Self-adaptive fixed time control method for bridge crane system with multiple uncertainties

Abstract

The invention discloses a self-adaptive fixed time control method for a multi-uncertainty bridge crane system, and belongs to the technical field of crane control. In order to solve the problems of quick positioning and swing elimination of a bridge crane trolley under the influence of multiple uncertainties, the control scheme is as follows: establishing a bridge crane model with multiple uncertainties, and establishing a state equation through coordinate transformation; coordinate transformation is defined; constructing a Lyapunov function, and designing a virtual controller of a first subsystem; introducing a neural network, constructing a Lyapunov function, and designing virtual controllers of a second subsystem and a third subsystem; proposing a variable gain control method, and designing an adaptive law; designing a sub-controller and a control input signal; according to the self-adaptive fixed time control method disclosed by the invention, rapid positioning and swing elimination of the bridge crane under the influence of multiple uncertainties are realized, the working efficiency of the bridge crane is improved, and the requirements of rapid and accurate positioning and swing elimination of the bridge crane are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of crane control, and more specifically, relates to an adaptive fixed-time control method for a bridge crane system with multiple uncertainties. Background Art

[0002] Bridge cranes are widely used in places such as ports and shipyards where heavy objects need to be moved over a large area, as well as in offshore engineering and material transportation. With the development of large-scale ships and container transportation, offshore bridge cranes are also constantly being updated to improve technical parameters and productivity to meet the needs of large-scale ships.

[0003] For the study of the control performance of the bridge crane system, the following two issues need to be considered: 1. During the transportation process, there are uncertain factors such as external interference and system friction parameters, and the trolley needs to be able to move to the desired position quickly and accurately; 2. While maintaining stable operation, the load swing during the movement of the trolley is required to be as small as possible, and can be in a "no swing" or "micro-swing" state, especially when the trolley moves to the target position, the residual swing of the load should be eliminated as much as possible.

[0004] At present, the backstepping method has been widely used in bridge crane systems. It can effectively solve the control problem of nonlinear systems and has the advantages of strong robustness and simple structure. At the same time, adaptive control can be used to solve the problem of uncertain parameters in bridge crane systems. The traditional adaptive backstepping method is only applicable to strict feedback systems. However, bridge cranes have strong nonlinearity and complex coupling relationships, which makes it impossible to directly apply traditional methods. Therefore, for bridge crane systems with multiple uncertainties and non-strict feedback structures, how to design a fast positioning and swing elimination control method is an urgent problem to be solved. Summary of the invention

[0005] The technical problem to be solved by the adaptive fixed-time control method for a bridge crane system with multiple uncertainties disclosed in the present invention is to ensure fast and accurate positioning and sway elimination of the bridge crane while enhancing its anti-interference ability so that it has a wider application scenario.

[0006] In order to achieve the above-mentioned invention objectives, the present application adopts the following technical solutions:

[0007] S1: Establish a dynamic model of a bridge crane with multiple uncertainties and construct its state equation through coordinate transformation;

[0008] S2: define system coordinate transformation;

[0009] S3: Construct Lyapunov function and design the virtual controller of the first subsystem;

[0010] S4: Introduce radial basis neural network, construct Lyapunov function, and design virtual controllers for the second and third subsystems;

[0011] S5: Propose a variable gain control method and design an adaptive law;

[0012] S6: Design sub-controllers and control input signals based on smooth nonlinear functions;

[0013] In step S1, the establishment of a dynamic model of a bridge crane with multiple uncertainties and the construction of its state equation through coordinate transformation specifically include:

[0014] The bridge crane is a nonlinear system with under-actuation and non-strict feedback. Its system dynamics model is:

[0015]

[0016] Where y and φ are the position of the trolley and the swing angle of the rope, respectively; u is the control input; M c and M p are the weights of the trolley and the load, respectively; l is the length of the rope; g is the gravitational constant; d is the external disturbance; f r is the friction and viscous damping force, which is expressed as:

[0017]

[0018] Among them, ρ1, ρ2 and v are friction parameters;

[0019] make and The original system can be rewritten as:

[0020]

[0021]

[0022] in,

[0023] Define auxiliary signal:

[0024]

[0025]

[0026]

[0027]

[0028] Calculating its derivative gives:

[0029]

[0030] in,

[0031] make and f4(z2,z3,z4)=H, then:

[0032]

[0033]

[0034] In step S2, the definition of system coordinate transformation specifically includes:

[0035] Define the following coordinate transformation:

[0036] e1=z1-y r ;

[0037] e2=z2-β1;

[0038] e3=z3-β2;

[0039] e4=z4-β3;

[0040] Among them, β1, β2 and β3 are virtual controllers; y r is the target location.

[0041] In step S3, constructing a Lyapunov function and designing a virtual controller for the first subsystem specifically includes:

[0042] Choose the following Lyapunov function:

[0043]

[0044] Taking its derivative, we get:

[0045]

[0046] Design the following virtual controller:

[0047]

[0048] in, is a design parameter; q = [(2τ + ι) / (2τ + 1)] > 1, τ > 0 and ι∈N + ;

[0049] According to the designed virtual controller and inequality theory, we can get:

[0050]

[0051] Among them, k11 >0 is a design parameter; 0 <p<1;

[0052] According to Young's inequality, we can get:

[0053]

[0054] Among them, l 11 >0 is the design parameter; but It can be calculated as:

[0055]

[0056] Where Φ1=l 12 ;k 12 > 11 .

[0057] In step S4, the radial basis function neural network is introduced, the Lyapunov function is constructed, and the virtual controllers of the second and third subsystems are designed, which specifically includes:

[0058] (1) Calculate the time derivative of e2 and we can get:

[0059]

[0060] in,

[0061] Consider the following radial basis neural network:

[0062]

[0063] Where W2=[w 21 ,…,w 2m ] T is the weight vector; ζ2(χ2)=[v1(χ2),…,v m (χ2)] T is the basis function vector, v j (χ2) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε2(χ2) is the approximation error; is the neural network input;

[0064] Next, choose the following Lyapunov function:

[0065]

[0066] in, is a positive constant; ω2=||W2|| 2 , is the estimated value of ω2;

[0067] By taking the derivative of the above Lyapunov function V2, we can get:

[0068]

[0069] According to Young's inequality, we can get:

[0070]

[0071] Where b2 is a positive constant;

[0072] By inequality We can get:

[0073]

[0075] in,

[0076] Design the following adaptive law and virtual controller respectively:

[0077]

[0078] in, and is the design parameter;

[0079] according to And β2 design, we can get:

[0080]

[0081] Among them, k 21 >0 is the design parameter;

[0082] Similar to S3, according to We can get:

[0083]

[0084] Among them, l 21 >0 is the design parameter;

[0085] (2) Calculate the time derivative of e3, and we can get:

[0086]

[0087] in,

[0088] Consider the following radial basis neural network:

[0089]

[0090] Where W3=[w 31 ,…,w 3m ] T is the weight vector; ζ3(χ3)=[v1(χ3),…,v m (χ3)] T is the basis function vector, v j (χ3) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε3(χ3) is the approximation error; is the neural network input;

[0091] Next, choose the following Lyapunov function:

[0092]

[0093] in, is a positive constant; ω3=||W3|| 2 , is the estimated value of ω3;

[0094] By taking the derivative of the above Lyapunov function V3, we can get:

[0095]

[0096] According to Young's inequality, we can get:

[0097]

[0098] Among them, b3 is a positive constant;

[0099] Depend on We can get:

[0100]

[0101] The following adaptive laws and virtual controllers are designed respectively:

[0102]

[0103] in, and is the design parameter;

[0104] according to And β3 design, we can get:

[0105]

[0106] Similar to S3, according to We can get:

[0107]

[0108] Among them, l 31 >0 is the design parameter;

[0109] In step S5, the variable gain control method is proposed and the adaptive law is designed, which specifically includes:

[0110] Calculating the time derivative of e4, we can get:

[0111]

[0112] in,

[0113] Consider the following radial basis neural network:

[0114]

[0115] Where W4 = [w 41 ,…,w 4m ] T is the weight vector; ζ4(χ4)=[v1(χ4),…,v m (χ4)] T is the basis function vector, v j (χ4) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε4(χ4) is the approximation error; is the neural network input;

[0116] Choose the following Lyapunov function:

[0117]

[0118] Among them, λ,δ γ and δ θ is a positive constant; and They are γ * and estimates of θ;

[0119] By taking the derivative of the Lyapunov function, we can obtain:

[0120]

[0121] in, is an unknown and bounded vector, Λ=[ζ4(x4) T ,1] T is a known vector;

[0122] According to inequality theory, e4Θ T Λ can be calculated as:

[0123]

[0124] in, σ satisfies is a positive constant;

[0125] Further, we can get:

[0126]

[0127] The following adaptive laws and control inputs are designed respectively:

[0128]

[0129] Among them, k θ >0 and is the design parameter; τ r is a robust term, given later, used to compensate for uncertainty;

[0130] but Can be rewritten as:

[0131]

[0132] Among them, k 41 >0 is the design parameter;

[0133] Similar to S3, according to We can get:

[0134]

[0135] Among them, l 41 >0 is the design parameter; l 41 <2 2q-2 ;Φ4=Φ3+l 42 +σθ;

[0136] definition We can get:

[0137]

[0138] make c is a positive constant, yes The upper bound of

[0139] Design the following adaptive law:

[0140]

[0141] in, k γ >0 and is a design parameter.

[0142] In step S5, the design of the sub-controller based on the smooth nonlinear function and the control input signal specifically includes:

[0143] Will and Substitution We can get:

[0144]

[0145] Then τ r Can be designed as:

[0146]

[0147] Among them, ε>0 is a design parameter;

[0148] Therefore, the control input signal is:

[0149]

[0150] Depend on We can get:

[0151]

[0153] Using Young's inequality, we can get:

[0154]

[0155] To obtain and Items include:

[0156]

[0157] Substituting the above inequality into We can get:

[0158]

[0159] in,

[0160] according to And its derivative, we can get:

[0161]

[0162] in,

[0164] Beneficial effects:

[0165] 1. The present invention discloses an adaptive fixed-time control method for a bridge crane system with multiple uncertainties, which applies the properties and inequalities of neural networks to the bridge crane and solves the non-strict feedback problem.

[0166] 2. The present invention discloses an adaptive fixed-time control method for a bridge crane system with multiple uncertainties, and proposes an adaptive fixed-time control method to achieve rapid positioning and sway elimination of the bridge crane. The proposed algorithm not only eliminates the constraints of finite-time control, but also solves the singularity problem in traditional fixed-time control.

[0167] 3. The present invention discloses an adaptive fixed-time control method for a bridge crane system with multiple uncertainties, and designs a variable gain controller with a robust term. Compared with fixed gain, the proposed method has better adaptability and robustness.

[0168] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become more clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0169] Figure 1 A flow chart of an adaptive fixed time control method for a bridge crane system with multiple uncertainties proposed by the present invention;

[0170] Figure 2 (a) and Figure 2 (b) is the trolley position and load swing angle curve of the bridge crane system according to the method of the present invention;

[0171] Figure 3 The adaptive control gain curve proposed by the present invention;

[0172] Figure 4 (a) and Figure 4 (b) is a comparison curve between the method of the present invention and the traditional backstepping method. DETAILED DESCRIPTION

[0173] In order to better illustrate the purpose and advantages of the present invention, the invention is compared with the traditional adaptive backstepping method and the invention is further described in detail in conjunction with the embodiments and corresponding drawings.

[0174] The present invention aims at the problem of rapid positioning and sway elimination of a bridge crane system with multiple uncertainties and non-strict feedback, adopts an adaptive fixed-time control strategy, introduces a radial basis neural network into the control of the bridge crane system, and introduces an adaptive control gain method to improve the adaptability and flexibility of the system. A method for adaptive fixed-time control of a bridge crane system with multiple uncertainties is proposed. The specific implementation method of the bridge crane system control method is described in detail below.

[0175] See also Figure 1 As shown, the present embodiment discloses an adaptive fixed time control method for a bridge crane system with multiple uncertainties, comprising the following steps:

[0176] Step S1: Establish a dynamic model of a bridge crane with multiple uncertainties and construct its state equation through coordinate transformation.

[0177] Specifically:

[0178] Step S11: The bridge crane is a nonlinear system with under-actuation and non-strict feedback, and its system dynamics model is:

[0179]

[0180] Where y and φ are the position of the trolley and the swing angle of the rope, respectively; u is the control input; M c and M p are the weights of the trolley and the load, respectively; l is the length of the rope; g is the gravitational constant; d is the external disturbance; f r is the friction and viscous damping force, which is expressed as:

[0181]

[0182] Among them, ρ1, ρ2 and v are friction parameters.

[0183] Step S12: Next, in order to facilitate the subsequent controller design, the following coordinate transformation is performed on the bridge crane system:

[0184] let and The original system can be rewritten as:

[0185]

[0186] in,

[0187] Define auxiliary signal:

[0188]

[0189]

[0190]

[0191]

[0192] Calculating its derivative gives:

[0193]

[0194] in,

[0195] make and f4(z2,z3,z4)=H, then:

[0196]

[0197]

[0198] Step S2: define system coordinate transformation;

[0199] Specifically:

[0200] Define the following coordinate transformation:

[0201] e1=z1-y t

[0202] e2=z2-β1

[0203] e3=z3-β2

[0204] e4=z4-β3 (7)

[0205] Among them, β1, β2 and β3 are virtual controllers; y r is the target location.

[0206] Step S3: Construct a Lyapunov function and design a virtual controller for the first subsystem.

[0207] Specifically:

[0208] Step S31: Select the following Lyapunov function:

[0209]

[0210] Step S32: Derivative it, we can get:

[0211]

[0212] Step S33: To achieve fixed-time convergence of the system and avoid singularity problems, the following virtual controller is designed:

[0213]

[0214] in, is a design parameter; q = [(2τ + ι) / (2τ + 1)] > 1, τ > 0 and ι∈N + .

[0215] According to the above design, we can get:

[0216]

[0217] Among them, k 11 >0 is a design parameter; 0 <p<1;

[0218] Step S34: According to Young's inequality, we can get:

[0219]

[0220] Among them, l 11 >0 is the design parameter;

[0221]

[0222] Where Φ1=l 12 ;k 12 > 11 .

[0223] Step S4: Introduce the radial basis neural network, construct the Lyapunov function, and design the virtual controllers of the second and third subsystems.

[0224] Specifically:

[0225] Step S41: Using a neural network to solve non-rigid problems and estimate virtual controller derivatives to simplify the controller design process.

[0226] Calculating the time derivative of e2, we can get:

[0227]

[0228] in,

[0229] Consider the following radial basis neural network:

[0230]

[0231] Where W2=[w 21 ,…,w 2m ]T is the weight vector; ζ2(χ2)=[v1(χ2),…,v m (χ2)] T is the basis function vector, v j (χ2) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε2(x2) represents the approximation error; Input to the neural network.

[0232] Step S42: Next, select the following Lyapunov function:

[0233]

[0234] in, is a positive constant; is an estimate of ω2.

[0235] By taking the derivative of the above Lyapunov function V2, we can get:

[0236]

[0237] According to Young's inequality, we can get:

[0238]

[0239] Where b2 is a positive constant.

[0240] By inequality We can get:

[0241]

[0242] in,

[0243] Step S43: To achieve fixed-time convergence of the system and avoid singularity problems, the following adaptive laws and virtual controllers are designed:

[0244]

[0245] in, and is a design parameter.

[0246] according to And β2 design, we can get:

[0247]

[0248] Among them, k 21 >0 is the design parameter;

[0249] Step S44: Similar to step S34, according to We can get:

[0250]

[0251] Among them, l 21 >0 is the design parameter;

[0252] Step S45: Similar to step S41, combined with the above coordinate transformation, the time derivative of e3 is calculated to obtain:

[0253]

[0254] in,

[0255] Consider the following radial basis neural network:

[0256]

[0257] Where W3=[w 31 ,…,w 3m ] T is the weight vector; ζ3(X3)=[v1(χ3),…,v m (χ3)] T is the basis function vector, v j (χ3) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε3(χ3) is the approximation error; is the neural network input.

[0258] Step S46: Next, select the following Lyapunov function:

[0259]

[0260] in, is a positive constant; ω3=‖W3|| 2 , is the estimated value of ω3.

[0261] By taking the derivative of the above Lyapunov function V3, we can get:

[0262]

[0263] According to Young's inequality, we can get:

[0264]

[0265] Among them, b3 is a positive constant;

[0266] From this we can get for:

[0267]

[0268] Step S47: Design the following adaptive law and virtual controller respectively:

[0269]

[0270] in, and is a design parameter.

[0271] according to And β3 design, we can get:

[0272]

[0273] Step S48: Similar to step S34, according to We can get:

[0274]

[0275] Among them, l 31 >0 is the design parameter;

[0276] Step S5: Propose a variable gain control method and design an adaptive law.

[0277] Specifically include:

[0278] Step S51: Calculate the time derivative of e4 as:

[0279]

[0280] in,

[0281] Consider the following radial basis neural network:

[0282]

[0283] Where W4 = [w 41 ,…,w 4m ] T is the weight vector; ζ4(χ4)=[v1(χ4),…,v m (χ4)] T is the basis function vector, v j (χ4) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε4(χ4) is the approximation error; is the neural network input.

[0284] Step S52: Select the following Lyapunov function:

[0285]

[0286] Among them, λ>0,δ γ >0 and δ θ >0 is the design parameter; and They are γ * and an estimate of θ.

[0287] By taking the derivative of the Lyapunov function, we can get:

[0288]

[0289] in, is an unknown and bounded vector, Λ=[ζ4(χ4) T ,1] T is a known vector.

[0290] According to inequality theory, e4Θ T Λ can be calculated as:

[0291]

[0292] in, σ satisfies is a normal number.

[0293] Further, we can get for:

[0294]

[0295] Step S53: Introduce adaptive control gain and sub-controller based on smooth nonlinear function into the control input to improve the adaptability and robustness of the system. Design the following adaptive law and control input respectively:

[0296]

[0297] Among them, k θ >0 and is the design parameter; τ r is a robust term, given later, used to compensate for uncertainty.

[0298] but Can be rewritten as:

[0299]

[0301] Among them, k 41 >0 is a design parameter.

[0302] Step S54: Similar to step S34, according to We can get:

[0303]

[0304] Among them, l 41 >0 is the design parameter; l 41 <2 2q-2 ;Φ4=Φ3+l 42 +σθ.

[0305] Step S55: Design an adaptive law and define We can get:

[0306]

[0307] make c is a positive constant, yes The upper bound of .

[0308] Design the following adaptive law:

[0309]

[0310] in, k γ >0 and is a design parameter.

[0311] Step S6: Design a sub-controller based on a smooth nonlinear function and a control input signal.

[0312] Specifically include:

[0313] Will and Substitution We can get:

[0314]

[0316] Step S61: Design a robust controller τ r , which is used to compensate for the uncertainty of the bridge crane system and the inevitable estimation error in the adaptive update process. Then τ r Can be designed as:

[0317]

[0318] Among them, ε>0 is a design parameter.

[0319] Therefore, the control input signal is:

[0320]

[0321] Depend on We can get:

[0322]

[0323] Step S62: Using Young's inequality, we can get:

[0324]

[0325] To obtain and Items include:

[0326]

[0327] Substituting the above inequality into We can get:

[0328]

[0330] in,

[0331] Step S63: Perform stability analysis on the system. And its derivative, we can get:

[0332]

[0333] in,

[0334] It follows that the bridge crane system is practically fixed-time bounded.

[0335] The parameters of the bridge crane system used in the embodiment are set as follows: c =1.852kg, M p =0.5kg, l=0.5m, g=9.8m / s 2 , ρ1=2.0, ρ2=-0,8, ∈=0.5.

[0336] The controller related parameters are set as follows: λ=1,δ γ =1,δ θ =1, b2=1, b3=1, σ=0.05e -0.5t , k θ =1, k γ =1, k ρ =1, ε=1, p=2.

[0337] The target position is set to: y r =0.3m.

[0338] The disturbance is defined as: d = 0.1sin 0.1t.

[0339] The initial conditions are:

[0340] The sampling time is 20ms.

[0341] Depend on Figure 2 It can be seen that: considering the uncertain parameters and disturbances, the fixed time control strategy proposed in the present invention can make the trolley reach the target position within 6 seconds, the load swing is between -1.5823deg and 0.3762deg, and there is no residual swing after the system reaches a steady state. Therefore, under the premise of ensuring safety, the fixed time control strategy proposed in the present invention can effectively improve the transportation efficiency of the bridge crane.

[0342] Depend on Figure 3 It can be seen that when the system tends to be stable, the adaptive adjustment gain parameter K4 quickly converges to between 0.0367 and 0.0748.

[0343] The fixed time control algorithm proposed in the present invention is compared with the traditional backstepping method for simulation, so as to verify the superiority of the algorithm proposed in the present invention. The control parameters of the traditional backstepping method are set as follows: k1=1, k2=1.8, k3=2, k4=1.5.

[0344] Depend on Figure 4 It can be seen that: Figure 4 (a) is the displacement curve of the trolley. Under the action of the present invention, the trolley reaches the target position within 6 seconds. The traditional backstepping method reaches the target position in about 15 seconds. Figure 4 (b) is the load swing angle variation curve. The load swing range of the present invention is [-1.5823, 0.3762] degrees and there is no residual swing. The load swing range of the traditional backstepping method is [-3.3157, 2.5226] degrees and there is residual swing after the trolley reaches the target position. From the above comparison results, it can be seen that compared with the traditional backstepping control method, the fixed time control strategy proposed by the present invention is superior to the traditional backstepping method in both trolley positioning and swing elimination.

[0345] This embodiment mainly uses the system trolley displacement and load swing angle as performance parameters. Figure 2 The displacement and load swing angle curves of the trolley under the adaptive fixed time control strategy are given. Figure 3 An adaptive adjustment gain curve is given. Figure 4 The comparison curve between the control method of the present invention and the traditional backstepping method is given. Figure 4 It can be seen that the control method provided by the present invention is capable of handling multiple uncertainties, improving the working efficiency of the bridge crane system, and effectively suppressing load swing.

[0346] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the embodiments are only used to explain the invention and are not used to limit the scope of protection of the invention. Any modifications, equivalent replacements, improvements, etc. under the same principles and concepts as the invention should be included in the scope of protection of the invention.

Claims

1. An adaptive fixed-time control method for a bridge crane system with multiple uncertainties, characterized in that: The following steps are involved: S1: Establish a dynamic model of a bridge crane with multiple uncertainties and construct its state equation through coordinate transformation; S2: define system coordinate transformation; S3: Construct Lyapunov function and design the virtual controller of the first subsystem; S4: Introduce radial basis neural network, construct Lyapunov function, and design virtual controllers for the second and third subsystems; S5: Propose a variable gain control method and design an adaptive law; S6: Design sub-controllers and control input signals based on smooth nonlinear functions.

2. The method for adaptive fixed-time control of a bridge crane system with multiple uncertainties according to claim 1, characterized in that: In S1, a dynamic model of a bridge crane with multiple uncertainties is established, and its state equation is constructed through coordinate transformation, including: The bridge crane is a nonlinear system with under-actuation and non-strict feedback. Its system dynamics model is: Where y and φ are the position of the trolley and the swing angle of the rope, respectively; u is the control input; M c and M p are the weights of the trolley and the load, respectively; l is the length of the rope; g is the gravitational constant; d is the external disturbance; f r is the friction and viscous damping force, which is expressed as: Among them, ρ1, ρ2 and ∈ are friction parameters; Let θ1 = y, θ3=φ and The original system can be rewritten as: in, Define auxiliary signals: z1=θ1+lln(secθ3+tanθ3); z3=-gtanθ3; Calculate its derivative as: in, make and f4(z2,z3,z4)=H, then:

3. The method for adaptive fixed-time control of a bridge crane system with multiple uncertainties according to claim 1, characterized in that: In S2, the system coordinate transformation is defined, including: Define the following coordinate transformation: e1=z1-y r ; e2=z2-β1; e3=z3-β2; e4=z4-β3; Among them, β1, β2 and β3 are virtual controllers; y r is the target location.

4. The method for adaptive fixed-time control of a bridge crane system with multiple uncertainties according to claim 1, characterized in that: In S3, construct the Lyapunov function and design the virtual controller of the first subsystem, including: Choose the following Lyapunov function: Taking its derivative, we get: Design the following virtual controller: in, is a design parameter; q = [(2τ + ι) / (2τ + 1)] > 1, τ > 0 and ι∈N + ; According to the designed virtual controller and inequality theory, we can get: Among them, k 11 >0 is a design parameter; 0 <p<1; According to Young's inequality, we can get: Among them, l 11 >0 is the design parameter; but It can be calculated as: Where Φ1=l 12 ;k 12 > 11 .

5. The method for adaptive fixed-time control of a bridge crane system with multiple uncertainties according to claim 1, characterized in that: In S4, radial basis neural network is introduced to construct Lyapunov function and design virtual controllers for the second and third subsystems, including: (1) Calculate the time derivative of e2 and we can get: in, Consider the following radial basis neural network: Where W2=[w 21 ,…,w 2m ] T is the weight vector; ζ2(χ2)=[υ1(χ2),…,υ m (χ2)] T is the basis function vector, υ j (χ2) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε2(χ2) is the approximation error; is the neural network input; Next, choose the following Lyapunov function: in, is a positive constant; is the estimated value of ω2; By taking the derivative of the above Lyapunov function V2, we can get: According to Young's inequality, we can get: Where b2 is a positive constant; By inequality We can get: in, Design the following adaptive law and virtual controller respectively: in, and is the design parameter; according to And β2 design, we can get: Among them, k 21 >0 is the design parameter; Similar to S3, according to We can get: Among them, l 21 >0 is the design parameter; (2) Calculate the time derivative of e3, and we can get: in, Consider the following radial basis neural network: Where W3=[w 31 ,…,w 3m ] T is the weight vector; ζ3(χ3)=[υ1(χ3),…,υ m (χ3)] T is the basis function vector, υ j (χ3) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε3(χ3) is the approximation error; is the neural network input; Next, choose the following Lyapunov function: in, is a positive constant; is the estimated value of ω3; By taking the derivative of the above Lyapunov function V3, we can get: According to Young's inequality, we can get: Among them, b3 is a positive constant; Depend on We can get: The following adaptive laws and virtual controllers are designed respectively: in, and is the design parameter; according to And β3 design, we can get: Similar to S3, according to We can get: Among them, l 31 >0 is the design parameter; 6. The method for adaptive fixed-time control of a bridge crane system with multiple uncertainties according to claim 1, characterized in that: In S5, a variable gain control method is proposed and an adaptive law is designed, which specifically includes: Calculating the time derivative of e4, we can get: in, Consider the following radial basis neural network: Where W4 = [w 41 ,…,w 4m ] T is the weight vector; ζ4(χ4)=[υ1(χ4),…,υ m (χ4)] T is the basis function vector, υ j (χ4) is a Gaussian function (j=1,...,m); m>1 is the number of neurons; ε4(χ4) is the approximation error; is the neural network input; Choose the following Lyapunov function: Among them, λ,δ γ and δ θ is a positive constant; and They are γ * and estimates of θ; By taking the derivative of the Lyapunov function, we can obtain: in, is an unknown and bounded vector, Λ=[ζ4(χ4) T ,1] T is a known vector; According to inequality theory, e4Θ T Λ can be calculated as: in, σ satisfies is a positive constant; Further, we can get: The following adaptive laws and control inputs are designed respectively: Among them, k θ >0 and is the design parameter; τ r is a robust term, given later, used to compensate for uncertainty; but Can be rewritten as: Among them, k 41 >0 is the design parameter; Similar to S3, according to We can get: Among them, l 41 >0 is the design parameter; l 41 <2 2q-2 ;Φ4=Φ3+l 42 +σθ; definition We can get: make c is a positive constant, yes The upper bound of Design the following adaptive law: in, k γ >0 and is a design parameter.

7. The method for adaptive fixed-time control of a bridge crane system with multiple uncertainties according to claim 1, characterized in that: In S6, the sub-controller and control input signal based on smooth nonlinear functions are designed, including: Will and Substitution We can get: Then τ r Can be designed as: Among them, ε>0 is a design parameter; Therefore, the control input signal is: Depend on We can get: Using Young's inequality, we can get: To obtain and Items include: Substituting the above inequality into We can get: in, according to And its derivative, we can get: in,

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