CN110471439B - Rigid aircraft fixed time attitude stabilization method based on neural network estimation - Google Patents

Rigid aircraft fixed time attitude stabilization method based on neural network estimation Download PDF

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CN110471439B
CN110471439B CN201910874872.3A CN201910874872A CN110471439B CN 110471439 B CN110471439 B CN 110471439B CN 201910874872 A CN201910874872 A CN 201910874872A CN 110471439 B CN110471439 B CN 110471439B
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陈强
谢树宗
孙明轩
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Zhejiang University of Technology ZJUT
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Abstract

A rigid aircraft fixed time attitude stabilization method based on neural network estimation is provided, aiming at the rigid aircraft attitude stabilization problem with centralized uncertainty, a fixed time sliding mode surface is designed, and the fixed time convergence of the state is ensured; and (3) introducing a neural network to approximate a total uncertain function, and designing a neural network fixed time controller. The method realizes the fixed time consistency and the final bounded control of the state of the aircraft system under the factors of external interference and uncertain rotational inertia.

Description

Rigid aircraft fixed time attitude stabilization method based on neural network estimation
Technical Field
The invention relates to a rigid aircraft fixed time attitude stabilization method based on neural network estimation, in particular to a rigid aircraft attitude stabilization method with external interference and uncertain rotational inertia matrix.
Background
Rigid aircraft attitude control systems play an important role in the healthy, reliable movement of rigid aircraft. In a complex aerospace environment, a rigid aircraft attitude control system can be affected by various external disturbances and uncertainty in the rotational inertia matrix. In order to effectively maintain the performance of the system, it needs to be robust to external interference and uncertainty of the rotational inertia matrix. The sliding mode variable structure control is taken as a typical nonlinear control method, can effectively improve the stability and the maneuverability of a rigid aircraft, and has stronger robustness, thereby improving the task execution capacity. Therefore, the sliding mode variable structure control method for researching the attitude control system of the rigid aircraft has very important significance.
Sliding mode control is considered to be an effective robust control method in solving system uncertainty and external disturbances. The sliding mode control method has the advantages of simple algorithm, high response speed, strong robustness to external noise interference and parameter perturbation and the like. Terminal sliding mode control is an improvement over conventional sliding mode control, which can achieve limited time stability. However, existing limited time techniques to estimate convergence time require knowledge of the initial information of the system, which is difficult for the designer to know. In recent years, a fixed time technique has been widely used, and a fixed time control method has an advantage of conservatively estimating the convergence time of a system without knowing initial information of the system, as compared with an existing limited time control method.
The neural network is one of linear parameterized approximation methods and can be replaced by any other approximation method, such as an RBF neural network, a fuzzy logic system, and the like. By utilizing the property that a neural network approaches uncertainty and effectively combining a fixed time sliding mode control technology, the influence of external interference and system parameter uncertainty on the system control performance is reduced, and the fixed time control of the attitude of the rigid aircraft is realized.
Disclosure of Invention
In order to overcome the problem of unknown nonlinearity of the existing rigid aircraft attitude control system, the invention provides a rigid aircraft fixed time attitude stabilization method based on neural network estimation, and under the condition that external interference and uncertain rotational inertia exist in the system, a control method with consistent fixed time and final bounded system state is realized.
The technical scheme proposed for solving the technical problems is as follows:
a rigid aircraft fixed time attitude stabilization method based on neural network estimation comprises the following steps:
step 1, establishing a kinematics and dynamics model of a rigid aircraft, initializing system states and control parameters, and carrying out the following processes:
1.1 the kinematic equation for a rigid aircraft system is:
Figure BDA0002203999370000021
Figure BDA0002203999370000022
wherein q isv＝[q1,q2,q3]TAnd q is4Vector part and scalar part of unit quaternion respectively and satisfy
Figure BDA0002203999370000023
q1,q2,q3Respectively mapping values on x, y and z axes of a space rectangular coordinate system;
Figure BDA0002203999370000024
are each qvAnd q is4A derivative of (a);
Figure BDA0002203999370000025
is qvTransposing; omega belongs to R3Is the angular velocity of the rigid aircraft; i is3Is R3×3A unit matrix;
Figure BDA0002203999370000026
expressed as:
Figure BDA0002203999370000027
1.2 the kinetic equation for a rigid aircraft system is:
Figure BDA0002203999370000028
wherein J ∈ R3×3Is the rotational inertia matrix of the aircraft;
Figure BDA0002203999370000029
is the angular acceleration of the aircraft; u is an element of R3And d ∈ R3Control moment and external disturbance; omega×Expressed as:
Figure BDA00022039993700000210
1.3 rotational inertia matrix J satisfies J ═ J0+ Δ J, wherein J0And Δ J represents the nominal and indeterminate portions of J, respectively, equation (4) is rewritten as:
Figure BDA0002203999370000031
further obtaining:
Figure BDA0002203999370000032
1.4 differentiating the formula (1) to obtain:
Figure BDA0002203999370000033
wherein
Figure BDA0002203999370000034
Is the total indeterminate set; omegaTIs a transposition of Ω;
Figure BDA0002203999370000035
is qvThe second derivative of (a);
Figure BDA0002203999370000036
is J0The inverse of (1);
Figure BDA0002203999370000037
expressed as:
Figure BDA0002203999370000038
Figure BDA0002203999370000039
are each q1,q2,q3A derivative of (a);
step 2, designing a required slip form surface aiming at a rigid aircraft system with uncertain external disturbance and moment inertia, wherein the process is as follows:
selecting a fixed-time sliding mode surface as follows:
Figure BDA00022039993700000310
wherein the content of the first and second substances,
Figure BDA00022039993700000311
sgn(qi)，
Figure BDA00022039993700000312
and sgn (q)i) Are all sign functions, λ1＞0,λ2＞0,a2＞1，
Figure BDA00022039993700000313
Figure BDA00022039993700000314
Is qiI ═ 1,2, 3;
definition S ═ S1,S2,S3]TAnd obtaining the following result by derivation of S:
Figure BDA0002203999370000041
substituting formula (8) into (11) to obtain:
Figure BDA0002203999370000042
step 3, designing a neural network fixed time controller, and the process is as follows:
3.1 define the neural network as:
Gi(Xi)＝Wi *TΦ(Xi)+εi (13)
wherein
Figure BDA0002203999370000043
For an input vector, [ phi ]i(Xi)∈R4Being basis functions of neural networks, Wi *∈R4The ideal weight vector is defined as:
Figure BDA0002203999370000044
wherein Wi∈R4Is a weight vector, εiTo approximate the error, | εi|≤εN,i＝1,2,3，εNIs a very small normal number; argmin {. is W {. DEG }i *Taking the set of all the minimum values;
3.2 consider that the fixed time controller is designed to:
Figure BDA0002203999370000045
wherein
Figure BDA0002203999370000046
Is a diagonal matrix of 3 x 3 symmetry,
Figure BDA0002203999370000047
is WiIs equal to [ phi (X) ]1),Φ(X2),Φ(X3)]T，
Figure BDA0002203999370000048
L＝[L1,L2,L3]T，
Figure BDA0002203999370000049
Figure BDA00022039993700000411
Γ＝diag(Γ1,Γ2,Γ3)∈R3×3Is a diagonal matrix of 3 x 3 symmetry,
Figure BDA00022039993700000410
0＜r1＜1，r2＞1，K1＝diag(k11,k12,k13)∈R3×3is a diagonal matrix with 3 multiplied by 3 symmetry; k2＝diag(k21,k22,k23)∈R3×3Is a diagonal matrix with 3 multiplied by 3 symmetry; k3＝diag(k31,k32,k33)∈R3×3A diagonal matrix of 3 × 3 symmetry;
Figure BDA0002203999370000051
is Wi(ii) an estimate of (d);
3.2 design update law:
Figure BDA0002203999370000052
wherein gamma isi＞0,pi＞0，
Figure BDA0002203999370000053
Is composed of
Figure BDA0002203999370000054
I ═ 1,2, 3; phi (X)i) Sigmoid function chosen as follows:
Figure BDA0002203999370000055
wherein l1,l2,l3And l4To approximate the parameter, [ phi ] (X)i) Satisfies the relation 0 < phi (X)i)＜Φ0And is and
Figure BDA0002203999370000056
step 4, the stability of the fixed time is proved, and the process is as follows:
4.1 demonstrates that all signals of the rigid aircraft system are consistent and finally bounded, and the Lyapunov function is designed to be of the form:
Figure BDA0002203999370000057
wherein
Figure BDA0002203999370000058
STIs the transpose of S;
Figure BDA0002203999370000059
is that
Figure BDA00022039993700000510
Transposing;
derivation of equation (18) yields:
Figure BDA00022039993700000511
wherein min {. cndot } represents a minimum value;
Figure BDA00022039993700000512
Figure BDA00022039993700000513
i | · | | represents a two-norm of the value;
determining that all signals of the rigid aircraft system are consistent and ultimately bounded;
4.2 prove the convergence of the fixed time, designing the Lyapunov function as follows:
Figure BDA00022039993700000514
derivation of equation (20) yields:
Figure BDA00022039993700000515
wherein
Figure BDA00022039993700000516
Figure BDA0002203999370000061
υ2An upper bound value greater than zero;
based on the above analysis, the rigid aircraft system state is consistently bounded at a fixed time.
Under the factors of external interference and uncertain rotational inertia, the method realizes the stable control of the system by applying the fixed-time attitude stabilization method of the rigid aircraft based on neural network estimation, and ensures that the system state realizes the consistent fixed time and is bounded finally. The technical conception of the invention is as follows: a neural network fixed time controller is designed by using a sliding mode control method and combining a neural network aiming at a rigid aircraft system containing external interference and uncertain rotational inertia. The design of the fixed-time sliding mode surface ensures the fixed-time convergence of the system state. The invention realizes the control method that the fixed time of the system state is consistent and the system is bounded finally under the condition that the system has external interference and uncertain rotational inertia.
The invention has the beneficial effects that: under the conditions that external interference exists in the system and the rotational inertia is uncertain, the fixed time for realizing the state of the system is consistent and finally bounded, and the convergence time is independent of the initial state of the system.
Drawings
FIG. 1 is a schematic representation of a rigid aircraft attitude quaternion of the present invention;
FIG. 2 is a schematic illustration of the angular velocity of a rigid aircraft of the present invention;
FIG. 3 is a schematic drawing of a sliding mode surface of the rigid aircraft of the present invention;
FIG. 4 is a schematic illustration of the rigid aircraft control moments of the present invention;
FIG. 5 is a schematic illustration of a rigid aircraft parameter estimation of the present invention;
FIG. 6 is a control flow diagram of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1-6, a method for rigid aircraft fixed-time attitude stabilization based on neural network estimation, the control method comprising the steps of:
step 1, establishing a kinematics and dynamics model of a rigid aircraft, initializing a system state and control parameters, and carrying out the following processes:
1.1 the kinematic equation for a rigid aircraft system is:
Figure BDA0002203999370000071
Figure BDA0002203999370000072
wherein q isv＝[q1,q2,q3]TAnd q is4Vector unit with unit quaternionDivide and sum scalar part and satisfy
Figure BDA0002203999370000073
q1,q2,q3Respectively mapping values on x, y and z axes of a space rectangular coordinate system;
Figure BDA0002203999370000074
are each qvAnd q is4A derivative of (d);
Figure BDA0002203999370000075
is qvTransposing; omega belongs to R3Is the angular velocity of the rigid aircraft; i is3Is R3×3An identity matrix;
Figure BDA0002203999370000076
expressed as:
Figure BDA0002203999370000077
1.2 the kinetic equation for a rigid aircraft system is:
Figure BDA0002203999370000078
wherein J ∈ R3×3Is the rotational inertia matrix of the aircraft;
Figure BDA0002203999370000079
is the angular acceleration of the aircraft; u is an element of R3And d ∈ R3Control moment and external disturbance; omega×Expressed as:
Figure BDA00022039993700000710
1.3 rotational inertia matrix J satisfies J ═ J0+ Δ J, wherein J0And Δ J represents the nominal and indeterminate portions of J, respectively, equation (4) is rewritten as:
Figure BDA00022039993700000711
further obtaining:
Figure BDA00022039993700000712
1.4 differentiating the formula (1) to obtain:
Figure BDA0002203999370000081
wherein
Figure BDA0002203999370000082
Is the total indeterminate set; omegaTIs a transposition of Ω;
Figure BDA0002203999370000083
is qvThe second derivative of (a);
Figure BDA0002203999370000084
is J0The inverse of (1);
Figure BDA0002203999370000085
expressed as:
Figure BDA0002203999370000086
Figure BDA0002203999370000087
are each q1,q2,q3A derivative of (a);
step 2, designing a required slip form surface aiming at a rigid aircraft system with uncertain external disturbance and moment inertia, wherein the process is as follows:
selecting a fixed-time sliding mode surface as follows:
Figure BDA0002203999370000088
wherein the content of the first and second substances,
Figure BDA0002203999370000089
sgn(qi)，
Figure BDA00022039993700000810
and sgn (q)i) Are all sign functions, λ1＞0,λ2＞0,a2＞1，
Figure BDA00022039993700000811
Figure BDA00022039993700000812
Is qiI ═ 1,2, 3;
definition S ═ S1,S2,S3]TAnd obtaining the following result by derivation of S:
Figure BDA00022039993700000813
substituting formula (8) into (11) to obtain:
Figure BDA00022039993700000814
Figure BDA0002203999370000091
step 3, designing a neural network fixed time controller, and the process is as follows:
3.1 define the neural network as:
Gi(Xi)＝Wi *TΦ(Xi)+εi (13)
wherein
Figure BDA0002203999370000092
For an input vector, [ phi ]i(Xi)∈R4Being basis functions of neural networks, Wi *∈R4The ideal weight vector is defined as:
Figure BDA0002203999370000093
wherein Wi∈R4Is a weight vector, εiFor approximation error, | εi|≤εN,i＝1,2,3，εNIs a very small normal number; argmin {. is W {. DEG }i *Taking the set of all the minimum values;
3.2 consider that the fixed time controller is designed to:
Figure BDA0002203999370000094
wherein
Figure BDA0002203999370000095
Is a diagonal matrix of 3 x 3 symmetry,
Figure BDA0002203999370000096
is WiIs equal to [ phi (X) ]1),Φ(X2),Φ(X3)]T，
Figure BDA0002203999370000097
L＝[L1,L2,L3]T，
Figure BDA0002203999370000098
Figure BDA0002203999370000099
Γ＝diag(Γ1,Γ2,Γ3)∈R3×3Diagonal moments of 3 x 3 symmetryThe number of the arrays is determined,
Figure BDA00022039993700000910
0＜r1＜1，r2＞1，K1＝diag(k11,k12,k13)∈R3×3is a diagonal matrix with 3 multiplied by 3 symmetry; k2＝diag(k21,k22,k23)∈R3×3A diagonal matrix of 3 × 3 symmetry; k3＝diag(k31,k32,k33)∈R3×3Is a diagonal matrix with 3 multiplied by 3 symmetry;
Figure BDA00022039993700000911
is Wi(ii) an estimate of (d);
3.2 design update law:
Figure BDA00022039993700000912
wherein gamma isi＞0,pi＞0，
Figure BDA00022039993700000913
Is composed of
Figure BDA00022039993700000914
I ═ 1,2, 3; phi (X)i) Sigmoid function chosen as follows:
Figure BDA00022039993700000915
wherein l1,l2,l3And l4To approximate the parameter, [ phi ] (X)i) Satisfies the relation 0 < phi (X)i)＜Φ0And is and
Figure BDA0002203999370000101
step 4, the stability of the fixed time is proved, and the process is as follows:
4.1 demonstrates that all signals of the rigid aircraft system are consistent and finally bounded, and the Lyapunov function is designed to be of the form:
Figure BDA0002203999370000102
wherein
Figure BDA0002203999370000103
STIs the transpose of S;
Figure BDA0002203999370000104
is that
Figure BDA0002203999370000105
Transposing;
derivation of equation (18) yields:
Figure BDA0002203999370000106
wherein min {. cndot } represents a minimum value;
Figure BDA0002203999370000107
Figure BDA0002203999370000108
i | · | | represents a two-norm of the value;
determining that all signals of the rigid aircraft system are consistent and ultimately bounded;
4.2 demonstrate fixed time convergence, designing the Lyapunov function to be of the form:
Figure BDA0002203999370000109
derivation of equation (20) yields:
Figure BDA00022039993700001010
wherein
Figure BDA00022039993700001011
Figure BDA00022039993700001012
υ2An upper bound value greater than zero;
based on the above analysis, the rigid aircraft system state is consistent at a fixed time and ultimately bounded.
In order to verify the effectiveness of the method, the method carries out simulation verification on the aircraft system. The system initialization parameters are set as follows:
initial values of the system: q (0) ═ 0.3, -0.2, -0.3,0.8832]T,Ω(0)＝[1,0,-1]TRadian/second; nominal part J of the rotational inertia matrix0＝[40,1.2,0.9；1.2,17,1.4；0.9,1.4,15]Kilogram square meter, uncertainty Δ J of inertia matrix, diag [ sin (0.1t),2sin (0.2t),3sin (0.3t)](ii) a External perturbation d (t) ═ 0.2sin (0.1t),0.3sin (0.2t),0.5sin (0.2t)]T(ii) newton-meters; the parameters of the slip form surface are as follows: lambda [ alpha ]1＝1,λ2＝1,a1＝1.5,a21.5; the parameters of the controller are as follows:
Figure BDA0002203999370000111
K1＝K2＝K3＝I3(ii) a The update law parameters are as follows: etai＝1,εi＝0.1,i＝1,2,3，
Figure BDA0002203999370000112
The parameters of the sigmoid function are selected as follows: l1＝2,l2＝8,l3＝4,l4＝-0.5。
The response diagrams of the attitude quaternion and the angular velocity of the rigid aircraft are respectively shown in fig. 1 and fig. 2, and it can be seen that both the attitude quaternion and the angular velocity can be converged into a zero region of a balance point within about 5 seconds; the sliding mode surface response diagram of the rigid aircraft is shown in fig. 3, and it can be seen that the sliding mode surface can be converged into a zero region of a balance point in about 3 seconds; the control moment and parameter estimation response diagrams of the rigid aircraft are shown in fig. 4 and 5, respectively.
Therefore, the invention realizes the consistency of the fixed time of the system state and the final limit under the condition that the system has external interference and uncertain rotational inertia, and the convergence time is independent of the initial state of the system.
While the foregoing has described a preferred embodiment of the invention, it will be appreciated that the invention is not limited to the embodiment described, but is capable of numerous modifications without departing from the basic spirit and scope of the invention as set out in the appended claims.

Claims (1)

1. A rigid aircraft fixed time attitude stabilization method based on neural network estimation is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a kinematics and dynamics model of a rigid aircraft, initializing system states and control parameters, and carrying out the following processes:
1.1 the kinematic equation for a rigid aircraft system is:
Figure FDA0003574545870000011
Figure FDA0003574545870000012
wherein q isv＝[q1,q2,q3]TAnd q is4Vector part and scalar part of unit quaternion respectively and satisfy
Figure FDA0003574545870000013
q1,q2,q3Respectively mapping values on x, y and z axes of a space rectangular coordinate system;
Figure FDA0003574545870000014
are each qvAnd q is4A derivative of (a);
Figure FDA0003574545870000015
is q isvTransposing; omega belongs to R3Is the angular velocity of the rigid aircraft; i is3Is R3×3An identity matrix;
Figure FDA0003574545870000016
expressed as:
Figure FDA0003574545870000017
1.2 the kinetic equation for a rigid aircraft system is:
Figure FDA0003574545870000018
wherein J ∈ R3×3Is the rotational inertia matrix of the aircraft;
Figure FDA0003574545870000019
is the angular acceleration of the aircraft; u is an element of R3And d ∈ R3Control moment and external disturbance; omega×Expressed as:
Figure FDA00035745458700000110
1.3 rotational inertia matrix J satisfies J ═ J0+ Δ J, wherein J0And Δ J represents the nominal and indeterminate portions of J, respectively, equation (4) is rewritten as:
Figure FDA00035745458700000111
further obtaining:
Figure FDA0003574545870000021
1.4 differentiating the formula (1) to obtain:
Figure FDA0003574545870000022
wherein
Figure FDA0003574545870000023
Is the total indeterminate set;
ΩTis a transposition of Ω;
Figure FDA0003574545870000024
is qvThe second derivative of (a);
Figure FDA0003574545870000025
is J0The inverse of (1);
Figure FDA0003574545870000026
expressed as:
Figure FDA0003574545870000027
Figure FDA0003574545870000028
are each q1,q2,q3A derivative of (a);
step 2, designing a required slip form surface aiming at a rigid aircraft system with uncertain external disturbance and moment inertia, wherein the process is as follows:
selecting a fixed-time sliding mode surface as follows:
Figure FDA0003574545870000029
wherein the content of the first and second substances,
Figure FDA00035745458700000210
Figure FDA00035745458700000211
Figure FDA00035745458700000212
and sgn (q)i) Are all sign functions, λ1＞0,λ2＞0,a2＞1，
Figure FDA00035745458700000213
Figure FDA00035745458700000214
Is qiI ═ 1,2, 3;
definition S ═ S1,S2,S3]TAnd obtaining the following result by derivation of S:
Figure FDA00035745458700000215
substituting formula (8) into (11) to obtain:
Figure FDA0003574545870000031
step 3, designing a neural network fixed time controller, and the process is as follows:
3.1 define the neural network as:
Gi(Xi)＝Wi *TΦ(Xi)+εi (13)
wherein
Figure FDA0003574545870000032
As an input vector, phi (X)i)∈R4Being basis functions of neural networks, Wi *∈R4The ideal weight vector is defined as:
Figure FDA0003574545870000033
wherein Wi∈R4Is a weight vector, εiFor approximation error, | εi|≤εN,i＝1,2,3，εNIs a very small normal number; argmin {. cndot } is Wi *Taking the set of all the minimum values;
3.2 consider that the fixed-time controller is designed to:
Figure FDA0003574545870000034
wherein
Figure FDA0003574545870000035
Is a diagonal matrix of 3 x 3 symmetry,
Figure FDA0003574545870000036
is WiIs equal to [ phi (X) ]1),Φ(X2),Φ(X3)]T，
Figure FDA0003574545870000037
L＝[L1,L2,L3]T，
Figure FDA0003574545870000038
i＝1,2,3；Γ＝diag(Γ1,Γ2,Γ3)∈R3×3Is a diagonal matrix of 3 x 3 symmetry,
Figure FDA0003574545870000039
0＜r1＜1，r2＞1，K1＝diag(k11,k12,k13)∈R3×3is a diagonal matrix with 3 multiplied by 3 symmetry; k2＝diag(k21,k22,k23)∈R3×3Is a diagonal matrix with 3 multiplied by 3 symmetry; k3＝diag(k31,k32,k33)∈R3×3Is a diagonal matrix with 3 multiplied by 3 symmetry;
Figure FDA00035745458700000310
is Wi(ii) an estimate of (d);
3.2 design update law:
Figure FDA00035745458700000311
wherein gamma isi＞0,pi＞0，
Figure FDA0003574545870000041
Is composed of
Figure FDA0003574545870000042
I ═ 1,2, 3; phi (X)i) Sigmoid function chosen as follows:
Figure FDA0003574545870000043
wherein l1,l2,l3And l4To approximate the parameter, phi (X)i) Satisfies the relation 0 < phi (X)i)＜Φ0And is and
Figure FDA0003574545870000044
step 4, the stability of the fixed time is proved, and the process is as follows:
4.1 demonstrates that all signals of the rigid aircraft system are consistent and finally bounded, and the Lyapunov function is designed to be of the form:
Figure FDA0003574545870000045
wherein
Figure FDA0003574545870000046
i＝1,2,3；STIs the transpose of S;
Figure FDA0003574545870000047
is that
Figure FDA0003574545870000048
Transposing;
derivation of equation (18) yields:
Figure FDA0003574545870000049
wherein min {. cndot } represents a minimum value;
Figure FDA00035745458700000410
i is 1,2, 3; i | · | | represents a two-norm of the value;
determining that all signals of the rigid aircraft system are consistent and ultimately bounded;
4.2 prove the convergence of the fixed time, designing the Lyapunov function as follows:
Figure FDA00035745458700000411
derivation of equation (20) yields:
Figure FDA00035745458700000412
wherein
Figure FDA00035745458700000413
i＝1,2,3；υ2An upper bound value greater than zero;
based on the above analysis, the rigid aircraft system state is consistently bounded at a fixed time.
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