Multi-unmanned ship formation fault-tolerant control method with input / state quantification

Abstract

The invention provides a multi-unmanned ship formation fault-tolerant control method with input / state quantification, and the method comprises the steps: obtaining the sea condition information of a surrounding environment and other surrounding ships, and building a trajectory control mathematical model of an under-actuated unmanned ship formation; a uniform quantizer is adopted to quantize control input and state variables in the control system; under the condition that virtual leader information is known, estimating quantization state information of each USV and uncertain items existing in the model by using an ESO technology; a hierarchical design method is adopted, a kinematics guidance law and a dynamics quantization tracking control law are designed, a linear model is introduced to describe a quantization process, and a designed controller does not need priori information of quantization parameters any more; and the stability of fault-tolerant control of the multi-unmanned ship formation with input / state quantification is proved by using an input-to-state stability theory.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a fault-tolerant control method for a multi-unmanned ship formation with input / state quantization. Background Art

[0002] In recent years, the emergence and rapid development of unmanned surface vehicles (USVs) are profoundly changing the way we explore and use the ocean. As an advanced navigation tool that integrates intelligent navigation, autonomous decision-making, remote control and other technologies, USVs can not only greatly improve the efficiency of ocean data collection and processing, but also perform various difficult tasks in complex and changeable marine environments, such as environmental monitoring, maritime rescue, and cargo transportation. However, with the continuous expansion of USV application scenarios, a single USV can no longer meet the needs of complex tasks, and USV formations have gradually become a research hotspot. USV formations can not only improve the efficiency and quality of overall mission execution through multi-ship collaborative operations, but also achieve a higher level of navigation control and autonomous decision-making through mutual cooperation within the formation. Therefore, USV formation tracking and control technology is the key to achieving efficient and safe operation of USV formations.

[0003] In navigation practice, control signals need to be transmitted through communication channels, and information must be quantized and encoded during the transmission of the channel. Quantization is the process of converting a continuous signal into a set of discrete symbols or integer values. Considering the limited bandwidth of maritime communications, and further saving communication resources while ensuring the normal operation of the system within a given bandwidth, considering the input and state quantization of USV formation tracking control with event triggering mechanism and actuator fault tolerance is more meaningful in navigation practice. Summary of the invention

[0004] According to the tracking control problem of USV formation under the unmanned ship formation control conditions based on event triggering and actuator fault tolerance proposed above, a multi-unmanned ship formation fault-tolerant control method with input / state quantization is provided.

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

[0006] A fault-tolerant control method for a multi-unmanned ship formation with input / state quantization, comprising:

[0007] S1. Obtain the sea condition information of the surrounding environment and other ships around, and establish a trajectory control mathematical model for the under-actuated unmanned ship formation;

[0008] S2, using a uniform quantizer to quantize the control input and state variables in the control system;

[0009] S3. When the virtual leader information is known, the ESO technology is used to estimate the quantitative state information of each USV and the uncertainties in the model;

[0010] S4. Use the hierarchical design method to design the kinematic guidance law and dynamic quantized tracking control law, introduce a linear model to describe the quantization process, so that the designed controller no longer needs the prior information of the quantized parameters;

[0011] S5. The stability of the fault-tolerant control system of a multi-unmanned ship formation with input / state quantization is proved using the input-to-state stability theory.

[0012] Furthermore, step S1 specifically includes:

[0013] S11. Given an underactuated USV formation, establish the kinematic model of the motion of the i-th unmanned ship in the USV formation system as follows:

[0014]

[0015] Among them, x i ,y i Indicates the coordinates of the ship's center of mass described in the geodetic coordinate system; Indicates the ship's heading angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively;

[0016] S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned ship as follows:

[0017]

[0018] in, Indicates the mass of the USV; Both represent the hydrodynamic derivative terms; I z represents the moment of inertia around the z-axis; function f iu (·),f iv (·),f ir (·) represents nonlinear uncertainties such as fluid dynamic damping and centripetal force; τ iuw ,τ ivw ,τ irw The disturbance caused by unknown ocean factors is represented by Q(τ iu ) and Q(τ ir ) represent the system control input τ iu and τ ir Quantified value of .

[0019] Further, step S2 specifically includes:

[0020] S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is described as follows:

[0021]

[0022] in, and χ>0 indicates the quantization step size, I1=χ and I i+1 =I i +χ; therefore, the quantization error of the uniform quantizer is bounded and is expressed as

[0023] S22, define the ideal trajectory as Where p0(t) represents a continuously differentiable parameter trajectory; the ideal parameter trajectory p0(t) is differentiable, and its first-order derivative and second-order derivative are bounded; this indicates that as time goes by, the ideal parameter trajectory is smooth and stable, that is, there is a constant p m satisfy

[0024] S23. Use a graph of Λ={T,Φ} to represent the relationship between N USVs and the virtual leader; where Φ=(i,j)∈Γ×Γ represents the set of edges, T=n0,n1,...,n N represents a set of points; in this case, n i ,n j represents the communication flow from node j to node i; the adjacency matrix is ​​expressed as If there is an edge (n j ,n i )∈Φ, then a ij =1; otherwise, a ij =0;

[0025] S24. The main control objective is to enable each USV in the ship formation system to track the ideal trajectory of time variation under the condition of communication bandwidth constraints, that is:

[0026]

[0027] Among them, P i (t) = [x i ,y i ] T represents the actual position of each USV in the formation, P 0id (t) represents the position deviation of each USV relative to the parameter trajectory of the virtual leader, and ζ represents a constant greater than zero.

[0028] Further, step S3 specifically includes:

[0029] S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows:

[0030]

[0031] in, ν i =[u i ,v i ,r i ] T , is a rotation matrix that satisfies:

[0032]

[0033] S32. Design ESO as follows:

[0034]

[0035] Among them, σ i represents a constant greater than 0, and is the observer state, and Represent the quantized state variables and Q(ν i )=[Q(u i ),Q(v i ),Q(r i )] T Observed value of Represents the uncertainty term of the system The observed value of Represents a rotation matrix based on state quantization and satisfies:

[0036]

[0037] S33. Definition And satisfy:

[0038]

[0039] Then we get:

[0040]

[0041]

[0042] S34. Due to That is, there is a constant greater than 0 and Make

[0043] S35. Define the dynamic error of ESO as follows:

[0044]

[0045] in,

[0046] S36. For the designed ESO, there exists a positive definite matrix Satisfy the given conditions so that the ESO error subsystem is input-state stable;

[0047] S37, Order in, And The derivative is:

[0048]

[0049] in,

[0050] S38, according to There is a constant greater than 0 satisfy

[0051] S39. In order to analyze the stability of the ESO error system, two inequalities are given as follows:

[0052]

[0053] Among them, ∈ i >0, represents the yaw angular velocity r i The upper bound of

[0054] S310. Design the Lyapunov function as follows:

[0055]

[0056] in, represents a positive definite matrix, and the derivative of the above formula is:

[0057]

[0058] S311, when satisfied Then we get:

[0059]

[0060] Among them, 0<o i <1, and satisfies in and The matrices are The maximum and minimum eigenvalues ​​of ;

[0061] S312, due to Then we get:

[0062]

[0063] Therefore, the error subsystem of the ESO is input-state stable.

[0064] Further, step S4 specifically includes:

[0065] S41. In the kinematic subsystem, the guidance law is designed based on the actuator to track the ideal trajectory of the unmanned ship formation;

[0066] S42. In the dynamics subsystem, a linear analytical model is used to describe the quantization process. At the same time, event-triggered drive and actuator fault-tolerant strategy are introduced into the system to save communication resources, and the system control law and adaptive law are designed based on the sliding mode control strategy.

[0067] Further, step S41 specifically includes:

[0068] S411. Define the distributed formation tracking error as follows:

[0069]

[0070] in, represents the estimated value of the actual position of USVs in the formation, P0 represents the actual position of the virtual leader, represents a rotation matrix and satisfies:

[0071]

[0072] S412, the distributed formation tracking error is derived to obtain:

[0073]

[0074] in,

[0075] S413. In order to eliminate the influence of under-actuation on the USV formation control system, the error transformation is set as follows:

[0076]

[0077] Wherein, δ0∈R is a constant greater than 0, and combined with step S412, we obtain:

[0078]

[0079] Among them, h i =diag{l i ,δ0};

[0080] S414. From step S2, it is known that the designed ESO is stable and the observation error can converge to a smaller residual set. Therefore, the kinematic guidance law based on the ESO is designed as follows:

[0081]

[0082] in, Λ i is a constant greater than 0; All are constants greater than 0;

[0083] S415. According to step S414, the kinematic error is expressed as

[0084] Further, step S42 specifically includes:

[0085] S421, according to the nonlinear dynamic mathematical model of the underactuated unmanned ship established in step S12, obtain:

[0086]

[0087] And simplify the above formula to:

[0088]

[0089] in, and

[0090] S422, let Q(τ iu )=q 11iu (t)τ iu +q 12iu (t), Q(τ ir )=q 11ir (t)τ ir +q 12ir (t), and:

[0091]

[0092] Among them, q 11iu (t) and q 11ir (t) is an unknown parameter; since the sign remains unchanged during the entire quantization process, it can be seen from the above formula that q 11iu (t)>0,q 11ir (t)>0; In addition, if |τ iu (t)|<b and |τ ir (t)|<b, considering Q(τiu (t)) and Q(τ ir (t)) is bounded, then q 12iu (t) and q 12ir (t) is also bounded and satisfies

[0093] S423. Considering the fault tolerance of the actuator, design the controller as follows:

[0094]

[0095] Where q1(t) = ρ0q 11 (t),q2(t)=ρ0q 12 (t),0<ρ0<1;

[0096] S424. Set the control target of the dynamics subsystem as follows:

[0097]

[0098] Wherein, a1 and a2 both represent small positive integers;

[0099] S425. Define the integral sliding film surface as follows:

[0100]

[0101] Among them, b iu >0 and b ir >0, taking the derivative of the above formula, we get:

[0102]

[0103] S426. According to step S425, obtain:

[0104]

[0105] Among them, ρ iu ,μ iu ,ρ ir ,μ ir Both represent constants greater than 0, μ iu ≥μ ud ,μ ir ≥μ rd And μ ud >0,μ rd >0;

[0106] S427, due to q 1iu (t) and q 1ir (t) is unknown and time-varying, so an adaptive method is used to estimate its boundary. In order to prevent the singular problem when the estimated value tends to zero, q 1iu(t) and q 1ir (t) is estimated; define the time-varying gain η iu =1 / q 1iu (t) min and η ir =1 / q 1ir (t) min , where q 1iu (t) min and q 1ir (t) min They are q 1iu (t) and q 1ir (t), therefore, the USV formation tracking control law is designed as follows:

[0107]

[0108] Among them, γ1,γ2,c iu ,c ir ,ω iu ,ω ir ,ε iu ,ε ir and All represent constants greater than 0;

[0109] S428. Based on the quantization of the control system, the event trigger mechanism of time-varying threshold is introduced to further save communication resources and reduce the burden of communication signal transmission. Definition:

[0110]

[0111] t1=0

[0112] Where m is the time constant, Indicates angle tracking, satisfying

[0113] S429, there exists a continuous time-varying coefficient θ i (t) satisfies θ i (t k )=0,θ i (t k+1 )=±1, and |θ i (t)|≤1, we can conclude Right now The analysis is as follows:

[0114] When θ i When (t) = 0, We get t = t k ,

[0115] When |θi (t)|<1, We get t∈[t k ,t k+1 );

[0116] When |θ i When (t)|=1, The corresponding time is t=t k+1 ,get For t∈[t k+1 ,t k+2 ] is the same as above, so at any time it satisfies Among them, θ i (t) satisfies θ i (t k )=0,θ(t k+1 )=±1, and |θ i (t)|≤1;

[0117] S4210, based on s iu ,s ir , The kinematic and dynamic error systems are expressed as:

[0118]

[0119] Furthermore, step S5 specifically includes:

[0120] S51. Considering the USV formation tracking control system with quantization, actuator fault tolerance and event triggering mechanism, combined with the designed ESO, kinematic guidance rate, dynamic control rate and adaptive law, with state s iu ,s ir , and input Ω iu ,Ω ir The formation tracking control system is stable in input state, the tracking error can converge to a small residual set, and all signals in the designed control system are uniformly and ultimately bounded;

[0121] S52. Define the Lyapunov function as follows:

[0122]

[0123] And the derivative of the defined Lyapunov function is:

[0124]

[0125] S53, combining step S426 and step S52 to obtain:

[0126]

[0127] S54. Combining the designed control law and adaptive law, we get:

[0128]

[0129] Among them, q 1i (t)>0 and

[0130] S55. Due to but make So we get:

[0131]

[0132] S56. Considering Then we get:

[0133]

[0134] S57. Due to and Then we get:

[0135]

[0136] S58. Due to Then we get:

[0137]

[0138] S59, Order Then we get:

[0139]

[0140] S510, Definitions u =[s 1u ,s 2u ,...,s Nu ] T ,s r =[s 1r ,s 2r ,...,s Nr ] T , Then we get:

[0141]

[0142] S511, note Then we get:

[0143]

[0144] in, Therefore, the designed error subsystem with event triggering, actuator fault tolerance, and input and state quantization is input-to-state stable and satisfies:

[0145]

[0146] in, R c =diag{1,1 / 2γ1η 1u ,...,1 / 2γ1η Nu ,1 / 2γ2η 1r ,...,1 / 2γ2η Nr};

[0147] S512, due to s iu ,s ir is bounded, so is bounded; according to step S414, the kinematic guidance signal u ic and r ic are all bounded, so we can prove that u i and r i is bounded; from step S3, it can be seen that ESO is stable when input to the state. According to the cascade system stability theory, combined with step S511, ‖W(t)‖ is bounded and satisfies:

[0148]

[0149] Compared with the prior art, the present invention has the following advantages:

[0150] 1. The present invention provides a fault-tolerant control method for a multi-unmanned ship formation with input / state quantization. Starting from input quantization and state quantization, it solves the problem of USV formation tracking control in a marine environment with limited communication bandwidth and a relatively complex quantization environment. In order to eliminate the need for quantizer parameter information, a linear model is used to describe the quantization process.

[0151] 2. The present invention provides a fault-tolerant control method for a multi-unmanned ship formation with input / state quantization, which combines the actuator input quantization with the fault-tolerant control strategy. By combining a complex quantization scheme with a robust fault-tolerant control framework, the reliability and accuracy of the actuator performance are improved, thereby significantly improving the overall control effect of the USV formation system under different operating conditions.

[0152] 3. The present invention provides a fault-tolerant control method for a multi-unmanned ship formation with input / state quantization, which adopts a linear analysis model to describe the input quantization process and designs an actuator fault-tolerant sliding mode control method with input and state quantization and based on event triggering. This method can further save the communication of control input signals and effectively reduce the number of communications with little system performance loss, thereby improving network utilization.

[0153] 4. The present invention provides a fault-tolerant control method for a multi-unmanned ship formation with input / state quantization. Based on the Matlab platform, a comparative experiment of the unmanned ship formation control system before and after quantization is carried out. At the same time, an adaptive quantization tracking controller is designed to track the trajectory of the unmanned ship formation. After considering the event trigger mechanism and the input and state quantization of the actuator fault tolerance, the execution frequency of the actuator is reduced, the control amplitude is reduced, and the system control input curve is more in line with the practice of navigation engineering.

[0154] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0155] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0156] Figure 1 The figure is a flow chart of the method of the present invention.

[0157] Figure 2 This is a diagram of the distributed formation tracking control results of unmanned ships provided in an embodiment of the present invention.

[0158] Figure 3 This is a lateral speed tracking diagram of five unmanned ships provided in an embodiment of the present invention.

[0159] Figure 4 This is a tracking diagram of the bow angular velocity of five unmanned ships provided in an embodiment of the present invention.

[0160] Figure 5 This is a diagram of the lateral tracking errors of five unmanned ships provided in an embodiment of the present invention.

[0161] Figure 6 This is a longitudinal tracking error diagram of five unmanned ships provided in an embodiment of the present invention.

[0162] Figure 7 This is a control input diagram of five unmanned ships in different communication environments provided by an embodiment of the present invention.

[0163] Figure 8 This is a control input diagram of five unmanned ships in different communication environments provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0164] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0165] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0166] like Figure 1 As shown, the present invention provides a fault-tolerant control method for a multi-unmanned ship formation with input / state quantization, comprising:

[0167] S1. Obtain the sea condition information of the surrounding environment and other ships around, and establish a trajectory control mathematical model for the under-actuated unmanned ship formation;

[0168] S2, using a uniform quantizer to quantize the control input and state variables in the control system;

[0169] S3. When the virtual leader information is known, the ESO technology is used to estimate the quantitative state information of each USV and the uncertainties in the model;

[0170] S4. A hierarchical design method is used to solve the under-actuation problem of USV, design the kinematic guidance law and the dynamic quantized tracking control law, and introduce a linear model to describe the quantization process, so that the designed controller no longer needs the prior information of the quantized parameters;

[0171] S5. The stability of the fault-tolerant control system of a multi-unmanned ship formation with input / state quantization is proved using the input-to-state stability theory.

[0172] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0173] S11. Given an underactuated USV formation, establish the kinematic model of the motion of the i-th unmanned ship in the USV formation system as follows:

[0174]

[0175] Among them, x i ,y i Indicates the coordinates of the ship's center of mass described in the geodetic coordinate system; Indicates the ship's heading angle; u i 、v i and r i They represent the surge speed, sway speed and rotational speed (ROT) of the ship respectively;

[0176] S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned ship as follows:

[0177]

[0178] in, Indicates the mass of the USV; Both represent the hydrodynamic derivative terms; I z represents the moment of inertia around the z-axis; function f iu (·),f iv (·),f ir (·) represents nonlinear uncertainties such as fluid dynamic damping and centripetal force; τ iuw ,τ ivw ,τ irw The disturbance caused by unknown ocean factors is represented by Q(τ iu ) and Q(τ ir ) represent the system control input τ iu and τ ir Quantified value of .

[0179] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0180] S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is described as follows:

[0181]

[0182] in, and χ>0 indicates the quantization step size, I1=χ and I i+1 =I i+χ; therefore, the quantization error of the uniform quantizer is bounded and is expressed as

[0183] S22, define the ideal trajectory as Where p0(t) represents a continuously differentiable parameter trajectory; the ideal parameter trajectory p0(t) is differentiable, and its first-order derivative and second-order derivative are bounded; this indicates that as time goes by, the ideal parameter trajectory is smooth and stable, that is, there is a constant p m satisfy

[0184] S23. Use a graph of Λ={T,Φ} to represent the relationship between N USVs and the virtual leader; where Φ=(i,j)∈Γ×Γ represents the set of edges, T=n0,n1,...,n N represents a set of points; in this case, n i ,n j represents the communication flow from node j to node i; the adjacency matrix is ​​expressed as If there is an edge (n j ,n i )∈Φ, then a ij =1; otherwise, a ij =0;

[0185] S24. The main control objective is to enable each USV in the ship formation system to track the ideal trajectory of time variation under the condition of communication bandwidth constraints, that is:

[0186]

[0187] Among them, P i (t) = [x i ,y i ] T represents the actual position of each USV in the formation, P 0id (t) represents the position deviation of each USV relative to the parameter trajectory of the virtual leader, and ζ represents a constant greater than zero.

[0188] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0189] S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows:

[0190]

[0191] in, ν i =[u i ,v i ,r i] T , is a rotation matrix that satisfies:

[0192]

[0193] S32. Design ESO as follows:

[0194]

[0195] Among them, σ i represents a constant greater than 0, and is the observer state, and Represent the quantized state variables and Q(ν i )=[Q(u i ),Q(v i ),Q(r i )] T Observed value of Represents the uncertainty term of the system The observed value of Represents a rotation matrix based on state quantization and satisfies:

[0196]

[0197] S33. Definition And satisfy:

[0198]

[0199] Then we get:

[0200]

[0201] S34. Due to That is, there is a constant greater than 0 and Make

[0202] S35. Define the dynamic error of ESO as follows:

[0203]

[0204] in,

[0205] S36. For the designed ESO, there exists a positive definite matrix Satisfy the given conditions so that the ESO error subsystem is input-state stable;

[0206] S37, Order in, And The derivative is:

[0207]

[0208] in,

[0209] S38, according to There is a constant greater than 0 satisfy

[0210] S39. In order to analyze the stability of the ESO error system, two inequalities are given as follows:

[0211]

[0212] Among them, ∈ i >0, represents the yaw angular velocity r i The upper bound of

[0213] S310. Design the Lyapunov function as follows:

[0214]

[0215] in, represents a positive definite matrix, and the derivative of the above formula is:

[0216]

[0217] S311, when satisfied Then we get:

[0218]

[0219] Among them, 0<o i <1, and satisfies in and The matrices are The maximum and minimum eigenvalues ​​of ;

[0220] S312, due to Then we get:

[0221]

[0222] Therefore, the error subsystem of the ESO is input-state stable.

[0223] In this embodiment, the introduction of ESO in the control system has two main purposes. First, it helps to obtain the state information of the USV in a quantitative environment and estimate the inherent uncertainties in the ship model. In addition, ESO also plays a role in filtering and smoothing the quantization curve, ensuring that the quantized state variables can be used as continuous differentiable variables, enhancing its applicability and feasibility in controller design.

[0224] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0225] S41. In the kinematic subsystem, the guidance law is designed based on the actuator to track the ideal trajectory of the unmanned ship formation;

[0226] S42. In the dynamics subsystem, a linear analytical model is used to describe the quantization process. At the same time, event-triggered drive and actuator fault-tolerant strategy are introduced into the system to save communication resources, and the system control law and adaptive law are designed based on the sliding mode control strategy.

[0227] In specific implementation, as a preferred embodiment of the present invention, step S41 specifically includes:

[0228] S411. Define the distributed formation tracking error as follows:

[0229]

[0230] in, represents the estimated value of the actual position of USVs in the formation, P0 represents the actual position of the virtual leader, represents a rotation matrix and satisfies:

[0231]

[0232] S412, the distributed formation tracking error is derived to obtain:

[0233]

[0234] in,

[0235] S413. In order to eliminate the influence of under-actuation on the USV formation control system, the error transformation is set as follows:

[0236]

[0237] Wherein, δ0∈R is a constant greater than 0, and combined with step S412, we obtain:

[0238]

[0239] Among them, h i=diag{l i ,δ0};

[0240] S414. From step S2, it is known that the designed ESO is stable and the observation error can converge to a smaller residual set. Therefore, the kinematic guidance law based on the ESO is designed as follows:

[0241]

[0242] in, Λ i is a constant greater than 0; All are constants greater than 0;

[0243] S415. According to step S414, the kinematic error is expressed as

[0244] In specific implementation, as a preferred embodiment of the present invention, step S42 specifically includes:

[0245] S421, according to the nonlinear dynamic mathematical model of the underactuated unmanned ship established in step S12, obtain:

[0246]

[0247] And simplify the above formula to:

[0248]

[0249] in, and

[0250] S422, let Q(τ iu )=q 11iu (t)τ iu +q 12iu (t), Q(τ ir )=q 11ir (t)τ ir +q 12ir (t), and:

[0251]

[0252] Among them, q 11iu (t) and q 11ir (t) is an unknown parameter; since the sign remains unchanged during the entire quantization process, it can be seen from the above formula that q 11iu (t)>0,q 11ir (t)>0; In addition, if |τ iu (t)|<b and |τ ir (t)|<b, considering Q(τ iu(t)) and Q(τ ir (t)) is bounded, then q 12iu (t) and q 12ir (t) is also bounded and satisfies

[0253] S423. Considering the fault tolerance of the actuator, design the controller as follows:

[0254]

[0255] Where q1(t) = ρ0q 11 (t),q2(t)=ρ0q 12 (t),0<ρ0<1;

[0256] S424. Set the control target of the dynamics subsystem as follows:

[0257]

[0258] Wherein, a1 and a2 both represent small positive integers;

[0259] S425. Define the integral sliding film surface as follows:

[0260]

[0261] Among them, b iu >0 and b ir >0, taking the derivative of the above formula, we get:

[0262]

[0263] S426. According to step S425, obtain:

[0264]

[0265] Among them, ρ iu ,μ iu ,ρ ir ,μ ir Both represent constants greater than 0, μ iu ≥μ ud ,μ ir ≥μ rd And μ ud >0,μ rd >0;

[0266] S427, due to q 1iu (t) and q 1ir (t) is unknown and time-varying, so an adaptive method is used to estimate its boundary. In order to prevent the singular problem when the estimated value tends to zero, q 1iu (t) and q1ir (t) is estimated; define the time-varying gain η iu =1 / q 1iu (t) min and η ir =1 / q 1ir (t) min , where q 1iu (t) min and q 1ir (t) min They are q 1iu (t) and q 1ir (t), therefore, the USV formation tracking control law is designed as follows:

[0267]

[0268] Among them, γ1,γ2,c iu ,c ir ,ω iu ,ω ir ,ε iu ,ε ir and All represent constants greater than 0;

[0269] S428. Based on the quantization of the control system, the event trigger mechanism of time-varying threshold is introduced to further save communication resources and reduce the burden of communication signal transmission. Definition:

[0270]

[0271] t1=0

[0272] Where m is the time constant, Indicates angle tracking, satisfying

[0273] S429, there exists a continuous time-varying coefficient θ i (t) satisfies θ i (t k )=0,θ i (t k+1 )=±1, and |θ i (t)|≤1, we can conclude Right now The analysis is as follows:

[0274] When θ i When (t) = 0, We get t = t k ,

[0275] When |θi (t)|<1, We get t∈[t k ,t k+1 );

[0276] When |θ i When (t)|=1, The corresponding time is t=t k+1 ,get For t∈[t k+1 ,t k+2 ] is the same as above, so at any time it satisfies Among them, θ i (t) satisfies θ i (t k )=0,θ(t k+1 )=±1, and |θ i (t)|≤1;

[0277] S4210, based on s iu ,s ir , The kinematic and dynamic error systems are expressed as:

[0278]

[0279] In specific implementation, as a preferred embodiment of the present invention, step S5 specifically includes:

[0280] S51. Considering the USV formation tracking control system with quantization, actuator fault tolerance and event triggering mechanism, combined with the designed ESO, kinematic guidance rate, dynamic control rate and adaptive law, with state s iu ,s ir , and input Ω iu ,Ω ir The formation tracking control system is stable in input state, the tracking error can converge to a small residual set, and all signals in the designed control system are uniformly and ultimately bounded;

[0281] S52. Define the Lyapunov function as follows:

[0282]

[0283] And the derivative of the defined Lyapunov function is:

[0284]

[0285] S53, combining step S426 and step S52 to obtain:

[0286]

[0287] S54. Combining the designed control law and adaptive law, we get:

[0288]

[0289] Among them, q 1i (t)>0 and

[0290] S55. Due to but make So we get:

[0291]

[0292] S56. Considering Then we get:

[0293]

[0294] S57. Due to and Then we get:

[0295]

[0296] S58. Due to Then we get:

[0297]

[0298] S59, Order Then we get:

[0299]

[0300] S510, Definitions u =[s 1u ,s 2u ,...,s Nu ] T ,s r =[s 1r ,s 2r ,...,s Nr ] T , Then we get:

[0301]

[0302] S511, note Then we get:

[0303]

[0304] in, Therefore, the designed error subsystem with event triggering, actuator fault tolerance, and input and state quantization is input-to-state stable and satisfies:

[0305]

[0306] in, R c =diag{1,1 / 2γ1η 1u ,...,1 / 2γ1η Nu ,1 / 2γ2η 1r ,...,1 / 2γ2η Nr};

[0307] S512, due to s iu ,s ir is bounded, so is bounded; according to step S414, the kinematic guidance signal u ic and r ic are all bounded, so we can prove that u i and r i is bounded; from step S3, it can be seen that ESO is stable when input to the state. According to the cascade system stability theory, combined with step S511, ||W(t)|| is bounded and satisfies:

[0308]

[0309] Example

[0310] In order to verify the effectiveness of the fault-tolerant control method for multiple unmanned ship formations with input / state quantization proposed in the present invention, this embodiment uses MATLAB / Simulink for computer simulation research. The parameters are set as follows:

[0311] The simulation object is the "Lanxin" unmanned surface ship of Dalian Maritime University. The parameters of the unmanned ship are: length 7.02m, width 2.6m, speed 35kn, full load draft 0.32m, full load displacement 2.73m 3 , square coefficient 0.6976. Other model parameters are selected as follows: m u =25.8kg, m v =33.8kg m r =2.76kg·m 2 , f v (·)=-36.5|v|v-0.8896v-0.805v|r|-m uu i r, f r (·)=-0.75|r|r-1.90r+0.08|v|r+(m u -m v ) i v-1.0948u i r.

[0312] The time-varying parameter trajectory of the virtual leader is designed as P0(t)=[0.8t,2sin(0.1t)] T The initial state of the five USVs in the formation is designed to be P1 = [0,0] T , P2=[-7,7] T , P3=[7,-7] T , P4=[-14,14] T and P5 = [14, -14] T The ideal initial position of the formation is designed as P 1d =[0,0] T ,P 2d =[-7,7] T ,P 3d =[7,-7] T , P 4d =[-14,14] T and P 5d =[14,-14] T The controller design parameters are ρ0=0.80, b iu =b ir =10,ρ iu =ρ ir =28,μ iu =μ ir =2, c iu =c ir =0.02,ω iu =ω ir =0.20, γ1=3, γ2=2, ε iu =ε ir =0.10,ε iu =ε ir =0.10, χ=0.1.

[0313] like Figure 2-8 Simulation results of the designed USV distributed formation tracking control strategy. Figure 2 The tracking results of the time-varying ideal trajectory by five underactuated USVs are shown in Figure 2. It can be seen that all USVs can track the ideal trajectory from the starting position in a short time. At the same time, after considering event triggering, actuator fault tolerance, and input and state quantization, the designed USV distributed formation tracking controller can still show good control performance. Figure 3 and Figure 4 The following are the tracking results of lateral velocity and angular velocity of 5 USVs. It can be seen that the USV can synchronize the velocity in a short time, and the velocity tracking error is convergent. Figure 5 and Figure 6 The lateral and longitudinal tracking errors of the five USVs are given respectively. It can be seen from the figure that although considering event triggering, actuator fault tolerance, and input and state quantization in the control system will lead to the loss of some control information, the control quality is not significantly sacrificed, and the lateral and longitudinal tracking errors of the five USVs can converge to a small neighborhood near 0. Figure 7 and Figure 8 The unquantized and quantized USV control inputs are shown. It can be seen that after considering the input and state quantization, the number of controller executions is significantly reduced, which is more in line with the offshore environment with limited communication bandwidth.

[0314] The simulation results show that the simulation results of the tracking control strategy designed by the present invention are relatively ideal. The controller can well realize the trajectory tracking of the USV distributed formation, and the tracking error can quickly converge to a smaller residual set. After considering the input and state quantization, the execution frequency of the actuator is reduced, the control amplitude is reduced, and the system control input curve is more in line with the practice of navigation engineering. This further verifies the effectiveness and rationality of the method of the present invention.

[0315] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fault-tolerant control method for a multi-unmanned ship formation with input / state quantization, characterized in that: include: S1. Obtain the sea condition information of the surrounding environment and other ships around, and establish a trajectory control mathematical model for the under-actuated unmanned ship formation; S2, using a uniform quantizer to quantize the control input and state variables in the control system; S3. When the virtual leader information is known, the ESO technology is used to estimate the quantitative state information of each USV and the uncertainties in the model; S4. Use the hierarchical design method to design the kinematic guidance law and dynamic quantized tracking control law, introduce a linear model to describe the quantization process, so that the designed controller no longer needs the prior information of the quantized parameters; S5. The stability of the fault-tolerant control system of a multi-unmanned ship formation with input / state quantization is proved using the input-to-state stability theory.

2. A fault-tolerant control method for a multi-unmanned ship formation with input / state quantization according to claim 1, characterized in that: Step S1 specifically includes: S11. Given an underactuated USV formation, establish the kinematic model of the motion of the i-th unmanned ship in the USV formation system as follows: Among them, x i ,y i Indicates the coordinates of the ship's center of mass described in the geodetic coordinate system; Indicates the ship's heading angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively; S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned ship as follows: in, Indicates the mass of the USV; Both represent the hydrodynamic derivative terms; I z Represents the moment of inertia around the z-axis; function f iu (·),f iv (·),f ir (·) represents nonlinear uncertainties such as fluid dynamic damping and centripetal force; τ iuw ,τ ivw ,τ irw The disturbance caused by unknown ocean factors is represented by Q(τ iu ) and Q(τ ir ) represent the system control input τ iu and τ ir Quantified value of .

3. The fault-tolerant control method for a multi-unmanned ship formation with input / state quantization according to claim 1 is characterized in that: Step S2 specifically includes: S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is described as follows: in, and χ>0 indicates the quantization step size, I1=χ and I i+1 =I i +χ; therefore, the quantization error of the uniform quantizer is bounded and is expressed as S22, define the ideal trajectory as Where p0(t) represents a continuously differentiable parameter trajectory; the ideal parameter trajectory p0(t) is differentiable, and its first-order derivative and second-order derivative are bounded; this indicates that as time goes by, the ideal parameter trajectory is smooth and stable, that is, there is a constant p m satisfy S23. Use a graph of Λ={T,Φ} to represent the relationship between N USVs and the virtual leader; where Φ=(i,j)∈Γ×Γ represents the set of edges, T=n0,n1,...,n N represents a set of points; in this case, n i ,n j represents the communication flow from node j to node i; the adjacency matrix is ​​expressed as If there is an edge (n j ,n i )∈Φ, then a ij =1; otherwise, a ij =0; S24. The main control objective is to enable each USV in the ship formation system to track the ideal trajectory of time variation under the condition of communication bandwidth constraints, that is: Among them, P i (t) = [x i ,y i ] T represents the actual position of each USV in the formation, P 0id (t) represents the position deviation of each USV relative to the parameter trajectory of the virtual leader, and ζ represents a constant greater than zero.

4. The fault-tolerant control method for a multi-unmanned ship formation with input / state quantization according to claim 1 is characterized in that: Step S3 specifically includes: S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows: in, ν i =[u i ,v i ,r i ] T , is a rotation matrix that satisfies: S32. Design ESO as follows: Among them, σ i represents a constant greater than 0, and is the observer state, and Represent the quantized state variables and Q(ν i )=[Q(u i ),Q(v i ),Q(r i )] T Observed value of Represents the uncertainty term of the system The observed value of Represents a rotation matrix based on state quantization and satisfies: S33. Definition And satisfy: Then we get: S34. Due to That is, there is a constant greater than 0 and Make S35. Define the dynamic error of ESO as follows: in, S36. For the designed ESO, there exists a positive definite matrix Satisfy the given conditions so that the ESO error subsystem is input-state stable; S37, Order in, And The derivative is: in, S38, according to There is a constant greater than 0 satisfy S39. In order to analyze the stability of the ESO error system, two inequalities are given as follows: Among them, ∈ i >0, represents the yaw angular velocity r i The upper bound of S310. Design the Lyapunov function as follows: in, represents a positive definite matrix, and the derivative of the above formula is: S311, when satisfied Then we get: Among them, 0<o i <1, and satisfies in and The matrices are The maximum and minimum eigenvalues ​​of ; S312, due to Then we get: Therefore, the error subsystem of the ESO is input-state stable.

5. The fault-tolerant control method of a multi-unmanned ship formation with input / state quantization according to claim 1 is characterized in that: Step S4 specifically includes: S41. In the kinematic subsystem, the guidance law is designed based on the actuator to track the ideal trajectory of the unmanned ship formation; S42. In the dynamics subsystem, a linear analytical model is used to describe the quantization process. At the same time, event-triggered drive and actuator fault-tolerant strategy are introduced into the system to save communication resources, and the system control law and adaptive law are designed based on the sliding mode control strategy.

6. A fault-tolerant control method for a multi-unmanned ship formation with input / state quantization according to claim 5, characterized in that: Step S41 specifically includes: S411. Define the distributed formation tracking error as follows: in, represents the estimated value of the actual position of USVs in the formation, P0 represents the actual position of the virtual leader, represents a rotation matrix and satisfies: S412, the distributed formation tracking error is derived to obtain: in, S413. In order to eliminate the influence of under-actuation on the USV formation control system, the error transformation is set as follows: Wherein, δ0∈R is a constant greater than 0, and combined with step S412, we obtain: Among them, h i =diag{l i ,δ0}; S414. From step S2, it is known that the designed ESO is stable and the observation error can converge to a smaller residual set. Therefore, the kinematic guidance law based on the ESO is designed as follows: in, Λ i is a constant greater than 0; All are constants greater than 0; S415. According to step S414, the kinematic error is expressed as 7. The fault-tolerant control method for a multi-unmanned ship formation with input / state quantization according to claim 5 is characterized in that: Step S42 specifically includes: S421, according to the nonlinear dynamic mathematical model of the underactuated unmanned ship established in step S12, obtain: And simplify the above formula to: in, and S422. Let Q(τ iu ) = q 11iu (t)τ iu + q 12iu (t), Q(τ ir ) = q 11ir (t)τ ir + q 12ir (t), and: Among them, q 11iu (t) and q 11ir (t) is an unknown parameter; since the sign remains unchanged during the entire quantization process, it can be seen from the above formula that q 11iu (t)>0,q 11ir (t)>0; In addition, if τ iu (t)|<b and τ ir (t)|<b, considering Q(τ iu (t)) and Q(τ ir (t)) is bounded, then q 12iu (t) and q 12ir (t) is also bounded and satisfies S423. Considering the fault tolerance of the actuator, design the controller as follows: where q1(t) = ρ0q 11 (t), q2(t) = ρ0q 12 (t), 0 < ρ0 < 1; S424, setting the control target of the dynamics subsystem as follows: Wherein, a1 and a2 both represent small positive integers; S425. Define the integral sliding film surface as follows: Among them, b iu >0 and b ir >0, taking the derivative of the above formula, we get: S426. According to step S425, obtain: Among them, ρ iu ,μ iu ,ρ ir ,μ ir Both represent constants greater than 0, μ iu ≥μ ud ,μ ir ≥μ rd And μ ud >0,μ rd >0; S427, due to q 1iu (t) and q 1ir (t) is unknown and time-varying, so an adaptive method is used to estimate its boundary. In order to prevent the singular problem when the estimated value tends to zero, q 1iu (t) and q 1ir (t) is estimated; define the time-varying gain η iu =1 / q 1iu (t) min and η ir =1 / q 1ir (t) min , where q 1iu (t) min and q 1ir (t) min They are q 1iu (t) and q 1ir (t), therefore, the USV formation tracking control law is designed as follows: Among them, γ1,γ2,c iu ,c ir ,ω iu ,ω ir ,ε iu ,ε ir and m both represent constants greater than 0; S428. Based on the quantization of the control system, the event trigger mechanism of time-varying threshold is introduced to further save communication resources and reduce the burden of communication signal transmission. Definition: Where m is the time constant, Indicates angle tracking, satisfying S429, there exists a continuous time-varying coefficient θ i (t) satisfies θ i (t k )=0,θ i (t k+1 )=±1, and |θ i (t)|≤1, we can conclude Right now The analysis is as follows: When θ i When (t) = 0, get When |θ i (t)|<1, We get t∈[t k ,t k+1 ); When |θ i When (t)|=1, The corresponding time is t=t k+1 ,get For t∈[t k+1 ,t k+2 ] is the same as above, so at any time it satisfies Among them, θ i (t) satisfies θ i (t k )=0,θ(t k+1 )=±1, and |θ i (t)|≤1; S4210, based on s iu ,s ir , The kinematic and dynamic error systems are expressed as:

8. The fault-tolerant control method for a multi-unmanned ship formation with input / state quantization according to claim 1 is characterized in that: Step S5 specifically includes: S51. Considering the USV formation tracking control system with quantization, actuator fault tolerance and event triggering mechanism, combined with the designed ESO, kinematic guidance rate, dynamic control rate and adaptive law, with state s iu ,s ir , and input Ω iu ,Ω ir The formation tracking control system is stable in input state, the tracking error can converge to a small residual set, and all signals in the designed control system are uniformly and ultimately bounded; S52. Define the Lyapunov function as follows: And the derivative of the defined Lyapunov function is: S53, combining step S426 and step S52 to obtain: S54. Combining the designed control law and adaptive law, we get: Among them, q 1i (t)>0 and S55. Due to but make So we get: S56. Considering Then we get: S57. Due to and Then we get: S58. Due to Then we get: S59, Order Then we get: S510、definitions u =[s 1u ,s 2u ,...,s Nu ] T ,s r =[s 1r ,s 2r ,...,s Nr ] T , =min i＝1,...,N (r iu ,r ir ,oh iu / 2nd iu ,oh ir / 2nd ir ,l min (a i )), get: S511, note , we get: in, Therefore, the designed error subsystem with event triggering, actuator fault tolerance, and input and state quantization is input-to-state stable and satisfies: Among them, R c =diag{1,1 / 2γ1η 1u ,...,1 / 2c1h Nu ,1 / 2c2h 1r ,...,1 / 2c2h Nr }; S512, due to s iu ,s ir is bounded, so is bounded; according to step S414, the kinematic guidance signal u ic and r ic are all bounded, so we prove that u i and r i is bounded; from step S3, it can be seen that ESO is stable when input to the state. According to the cascade system stability theory, combined with step S511, ||W(t)|| is bounded and satisfies:

Images