Self-adaptive discrete observer-based unmanned surface vehicle fault estimation method

Abstract

The invention discloses an unmanned surface vehicle fault estimation method based on a self-adaptive discrete observer, and belongs to the technical field of unmanned surface vehicle fault diagnosis. Comprising the steps of discretizing a continuous state space model containing a sensor fault, a steering engine additive fault and external disturbance in the unmanned surface vehicle and augmenting the continuous state space model into a new discrete time augmented state space model containing a fault vector, and establishing a self-adaptive discrete fault estimation observer of the discrete time augmented state space model; the discrete state space model and the self-adaptive discrete observer are combined, an error system dynamic equation is constructed, a condition for judging the stability of an error system is given, a parameter matrix of the self-adaptive discrete observer is solved, and an estimated value of the fault of the unmanned surface vehicle is obtained through the self-adaptive discrete observer; according to the unmanned surface vehicle fault estimation method based on the self-adaptive discrete observer, the influence of a sampling behavior on unmanned surface vehicle fault estimation is overcome, and the design difficulty and the calculation complexity are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned boat fault diagnosis, and in particular to a surface unmanned boat fault estimation method based on an adaptive discrete observer. Background Art

[0002] Surface unmanned vessels, with their features of autonomous navigation, remote control and multi-functional payload integration, can perform efficient and precise tasks in complex marine environments, significantly reducing personnel risks and improving operational efficiency. Therefore, they play an important role in marine exploration, environmental monitoring, military reconnaissance and search and rescue.

[0003] When unmanned surface vehicles (USVs) perform their missions, the complex marine environment, high loads, and long hours of operation increase the risk of sensor and steering gear failures. This can severely impact system stability and even cause system loss of control, posing a serious threat to the safe navigation of the USVs. Therefore, using fault estimation technology to determine the location and severity of faults in real time is crucial for ensuring the reliability and safety of USVs.

[0004] Fault estimation technology for unmanned surface vehicles (UUVs) has long been a hot topic in the UUV research field. For example, patent application number 201911373563.4, titled "Unmanned Vessel Fault Estimation Method Based on Iterative Adaptive Observer," proposes an observer-based iterative fault estimation method to address multiplicative servo and sensor failure estimation. However, this method suffers from three major issues: First, the proposed method designs a fault estimation observer for UUV systems operating in the continuous-time domain. However, in practical engineering applications, since digital control systems generally employ periodic sampling mechanisms, the measured signals must be discretized before being input into a digital computer for observer implementation. This sampling process destroys the temporal continuity of the measured signals, potentially breaking the stability requirements of the adaptive laws and iterative algorithms designed in the continuous-time fault estimation method after discretization. This makes the method difficult to apply to UUV digital control platforms. Second, the proposed method requires the construction of multiple iterative observers to achieve fault estimation when estimating sensor faults. Given the limited computing resources inherent in UUVs, this multiple-observer iterative approach inevitably wastes computing resources. Finally, the method proposed in the above patent mainly reconstructs the efficiency factor for the partial failure of the servo when dealing with servo failures, but it is difficult to provide information such as the amplitude and frequency of additive failures such as servo jamming and drifting. Summary of the Invention

[0005] The purpose of the present invention is to provide a surface unmanned vehicle fault estimation method based on an adaptive discrete observer to solve the problem that the surface unmanned vehicle fault estimation algorithm based on a continuous-time system is difficult to be directly applied to a digital control system with discrete measurement characteristics.

[0006] To achieve the above object, the present invention proposes a method for estimating faults of an unmanned surface vehicle based on an adaptive discrete observer, comprising the following steps:

[0007] S1. Discretize the continuous state space model of the surface unmanned vehicle containing sensor faults, steering gear additive faults and external disturbances and augment it into a new discrete time augmented state space model containing the fault vector;

[0008] S2, establish an adaptive discrete fault estimation observer for the discrete-time augmented state space model;

[0009] S3. Combine the discrete-time augmented state-space model and the adaptive discrete fault estimation observer to construct the error system dynamic equation, provide the conditions for judging the stability of the error system, and solve the parameter matrix of the adaptive discrete fault estimation observer;

[0010] S4. Obtain an estimated value of the surface unmanned vehicle fault through an adaptive discrete fault estimation observer.

[0011] Preferably, the specific steps of S1 are as follows:

[0012] S11. Establish a continuous state space model of the surface unmanned vehicle containing sensor fault vectors, steering gear fault vectors and external disturbance vectors:

[0013]

[0014] Where t represents time, is the state vector of the unmanned boat, which is respectively generated by the lateral velocity v(t), panning velocity r(t), heading angle ψ(t), rolling velocity ρ(t) and rolling angle constitute, is the first-order derivative of x(t), u(t)=χ(t) is the control input of the servo, χ(t) represents the rudder angle, is the disturbance vector of the surface unmanned vehicle, and the heading angle disturbance w caused by the waves is ψ (t) and roll angle disturbance constitute, This is the steering gear fault vector of the surface unmanned boat, such as the steering gear stuck or drifting. is the measurable output signal vector of the surface unmanned vehicle, is the sensor fault vector of the surface unmanned vehicle, A, B, G1 and C are system matrices, and E is the steering gear fault matrix, satisfying where n a ≤5 holds true, G2 is the sensor fault matrix, satisfying where n s ≤5 is established;

[0015] S12. Discretize the continuous state space model of the unmanned surface vehicle to obtain the discrete state space equation of the unmanned surface vehicle:

[0016]

[0017] Among them, the discrete time moment k is a simplified representation of kT, T is the discrete sampling period, x(k+1) is the discrete system state vector at time k+1, x(k) is the discrete system state vector at time k, u(k) is the control input variable of the discrete system at time k, d(k) is the disturbance vector of the discrete system at time k, and f a (k) is the servo fault vector of the discrete system at time k, satisfying h=1,2,...,n a , is an unknown positive number, y(k) is the measurable output signal vector of the discrete system at time k, f s (k) is the sensor fault vector of the discrete system at time k, A o 、B o , G 1o and C o is the discretized system matrix, E o is the discretized servo fault matrix, G 2o is the discretized sensor fault matrix;

[0018] S13. Augment the state space equation of the unmanned surface vehicle, and let The augmented discrete-time augmented state space model is obtained:

[0019]

[0020] Among them, U is the state transfer matrix, is the augmented state vector, is the augmented perturbation vector, and is the augmented system matrix, is the augmented servo fault matrix.

[0021] Preferably, the system matrix in S11 is specifically expressed as:

[0022]

[0023]

[0024] Among them, T v and T r is the time constant, K vr , K vp , K dv , K dr and K dp is a known gain, w n is the undamped natural frequency, and ζ is the damping ratio.

[0025] Preferably, the discretized system matrix in S12 satisfies A o =e AT , B o =A -1 (A o -I5)B,G 1o =A -1 (A o -I5)G1,E o =A -1 (A o -I5)E,C o =C,G 2o =G2;

[0026] Where I5 is the 5-dimensional identity matrix.

[0027] Preferably, the matrix in S13 is specifically expressed as:

[0028]

[0029] in, satisfy d * is an unknown positive number.

[0030] Preferably, the adaptive discrete fault estimation observer equation established by S2 is as follows:

[0031]

[0032] Among them, S, N and is the observer parameter matrix for adaptive discrete fault estimation, is k moment The estimated value of z(k)∈R 10 is the intermediate variable of the adaptive discrete fault estimation observer, is the servo fault vector f at time k a The estimated value of (k), and is the injection term of the adaptive discrete fault estimation observer at time k, and K is the designed matrix.

[0033] Preferably, the injection item u in S2 d (k) with The specific design is:

[0034]

[0035] Among them, β 1h and is a given positive number, and is the designed matrix, yes The hth element of .

[0036] Preferably, the parameter matrix of the adaptive discrete fault estimation observer in S2 is is a reversible matrix,

[0037] N∈R 10×10 、 and S -1 ∈R 10×10 Specifically expressed as:

[0038]

[0039] The adaptive law is designed as:

[0040]

[0041] Among them, β 1h and α h is a given positive number, yes The hth element of .

[0042] Preferably, the specific steps of S3 are as follows:

[0043] S31, based on the discrete time augmented state space model in S13, Substituting into the equation we get the following;

[0044]

[0045] S32, reintegrate the adaptive discrete fault estimation observer equation of S2, substitute the second equation of formula (16) into the first equation, and obtain the following equation;

[0046]

[0047] S33. Define the estimation error as:

[0048]

[0049] Combining the equations of S31 and S32, we get the error system dynamic equation:

[0050]

[0051] S34. Give the judgment conditions for the stability of the error system dynamic equation and solve the parameter matrix K of the adaptive discrete fault estimation observer in S2.

[0052] Preferably, the judgment condition of S34 is:

[0053] Given a positive constant 1 / 4<α h <2 / 3,γ<1 / 4,if there exists a positive definite matrix Z∈R 10×5 ,matrix matrix The constant δ>0 satisfies:

[0054]

[0055] in, I 10 is a 10-dimensional identity matrix;

[0056] Then the error system dynamic equation is bounded and stable, and the parameter matrix K∈R 10×5 It can be solved as

[0057] Therefore, the present invention adopts the above-mentioned surface unmanned vehicle fault estimation method based on adaptive discrete observer, which has the following beneficial effects:

[0058] (1) An adaptive discrete fault estimation observer design architecture for the discrete-time system of an unmanned vehicle was constructed, which effectively solved the model mismatch problem of the traditional continuous-time fault estimation method in the digital control platform and realized the estimation of sensor faults and steering gear faults of the unmanned vehicle in the discrete-time domain.

[0059] (2) The collaborative estimation of servo actuator faults and sensor measurement faults is achieved within a single observer framework, which reduces the design difficulty and computational complexity and can provide estimated values for additive faults such as servo jamming and drifting.

[0060] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a flow chart of a method for estimating a fault of an unmanned surface vehicle based on an adaptive discrete observer according to the present invention;

[0062] Figure 2 Schematic diagram of actual sensor failure (solid line) and sensor failure estimation value (dashed line) of a simulation example in an embodiment of the present invention;

[0063] Figure 3 Schematic diagram of actual steering gear fault (solid line) and steering gear fault estimation value (dashed line) of a simulation example in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0065] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0066] Example

[0067] like Figure 1 As shown, the present invention provides a method for estimating faults of an unmanned surface vehicle based on an adaptive discrete observer, comprising the following steps:

[0068] S1. The continuous state space model of the surface unmanned vehicle containing sensor faults, additive steering gear faults and external disturbances is discretized and augmented into a new discrete-time augmented state space model containing a fault vector.

[0069] S11. Establish a continuous state space model of the surface unmanned vehicle containing sensor fault vectors, steering gear fault vectors and external disturbance vectors:

[0070]

[0071] Where t represents time, is the state vector of the unmanned boat, which is respectively generated by the lateral velocity v(t), panning velocity r(t), heading angle ψ(t), rolling velocity ρ(t) and rolling angle constitute, is the first-order derivative of x(t), u(t)=χ(t) is the control input of the servo, χ(t) represents the rudder angle, is the disturbance vector of the surface unmanned vehicle, and the heading angle disturbance w caused by the waves is ψ (t) and roll angle disturbance constitute, This is the steering gear fault vector of the surface unmanned boat, such as the steering gear stuck or drifting. is the measurable output signal vector of the surface unmanned vehicle, is the sensor fault vector of the surface unmanned vehicle, A, B, G1 and C are system matrices, and E is the steering gear fault matrix, satisfying where n a ≤5 holds true, G2 is the sensor fault matrix, satisfying where n s ≤5 is true.

[0072] In this embodiment, n a =1,n y =5,n s =1.

[0073] The system matrix is specifically expressed as:

[0074]

[0075] Among them, T v and T r is the time constant, K vr , K vp , K dv , K dr and K dp is a known gain, w n is the undamped natural frequency, and ζ is the damping ratio.

[0076] In this embodiment, the given parameters are: T r =1.667, T v =10,K vr =-0.46m / s, K dv =0.7780, K dr =-0.0211, K dp =-0.0852, K vp =1.6380,w n =0.63rad / s, ζ =0.0936, the following system matrix can be obtained:

[0077]

[0078] B=[0.0078 -0.0127 0.0000 -0.0338 0.0000] T ;

[0079]

[0080] The servo fault matrix is assumed to be E = [-0.09 0 -0.02 0 0.1] T , the sensor fault matrix is assumed to be G2 = [0.5 -0.1 0.01 -0.02 -0.1] T .

[0081] S12. Discretize the continuous state space model of the unmanned surface vehicle to obtain the discrete state space equation of the unmanned surface vehicle:

[0082]

[0083] Among them, the discrete time moment k is a simplified representation of kT, T is the discrete sampling period, x(k+1) is the discrete system state vector at time k+1, x(k) is the discrete system state vector at time k, u(k) is the control input variable of the discrete system at time k, d(k) is the disturbance vector of the discrete system at time k, and f a (k) is the servo fault vector of the discrete system at time k, satisfying h=1,2,...,n a , is an unknown positive number, y(k) is the measurable output signal vector of the discrete system at time k, f s (k) is the sensor fault vector of the discrete system at time k, A o 、B o , G 1o and C o is the discretized system matrix, E o is the discretized servo fault matrix, G 2o is the discretized sensor fault matrix.

[0084] In this embodiment, T=0.5s; A o 、B o , G 1o 、E o 、C o and G 2o is the system state matrix after discretization using the zero-order holder, satisfying A o =e AT , B o =A -1 (A o -I5)B,G 1o =A -1 (A o -I5)G1,E o =A -1 (A o -I5)E,C o =C,G 2o =G2;

[0085] Where I5 is the 5-dimensional identity matrix.

[0086] According to the system state matrix solved by S11, the discretized system state matrix can be obtained as follows:

[0087]

[0088] B o =[0.0038 -0.0057 -0.0015 -0.0155 -0.0040] T ;

[0089]

[0090] E o =[-0.0439 0.0028 -0.0095 -0.0070 -0.0012] T ;

[0091]

[0092] G 2o =[0.5 -0.1 0.01 -0.02 -0.1] T ;

[0093] S13. Augment the state space equation of the unmanned surface vehicle, and let The augmented discrete-time augmented state space model is obtained:

[0094]

[0095] Among them, U is the state transfer matrix, is the augmented state vector, is the augmented perturbation vector, and is the augmented system matrix, is the augmented servo fault matrix.

[0096] The matrix in formula (3) is specifically expressed as:

[0097]

[0098]

[0099] in, satisfy d * is an unknown positive number.

[0100] S2. Establish an adaptive discrete fault estimation observer for the discrete-time augmented state space model.

[0101] The established adaptive discrete fault estimation observer equation is as follows:

[0102]

[0103] Among them, S, N and is the observer parameter matrix for adaptive discrete fault estimation, is k moment The estimated value of z(k)∈R 10 is the intermediate variable of the adaptive discrete fault estimation observer, is the servo fault vector f at time k a The estimated value of (k), and is the injection term of the adaptive discrete fault estimation observer at time k, K∈R 10×5 It is the matrix that needs to be designed in S34.

[0104] Injection item u d (k) with The specific design is:

[0105]

[0106] Among them, β 1h and is a given positive number, and This is the matrix that needs to be designed in S34 later. yes The hth element of .

[0107] Adaptive discrete fault estimation observer parameter matrix is a reversible matrix,

[0108] N∈R 10×10 、 and S -1 ∈R 10×10 Specifically expressed as:

[0109]

[0110] The adaptive law is designed as:

[0111]

[0112] Among them, β 1h and α h is a given positive number, yes The h-th element of , in this embodiment, h=1.

[0113] S3. Combine the discrete-time augmented state-space model and the adaptive discrete fault estimation observer to construct the dynamic equation of the error system, give the conditions for judging the stability of the error system, and solve the parameter matrix of the adaptive discrete fault estimation observer.

[0114] S31, based on the discrete time augmented state space model in S13, Substituting into the equation we get the following;

[0115]

[0116] S32, reintegrate the adaptive discrete fault estimation observer equation of S2, substitute the second equation of formula (16) into the first equation, and obtain the following equation;

[0117]

[0118] S33. Define the estimation error as:

[0119]

[0120] Combining the equations of S31 and S32, we get the error system dynamic equation:

[0121]

[0122] S34. Give the judgment conditions for the stability of the error system dynamic equation and solve the parameter matrix K of the adaptive discrete fault estimation observer in S2.

[0123] The judgment conditions are:

[0124] Given a positive constant 1 / 4<α h <2 / 3,γ<1 / 4,if there exists a positive definite matrix Z∈R 10×5 ,matrix matrix The constant δ>0 satisfies:

[0125]

[0126] in, I 10 is a 10-dimensional identity matrix;

[0127] Then the error system dynamic equation is bounded and stable, and the parameter matrix K∈R 10×5 It can be solved as

[0128] Select γ=0.2, parameter matrix Z∈R 10×5 , as well as It can be solved as:

[0129]

[0130] J1=[0.0054 0.0061 -0.0118 -0.0251 0.0095];

[0131]

[0132] Given parameters Given the adaptive parameter β 11 =30,α1=0.6.

[0133] S4. Obtain an estimated value of the surface unmanned vehicle fault through an adaptive discrete fault estimation observer.

[0134] In order to verify the effect of this example, the following simulation example is used to verify it, assuming that the sensor failure and the servo failure are:

[0135]

[0136] The heading angle disturbance caused by the waves is w ψ (k) = 0.2sin(0.3k), the roll angle disturbance is The control input is u(k)=χ(t)=50cos(0.2k).

[0137] The simulation results are as follows Figure 2 and Figure 3 As shown, Figure 2 is the sensor fault curve, the solid line is the true curve of sensor fault, and the dotted line is the estimated value of sensor fault obtained by the adaptive discrete observer. Figure 3 is the steering gear fault curve, the solid line is the true curve of the steering gear fault, and the dotted line is the estimated value of the steering gear fault obtained by the adaptive discrete observer. From the simulation results, it can be seen that there are some errors in the early estimation of this embodiment. With the improvement of the robustness of the adaptive discrete fault estimation observer, the fault estimation can be accurately and quantitatively realized, which facilitates the efficient operation of the surface unmanned vehicle.

[0138] Therefore, the present invention adopts the above-mentioned surface unmanned boat fault estimation method based on adaptive discrete observer, overcomes the influence of sampling behavior on unmanned boat fault estimation, and ensures the applicability of this method in digital control systems; the present invention only needs to design a unique observer to achieve simultaneous estimation of unmanned boat sensor and servo faults, effectively reducing the complexity of observer design and improving computational efficiency.

[0139] 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 the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for fault estimation of unmanned surface vehicles based on an adaptive discrete observer, characterized in that: The following steps are involved: S1. Discretize the continuous state space model of the surface unmanned vehicle containing sensor faults, steering gear additive faults and external disturbances and augment it into a new discrete time augmented state space model containing the fault vector; S2, establish an adaptive discrete fault estimation observer for the discrete-time augmented state space model; S3. Combine the discrete-time augmented state-space model and the adaptive discrete fault estimation observer to construct the error system dynamic equation, provide the conditions for judging the stability of the error system, and solve the parameter matrix of the adaptive discrete fault estimation observer; S4. Obtain an estimated value of the surface unmanned vehicle fault through an adaptive discrete fault estimation observer.

2. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 1, characterized in that: The specific steps of S1 are as follows: S11. Establish a continuous state space model of the surface unmanned vehicle containing sensor fault vectors, steering gear fault vectors and external disturbance vectors: Where t represents time, is the state vector of the unmanned boat, which is respectively generated by the lateral velocity v(t), panning velocity r(t), heading angle ψ(t), rolling velocity ρ(t) and rolling angle constitute, is the first-order derivative of x(t), u(t)=χ(t) is the control input of the servo, χ(t) represents the rudder angle, is the disturbance vector of the surface unmanned vehicle, and the heading angle disturbance w caused by the waves is ψ (t) and roll angle disturbance constitute, is the fault vector of the servo of the surface unmanned vehicle, is the measurable output signal vector of the surface unmanned vehicle, is the sensor fault vector of the surface unmanned vehicle, A, B, G1 and C are system matrices, E is the steering gear fault matrix, and G2 is the sensor fault matrix; S12. Discretize the continuous state space model of the unmanned surface vehicle to obtain the discrete state space equation of the unmanned surface vehicle: Among them, the discrete time moment k is a simplified representation of kT, T is the discrete sampling period, x(k+1) is the discrete system state vector at time k+1, x(k) is the discrete system state vector at time k, u(k) is the control input variable of the discrete system at time k, d(k) is the disturbance vector of the discrete system at time k, and f a (k) is the servo fault vector of the discrete system at time k, satisfying h=1,2,...,n a , is an unknown positive number, y(k) is the measurable output signal vector of the discrete system at time k, f s (k) is the sensor fault vector of the discrete system at time k, A o 、B o , G 1o and C o is the discretized system matrix, E o is the discretized servo fault matrix, G 2o is the discretized sensor fault matrix; S13. Augment the state space equation of the unmanned surface vehicle, and let The augmented discrete-time augmented state space model is obtained: Among them, U is the state transfer matrix, is the augmented state vector, is the augmented perturbation vector, and is the augmented system matrix, is the augmented servo fault matrix.

3. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 2, characterized in that: The system matrix in S11 is specifically expressed as: Among them, T v and T r is the time constant, K vr , K vp , K dv , K dr and K dp is a known gain, w n is the undamped natural frequency, and ζ is the damping ratio.

4. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 2, characterized in that: The discretized system matrix in S12 satisfies A o =e AT , B o =A -1 (A o -I5)B,G 1o =A -1 (A o -I5)G1,E o =A -1 (A o -I5)E,C o =C,G 2o =G2; Where I5 is the 5-dimensional identity matrix.

5. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 2, characterized in that: The matrix in S13 is specifically expressed as: in, satisfy d * is an unknown positive number.

6. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 5, characterized in that: The adaptive discrete fault estimation observer equation established by S2 is as follows: Among them, S, N and is the observer parameter matrix for adaptive discrete fault estimation, R 10 is k moment The estimated value of z(k)∈R 10 is the intermediate variable of the adaptive discrete fault estimation observer, is the servo fault vector f at time k a The estimated value of (k), and is the injection term of the adaptive discrete fault estimation observer at time k, and K is the designed matrix.

7. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 6, characterized in that: Injection item u in S2 d (k) with The specific design is: Among them, β 1h and is a given positive number, and is the designed matrix, yes The hth element of .

8. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 6, characterized in that: Parameter Matrix of Adaptive Discrete Fault Estimation Observer in S2 is a reversible matrix, N∈R 10×10 、 and S -1 ∈R 10×10 Specifically expressed as: The adaptive law is designed as: Among them, β 1h and α h is a given positive number, yes The hth element of .

9. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 8, characterized in that: The specific steps for S3 are as follows: S31, based on the discrete time augmented state space model in S13, Substituting into the equation we get the following; S32, reintegrate the adaptive discrete fault estimation observer equation of S2, substitute the second equation of formula (16) into the first equation, and obtain the following equation; S33. Define the estimation error as: Combining the equations of S31 and S32, we get the error system dynamic equation: S34. Give the judgment conditions for the stability of the error system dynamic equation and solve the parameter matrix K of the adaptive discrete fault estimation observer in S2.

10. A method for estimating faults of unmanned surface vehicles based on an adaptive discrete observer according to claim 9, characterized in that: The judgment conditions of S34 are: Given a positive constant 1 / 4<α h <2 / 3,γ<1 / 4,if there exists a positive definite matrix Z∈R 10×5 ,matrix matrix The constant δ>0 satisfies: in, I 10 is a 10-dimensional identity matrix; Then the error system dynamic equation is bounded and stable, and the parameter matrix K∈R 10×5 It can be solved as

Images