Global finite time ship trajectory tracking control method considering input limitation

Abstract

The invention discloses a global finite time ship trajectory tracking control method considering input limitation, and the method comprises the steps: obtaining a longitudinal trajectory tracking error xe and a transverse trajectory tracking error ye through an actual trajectory and an expected trajectory of a ship, combining the longitudinal trajectory tracking error xe with a piecewise function kz to design a first new error zx, designing a second new error zy by combining the transverse trajectory tracking error ye with the piecewise function kz, and designing an expected longitudinal speed ud and an expected transverse speed vd through the first new error zx and the second new error zy; designing a first finite time sliding mode surface s1 through the difference ue between the actual longitudinal speed u and the expected longitudinal speed ud, and designing a second finite time sliding mode surface s2 through the difference ve between the actual transverse speed v and the expected transverse speed vd; longitudinal control force Tuc is designed based on s1, yawing control torque Trc is designed based on s2, ue and ve are converged through the longitudinal control force Tuc and the yawing control torque Trc, and when ue and ve are converged, trajectory tracking of the ship is achieved.

Description

Technical Field

[0001] The present invention relates to the field of ship trajectory tracking, and in particular to a global finite-time ship trajectory tracking control method considering input restrictions. Background Art

[0002] In recent years, with the continuous development of marine resources, higher technical requirements have been put forward for the intelligence of ships. Among them, surface ships play an important role in water monitoring, environmental protection and military missions. The accuracy of their trajectory is closely related to the efficiency of engineering operations. Ship trajectory tracking control refers to the design of controllers to make ships sail according to the expected trajectory. Its purpose is to promote the intelligence of ships, ensure navigation safety, and reduce the burden on sailors. Ships themselves have the characteristics of nonlinearity, strong coupling, and large inertia, which often makes it difficult to obtain accurate mathematical models. In addition, the sea conditions in which ships are located are relatively complex and are easily affected by unknown external interference.

[0003] When a ship is sailing on the sea, it will face various internal and external disturbances. External disturbances are manifested as deviations, speed changes, and shaking caused by the wind, waves, and currents acting on the ship. Internal disturbances are model uncertainties caused by changes in ship parameters due to various consumptions such as cargo loading and unloading, fuel, and food, but internal and external disturbances are not considered when designing the controller. At the same time, how to make the ship have a faster convergence rate in the process of tracking the desired trajectory has always been a key research topic in the field of ship motion control. The increase in convergence rate will inevitably increase the control input, but due to the inherent characteristics of the ship's actuator, there will be certain limits on the control input. Therefore, the input limit must be taken into account when designing the controller, otherwise it will be out of touch with reality and lose its meaning. At present, most methods to speed up the convergence rate are to design the controller in combination with finite time convergence in the approaching stage, while ignoring the sliding stage, which has the problem of slow convergence. Summary of the invention

[0004] The present invention provides a global finite-time ship trajectory tracking control method considering input constraints to overcome the above technical problems.

[0005] The global finite-time ship trajectory tracking control method considering input constraints includes:

[0006] S1, the longitudinal trajectory tracking error x is obtained by the actual trajectory and the expected trajectory of the ship. e and the lateral trajectory tracking error y e , the longitudinal trajectory tracking error x e Combined with piecewise function k z Design the first new error z x , the lateral trajectory tracking error y e Combined with piecewise function k zDesign the second new error z y , through the first new error z x and the second new error z y Design the expected longitudinal velocity u d and the desired lateral velocity v d ;

[0007] S2, through the actual longitudinal speed u and the expected longitudinal speed u d The difference u e Design the first finite time sliding surface s 1 , through the actual lateral velocity v and the expected lateral velocity v d Difference v e Design the second finite time sliding surface s 2 ;

[0008] S3, based on the first finite time sliding surface s 1 Design longitudinal control force T uc , based on the second finite-time sliding surface s 2 Designed yaw control moment T rc , by the longitudinal control force T uc and the yaw control torque T rc Make u e and v e Convergence, when u e and v e When converged, the ship can achieve trajectory tracking.

[0009] Preferably, the S1 includes:

[0010] S11, determining a mathematical model of an underactuated ship with limited input, wherein the mathematical model of an underactuated ship with limited input is formula (1),

[0011]

[0012] in:

[0013]

[0014] Where x, y, ψ are the forward displacement, drift displacement and heading angle of the ship respectively; u, v, r are the longitudinal velocity, transverse velocity and bow angular velocity of the ship in the appendage coordinate system respectively, T u1 To consider the actual longitudinal control force of the ship after limitation, T r1 is the actual yaw control moment after considering the limitation, m 11 ,m 22 ,m 33 is the inertia parameter, d 11 ,d 22 ,d 33 is the hydrodynamic parameter, Δfu ,Δf v ,Δf r is the uncertainty term of the ship model, τ wu, τ wv, τ wr is the external unknown disturbance, τ im is the upper bound of the control input, T uc is the ideal longitudinal control force of the ship, T rc is the ideal yaw control torque, ΔT u and Δτ r is the difference between the actual control input and the ideal input,

[0015] S12. Define tracking error:

[0016]

[0017] Where x d ,y d are the ordinate and abscissa of the expected trajectory of the ship, x e ,y e is the longitudinal and lateral position error, let

[0018]

[0019] Where α 1 ,p, is a positive parameter, and the expression of z(t) is shown in formula (5):

[0020]

[0021] Where t is time, β 1 ,T is a positive parameter,

[0022] make

[0023]

[0024] Where z x is the first new error, z y is the second new error,

[0025] By taking the derivative of formula (6) and combining it with formula (1), we can get:

[0026]

[0027] According to formula (7), if we want to make the first new error and the second new error z x ,z y Both tend to 0, and the expected forward speed u d and the desired drift velocity v d for:

[0028]

[0029] Where c 1 ,c 2 ,c 3 ,c 4 ,ε 1 ,ε 2 is the positive parameter to be designed.

[0030] Preferably, the actual longitudinal speed u and the expected longitudinal speed u d The difference u e Design the first finite time sliding surface s 1 include:

[0031] make

[0032] u e =uu d (9)

[0033] Define the first finite time sliding surface s 1 As shown in formula (10):

[0034]

[0035] In the formula, λ 1 ,λ 2 is a positive parameter and t is time.

[0036] Preferably, the actual lateral velocity v and the expected lateral velocity v d Difference v e Design the second finite time sliding surface s 2 include:

[0037] make

[0038] v e =vv d (11)

[0039] Define the second finite time sliding surface s 2 As shown in formula (12):

[0040]

[0041] In the formula, λ 3 ,λ 4 is a positive parameter.

[0042] Preferably, S3 includes:

[0043] For the first finite-time sliding surface s 1 Taking the derivative and combining equation (1) and equation (9), we can get:

[0044]

[0045] In the formula, u e is the actual longitudinal velocity u and the expected longitudinal velocity u d The difference, λ 1 ,λ 2 is a positive parameter, u, v, r are the longitudinal velocity, transverse velocity, and bow angular velocity of the ship in the appendage coordinate system, respectively, u d Indicates the expected longitudinal speed of the ship, m 11 and m 22 is the inertia parameter, d 11 is the hydrodynamic parameter, T wu ,T wv ,T wr is the external unknown disturbance, T uc is the ideal longitudinal control force of the ship, ΔT u is the difference in actual control input, Δf u As an unknown term, RBF neural network is used to calculate Δf u Estimate the unknown term Δf u The output expression of the neural network is shown in formula (14), h u (x) is the first Gaussian function, o 1 is the first approximation error:

[0046] Δf u =W u T h u (x)+o 1 (14)

[0047] According to equation (13) and combined with finite time convergence, the longitudinal control force T is designed uc ,

[0048]

[0049] In the formula, μ 1 =D 1 -o 1 +ΔT u , μ 1 The estimated value of 5 , c 6 , ε 3 is a positive parameter; parameter and The adaptive law is shown in formula (16):

[0050]

[0051] Where η 1 ,η 2 ,σ 1 ,σ2 is a positive design parameter;

[0052] For the second finite time sliding surface s 2 Taking the derivative and combining equation (1) and equation (11), we can get:

[0053]

[0054] make

[0055]

[0056] According to equation (17) and combined with finite time convergence, the bow control torque T is designed rc :

[0057]

[0058] In the formula, μ 2 =D 2 -o 2 +ΔT r , μ 2 The estimated value of 7 , c 8 , ε 4 is a positive design parameter; parameter and The adaptive law is shown in formula (21):

[0059]

[0060] Where η 3 ,η 4 ,σ 3 ,σ 4 is a positive parameter.

[0061] The present invention provides a global finite-time ship trajectory tracking control method considering input constraints, by designing the expected longitudinal velocity u d and the desired lateral velocity v d , so that the control system can achieve finite time convergence, and then the first finite time sliding surface and the second finite time sliding surface are designed in the process of subsequent control input. The longitudinal control force is designed based on the first finite time sliding surface, and the bow control torque is designed based on the second finite time sliding surface, which further accelerates the convergence speed of the error and improves the ship trajectory tracking accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0063] Figure 1 is a flow chart of the method of the present invention;

[0064] Figure 2 It is the basic framework of the control method in the embodiment of the present invention;

[0065] Figure 3 is a phase plane diagram in an embodiment of the present invention;

[0066] Figure 4 is a comparison diagram of the expected trajectory and the actual trajectory of the ship in the plane in an embodiment of the present invention;

[0067] Figure 5 is a comparison diagram of the effect of lateral position error in an embodiment of the present invention;

[0068] Figure 6 is a comparison diagram of the longitudinal position error effect in an embodiment of the present invention;

[0069] Figure 7 is a comparison diagram of lateral velocity errors in an embodiment of the present invention;

[0070] Figure 8 is a longitudinal velocity error comparison diagram in an embodiment of the present invention;

[0071] Fig. 9 is a graph of longitudinal control force input in an embodiment of the present invention;

[0072] Fig.10 is a curve diagram of the yaw control torque input in an embodiment of the present invention;

[0073] Fig.11 This is a neural network fitting curve effect diagram in an embodiment of the present invention;

[0074] Fig.12 It is an upper bound adaptive estimation graph in an embodiment of the present invention. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0076] Figure 1 It is a flow chart of the method of the present invention, such as Figure 1 As shown, the method of this embodiment includes:

[0077] S1, the longitudinal trajectory tracking error x is obtained by the actual trajectory and the expected trajectory of the ship. e and the lateral trajectory tracking error y e , the longitudinal trajectory tracking error x e Combined with piecewise function k z Design the first new error z x , the lateral trajectory tracking error y e Combined with piecewise function k z Design the second new error z y , through the first new error z x and the second new error z y Design the expected longitudinal velocity u d and the desired lateral velocity v d ;

[0078] S2, through the actual longitudinal speed u and the expected longitudinal speed u d The difference u e Design the first finite time sliding surface s 1 , through the actual lateral velocity v and the expected lateral velocity v d Difference v e Design the second finite time sliding surface s 2 ;

[0079] S3, based on the first finite time sliding surface s 1 Design longitudinal control force T uc , based on the second finite-time sliding surface s 2 Designed yaw control moment T rc , by longitudinal control force T uc and the yaw control torque T rc Make u e and v e Convergence, when u e and v e When converged, the ship can achieve trajectory tracking.

[0080] Based on the above content, the present invention provides a global finite-time ship trajectory tracking control method considering input restrictions. For unknown external disturbances, the RBF neural network is used to approximate the uncertain terms, and the adaptive law is used to estimate the total disturbance formed by the nonlinear terms caused by the input restrictions and the external disturbances and the neural network approximation errors. Finally, the dynamic surface technology is used to solve the differential explosion problem. In order to speed up the convergence speed, a finite-time term is designed, and a finite-time sliding surface is used to further speed up the convergence speed of the error.

[0081] Specifically, this embodiment provides a basic framework of the ship trajectory tracking control method, such as Figure 2 As shown in the figure, the specific process is to first pass the actual trajectory (x, y) of the ship and the expected trajectory (x d ,y d ) to obtain the trajectory tracking error x e and e , and then combine the error with the piecewise function k z Design a new error z x and z y , through the new error z x and z y Design the expected longitudinal velocity u d and the desired lateral velocity v d ; Then, the actual longitudinal velocity u and the expected longitudinal velocity u d The finite time sliding surface s 1 , the lateral velocity v and the expected lateral velocity v d The finite time sliding surface s 2 ; Finally combine Design the longitudinal control force T using the backstepping method uc and the yaw control torque T rc Make the sliding surface s 1 ,s 2 Converge to the stable region. After convergence, the error will be on the sliding surface s 1 and 2 Slide on the surface to make the speed error converge. The details of the present invention include:

[0082] First, the ship mathematical model used in this embodiment is determined. After considering the input limitation, the underactuated ship mathematical model can be written as follows:

[0083]

[0084] in,

[0085]

[0086] Where x, y, ψ are the forward displacement, drift displacement and heading angle of the ship respectively; u, v, r are the longitudinal velocity, transverse velocity and bow angular velocity of the ship in the appendage coordinate system respectively, T u1 To consider the actual longitudinal control force of the ship after limitation, T r1 is the actual yaw control moment after considering the limitation, m 11 ,m 22 ,m 33 is the inertia parameter, d 11 ,d 22 ,d 33 is the hydrodynamic parameter, Δf u ,Δf v ,Δf r is the uncertainty of the ship model, T wu ,T wv ,T wr is the external unknown disturbance, T im is the upper bound of the control input, T uc is the ideal longitudinal control force of the ship, T rc is the ideal yaw control torque, ΔT u and ΔT r is the difference between the actual control input and the ideal input.

[0087] This embodiment provides the following related content of the prior art, including:

[0088] 1) Lemma:

[0089] Lemma 1: For any ε>0, there exists the following inequality:

[0090] 0≤|s|-stanh(s / ε)≤0.2785ε (3)

[0091] Where s is an arbitrary variable.

[0092] Lemma 2: For any defined on a compact set The continuous smooth function f(x) on has:

[0093]

[0094] Where o is the approximation error. For all x∈Ω, there exists a vector o ＊ >0, and satisfies o|≤o ＊ ; W is the weight vector under ideal conditions, which is usually difficult to obtain and is an unknown variable, so it needs to be estimated. h(x) is a Gaussian function, and its expression is shown in formula (5).

[0095]

[0096] Where: j = 1, 2, 3, ... n, is the number of network nodes; m j is the input center vector; b j is the standard deviation of the Gaussian function.

[0097] Lemma 3: Consider a system x = f(x), f(0) = 0, x∈R n , where f(x) is a continuous function. Assume that there exists a continuous Lyapunov function V:D→R that satisfies the following conditions: V is a positive definite function, and there exists a real number ρ 1 >0,ρ 2 >0, θ l >0 and an open-loop neighborhood near the origin satisfies Then the system is practically finite-time stable, and the stability time T r satisfy:

[0098]

[0099] Where V(0) is the initial value of the system V(x).

[0100] 2) Assumptions:

[0101] Assumption 1: The external disturbance to the ship is time-varying and satisfies:

[0102] |T wu |≤D 1 ,|T wr |≤D 2

[0103] Where D 1 ,D 2 All are greater than 0, indicating interference τ wu ,T wr The upper bound of and limit of are unknown.

[0104] Assumption 2: The expected trajectory of the ship (x d ,y d ) is smooth and has first- and second-order derivatives.

[0105] Define tracking error:

[0106]

[0107] Where x d ,y d x is the ordinate and abscissa of the ship’s expected trajectory. e ,y e is the longitudinal and lateral position error.

[0108] make

[0109]

[0110] Where α 1 ,p, is the positive parameter to be designed, and the expression of z(t) is shown in formula (8):

[0111]

[0112] Where t is time, β 1 ,T is the positive parameter that needs to be designed.

[0113] make

[0114]

[0115] By taking the derivative of formula (9) and combining it with formula (1), we can get:

[0116]

[0117] According to formula (10), if we want to make the first new error and the second new error z x ,z y Both tend to 0, then the expected forward speed u d and the desired drift velocity v d Can be designed as:

[0118]

[0119] Where c 1 ,c 2 ,c 3 ,c 4 ,ε 1 ,ε 2 is the positive parameter to be designed.

[0120] When u e With v e When both tend to 0, formula (10) can be simplified as:

[0121]

[0122] Construct the following Lyapunov function:

[0123]

[0124] Deriving formula (13) and combining it with formula (12), we can obtain:

[0125]

[0126] According to Lemma 1,

[0127] -s tanh(s / ε)≤0.2785ε-|s|

[0128] Therefore

[0129]

[0130] Substituting formula (15) into formula (14), we can obtain:

[0131]

[0132] in,

[0133]

[0134] Because 1 , ρ 2 ,θ 1 are all greater than 0, so according to Lemma 3, V 1 It can achieve finite time convergence, and time T r1 satisfy:

[0135]

[0136] By taking the derivative and simplifying formula (11), we can get:

[0137]

[0138] make

[0139] u e =uu d (twenty two)

[0140] Define the sliding surface s 1 As shown in formula (23):

[0141]

[0142] In the formula, λ 1 ,λ 2 is the positive parameter to be designed. Specifically, Figure 3 is the phase plane diagram, where e is the state variable, is the derivative of e. Sliding mode control consists of two stages, the approach stage and the sliding stage. Under the action of the controller, the system will converge from any state to the sliding surface, this stage is called the approach stage; and once it reaches the sliding surface, the system will slide to the equilibrium point under the action of the sliding surface, this stage is called the sliding stage. The reason why sliding mode control is so robust is that once the system reaches the sliding surface, its motion performance only depends on the design parameters of the sliding surface, and has nothing to do with the system parameters and external disturbances.

[0143] Deriving formula (23) and combining formula (1) and formula (22) yields:

[0144]

[0145] Since RBF neural network has the universal approximation characteristic for any function, RBF neural network is used here to approximate Δf u According to Lemma 2, the unknown term Δf u The output expression of the neural network is shown in formula (25):

[0146] Δf u =W u T h u (x)+o 1 (25)

[0147] By combining (24) and finite time convergence, the longitudinal control force T can be designed uc ,

[0148]

[0149] In the formula, μ 1 =D 1 -o 1 +ΔT u , μ 1 The estimated value of 5 , c 6 , ε 3 is a positive design parameter; parameter and The adaptive law of is shown in formula (27):

[0150]

[0151] Where η 1 ,η 2 ,σ 1 ,σ 2 is a positive design parameter;

[0152] make

[0153] v e =vv d (28)

[0154] Define the sliding surface s 2 As shown in formula (29):

[0155]

[0156] In the formula, λ 3 ,λ 4 is the positive parameter to be designed.

[0157] In order to facilitate the subsequent controller writing, let:

[0158]

[0159] but

[0160]

[0161] In order to avoid the differential explosion phenomenon when directly derivatizing f, the dynamic surface technology is used to use the output of the first-order filter to avoid directly derivatizing f, so a new variable f is introduced r And as the output of the first-order low-pass filter of f, its expression is as follows:

[0162]

[0163] Where T r >0 is the design parameter.

[0164] Deriving formula (29) and combining formula (1) and formula (28) we can obtain:

[0165]

[0166] make

[0167]

[0168] Unknown term Δf r The output expression of the neural network is:

[0169] Δf r =W r T h r (x)+o 2 (35)

[0170] By combining (33) and finite time convergence, the yaw control torque T can be designed: rc ,

[0171]

[0172] In the formula, μ 2 =D 2 -O 2 +ΔT r , μ 2 The estimated value of 7 , c 8 , ε 4 is a positive design parameter; parameter and The adaptive law of is shown in formula (37):

[0173]

[0174] Where η 3 ,η 4 ,σ 3 ,σ 4 is a positive design parameter.

[0175] In summary, the design of the controller in this embodiment can be divided into two steps. The first step is to design the expected forward speed u d and the drift speed v d Make the actual trajectory of the ship track to the desired trajectory within a limited time; the second step is to design the longitudinal control force T of the ship uc and the yaw control torque T rc Make u approach u d and v approaches v d . When u e and v e When it converges to 0, the ship can achieve trajectory tracking.

[0176] In order to verify the stability of the controller designed by the present invention, the Lyapunov function shown in formula (38) is defined.

[0177]

[0178] In the formula,

[0179] Taking the derivative of both sides of equation (38) and substituting equations (23) to (27) and (33) to (37) into equation (38), we can obtain

[0180]

[0181] Consider formula (39)

[0182]

[0183] According to Lemma 1, we know

[0184]

[0185] because

[0186]

[0187] Combining equations (40), (41) and (42), equation (39) can be simplified to

[0188]

[0189] in

[0190]

[0191] According to formula (43), we can get

[0192]

[0193] where ρ 5 ≤ρ 4 ,when When Therefore, according to Lemma 3, V 2 Can converge to the set area within a limited time And time T r2 satisfy

[0194]

[0195] Since V 2 is bounded, so V 2 The s 1 ,s 2 , are bounded, so u e , v e is also bounded. And because μ 1 , μ 2 , W u , W r Bounded, so It is also bounded, thus ensuring that all error signals in the underactuated ship trajectory tracking control system are ultimately bounded.

[0196] Next, the speed error u e and v e Perform a finite-time stability analysis:

[0197] Due to s 1 and 2 are bounded, so s 1 and 2 The derivative of is also bounded, assuming that it is less than Δ s ,but

[0198]

[0199] Define the following Lyapunov function, as shown in formula (50):

[0200]

[0201] By taking the derivative of formula (50) and combining it with formula (49), we can obtain:

[0202]

[0203] According to Lemma 1 and Young's inequality, equation (51) can be transformed into

[0204]

[0205] in

[0206]

[0207] θ 3 =Δ s 2 +0.2785λ 2 +0.2785λ 4 (55)

[0208] Therefore, according to Lemma 3, V 3 It can achieve finite time convergence, and time T r3 satisfy

[0209]

[0210] In summary, the position tracking error x e and e It can converge within a limited time, and the convergence time T r =T r1 +T r2 +T r3 , T r2 is the time spent in the approaching stage, during which the controller makes the system state approach the sliding surface from any state; T r3 is the time spent in the sliding stage. When the system state approaches the sliding surface, the velocity tracking error u e and v e It will converge near the sliding surface in a finite time; when the velocity tracking error u e and v e When it approaches 0, the ship’s position tracking error x e and e In a limited time T r1 Convergence is achieved within.

[0211] In order to verify the effectiveness of the control scheme designed by the present invention, a computer simulation experiment was conducted with a patrol boat named BAY CLASS of Singapore Customs as the simulation object. The boat is 38m long and has a mass of m=1.18×10 5 kg, other parameters are m 11 =1.2×10 5 kg, m 22 =1.779×10 5 kg, m 33 =6.36×10 7 kg, d 11 =2.15×10 4 kg / s,d 22 =1.47×105 kg / s,d 33 =8.02×10 6 kg / s.

[0212] In order to verify the effect of the control strategy proposed in this invention on the ship, this simulation experiment is divided into three groups. The first group does not add the finite time term. d With v d , sliding surface, control law, parameters The adaptive laws are shown in equations (57), (58), (59) and (60); the second group is to add a finite time term in the approaching stage, and its specific u d With v d , sliding surface, control law, parameters The adaptive law is shown in equations (57), (58), (61), and (60), and the other parts are consistent with the present invention; the third group is the effect of the controller of the present invention. The comparison between the first group and the second group mainly highlights the effect of using finite time convergence in the approaching stage; the comparison between the second group and the third group highlights the influence of using finite time sliding mode on the convergence rate.

[0213]

[0214] Remark. In formula (58), ξ 1 and 2 The introduction is to eliminate the nonlinear term caused by saturation of the input, and the processing method of the present invention is to set the nonlinear term, the external disturbance and the neural network approximation error as a total disturbance and use the adaptive law to estimate it.

[0215]

[0216]

[0217] In order to simulate the sea conditions, the external time-varying disturbance is expressed by equation (62).

[0218]

[0219] Set parameter c 1 =2, c 2 =0.7, c 3 =1, c 4 =0.2, c 5 =5×10 5 , c 6 =2×10 7 , c 7 =5×10 2 , c 8 =5×104 , λ 1 = 10, λ 2 = 2, λ 3 = 5, λ 4 = 3, ε 1 = ε 3 = 0.1, ε 2 = ε 4 = 0.05, α 1 = 15, β 1 = 0.5, T = 20, T r = 0.1, p = 5, η 1 = 5×10 4 , η 2 = 7×10 3 , η 3 = 1.2×10 3 , η 4 = 1.3×10 7 , η 5 = 6×10 3 , η 6 = 5×10 4 , η 7 = 1.3×10 3 , η 8 = 1.2×10 3 , σ 1 = 2×10 -7 , σ 2 = 1×10 -6 , σ 3 = 1×10 -1 , σ 4 = 8×10 -6 , σ 5 = 1.8×10 -6 , σ 6 = 2×10 -7 , σ 7 = 8×10 -8 , σ 8 = 1×10 -1 。

[0220] The uncertainty term of the model is set as Δf u = 0.2d 11 u 2 + 0.1d 11 u 3 , Δf v = 0.2d 22 v 2 + 0.1d 22 v 3 , Δf r = 0.2d 33 r2 +0.2d 33 r 3 . Set the input upper limit T um =6.5×10 6 N, T rm =4×10 8 (N·m).

[0221] The number of hidden layer nodes of the neural network is 41. The first one is uniformly distributed with the center point on [-6,6], and the second one is uniformly distributed with the center point on [-1,1]. Gaussian basis function width b 1 =35, b 2 =20, the initial value of the estimated weight Set the expected sine trajectory to x d =300sin(0.03t),y d =10t. Select the initial position and speed of the ship as (x 0 ;y 0 ψ 0 ;u 0 ;v 0 ; r 0 )=(40;0;0;0.1;0;0).

[0222] The simulation results are as follows Figures 4 to 12 As shown. Figure 4 It can be seen that under the action of three different control strategies, the actual trajectory of the ship can track the expected trajectory.

[0223] First, the second group is compared with the first group to highlight the effect of adopting finite time convergence in the approach phase. Figure 5 and Figure 6 It can be seen that under the two different control strategies, the lateral position error of the ship can converge in about 12 seconds, and the longitudinal position error can converge in about 10 seconds. It can also be seen that after adopting finite time convergence in the approaching stage, the convergence speed of the second group of errors is slightly faster than that of the first group, both in the lateral and longitudinal positions. Figure 7 and Figure 8 It can be seen that the speed tracking error of the ship under the two different control strategies is not much different. Fig. 9 and Fig.10 It can be seen that the control inputs of the two different control strategies are within the limits and the difference is not large. Therefore, it can be concluded that under the premise of input constraints, the use of finite time convergence in the approaching stage can still accelerate the convergence rate of the tracking error.

[0224] Then, the second group is compared with the third group to highlight the effect of using the finite-time sliding surface during the sliding stage. Figure 5 and Figure 6 It can be seen that after the finite time sliding surface is used in the sliding stage, the stabilization time of the lateral position error is shortened from the original 12s to 9s, an increase of 25%. The convergence rate of the longitudinal position error is also accelerated. Figure 7 and Figure 8 It can be seen from the figure that after adopting the finite time sliding surface, the velocity error stabilization time is shorter in both the longitudinal and lateral directions. Fig. 9 and Fig.10 It can be seen that the control input of this control strategy is always within the limit and is not much different from the first group and the second group, highlighting the superiority of the control strategy of the present invention.

[0225] Finally, from Fig.11 From the neural network fitting curve, we can see that the neural network can better estimate the uncertainty of the ship model and show good fitting performance. Fig.12 It can be obtained that the adaptive law designed in the present invention can better estimate the total disturbance μ i , i=1,2, thereby improving the tracking accuracy of the controller of the present invention.

[0226] Through the comparative simulation experiment between the above invention and the existing research, the beneficial effects brought by the present invention are summarized into the following two points:

[0227] (1) In order to solve the problems of unknown external disturbances, uncertainties in the ship model and differential explosion, the RBF neural network is used to approximate the uncertainties, and the adaptive law is used to estimate the total disturbance caused by the nonlinear terms caused by the input restrictions, the external disturbances and the neural network approximation error. Finally, the dynamic surface technology is used to solve the differential explosion problem.

[0228] (2) To speed up the convergence, we will design the controller based on the finite time convergence theory and use the finite time sliding surface to achieve global finite time convergence. First, we design the expected forward speed u by combining the hyperbolic tangent function. d And the drift speed v d , so that z x With z y Finite-time convergence can be achieved, and constructing finite-time convergence through the hyperbolic tangent function can effectively avoid the subsequent inability to differentiate caused by using the symbolic function to construct finite-time convergence; then, in the process of subsequent control input, the finite-time term is also designed, and the finite-time sliding surface is used to further accelerate the convergence speed of the error.

[0229] The global finite-time ship trajectory tracking control method considering input constraints proposed in the present invention can effectively solve the problem of ships being under external unknown disturbances and the existence of model uncertainties, accelerate the convergence rate of errors, and handle nonlinear terms caused by input constraints. Through the Lyapunov theory, it is proved that all signals of the ship system are bounded and the tracking error can converge within a finite time. By comparing with various control strategies, it is verified that this control strategy can achieve finite-time convergence in both the approaching stage and the sliding stage, and can achieve global finite-time convergence. Theoretical analysis and simulation experimental results show that the feasibility of the global finite-time ship trajectory tracking control method considering input constraints proposed in the present invention is confirmed.

[0230] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A global finite-time ship trajectory tracking control method considering input constraints, characterized in that: include: S1, the longitudinal trajectory tracking error x is obtained by the actual trajectory and the expected trajectory of the ship. e and the lateral trajectory tracking error y e , the longitudinal trajectory tracking error x e Combined with piecewise function k z Design the first new error z x , the lateral trajectory tracking error y e Combined with piecewise function k z Design the second new error z y , through the first new error z x and the second new error z y Design the expected longitudinal velocity u d and the desired lateral velocity v d ; S2, through the actual longitudinal speed u and the expected longitudinal speed u d The difference u e The first finite-time sliding surface s1 is designed by comparing the actual lateral velocity v with the expected lateral velocity v d Difference v e Design a second finite-time sliding surface s2; S3, design the longitudinal control force T based on the first finite time sliding surface s1 uc , based on the second finite time sliding surface s2, the yaw control torque T is designed rc , by the longitudinal control force T uc and the yaw control torque T rc Make u e and v e Convergence, when u e and v e When converged, the ship can achieve trajectory tracking.

2. The global finite-time ship trajectory tracking control method considering input constraints according to claim 1 is characterized in that: The S1 includes: S11, determining a mathematical model of an underactuated ship with limited input, wherein the mathematical model of an underactuated ship with limited input is formula (1), in: Where x, y, ψ are the forward displacement, drift displacement and heading angle of the ship respectively; u, v, r are the longitudinal velocity, transverse velocity and bow angular velocity of the ship in the appendage coordinate system respectively, T u1 To consider the actual longitudinal control force of the ship after limitation, T r1 is the actual yaw control moment after considering the limitation, m 11 ,m 22 ,m 33 is the inertia parameter, d 11 ,d 22 ,d 33 is the hydrodynamic parameter, Δf u ,Δf v ,Δf r is the uncertainty of the ship model, T wu ,T wv ,T wr is the external unknown disturbance, T im is the upper bound of the control input, T uc is the ideal longitudinal control force of the ship, T rc is the ideal yaw control torque, ΔT u and ΔT r is the difference between the actual control input and the ideal input, S12. Define tracking error: Where x d ,y d are the ordinate and abscissa of the ship’s expected trajectory, x e ,y e are the longitudinal and lateral position errors, make k z =α1z(t) p i (4) Where a1, p, θ are positive parameters, and the expression of z(t) is shown in formula (5): Where t is time, β1,T is a positive parameter, make Where z x is the first new error, z y is the second new error, By taking the derivative of formula (6) and combining it with formula (1), we can get: According to formula (7), if we want to make the first new error and the second new error z x ,z y Both tend to 0, and the expected forward speed u d and the desired drift velocity v d for: In the formula, c1, c2, c3, c4, ε1, ε2 are the positive parameters that need to be designed.

3. The global finite-time ship trajectory tracking control method considering input constraints according to claim 2 is characterized in that: The actual longitudinal velocity u and the expected longitudinal velocity u d The difference u e Designing the first finite-time sliding surface s1 includes: make in e =uuu d (9) The first finite-time sliding surface s1 is defined as shown in formula (10): Where λ1, λ2 are positive parameters and t is time.

4. The global finite-time ship trajectory tracking control method considering input constraints according to claim 3 is characterized in that: The actual lateral velocity v and the expected lateral velocity v d Difference v e Designing the second finite-time sliding surface s2 includes: make v e =vv d (11) The second finite time sliding surface s2 is defined as shown in formula (12): Where λ3 and λ4 are positive parameters.

5. The global finite-time ship trajectory tracking control method considering input constraints according to claim 4 is characterized in that: The S3 includes: By taking the derivative of the first finite-time sliding surface s1 and combining equation (1) and equation (9), we can obtain: In the formula, u e is the actual longitudinal velocity u and the expected longitudinal velocity u d The difference between the two, λ1 and λ2 are positive parameters, u, v, and r are the longitudinal velocity, transverse velocity, and bow angular velocity of the ship in the appendage coordinate system, respectively. d Indicates the expected longitudinal speed of the ship, m 11 and m 22 is the inertia parameter, d 11 is the hydrodynamic parameter, T wu ,T wv ,T wr is the external unknown disturbance, T uc is the ideal longitudinal control force of the ship, ΔT u is the difference in actual control input, Δf u As an unknown term, RBF neural network is used to calculate Δf u Estimate the unknown term Δf u The output expression of the neural network is shown in formula (14), h u (x) is the first Gaussian function, and o1 is the first approximation error: Δf u =W u T h u (x)+o1 (14) According to formula (13) and combined with finite time convergence, the longitudinal control force T is designed uc , Where, μ1=D1-O1+ΔT u , is the estimated value of μ1, c5, c6, ε3 are positive parameters; parameter and The adaptive law is shown in formula (16): Where η1, η2, σ1, σ2 are positive design parameters; By taking the derivative of the second finite-time sliding surface s2 and combining equation (1) and equation (11), we can obtain: make According to equation (17) and combined with finite time convergence, the bow control torque T is designed rc : Where, μ2=D2-o2+ΔT r , is the estimated value of μ2, c7, c8, ε4 are positive design parameters; and The adaptive law is shown in formula (21): In the formula, η3, η4, σ3, σ4 are positive parameters.

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