An unmanned ship course fault-tolerant control method with input and state quantization

Abstract

The application provides a kind of unmanned ship heading fault-tolerant control method with input and state quantization, comprising: considering the fault factors of sensors and actuators in USV fault-tolerant system, designing controller;Using extended state observer, estimate the state variables and uncertainty of the system, and reconstruct the quantized state variables;Linearly describe the process of input quantization, the controller does not need any prior information of quantization parameter;The stability of the controller and observer is proved by Lyapunov stability theory, and the whole closed-loop system is finally consistent bounded.The application considers the fault factors in the process of ship motion control, and uses quantization technology to process the control input and state variables of the system.In the simulation process, the saturation function is used instead of the sign function in the control law to prevent chattering, and the effectiveness of the unmanned ship heading fault-tolerant control strategy with input and state quantization is verified.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of artificial intelligence, in particular, especially relates to a USV heading fault-tolerant control method with input and state quantization. BACKGROUND

[0002] With the development of shipping industry, the research of unmanned surface vehicle (USV) has attracted extensive attention of many experts and scholars. Compared with the traditional human control system, the characteristics of USV are small size, high mobility and high speed, and now it is mainly used to perform those tasks that are dangerous or not suitable for human participation. Heading control as the basis of USV motion control has important research significance. In the actual navigation process, the motion parameters of USV will change with the navigation ocean environment and the navigation conditions of the ship, therefore, USV shows high nonlinear characteristics.

[0003] However, in the control process, the system may not work normally due to the occurrence of faults; and in the process of navigation practice, the communication bandwidth is limited, and the control signal needs to be transmitted in the given communication bandwidth. In addition, in the process of navigation practice, the control signal needs to be transmitted through the communication channel, and since the communication bandwidth is limited at sea, it is meaningful to quantize the input and state of the USV heading control process. Through the quantization technology, the system can be ensured to operate normally within the given communication bandwidth. At present, there are few researches on the fault tolerance of sensors and actuators at the same time. SUMMARY

[0004] In view of the above-mentioned technical problems existing in the motion control of the existing USV, a USV heading fault-tolerant control method with input and state quantization is provided. The present application considers the fault factors of the sensors and actuators in the USV motion control process, and adopts the quantization technology to process the control input and state variables of the system.

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

[0006] A USV heading fault-tolerant control method with input and state quantization comprises:

[0007] S1, considering the fault factors of the sensors and actuators in the USV fault-tolerant system, a controller is designed;

[0008] S2, an extended state observer is adopted to estimate the state variables and uncertainties of the system, and the quantized state variables are reconstructed;

[0009] S3, the process of input quantization is linearly described, and the controller does not need any prior information of the quantization parameters;

[0010] S4, the stability of the controller and the observer is proved by using Lyapunov stability theory, and the whole closed-loop system is finally uniformly bounded.

[0011] Further, the step S1 specifically comprises:

[0012] S11, constructing a ship mathematical model, as follows:

[0013]

[0014] wherein ψ represents the heading of the USV, r represents the turning angle velocity of the USV; a represents a nonlinear coefficient of the Norrbin model, b represents a gain of the control system, K represents a turning index, T represents a following index, ω represents an unknown disturbance of the system, τ represents a control input of the system, δ represents a rudder angle of the system, and |ω|≤D;

[0015] S12, selecting (ψ, r) as state variables, and defining x1=ψ, f(x, t)=a1r+a2r 3 , taking τ=δ, and Q(τ) is a control input of the quantized system; quantization converts continuous signals into segmented signals, thereby introducing an input-quantized USV heading control mathematical model, as follows:

[0016]

[0017] S13, based on fault factors, considering the fault tolerance of sensors and actuators, designing a fault-tolerant subsystem, as follows:

[0018]

[0019] τ=ρ0ν

[0020] wherein ρ0 and ρ i represent unknown parameters, 0<ρ i0 ≤ρ i ≤1, 0<ρ 00 ≤ρ0≤1; the instruction of x1 is y d , and represent the output of the sensor; the control target is to design the control rate ν to make the signals of the entire closed-loop system bounded, and when t→∞,

[0021] Further, the step S2 specifically comprises:

[0022] S21, quantizing the state variables x1, x2 and the control input τ of the USV through a uniform quantizer, the uniform quantizer being as follows:

[0023]

[0024] wherein, γ>0 is quantization step, H1=γ, H i+1 =H i +γ;

[0025] S22, quantization error of uniform quantizer is bounded and can guarantee Let Q(τ)=q1(t)τ+q2(t), then:

[0026]

[0027] Wherein, q1(t) represents unknown parameters, since the sign remains unchanged in the quantization process, if |τ|<κ, q1(t)>0 is obtained, considering that Q(τ(t)) is bounded, q2(t) is also bounded, and

[0028] S23, design extended state observer, as follows:

[0029]

[0030] Wherein, ε represents a constant greater than zero, All represent the state of the observer, Using the designed extended state observer, when t→∞,

[0031] Further, step S3, specifically comprising:

[0032] Let Q(τ)=q1(t)τ+q2(t), and:

[0033]

[0034] Wherein, q1(t) represents unknown parameters, since the sign remains unchanged in the quantization process, q1(t)>0 is obtained from the above formula, if |τ(t)|<κ, considering that Q(τ(t)) is bounded, q2(t) is also bounded, and

[0035] Further, step S4, specifically comprising:

[0036] S41, define Then

[0037] S42, design Lyapunov function, as follows:

[0038]

[0039] And the derivative of the designed Lyapunov function is obtained:

[0040]

[0041] Since then:

[0042]

[0043] S43, since 0 < p 20 ≤ p2≤ 1, then that is then:

[0044]

[0045] S44, define a1= -c1z1, c1> 0, then:

[0046]

[0047] wherein,

[0048] S45, according to the definition in step S41, we get:

[0049]

[0050] S46, design Lyapunov function, as follows:

[0051]

[0052] Since then:

[0053]

[0054] wherein, μ2= p2p0,

[0055] S47, since is an unknown constant, then use adaptive method, design Lyapunov function, as follows:

[0056]

[0057] wherein, γ1> 0, then:

[0058]

[0059] S48, since μ3= p2p0 is unknown, design control law and adaptive law as follows:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] S49, the extended state observer designed according to step S23 is defined as

[0066]

[0067]

[0068] S410, the error state equation of the observer is defined as follows:

[0069]

[0070] wherein,

[0071] S411, for any given positive definite matrix Q, there is a symmetric positive definite matrix P that satisfies the following Lyapunov equation as follows:

[0072] B T P + PB + Q = 0

[0073] S412, the Lyapunov function of the extended state observer is defined as follows:

[0074]

[0075] S413, the derivative of the defined Lyapunov function of the extended state observer is taken to obtain:

[0076]

[0077]

[0078] wherein, λ min (Q) represents the minimum eigenvalue of Q;

[0079] S414, it is known from that the convergence condition of the observer is as follows:

[0080]

[0081] The convergence speed of the observer error depends on ε, the smaller ε is, the faster the convergence is, and as ε decreases, will converge to 0 gradually;

[0082] S415, Lyapunov function set by the design controller process:

[0083]

[0084] Since q1≥q 1min =1 / ∈>0, then:

[0085]

[0086] where, Since Take y d =sint, then:

[0087]

[0088] S416, calculate the inequality equation solution as follows:

[0089]

[0090] where a represents any constant;

[0091] S417, if V(t) and k(·) are smooth functions on V(t)≥0, N(·) is a smooth N function, θ0 is a non-zero constant, if c1>0, c0 is a constant, θ0(t) is an unknown time-varying parameter, then V(t), k(t) and bounded on ;

[0092] S418, from step S416:

[0093]

[0094] where, From step S417, V(t) is bounded on Therefore, z1 and z2 are bounded on By taking a large enough λ and γ2 value, ensure that t→∞, z1, z2 is small enough, so that

[0095] S419, Lyapunov function for the entire closed loop system design, as follows:

[0096] V o =V+Ve

[0097] And by differentiating the designed Lyapunov function, we obtain:

[0098]

[0099] This proves that the entire closed-loop system is eventually uniformly bounded.

[0100] Compared with the prior art, the present invention has the following advantages:

[0101] 1. The present invention provides a fault-tolerant control method for unmanned surface vessel (USV) heading with input and state quantization, which addresses the heading control problem of USV by simultaneously considering the fault tolerance issues of actuator input quantization and sensor state quantization.

[0102] 2. The present invention provides a course fault-tolerant control method for unmanned vessels with input and state quantization. The method quantizes the control input of the system and the state variables of the unmanned vessel. In addition, since the input quantization process is linearly described, the controller does not need to obtain any prior information of the quantization parameters.

[0103] 3. The present invention provides a course fault-tolerant control method for unmanned vessels with input and state quantization. It uses an extended state observer (ESO) to explore the impact of quantized state variables on the control system, and verifies the effectiveness of the course fault-tolerant control strategy for unmanned vessels with input and state quantization through simulation experiments.

[0104] Based on the above reasons, this invention can be widely applied in fields such as artificial intelligence. Attached Figure Description

[0105] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0106] Figure 1 This is a flowchart of the method of the present invention.

[0107] Figure 2 The heading tracking result diagram is provided for an embodiment of the present invention.

[0108] Figure 3 The control input diagram provided in this embodiment of the invention.

[0109] Figure 4 A quantized heading tracking result diagram provided for an embodiment of the invention.

[0110] Figure 5 Quantized control input map provided for the embodiment of the present application.

[0111] Figure 6 Tracking error map provided for the embodiment of the present application.

[0112] Figure 7 ESO observation map provided for the embodiment of the present application. DETAILED DESCRIPTION

[0113] In order to make the personnel in the technical field better understand the present application scheme, the technical scheme in the embodiment of the present application will be described clearly and completely in combination with the drawings in the embodiment of the present application. Obviously, the described embodiment is only a part of the embodiment of the present application, not all. Based on the embodiment in the present application, all other embodiments obtained by the person skilled in the art without creative labor should belong to the protection scope of the present application.

[0114] It should be noted that the terms "first", "second" and the like in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or a chronological 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 that 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 necessarily limit to 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.

[0115] As shown in Figure 1 The present application provides an unmanned ship heading fault-tolerant control method with input and state quantization, which comprises:

[0116] S1, considering the fault factors of sensors and actuators in the USV fault-tolerant system, designing a controller;

[0117] S2, using an extended state observer (ESO) to estimate the state variables and uncertainties of the system, and reconstructing the quantized state variables;

[0118] S3, linearly describing the input quantization process, and the controller does not need any prior information of quantization parameters;

[0119] S4, using Lyapunov stability theory to prove the stability of the controller and observer, and the whole closed-loop system is ultimately uniformly bounded.

[0120] In specific implementation, as the preferred embodiment of the present application, step S1 specifically comprises:

[0121] S11, a ship mathematical model is constructed, as follows:

[0122]

[0123] wherein, ψ represents the heading of the USV, r represents the turning angle velocity of the USV; a represents the nonlinear coefficient of the Norrbin model, b represents the gain of the control system, K represents the turning index, T represents the following index, ω represents the unknown disturbance of the system, τ represents the control input of the system, δ represents the rudder angle of the system, and |ω|≤D;

[0124] S12, (ψ, r) is selected as the state variable, and x1=ψ is defined, f(x, t)=a1r+a2r 3 , τ=δ is taken, and Q(τ) is the control input of the quantized system; quantization converts continuous signals into segmented signals, thereby introducing the USV heading control mathematical model after input quantization, as follows:

[0125]

[0126] S13, based on the fault factors, the fault tolerance of the sensor and the actuator is considered, and a fault tolerance subsystem is designed, as follows:

[0127]

[0128] τ=ρ0ν

[0129] wherein, ρ0 and ρ i both represent unknown parameters, 0<ρ i0 ≤ρ i ≤1, 0<ρ 00 ≤ρ0≤1; the instruction of x1 is y d , and represent the output of the sensor; the control target is to design the control rate ν to make the signals of the whole closed-loop system bounded, and when t→∞,

[0130] In specific implementation, as the preferred embodiment of the present application, step S2 specifically comprises:

[0131] S21, the state variables x1, x2 and the control input τ of the USV are quantized by a uniform quantizer, and the uniform quantizer is as follows:

[0132]

[0133] wherein, γ>0 is quantization step, H1=γ, H i+1 =H i +γ;

[0134] S22, quantization error of the uniform quantizer is bounded and can guarantee Let Q(τ)=q1(t)τ+q2(t), then:

[0135]

[0136] Wherein, q1(t) represents unknown parameters, since the sign remains unchanged in the quantization process, if |τ|<κ, q1(t)>0 is obtained, considering that Q(τ(t)) is bounded, q2(t) is also bounded, and

[0137] S23, design extended state observer (ESO), as follows:

[0138]

[0139] Wherein, ε represents a constant greater than zero, All represent the state of the observer, Using the designed extended state observer, when t→∞,

[0140] In specific implementation, as a preferred embodiment of the application, step S3 specifically comprises:

[0141] Let Q(τ)=q1(t)τ+q2(t), and:

[0142]

[0143] Wherein, q1(t) represents unknown parameters, since the sign remains unchanged in the quantization process, q1(t)>0 is obtained from the above formula, if |τ(t)|<κ, considering that Q(τ(t)) is bounded, q2(t) is also bounded, and

[0144] In specific implementation, as a preferred embodiment of the application, step S4 specifically comprises:

[0145] S41, define Then

[0146] S42, design Lyapunov function, as follows:

[0147]

[0148] And the derivative of the designed Lyapunov function is obtained:

[0149]

[0150] Since Then:

[0151]

[0152] S43, since 0 < p < 1, 20 ≤ p2 ≤ 1, then That is Then:

[0153]

[0154] S44, define a1 = -c1z1, c1 > 0, then:

[0155]

[0156] Where,

[0157] S45, according to the definition in step S41, we get:

[0158]

[0159] S46, design Lyapunov function, as follows:

[0160]

[0161] Since Then:

[0162]

[0163] Where, μ2 = p2 p0,

[0164] S47, since Is an unknown constant, then use adaptive method, design Lyapunov function, as follows:

[0165]

[0166] Where, γ1 > 0, then:

[0167]

[0168] S48, since μ3 = p2 p0 is unknown, the control law and adaptive law are designed as follows:

[0169]

[0170]

[0171]

[0172]

[0173]

[0174] S49, the extended state observer designed according to step S23 is defined as

[0175]

[0176]

[0177] S410, the error state equation of the observer is defined as follows:

[0178]

[0179] wherein,

[0180] S411, for any given positive definite matrix Q, there is a symmetric positive definite matrix P satisfying the following Lyapunov equation, as follows:

[0181] B T P + PB + Q = 0

[0182] S412, the Lyapunov function of the extended state observer is defined as follows:

[0183]

[0184] S413, the derivative of the Lyapunov function of the defined extended state observer is taken to obtain:

[0185]

[0186] wherein, λ min (Q) represents the minimum eigenvalue of Q;

[0187] S414, it is known from that the convergence condition of the observer is as follows:

[0188]

[0189] The convergence speed of the observer error depends on ε, the smaller ε is, the faster the convergence is, and as ε decreases, It will gradually converge to 0;

[0190] S415, Lyapunov function set by the design controller process:

[0191]

[0192] Since q1≥q 1min =1 / ∈>0, then:

[0193]

[0194] Where, Since Take y d =sint, then:

[0195]

[0196] S416, calculate the solution of inequality equation As follows:

[0197]

[0198] Where, a represents any constant;

[0199] S417, if V(t) and k(·) are smooth functions on V(t)≥0, N(·) is a smooth N function, θ0 is a non-zero constant, if it satisfies c1>0, c0 is a constant, θ0(t) is an unknown time-varying parameter, then V(t), k(t) and It is bounded on

[0200] S418, from step S416:

[0201]

[0202] Where, From step S417, V(t) is bounded on Therefore, z1 and z2 are bounded on By taking a large enough λ and γ2 value, it is guaranteed that z1, z2 are small enough as t→∞, so that

[0203] S419, design Lyapunov function for the entire closed-loop system, as follows:

[0204] V o =V+V​e

[0205] And by differentiating the designed Lyapunov function, we obtain:

[0206]

[0207] This proves that the entire closed-loop system is eventually uniformly bounded.

[0208] Example

[0209] To verify the effectiveness of the present invention, this embodiment uses MATLAB for simulation study, with the parameters set as follows:

[0210] Taking the "Lanxin" unmanned surface vessel from Dalian Maritime University as an example: the unmanned vessel is 7.02 meters long, 2.60 meters wide, has a full-load draft of 0.32 meters, and a block coefficient of 0.6976. The vessel's model parameters are K = 0.71, T = 0.32, and the Norrbin motion model is adopted with a nonlinear coefficient a = 0.001.

[0211] Set the ideal heading instruction y d = sint, ω = -0.01. Set ρ0 = 0.50, ρ1 = 0.95, ρ2 = 0.95. The initial state of the controlled object is ψ = 0.2 rad, r = 0.1 rad·s -1 To meet μ2=ρ2ρ0>0, k1=4, k2=1, c1=20. According to the Nussbaum function, N(k)=k 2 cosk. The parameters of the control law and the adaptive law are chosen as γ1=γ2=1.0, η=D+0.10=1.1.

[0212] The ESO parameter is set to ε = 0.01. To prevent chattering, the saturation function satz2 is used instead of the sign function sgnz2 in the controller.

[0213]

[0214] Where Δ represents the boundary layer, and Δ = 0.05 is taken.

[0215] like Figures 2-7 As shown, Figure 2 The course tracking results are shown in the image. Figure 4 The quantized heading tracking results are shown in the image. Figure 3 The control input diagram is shown. Figure 5 The quantized control input diagram is shown. Figure 6 The tracking error graph is shown. Figure 7The ESO observation result graph is displayed, a saturation function is used instead of a sign function in the control law in the simulation process to prevent chattering, and the effectiveness of the method is verified.

[0216] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not limited to them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for unmanned ship course-keeping fault-tolerant control with input and state quantization, characterized by, Comprise: S1, considering the fault factors of sensors and actuators in the USV fault-tolerant system, design the controller, including: S11, construct the ship mathematical model, as follows: where ψ represents the heading of the USV, r represents the turning angle velocity of the USV, a represents the nonlinear coefficient of the Norrbin model, b represents the gain of the control system, K represents the turning index, T represents the following index, ω represents the unknown disturbance of the system, τ represents the control input of the system, δ represents the rudder angle of the system, and |ω|≤D. S12, select (ψ, r) as state variable, define x1=ψ, f(x, t) = a1r + a2r 3 , take τ=δ, Q(τ) is the control input of the quantized system; quantization converts continuous signals into segmented signals, thereby introducing the USV course control mathematical model after input quantization, as follows: S13, based on the fault factors, consider the fault tolerance of sensors and actuators, design the fault-tolerant subsystem, as follows: τ = ρ0ν where p0and p i are unknown parameters, 0 < p i0 ≤ p i ≤ 1, 0 < p 00 ≤ p0≤ 1; the instruction of x1is y d , and represent the output of the sensor; the control objective is to design the control rate v such that the signal of the entire closed-loop system is bounded, when t→∞, S2, adopt the extended state observer to estimate the state variables and uncertainties of the system, and reconstruct the quantized state variables, and linearly describe the input quantization process, the controller does not need any prior information of quantization parameters, including: S21, quantize the state variables x1, x2 and control input τ of the USV through the uniform quantizer, the uniform quantizer is as follows: where χ = x1, x2, τ, γ > 0 is the quantization step size, H1= γ, H i+1 = H i + γ ; S22, the quantization error of the uniform quantizer is bounded and can guarantee Let Q(τ) = q1(t)τ + q2(t), then: where q1(t) represents an unknown parameter, and since the sign is preserved during quantization, if |τ(t)| < κ, then q1(t) > 0. Considering that Q(τ(t)) is bounded, then q2(t) is also bounded, and S23, design the extended state observer, as follows: where ε denotes a constant greater than zero, all denote the state of the observer, using a design extended state observer to achieve S3, the stability of the controller and observer is proved by using Lyapunov stability theory, the whole closed-loop system is ultimately uniformly bounded, including: S31, define then S32, design the Lyapunov function, as follows: And take the derivative of the designed Lyapunov function, get: Because then: S33, since 0 < p 20 ≤ p2≤ 1, then That is Then: S34, define α1 =-c1z1, c1>0, then: wherein S35, according to the definition in step S31, get: S36, design the Lyapunov function, as follows: Because then: wherein μ2= p2p0, S37、Since is an unknown constant, an adaptive method is used to design the Lyapunov function as follows: wherein γ1> 0, then: S38, since μ3 = ρ2ρ0 is unknown, the control law and adaptive law are designed as follows: S39. Designing an augmented state observer according to step S23, defined as S310, define the error state equation of the observer, as follows: wherein S311, for any given positive definite matrix Q, there exists a symmetric positive definite matrix P that satisfies the following Lyapunov equation, as follows: B T P + PB + Q = 0 S312, define the Lyapunov function of the extended state observer, as follows: S313, take the derivative of the defined Lyapunov function of the extended state observer, get: where λ min (Q) denotes the minimum eigenvalue of Q; S314、by The convergence condition of the observer is known as follows: Observer error The convergence speed of the observer error depends on ε, the smaller ε is, the faster the convergence is, and as ε decreases, the observer error will gradually converge to 0; S315, get from the Lyapunov function designed in the process of designing the controller: Due to q1≥q 1min = 1 / ∈ > 0, then: wherein Since Take y d = sint, then: S316, compute the solution of the inequality equation as follows: Where a represents any constant; S317、if V(t) and k(·) are smooth functions on V(t) ≥ 0, N(·) is a smooth N-function, and θ0 is a non-zero constant, if c1>0, c0 is a constant, and θ0(t) is an unknown time-varying parameter, then V(t), k(t), and are bounded on ; S318, it can be known from step S316: wherein, From step S317, V(t) is bounded on , thus z1 and z2 are bounded on , by taking sufficiently large values of λ and γ2, it is guaranteed that z1, z2 are sufficiently small as t→∞, thus S319, design the Lyapunov function for the whole closed-loop system, as follows: V o = V + V e And take the derivative of the designed Lyapunov function, get: Then it is proved that the whole closed-loop system is ultimately uniformly bounded.

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