Unmanned ship power positioning integral sliding mode fault-tolerant control method based on fuzzy system

Abstract

The application discloses an unmanned ship power positioning integral sliding mode fault-tolerant control method based on a fuzzy system, and comprises the following steps: a mathematical model of unmanned ship movement under an actuator fault is established; a T-S fuzzy model of the unmanned ship corresponding to the mathematical model is established; based on the established T-S fuzzy model of the unmanned ship, an integral sliding mode surface with fault information is constructed; and the asymptotic stability of the sliding mode dynamics of the system is proved by combining the definition of performance index and related lemmas.Aiming at the nonlinear term in the T-S fuzzy model of the unmanned ship, a fuzzy logic method is used to approximate the unknown smooth nonlinear term; based on the constructed integral sliding mode surface with fault information, a suitable Lyapunov function is selected, a fault-tolerant controller and an adaptive law are designed, and the reachability of the system is proved.The application can solve the problem that the resolution and complexity of the T-S model of the unmanned ship are difficult to balance, and can also ensure that the system has robustness from the initial stage.

Description

Technical Field

[0001] This invention relates to the field of unmanned vessel dynamic positioning fault-tolerant control technology, and in particular to an integral sliding mode fault-tolerant control method for unmanned vessel dynamic positioning based on fuzzy systems. Background Technology

[0002] In recent years, the dynamic positioning control problem of unmanned vessels based on the TS fuzzy model has been studied in depth. W.-H. Ho et al. used the orthogonal function method and the hybrid Taguchi genetic algorithm to solve the quadratic finite-time optimal controller design problem for the dynamic positioning system control system based on the TS fuzzy model. WENgongi et al. designed a controller based on the TS fuzzy model and optimal... Robust dynamic positioning controllers for control technology. Y.-L. Wang et al. studied network modeling, stability analysis, and controller design for an observer-based TS fuzzy dynamic positioning system for unmanned surface vessels (USVs). Although the aforementioned TS fuzzy models achieved good results, they simplified the original nonlinear system as much as possible, resulting in a loss of resolution. However, when the resolution of the TS model is improved by increasing the number of fuzzy local models, the complexity of the TS model also increases, making stability analysis and control synthesis of the TS fuzzy model very difficult. Therefore, achieving a good balance between the resolution and complexity of the TS model for USVs has become a pain point in practical applications.

[0003] On the other hand, in complex marine environments, propulsion failures of unmanned surface vessels (USVs) are inevitable. Propulsion failures can lead to significant performance degradation or mission cancellation, and even serious consequences for navigation safety. Therefore, research on fault-tolerant control for USVs is essential. Currently, some progress has been made in this field. G. Zhang et al. designed a fault-tolerant controller that does not rely on fault detection and identification modules, and H. Zhang et al. presented a fault-tolerant control design scheme for USVs within the framework of the TS fuzzy model. However, traditional sliding mode control design schemes cannot guarantee that the system will always meet the desired robustness from the initial stage. Therefore, it is very meaningful to design a fault-tolerant controller for USVs based on the TS fuzzy model that can guarantee robustness from the initial stage. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention discloses an unmanned surface vessel dynamic positioning integral sliding mode fault-tolerant control method based on the TS fuzzy model, comprising the following steps:

[0005] S1. Analyze the motion of the unmanned vessel and, in conjunction with the thruster failure model, establish a mathematical model of the motion of the unmanned vessel under thruster failure.

[0006] S2, according to the mathematical model of the unmanned ship motion, the corresponding unmanned ship T-S fuzzy model is established;

[0007] S3, based on the unmanned ship T-S fuzzy model established in step S2, an integral sliding mode surface with fault information is constructed;

[0008] S4, based on the integral sliding mode surface with fault information constructed in step S3, combined with The definition of performance index and related lemmas are proved, and the sliding mode dynamics of the system has asymptotic stability;

[0009] S5, for the nonlinear term in the T-S fuzzy model of the unmanned ship in S2, fuzzy logic method is used to approximate.

[0010] S6, based on the integral sliding mode surface with fault information constructed in step S3, select the appropriate Lyapunov function, design fault-tolerant controller and adaptive law, and prove the reachability of the system.

[0011] S1 is as follows:

[0012] S11, analyze the motion model of the unmanned ship, as follows:

[0013]

[0014] where, is the linear velocity and angular velocity vector of the unmanned ship defined in the body coordinate system, θ(t) v(t) and r(t) represent the forward speed, lateral drift speed and yaw angular velocity respectively; and is the direction vector in the fixed coordinate system, x p (t) and y p (t) represent the horizontal position of the unmanned ship, ψ(t) represents the heading angle of the unmanned ship. w(t) represents the ocean disturbance; M represents the inertia matrix; N represents the damping matrix; G represents the mooring force, and the thruster configuration matrix E with arbitrary angle Θ is defined as

[0015]

[0016] where, and represent the moment arm in yaw.

[0017] S12, analyze the thruster fault model of the unmanned ship, as follows:

[0018] u F (t) is a unified thruster fault model, described as follows:

[0019] u F (t) = ρu(t) + σu s (t) (2)

[0020] where p is a diagonal positive semi-definite weight matrix, belonging to the set where the element For l e {1, …, m} and j e {1, …, n}, l is the lth thruster, j is the jth fault model, m and n represent the number of all thrusters and the number of fault modes, respectively, and u s (t) satisfies where denotes the unknown upper bound of the thruster time-varying stuck fault.

[0021] S13, establish the unmanned ship motion mathematical model under thruster fault, as follows:

[0022]

[0023]

[0024] Let g(t, v) = η(t), where g(t, v) denotes a time-varying, nonlinear vector-valued function of v(t). At this time, the unmanned ship system can be rewritten as

[0025]

[0026] where u(t) = u0(t) + u1(t)

[0027]

[0028]

[0029] S2 is specifically adopted as follows:

[0030] S21, expand the above unmanned ship mathematical model, as follows:

[0031] Let From (3) and (4), we can get:

[0032]

[0033] S22, select the antecedent variable of fuzzy rule, establish the T-S fuzzy model of unmanned ship, as follows: Let ψ assume that the heading angle changes from to Further, we can get Then by introducing the following rules we can get the T-S fuzzy unmanned ship system.

[0034]

[0035] where i = 1, 2, 3, 4, Q i1 and Q i2 is a fuzzy set, z(t) is the control output,

[0036]

[0037]

[0038]

[0039] C i is a known matrix, for convenience, g(t, x) is simply denoted as g(x). In summary, the T-S fuzzy global model of the unmanned ship can be described as

[0040]

[0041] where,

[0042] In S3, the following method is used:

[0043] S3, construct an integral sliding mode surface with fault information as follows:

[0044] According to the definition of the sliding mode surface

[0045]

[0046] The integral sliding mode surface construction method in this method is as follows:

[0047]

[0048] where, is a free design matrix that satisfies the condition , in the above formula is an estimated matrix of the unknown actuator failure level p, which is updated by the following projection algorithm

[0049]

[0050] where, is the i-th column of the input matrix B2, K i is the i-th row of the gain matrix K, and γ0 is a tunable parameter.

[0051] Because the term -Gx(t0) has the property α(x(t0), t0) = 0, the reaching phase is eliminated.

[0052] In S4, the following method is used:

[0053] S4, prove that the sliding mode dynamics of the system have asymptotic stability as follows:

[0054] Taking the derivative of the integral sliding surface, we have

[0055]

[0056] Let Then the equivalent control is

[0057]

[0058] Substituting the system equation, we have

[0059]

[0060] Let From The definition and related lemmas, we have

[0061] If there exist P = P T > 0 and matrix such that the following inequality holds for the constructed integral sliding surface, then there exists asymptotically stable sliding mode dynamics from the initial time and The performance index is not greater than the positive scalar γ'0

[0062]

[0063] In S5, the following method is used:

[0064] In S5, the fuzzy logic method is used to approximate the unknown smooth function g(x), as follows:

[0065] The fuzzy logic method is used to approximate the unknown smooth function g(x) in the T-S fuzzy model of the unmanned ship. They have the ability to uniformly approximate any nonlinear smooth function defined on a compact set. Therefore, the fuzzy logic method can be used to obtain the following equation

[0066] g(x) = θ T ξ(x) + δ(x) (15)

[0067] where θ ∈ R n is an unknown adjustable parameter vector ξ(x) is a fuzzy basis function vector, usually a Gaussian function is selected so that the future basis vector is positive, and δ(x) is the approximation error, whose bound is an unknown constant δ0, i.e., the following inequality can be obtained

[0068] ||δ(x)|| ≤ δ0 (16)

[0069] In S6, the following method is used:

[0070] In S61, a fault-tolerant controller is designed, as follows:

[0071] The integral sliding mode controller designed in this method consists of two parts

[0072] u(t) = u0(t) + ui(t) (17)

[0073] where,

[0074]

[0075] In the above equation, K j = L j P -1 , and The term u0(t) is used to suppress the disturbance, while ui(t) is a designed discontinuous control action to compensate for the actuator faults and reject the nonlinear term, forcing the system state to stay on the integral sliding surface constructed in this method. Let μ be a positive parameter. In particular, is the inverse of μ0, i.e., μ0 = 1 / μ, and

[0076]

[0077] where, λ N is the smallest eigenvalue of the matrix NN T , parameters and are the weight matrix θ, the reconstruction error upper bound δ0, the fault failure factor σ, and the stuck fault upper bound and the disturbance upper bound ∈ is an arbitrary positive scalar.

[0078] S62, design the adaptive law as follows:

[0079] The matrix decomposition form used in the subsequent analysis is as follows

[0080] F1= [F 11 F 12 … F 1q ], N = [N1 N2 … N m ],

[0081] θ = [θ1 θ2 … θ M ] T , ξ(x) = [ξ1(x) ξ2(x) … ξ M (x)] T

[0082] where, and θ,

[0083] The adaptive law is as follows:

[0084]

[0085] where i = 1,...,m, k = 1,...,q, r = 1,...,M, μ 00 , σ i0 , θ r0 and δ 00 are bounded initial values of and . Constants γ, γ 1i , γ 2i , γ 3k , γ 4r and γ5are positive design parameters.

[0086] Let

[0087]

[0088] Since ρ, μ0, σ i , θ and δ0are unknown parameters, the error system can be rewritten as

[0089]

[0090] S63, To analyze the reachability, a Lyapunov function is constructed:

[0091] Let then

[0092]

[0093] where V0(t) = (1 / 2)α T (x)α(x), the derivative of the Lyapunov function is taken, and the constructed integral sliding mode surface, fuzzy logic approximator, adaptive law and control law are brought into the formula after the derivative of the Lyapunov function, to obtain:

[0094]

[0095] From the above formula, it can be obtained that is a non-increasing function of time and Therefore, V, α(x), when t→∞, there exists, the integral operation is performed on both sides of the above formula, to obtain where Further, when t→∞, therefore, This means that alpha is a uniformly continuous function. In combination with the Barbalat lemma, the system trajectory will remain on the integral sliding surface

[0096] Further, the step S6 further comprises:

[0097] S7, the mathematical model of the unmanned ship motion under the fault of the unmanned ship dynamic positioning integral sliding mode fault-tolerant control method based on T-S fuzzy model, the integral sliding surface considering the fault information, the fault-tolerant controller and the adaptive law are simulated and verified, and compared with conventional methods, and the effectiveness and superiority are further verified.

[0098] Since the above technical solutions are adopted, the unmanned ship dynamic positioning integral sliding mode fault-tolerant control method based on T-S fuzzy model provided by the application uses a fuzzy logic method to approximate the local nonlinear term in the T-S fuzzy model of the unmanned ship, and then balances the resolution and complexity of the T-S fuzzy model of the unmanned ship. In addition, the integral sliding mode control method with fault information is used to design the fault-tolerant controller of the T-S fuzzy model of the unmanned ship, so that the conservativeness of the controller is reduced, and the robustness and fault-tolerant capability of the unmanned ship are maintained from the initial time. BRIEF DESCRIPTION OF DRAWINGS

[0099] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments described in the present application, and those skilled in the art can also obtain other drawings according to these drawings without creating any creative labor.

[0100] Figure 1 The method flowchart of the present application.

[0101] Figure 2 The state simulation diagram provided by the embodiment of the present application.

[0102] Figure 3 The adaptive law simulation diagram provided by the embodiment of the present application.

[0103] Figure 4 The adaptive law simulation diagram provided by the embodiment of the present application.

[0104] Figure 5 The adaptive law simulation diagram provided by the embodiment of the present application.

[0105] Figure 6 The adaptive law simulation diagram provided by the embodiment of the present application.

[0106] Figure 7 The adaptive law simulation diagram provided by the embodiment of the present application.

[0107] Figure 8 An adaptive law simulation diagram provided for the embodiment of the present application. DETAILED DESCRIPTION

[0108] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in 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. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should fall within the scope of protection of the present application.

[0109] It should be noted that the terms "first", "second", and the like in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device including a series of steps or units does not have to be limited to only those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0110] As shown in Figure 1 , the present application provides a fuzzy system-based unmanned ship dynamic positioning integral sliding mode fault-tolerant control method, comprising the following steps:

[0111] S1, analyzing the motion of the unmanned ship, and combining the propeller fault model, establishing a mathematical model of the unmanned ship motion with propeller faults;

[0112] S2, establishing a T-S fuzzy model corresponding to the mathematical model of the unmanned ship motion according to the mathematical model of the unmanned ship motion;

[0113] S3, based on the T-S fuzzy model of the unmanned ship established in step S2, constructing an integral sliding surface with fault information;

[0114] S4, based on the integral sliding surface with fault information constructed in step S3, combining the definition of performance index and related lemmas, proving that the sliding mode dynamics of the system have asymptotic stability.

[0115] S5, for the nonlinear term in the T-S fuzzy model of the unmanned ship in S2, a fuzzy logic method is used to approximate.

[0116] S6, based on the integral sliding surface with fault information constructed in step S3, selecting a suitable Lyapunov function, designing a fault-tolerant controller and an adaptive law, and proving the reachability of the system.

[0117] The specific process of step S1 is as follows:

[0118] S11, analyze the motion model of the unmanned ship as follows:

[0119]

[0120] wherein, is the linear velocity and angular velocity vector of the unmanned ship defined in the body coordinate system, θ(t) v(t) and r(t) represent the forward speed, lateral drift speed, and yaw angular velocity, respectively; and is the direction vector in the fixed coordinate system, x p (t) and y p (t) represent the horizontal position of the unmanned ship, ψ(t) represents the heading angle of the unmanned ship, w(t) represents the ocean disturbance, M represents the inertia matrix, N represents the damping matrix, G represents the mooring force, and the thruster configuration matrix E with an arbitrary angle Θ is defined as

[0121]

[0122] wherein, and represent the moment arm in yaw.

[0123] S12, analyze the thruster fault model of the unmanned ship as follows:

[0124] u F (t) is a unified thruster fault model representing the description as follows:

[0125] u F (t) = ρu(t) + σu s (t) (2)

[0126] wherein, ρ is a diagonal positive semi-definite weight matrix, belonging to the set wherein, the element for l∈{1,…,m} and j∈{1,…,n}, l is the lth thruster, j is the jth fault model, m and n represent the number of all thrusters and the number of fault modes, respectively, and u s (t) satisfies wherein, represents the unknown upper bound of the thruster time-varying stuck fault.

[0127] S13, establish the unmanned ship motion mathematical model under thruster fault as follows:

[0128]

[0129]

[0130] Let g(t, v) = η(t), where g(t, v) represents a time-varying, nonlinear vector-valued function of v(t). In this case, the unmanned ship system can be rewritten as

[0131]

[0132] where u(t) = u0(t) + u1(t)

[0133]

[0134] The specific process of step S2 is as follows:

[0135] The following method is specifically used in S2:

[0136] S21, expand the above unmanned ship mathematical model, as follows:

[0137] Let From (3) and (4), we can get:

[0138]

[0139] S22, select the antecedent variables of the fuzzy rule, and establish the T-S fuzzy model of the unmanned ship, as follows: Let ψ assume that the heading angle changes from to Further, we can get Then by introducing the following rules, we can get the T-S fuzzy unmanned ship system.

[0140]

[0141] where i = 1, 2, 3, 4, Q i1 and Q i2 are fuzzy sets, z(t) is the control output,

[0142]

[0143]

[0144]

[0145] C i is a known matrix, and for convenience of representation, g(t, x) is simply denoted as g(x). Based on the above, the T-S fuzzy global model of the unmanned ship can be described as

[0146]

[0147] wherein,

[0148] The specific process of step S3 is as follows:

[0149] S3, construct the integral sliding mode surface with fault information, as follows:

[0150] According to the definition of the sliding mode surface

[0151]

[0152] The integral switching surface construction method in the method is as follows:

[0153]

[0154] wherein, is a free design matrix satisfying the condition , wherein is an estimation matrix of the unknown actuator failure level p, which is updated by the following projection algorithm

[0155]

[0156] wherein, is the i-th column of the input matrix B2, K i is the i-th row of the gain matrix K, and γ0 is an adjustable parameter.

[0157] Because the term -Gx(t0) has the property α(x(t0),t0)=0, the reaching phase is eliminated.

[0158] S4, prove that the sliding mode dynamics of the system has asymptotic stability, as follows:

[0159] Taking the derivative of the integral switching surface, we have

[0160]

[0161] Let then the equivalent control is

[0162]

[0163] Substituting the system equation, we have

[0164]

[0165] Let by definition and related lemmas, it is not difficult to obtain:

[0166] If P = P T >0 and matrix If the following inequality holds for the constructed integral sliding surface, then there exists an asymptotically stable sliding dynamic from the initial time. The performance index is no greater than the positive scalar γ′0

[0167]

[0168] S5. The fuzzy logic method approximates the unknown smooth function g(x), as shown below:

[0169] By using FLS to approximate the unknown smooth function g(x) in the TS fuzzy model of the unmanned vessel, it is possible to uniformly approximate any nonlinear smooth function defined on a compact set. Therefore, the following equation can be obtained using fuzzy logic methods.

[0170] g(x)=θ T ξ(x)+δ(x) (15)

[0171] Where, θ∈R n Let ξ(x) be an unknown, adjustable parameter vector, and let δ(x) be a fuzzy basis function vector, typically chosen as a Gaussian function so that future basis vectors are positive. Let δ(x) be the approximation error, bounded by an unknown constant δ0. Then, the following inequality can be obtained.

[0172] ||δ(x)||≤δ0 (16)

[0173] S61. Design a fault-tolerant controller as shown below:

[0174] The integral sliding mode controller designed using this method consists of the following two parts.

[0175] u(t)=u0(t)+u1(t) (17)

[0176] in,

[0177]

[0178] In the above formula, K j =L j P -1 , and The term u0(t) is used to suppress disturbances, while u1(t) is a designed discontinuous control behavior to compensate for actuator failures and reject nonlinear terms, forcing the system state to remain on the integral sliding surface constructed by this method. Let μ be a positive parameter. In particular, It is an estimate of the reciprocal of μ0, that is, μ0 = 1 / μ, and

[0179]

[0180] where λ N is the minimum eigenvalue of the matrix NN T , the parameter and are the weight matrix θ, the reconstruction error upper bound δ0, the failure factor σ, and the stuck fault upper bound u s , respectively, and the disturbance upper bound ∈ is an arbitrary positive scalar.

[0181] S62, design the adaptive law as follows:

[0182] The matrix decomposition form used in the subsequent analysis is as follows

[0183] F1=[F 11 F 12 … F 1q ],N=[N1 N2 … N m ],

[0184] θ=[θ1 θ2 … θ M ] T ,ξ(x)=[ξ1(x) ξ2(x) … ξ M (x)] T

[0185] where, and θ,

[0186] The adaptive law is as follows:

[0187]

[0188] where i=1,...,m, k=1,...,q, r=1,...,M, μ 00 , σ i0 , θ r0 and δ 00 are the bounded initial values of and . The constants γ, γ 1i , γ 2i , γ 3k , γ 4r and γ5 are positive design parameters.

[0189] Let

[0190]

[0191] Because ρ, μ0, σ i , θ and δ0 are unknown parameters, so the error system can be rewritten as

[0192]

[0193] S63, in order to analyze the accessibility, the Lyapunov function is constructed:

[0194] Let Then

[0195]

[0196] Wherein, V0(t)=(1 / 2)α T (x)α(x), the derivative of the Lyapunov function is taken, and the constructed integral sliding surface, fuzzy logic approximator, adaptive law and control law are brought into the formula after the derivative of the Lyapunov function, to obtain:

[0197]

[0198] From the above formula, it can be obtained that is a non-increasing function of time and Therefore, V, α(x), When t→∞, There exists, the integral operation is carried out on both sides of the above formula, to obtain Wherein, Further, when t→∞, there is Therefore, This means that α is a uniformly continuous function. Combined with the Barbalat lemma, the system trajectory will be kept on the integral sliding surface

[0199] The method further comprises:

[0200] S7, the mathematical model of the unmanned ship motion under the fault of the integral sliding mode fault-tolerant control method for the dynamic positioning of the unmanned ship based on the T-S fuzzy model, the integral sliding surface considering the fault information, the fault-tolerant controller and the adaptive law are simulated and verified, and compared with the conventional method, to further verify the effectiveness and superiority.

[0201] In order to verify the effectiveness of the integral sliding mode fault-tolerant control method for the dynamic positioning of the unmanned ship based on the T-S fuzzy model provided in the embodiment, matlab is used for simulation experiment verification, and detailed description is made.

[0202] Specifically, in the embodiment, the parameter matrix of the T-S fuzzy UMVs model is

[0203]

[0204]

[0205] Without loss of generality, the ocean disturbance is where, and are the shaping filters; and denote the dominant wave intensity coefficients; ε1=0.5 and ε2=1.7 are the damping coefficients; and denote the frequency of the wave encountered; and denote band-limited white noises with power 2.69 and 1.56, respectively, and

[0206] In this case, the nonlinear term g(t,x(t)) is expressed as g2=sin(v(t)); g3=0.02r(t), and in the simulation, x(0)=[0.1-0.01-0.050.11-0.070.07] T , The performance index is chosen as γ'0=1, and the thruster failure settings after 30 seconds are set as: the front tunnel thruster fails by 40%, the rear tunnel thruster I simultaneously fails by 0.1sin(2t), B 2v is chosen as

[0207] It is not difficult to prove that rank(B 2v ) = rank(N) = 3 < 6 = m. Moreover, some initial values of the estimated parameters and the adjustment gains are as follows:

[0208]

[0209]

[0210] γ = 10,

[0211] γ 01 = γ 02 = γ 03 = γ 04 = γ 05 = γ 06 = 0.01, γ 11 = γ 12 = γ 13 = γ 14 = γ 15 = γ 16 = 0.001,

[0212] γ 21 = γ 22 = γ 23 = γ24 = 0.001, gamma 25 = 0.001, gamma 26 = 0.001, gamma 31 = 0.001, gamma 32 = 0.001, gamma 33 = 0.001, gamma

[0213] gamma 41 = 0.001, gamma 42 = 0.001, gamma 43 = 0.001, gamma 44 = 0.001, gamma 45 = 0.001, gamma 46 = 0.001, gamma

[0214] Based on the above parameters, the simulation verification of an integral sliding mode fault-tolerant control method for the dynamic positioning of an unmanned ship based on a T-S fuzzy model is as shown in Figures 2-8 The state of the T-S fuzzy unmanned ship system is as shown in Figure 2 It can be seen from Figure 2 that when the fault occurs at t=30s, the fault-tolerant controller designed by the method makes the state tend to zero ultimately. Figures 3-8 The changes of adaptive parameters are shown. It can be seen that they are convergent, which meets our expectation. Thus, the digital simulation of the algorithm is completed, and its effectiveness is verified.

[0215] The above embodiment numbers of the application are only for description, and do not represent the advantages and disadvantages of the embodiments.

[0216] In the above embodiments of the application, the description of each embodiment has its own emphasis, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0217] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the above embodiments, those skilled in the art should understand that: they can still modify the technical solutions recorded in the above embodiments, or make equivalent replacement for 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 application.

Claims

1. A T-S fuzzy model-based integral sliding mode fault-tolerant control method for dynamic positioning of an unmanned ship, characterized in that, The method comprises the following steps: analyzing the motion state of the unmanned ship, and establishing an unmanned ship motion mathematical model under propeller failure in combination with a propeller failure model; establishing an unmanned ship T-S fuzzy model corresponding to the model according to the unmanned ship motion mathematical model; constructing an integral sliding mode surface with fault information based on the unmanned ship T-S fuzzy model; Combining The definition of performance index and related lemma are given, and the asymptotic stability of the sliding mode dynamics of the T-S fuzzy model of the unmanned ship is proved. approximating nonlinear terms in the unmanned ship T-S fuzzy model by using a fuzzy logic method; selecting a suitable Lyapunov function, designing a fault-tolerant controller and an adaptive law, constructing an integral sliding mode surface with fault information, and proving the reachability of the unmanned ship T-S fuzzy model; the specific process of establishing the unmanned ship T-S fuzzy model is as follows: equivalent rewriting is performed on the unmanned ship motion mathematical model; Select As the antecedent variable of the fuzzy rule, the fuzzy model of the unmanned ship T-S is obtained, and after a series of operations, the following T-S fuzzy unmanned ship global model is obtained: wherein, , and are fuzzy sets, is a control output, ; the integral sliding mode surface is as follows: wherein is a freely designed matrix satisfying the condition is an estimate matrix of unknown actuator failure levels is an estimate matrix of unknown actuator failure levels is an estimate matrix of unknown actuator failure levels when the sliding mode dynamics of the unmanned ship T-S fuzzy model is proved to have asymptotic stability: derivation is performed on the integral sliding mode surface to obtain Let The equivalent control is then substitution into the unmanned ship T-S fuzzy model equation obtains Let By the definition and related lemmas, we obtain the following theorem If there exists and a matrix such that the following inequality holds for the constructed integral sliding surface the asymptotically stable sliding mode dynamics exist from the initial time and Approximating unknown smooth functions in T-S fuzzy model of unmanned surface vehicle using fuzzy logic approach Using fuzzy logic approach, the following equation is obtained where is an unknown adjustable parameter vector, is a vector of blurring basis functions, the Gaussian functions are chosen so that the future basis vector is positive, and is an approximation error whose bound is an unknown constant i.e. the following inequality is obtained the integral sliding mode controller of the unmanned ship T-S fuzzy model is composed of the following two parts wherein, In the above equation, and , the term is used to suppress the disturbance, while is a designed discontinuous control action to compensate for actuator faults and reject the nonlinear term, forcing the system state to remain on the integral sliding surface constructed by the proposed method, i.e. is a positive parameter, is the inverse of the estimation, i.e., , and wherein is the smallest eigenvalue of the matrix , the parameters and are weight matrices , the reconstruction error upper bound , the failure factor of fault , the stuck-at fault upper bound and the perturbation upper bound , is an arbitrary positive scalar; wherein the adaptive law is designed as follows: wherein, and are respectively and bounded initial values, constants and are positive design parameters; in order to analyze the reachability, a Lyapunov function is constructed: Let then there are wherein, Taking the derivative of the Lyapunov function and bringing the constructed integral sliding surface, fuzzy logic approximator, adaptive law and control law into the formula after the derivative of the Lyapunov function, we get: From the above equation, we have is a non-increasing function of time and , so , when , there exists, integrating both sides of the above equation, we have where , when , we have , so , i.e. is uniformly continuous, and combined with Barbalat lemma, the system trajectory will be kept on the integral sliding surface .

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