that:

[0030]

[0031] wherein, λ max (M) represents the maximum eigenvalue of the inertia matrix M, the time-varying control gain parameter γ ≥ 0, the adjustable parameter d0 > 0, and t represents time;

[0032] V is arranged as follows:

[0033]

[0034] The tracking controller u is expressed as:

[0035]

[0036] wherein, u0 represents a control term containing a time-varying control gain, u1 represents a control term containing a non-time-varying control gain, and the controller parameter matrix C2 = diag{c 21 ,c 22 ,c 23} with c 2j > 0 (j = 1, 2, 3).

[0037] Further, the Lyapunov stability theory is adopted to analyze the asymptotic tracking performance and practical tracking performance of the tracking controller, specifically including:

[0038] V is converted into the following by the tracking controller u:

[0039]

[0040] wherein, c = min{2c1, 2c2}, c i = min{c i1 ,c i2 ,c i3} (i = 1, 2);

[0041] Since m1 = min{1 / 2, λ min (M) / 2}, m2 = max{1 / 2, λ max (M) / 2}, and λ max (M) ≥ λmin (M)>0, proceed

[0042] Obtain the closed-loop system:

[0043]

[0044] according to It can be deduced that:

[0045]

[0046] Using L'Hôpital's rule, we have:

[0047]

[0048] When γ > 0 And combined with |z(t)| 2 The nonnegativity of gives us The tracking controller has the ability to asymptotically track the tracking signal;

[0049] When γ = 0 Right now d0 and c are independent adjustable parameters, and the tracking controller has practical tracking performance for tracking signals.

[0050] Furthermore, the boundedness of the analysis tracking controller specifically includes:

[0051] Analyze the boundedness of the control term u0, which includes time-varying control gain, for the subsystem Introducing Lyapunov functions

[0052]

[0053] Conclusion:

[0054]

[0055] Combining L'Hôpital's rule, we can further deduce:

[0056]

[0057] Therefore, the control term u0, which includes time-varying control gain, is bounded;

[0058] The boundedness of the control term u1, which includes time-invariant control gain, is determined by... roll out:

[0059]

[0060] In the closed-loop state, both z1 and z2 are bounded, and this is consistent with η = z1 + η.r , and the boundedness of r and , it is concluded that both η and v are bounded, and further, the control term u1 containing the non-time-varying control gain is bounded.

[0061] Compared with the prior art, the present application has the following advantages:

[0062] The present application provides a tracking control method for a full-drive water surface ship with time-varying control gain, which comprises: establishing a full-drive water surface ship system model considering external disturbance; designing a tracking controller combining time-varying control gain and non-time-varying control gain by using vector backstepping method; analyzing the asymptotic tracking performance and practical tracking performance of the tracking controller by using L'Hopital's rule; analyzing the boundedness of the control term containing time-varying control gain and the control term containing non-time-varying control gain in the tracking controller, and realizing tracking control of the full-drive water surface ship. On one hand, based on unknown bounded external disturbance, the present application designs a tracking control method containing time-varying control gain, which is used to realize the asymptotic tracking performance of the system and the stability of the closed-loop system; on the other hand, by adjusting the value of the time-varying control gain, the closed-loop performance of the system in asymptotic tracking or practical tracking can be realized. Based on the above reasons, the present application can be widely popularized in the field of intelligent tracking control of full-drive water surface ship. BRIEF DESCRIPTION OF DRAWINGS

[0063] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative labor.

[0064] Figure 1 The flow chart of the tracking control method for the full-drive water surface ship with time-varying control gain in the present application.

[0065] Figure 2 The schematic diagram of the earth coordinate system and the body coordinate system of the water surface ship in the present application.

[0066] Figure 3 The decomposition schematic diagram of the external disturbance acceleration in the earth coordinate system of the water surface ship in the present application in the body coordinate system.

[0067] Figure 4 The control input signal trajectory diagram of the water surface ship in the present application under the condition of time-varying control gain γ=0.5.

[0068] Figure 5 The tracking error trajectory diagram of the water surface ship in the present application under the condition of time-varying control gain γ=0.5.

[0069] Figure 6 Tracking performance plot for the water surface vessel of the present invention with time-varying control gain γ = 0.5.

[0070] Figure 7 Control input signal trajectory plot for the water surface vessel of the present invention with time-varying control gain γ = 0.

[0071] Figure 8 Tracking error trajectory plot for the water surface vessel of the present invention with time-varying control gain γ = 0.

[0072] Figure 9 Tracking performance plot for the water surface vessel of the present invention with time-varying control gain γ = 0. DETAILED DESCRIPTION

[0073] It should be noted that the embodiments and features of the embodiments in the present application can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0074] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. The description of the at least one exemplary embodiment is actually only illustrative, but not intended to limit the present application and its application or use in any way. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0075] It should be noted that the terms used herein are only intended to describe specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a feature, step, operation, device, component and / or combination thereof.

[0076] The foregoing is considered as illustrative only of the principles of the application. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the application to the exact construction and practice described. Accordingly, all suitable modifications and equivalents can be resorted to falling within the scope of the application. Unless otherwise indicated herein, the contents of all patents, patent applications, publications, and test methods cited herein are hereby incorporated by reference in their entirety for all purposes.

[0077] In the description of the present application, it is to be understood that the orientation or positional relationships indicated by terms such as "front", "back", "up", "down", "left", "right", "lateral", "vertical", "horizontal", "top", "bottom", and the like are generally based on the orientation or positional relationships shown in the drawings, and are merely intended to facilitate the description and simplify the description, and do not indicate or imply that the device or element referred to must have a particular orientation or be constructed and operated in a particular orientation, and therefore cannot be construed as limiting the scope of protection of the present application. The orientation terms "inner", "outer" refer to the inner and outer relative to the contour of the parts themselves.

[0078] For the convenience of description, spatial relative terms such as "over", "above", "upper surface", "upper", and the like can be used herein to describe the spatial positional relationship of one device or feature with respect to other devices or features as shown in the drawings. It should be understood that the spatial relative terms are intended to include different orientations in use or operation in addition to the orientation of the device as described in the drawings. For example, if the device in the drawings is inverted, the device described as "above" or "over" other devices or structures will be positioned "below" or "under" the other devices or structures. Thus, the exemplary term "above" can include both "above" and "below" orientations. The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein are interpreted accordingly.

[0079] In addition, it should be noted that the use of the terms "first", "second", and the like, to describe various components, do not necessarily indicate any special significance, and are merely intended to distinguish the corresponding components, and therefore cannot be construed as limiting the scope of protection of the present application.

[0080] As Figure 1As shown, the application provides a full-drive surface ship tracking control method with time-varying control gain, characterized in that it comprises:

[0081] A full-drive surface ship system model considering external disturbance is established.

[0082] In specific implementation, as a preferred embodiment of the application, the full-drive surface ship system model considering external disturbance is expressed as:

[0083]

[0084] Wherein, η=(x, y, ψ) T represents the position and attitude of the surface ship in the earth coordinate system, (x, y) T represents the position of the surface ship, and ψ represents the yaw angle of the surface ship, v=(v1, v2, v3) T represents the speed of the surface ship, (v1, v2) T represents the linear speed of the surface ship, and v3 represents the yaw angular velocity, u=(u1, u2, u3) T represents the driving force and torque provided by the power system of the surface ship, u1, u2, and u3 represent surge force, sway force, and yaw torque respectively, the inertia matrix M is a positive definite symmetric matrix, M=diag{m 11 ,m 22 ,m 33}, m ii >0 (i=1, 2, 3), R is a rotation matrix, satisfying R T R=RR T =I3, D(v) is a damping matrix, D(v)=diag{d 11 (v), d 22 (v), d 33 (v)}, wherein d 11 (v)=-l 11 -l 12 |v1|-l 13 |v1| 2 , d ii (v)=-l i1 -l i2 |v2|-l i3 |v3| 2 (i=2, 3); ξ represents the disturbance acceleration of the surface ship caused by unknown bounded disturbance from the external environment in the earth coordinate system, such as Figure 3 As shown, ξ=ξ(t)=(ξ1(t), ξ2(t), ξ3(t)) T , satisfying |ξ(t)|≤K0, K0 is a constant.

[0085] The tracking controller designed by using the vector backstepping method combines time-varying control gain and non-time-varying control gain;

[0086] In the implementation, as a preferred embodiment of the present application, the tracking controller designed by using the vector backstepping method combines time-varying control gain and non-time-varying control gain, and specifically comprises:

[0087] A given tracking signal η r =(x r ,y r ,ψ r ) T A coordinate transformation is introduced as shown in the following formula: Figure 2

[0088]

[0089] Wherein, α represents a virtual control;

[0090] Selecting then:

[0091]

[0092] Wherein, V1 represents a first candidate Lyapunov function, is the derivative of V1; according to Young inequality, and in combination with R T R=I3, we have:

[0093]

[0094] The virtual control α=-R T C0z1 is designed, wherein the controller parameter matrix C0=C1+d1I3 / 2λ min (M), I3=diag{1,1,1}, λ min (M) represents the minimum eigenvalue of the inertia matrix M, the controller parameter matrix C1 to be designed=diag{c 11 ,c 12 ,c 13}, c 1j >0 (j=1,2,3), and the controller design parameter d1>0;

[0095] Rewrite as:

[0096]

[0097] Let V=V1+V2, then:

[0098]

[0099] ​Wherein, V represents Lyapunov function, V2 represents second candidate Lyapunov function, S is third order matrix, S=(s ij ) 3×3 And s 12 =-s 21 =1, s ii =0 (i=1, 2, 3) and s 13 =s 31 =s 23 =s 32 =0;

[0100] According to Young inequality, it is known that:

[0101]

[0102] Wherein, λ max (M) represents the maximum eigenvalue of inertia matrix M, time-varying control gain parameter γ≥0, adjustable parameter d0>0, and t represents time;

[0103] V is arranged as follows:

[0104]

[0105] The tracking controller u is represented as:

[0106]

[0107] Wherein, u0 represents a control term containing time-varying control gain, u1 represents a control term containing non-time-varying control gain, controller parameter matrix C2=diag{c 21 ,c 22 ,c 23} and c 2j >0 (j=1, 2, 3).

[0108] Lyapunov stability theory is used to analyze the asymptotic tracking performance and practical tracking performance of the tracking controller;

[0109] In specific implementation, as a preferred embodiment of the present application, the Lyapunov stability theory is used to analyze the asymptotic tracking performance and practical tracking performance of the tracking controller, and specifically includes:

[0110] V is converted into the following form through the tracking controller u:

[0111]

[0112] Wherein, c=min{2c1,2c2}, c i =min{c i1 ,c i2 ,c i3(i = 1, 2);

[0113] Since m1 = min{1 / 2, λ min (M) / 2} and m2 = max{1 / 2, λ max (M) / 2}, and λ max (M) ≥ λ min (M) > 0, it is concluded that

[0114] The closed-loop system is obtained as:

[0115]

[0116] The closed-loop system is practically stable.

[0117] According to It can be deduced that:

[0118]

[0119] Using the L'Hopital rule, we have:

[0120]

[0121] When γ > 0, and combining the non-negativity of |z(t)| 2 , we obtain The tracking controller has the asymptotic tracking performance for the tracking signal;

[0122] When γ = 0, i.e. d0 and c are mutually independent adjustable parameters, and the tracking controller has the practical tracking performance for the tracking signal.

[0123] The boundedness of the control term containing the time-varying control gain u0 and the control term containing the non-time-varying control gain in the tracking controller is analyzed, and the boundedness of the tracking controller is proved to realize the tracking control of the fully-driven surface ship.

[0124] The boundedness of the control term containing the time-varying control gain u0 is analyzed, and the subsystem A Lyapunov function V is introduced

[0125]

[0126] It is concluded that:

[0127]

[0128] Combining the L'Hopital rule, it is further concluded that:

[0129]

[0130] Therefore, the time-varying control term u0 is bounded;

[0131] The boundedness of the control term u1, which includes time-invariant control gain, is determined by... roll out:

[0132]

[0133] In the closed-loop state, both z1 and z2 are bounded, and this is consistent with η = z1 + η. r , and η r and The boundedness of η and v leads to the conclusion that both η and v are bounded. Furthermore, the time-invariant control term u1 is bounded.

[0134] It should be noted that the designed controller u can be divided into a control term u0 containing time-varying control gain and a control term u1 containing non-time-varying control gain. In fact, both are bounded, meaning that the designed controller u is bounded.

[0135] Example

[0136] like Figure 1 As shown, this invention provides a tracking control method for all-wheel-drive surface vessels with time-varying control gain. In this embodiment, hull parameter data of the all-wheel-drive surface vessel system, unknown external disturbance acceleration, tracking signal, and control parameters are provided. Experiments were conducted under different time-varying control gain values, demonstrating that the tracking control method for all-wheel-drive surface vessels in this invention has asymptotic tracking performance and practical tracking performance.

[0137] The hull parameters of the fully driven surface vessel system are as follows:

[0138] m 11 =26,m 22 =34,m 33 =2.8

[0139] l 11 =-0.7,l 12 =-1.3,l 13 =-5.9,l 21 =0.9,l 22 =-36,l 23 =l 31 =l 32 =0,l 31 =0.1,

[0140] The unknown external disturbance acceleration is set as follows:

[0141] ξ1(t) = 0.1 sin(0.4t) + 0.25 cos(0.8t)

[0142] ξ2(t) = 0.15 sin(0.3t) + 0.25 cos(0.6t)

[0143] ξ3(t) = 0.015 cos(0.5t) + 0.01 sin(t)

[0144] Initial values:

[0145] η(0) = (0.3, -0.8, 1) T v(0) = (0.3, 1.5, 0.4) T

[0146] Tracking signals:

[0147] η r1 = 0.2 sin(0.1t) + 0.1 cos(0.1t)

[0148] η r2 = 0.25 sin(0.1t) - 0.15 cos(0.1t)

[0149] η r3 = 0.3 sin(0.1t) + 0.2 cos(0.1t)

[0150] Control parameters:

[0151] c 11 = 4, c 12 = 4, c 13 = 0.3, c 21 = 4, c 22 = 4, c 23 = 0.3, d1 = 1, d0 = 1, γ = 0.5 or γ = 0

[0152] In the case of time-varying control gain γ = 0.5, Figure 4 represents the system control input signal, under the input signal shown in Figure 4 , the tracking error and tracking performance of the system are shown in Figure 5 and Figure 6 respectively. From the tracking error curve, it is clear that the designed control signal achieves the asymptotic tracking performance of the system.

[0153] In the case of time-varying control gain γ = 0, Figure 7 represents the system control input signal, under the input signal shown in Figure 7 , the tracking error and tracking performance of the system are shown in Figure 8 and Figure 9The tracking error and the tracking performance of the system are shown respectively. From the tracking error curve, it is clear that the designed control signal achieves the practical tracking performance of the system.

[0154] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not limited to them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A tracking control method for all-wheel-drive surface vessels with time-varying control gain, characterized in that, include: Establish a system model for all-wheel-drive surface vessels that takes into account external interference; The model of the all-wheel-drive surface vessel system considering external disturbances is represented as follows: in, This indicates the position and attitude of a ship on the water surface in the Earth coordinate system. Indicates the position of ships on the water. Indicates the yaw angle of a surface vessel. Indicates the speed of ships on the water. This represents the linear velocity of a vessel moving on water. Indicates yaw rate, This refers to the driving force and torque provided by the propulsion system of a surface vessel. Representing surge force, sway force, and yaw moment respectively, and inertia matrix It is a positive definite symmetric matrix. , , Let be a rotation matrix, satisfying , Here is the damping matrix. ,in, , ; This represents the acceleration caused by unknown, bounded disturbances from the external environment to a ship on the water surface, in the Earth coordinate system. ,satisfy , It is a constant; A tracking controller combining time-varying and non-time-varying control gains is designed using the vector backpropagation method. Given tracking signal The following coordinate transformation is introduced: in, Indicates virtual control; Select ,but: in, This represents the first candidate Lyapunov function. for The derivative; according to Young's inequality, and combined with get: Design virtual control , where the controller parameter matrix , , Representing the inertia matrix The minimum eigenvalue, the controller parameter matrix to be designed , Controller design parameters ; Will Rewritten as: make , ,but: in, This represents a Lyapunov function. This indicates the second candidate Lyapunov function. It is a third-order matrix. and , and ; According to Young's inequality, we can infer that: in, Representing the inertia matrix Maximum eigenvalue, time-varying control gain parameter Adjustable parameters , Indicates time; Will Rearranged as follows: Tracking Controller Represented as: in, This indicates a control term that includes time-varying control gain. This represents the control term containing time-invariant control gain, and the controller parameter matrix. , ; The asymptotic tracking performance and practical tracking performance of the tracking controller are analyzed using Lyapunov stability theory; The boundedness of the tracking controller is analyzed to achieve tracking control of all-wheel-drive surface vessels.

2. The tracking control method for all-wheel-drive surface vessels with time-varying control gain according to claim 1, characterized in that, The analysis of the asymptotic and practical tracking performance of the tracking controller using Lyapunov stability theory specifically includes: By tracking controller Will Transform into: in, , ; because , , , ,and ,roll out ; Obtain the closed-loop system: according to It can be deduced that: Using L'Hôpital's rule, we have: when hour, and combined The nonnegativity of gives us The tracking controller has the ability to asymptotically track the tracking signal; when hour, ,Right now , and With independently adjustable parameters, the tracking controller possesses practical tracking performance for tracking signals.

3. The tracking control method for all-wheel-drive surface vessels with time-varying control gain according to claim 2, characterized in that, The boundedness of the analysis tracking controller specifically includes: Analysis of the control term containing time-varying control gain The boundedness of the subsystem Introducing Lyapunov functions : Conclusion: Combining L'Hôpital's rule, we can further deduce: Therefore, the control term includes time-varying control gain. It possesses boundedness; The control term that includes time-invariant control gain The boundedness of roll out: In a closed-loop state and Both are bounded, and their combination... , as well as and The boundedness of , yields and All are bounded; furthermore, control terms that include time-invariant control gains. It is bounded.

Images