CN109189080A - How autonomous ocean navigation device system distributed control method based on fuzzy theory - Google Patents
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Abstract
The technical issues of the invention discloses a kind of how autonomous ocean navigation device system distributed control method based on fuzzy theory, the practicability is poor for solving existing ocean navigation device control method.Technical solution is a series of fuzzy model for being configured to be made of fuzzy logics by more aircraft kinematics and dynamic system using fuzzy system theory, distributed director is designed for the fuzzy model constructed, obtain closed loop fuzzy system, using the stability of Lyapunov stability theory analysis closed-loop system, and use Algebraic Riccati equations method optimal control gain parameter.The method of the present invention can input controller and optimize, and realize that desired control performance, practicability are good with lesser control force.By taking two aircraft as an example, for the state error curve of each aircraft in the case where converging to zero within 40 seconds, the maximum value of control force input is reduced to 12N and 8N by the 55N of background technique and 13N respectively.
Description
Technical field
The present invention relates to a kind of ocean navigation device control method, in particular to a kind of how autonomous ocean based on fuzzy theory
Aircraft systems distributed control method.
Background technique
Document " the submarine navigation device motion control simulation study based on Sliding mode control, naval vessel science and technology, 2016,
38 (6), 92-96 " disclose a kind of single ocean navigation device control method based on nonlinear compensation.This method has studied single sea
The motor control problems of foreign aircraft devise STATE FEEDBACK CONTROL algorithm, compensate the nonlinear terms in system as control
Item feedback is into control input.Method advantage described in document based on Nonlinear compensation control is that controller is easy to set
Meter is not carrying out control input using optimization algorithm more mature in linear control method excellent
Change, causes controller that can not input with optimal control to realize desired control performance；The requirement of Nonlinear compensation control method
The oneself state information of all aircraft be all it is measurable, between aircraft topological structure it is restricted relatively strong.
Summary of the invention
In order to overcome the shortcomings of existing ocean navigation device control method, the practicability is poor, and the present invention provides a kind of based on fuzzy reason
The how autonomous ocean navigation device system distributed control method of opinion.This method utilizes fuzzy system theory by more aircraft kinematics
And dynamic system is configured to a series of fuzzy model being made of fuzzy logics, for the fuzzy model design distribution constructed
Formula controller obtains closed loop fuzzy system, using the stability of Lyapunov stability theory analysis closed-loop system, and uses
Algebraic Riccati equations method optimal control gain parameter.Method provided by the invention can be inputted to optimize and be set to controller
Meter realizes that desired control performance, practicability are good with lesser control force.By taking two aircraft as an example, the shape of each aircraft
In the case where converging to zero within 40 seconds, the maximum value of control force input is dropped by the 55N of background technique and 13N state error curve respectively
Low is 12N and 8N.
A kind of the technical solution adopted by the present invention to solve the technical problems: how autonomous ocean navigation based on fuzzy theory
Device system distributed control method, its main feature is that the following steps are included:
Step 1: more ocean navigation device kinematics and dynamic system are configured to by a series of using fuzzy system theory
The fuzzy system of fuzzy logic composition, establishes more aircraft kinematics and kinetic model:
In formula,Indicate the position vector of aircraft under inertial coodinate system, ψiIndicate yaw angle；uiIt indicates
Act on the control input quantity of aircraft；vi=[ρi υi ri]TIndicate the velocity vector under aircraft body coordinate system, ρiFor boat
To speed, υiFor lateral velocity, riFor yaw rate；Ω(ψi) indicate between inertial coodinate system and aircraft body coordinate system
State-transition matrix；M indicates that inertial matrix, D indicate damping matrix；Subscript i indicates that i-th of aircraft, N indicate aircraft
Total number.M,D,Ω(ψi) expression formula difference it is as follows:
In formula, m11、m22、m23、m33For inertial matrix parameter, d11、d22、d23、d33For damping matrix parameter, sin (ψi) and
cos(ψi) be yaw angle sine and cosine value.Enable A=-M-1D, B=M-1, so that more aircraft power models is turned into following form:
Define ξi=[xi yi ψi ρi υi ri]T, more aircraft kinematics and dynamic (dynamical) overall model are turned into as follows
Form:
In formula,
Using fuzzy system criterion, nonlinear system shown in formula (4) is turned into following fuzzy system:
System ambiguous rule miIf: ξi1It isAnd ... and ξi6It isSo
Wherein,The fuzzy set of expression system, miIndicate miA fuzzy rule, ξi1,...,ξi6It indicates
Vector ξi6 components,Indicate miThe corresponding state parameter matrix of a fuzzy rule, r indicate the total number of fuzzy rule.
Using the weighted average of each linear subsystem, whole fuzzy system as follows is obtained:
In formula,
Step 2: obtaining closed loop for whole fuzzy system formula (6) the design distributed director constructed in step 1
The system is carried out conversion of equal value, obtains one group of fuzzy system of equal value for being more easily performed stability analysis by fuzzy system.First
Design following distributed director:
Wherein, K is control gain matrix to be solved, aijIndicate the communication state weight between each aircraft, aiiIt indicates
Acquisition capability of i-th of aircraft to oneself state information.Formula (7) is updated in formula (6), closed loop system as follows is obtained
System:
In formula, ζ=[ξ1 T,...,ξN T]T；Indicate that i-th of diagonal variable matrix isRemaining matrix element is 0
Matrix；The corresponding Laplacian Matrix of communication topological structure between aircraft.Since the structure of formula (8) is complex,
It is difficult to carry out it stability analysis, therefore utilizes FUZZY WEIGHTED itemProperty, by formula (8) equivalence transformation be following shape
Formula:
In formula,
Step 3: designing distributed AC servo system algorithm for the fuzzy system formula (9) of equal value being converted in step 2, obtaining
Closed-loop system is provided the adequate condition for guaranteeing that closed-loop system is stable using Lyapunov stability theory, and utilizes algebra multitude
Riccati equation optimizes control gain parameter, guarantees that control input is optimal.For the fuzzy system formula after equivalence transformation
(9), liapunov function V=ζ is chosenTP ζ, whereinP2For positive definite symmetric matrices, INIndicate N rank unit square
Battle array.It is obtained using Lyapunov stability theory and infinite horizon optimal control theory, when following Algebraic Riccati equations
When having feasible solution:
Systematic (9) asymptotically stability, and following performance indicator is minimum:
In formula, U=[u1 T,...,uN T]T,Wherein R2And Q2It is the symmetrical square of positive definite
Battle array, and the minimum value for having performance indicator J is Jmin=V (0), and V (0) indicates liapunov function V in the initial value of zero moment.
Step 4: being increased based on adequate condition obtained in step 3 using linear matrix inequality approach simplified control device
Beneficial parametric solution process.Lemma is mended using the Shu Er in linear matrix inequality approach, formula (10) is equivalent to following linear moment
The form of battle array inequality:
In formula,Wherein ε is sufficiently small positive number, I6Indicate 6 ranks list
Bit matrix.In addition, recycling following two groups of linear matrix inequality to limit the value of (0) V, guarantee V (0)≤δ, wherein δ is one
A positive number:
-δ+αφ≤0, (13)
Wherein, φ is scalar, α >=ζT(0) (0) ζ, ζ (0) indicate ζ in the initial value of zero moment.It recycles under constraint condition
Method for optimally controlling solves and guarantees inequality (12), (13), (14) while the minimum δ set up.
The beneficial effects of the present invention are: this method utilizes fuzzy system theory by more aircraft kinematics and dynamic system
It is configured to a series of fuzzy model being made of fuzzy logics, distributed director is designed for the fuzzy model constructed, obtains
To closed loop fuzzy system, mentioned using the stability of Lyapunov stability theory analysis closed-loop system, and using algebra multitude card
Equation method optimal control gain parameter.The method of the present invention can input controller and optimize, with lesser control
Power realizes desired control performance.
Due to using the distributed control method based on fuzzy theory and the parameter optimization side based on Algebraic Riccati equations
Method can optimize control input, demand of the system to control input is greatly reduced under the premise of guaranteeing system performance；
To the restricted weaker of topology is communicated between more ocean navigation devices, can be suitable for only part aircraft can obtain oneself state
The case where information.By taking two aircraft as an example, the state error curve of background technique method, each aircraft can be received at 40 seconds
It holds back to zero, the maximum value of control force input is respectively 55N and 13N；The method of the present invention, the state error curve of each aircraft is still
Zero was converged at 40 seconds, the maximum value of control force input is respectively 12N and 8N.
It elaborates with reference to the accompanying drawings and detailed description to the present invention.
Detailed description of the invention
Fig. 1 is more aircraft in the how autonomous ocean navigation device system distributed control method the present invention is based on fuzzy theory
System coordinate system structural schematic diagram, X are the horizontal axis of inertial coodinate system, and Y is the longitudinal axis of inertial coodinate system, and Z is inertial coodinate system
Vertical pivot, X1For the horizontal axis of first aircraft body coordinate system, Y1For the longitudinal axis of first aircraft body coordinate system, Z1It is
The vertical pivot of one aircraft body coordinate system, X2For the horizontal axis of second aircraft body coordinate system, Y2For second aircraft sheet
The longitudinal axis of body coordinate system, Z2For the vertical pivot of second aircraft body coordinate system；
Fig. 2 be in situation of embodiment of the present invention I two aircraft existing Nonlinear compensation control method effect under
State error curve；
Fig. 3 be in situation of embodiment of the present invention I two aircraft in the controlling party proposed by the present invention based on fuzzy theory
State error curve under method effect；
Fig. 4 be in situation of embodiment of the present invention I two aircraft existing Nonlinear compensation control method effect under
Control input curve；
Fig. 5 be in situation of embodiment of the present invention I two aircraft in the controlling party proposed by the present invention based on fuzzy theory
Control input curve under method effect；
Fig. 6 be in situation of embodiment of the present invention II two aircraft in the controlling party proposed by the present invention based on fuzzy theory
State error curve under method effect；
Fig. 7 be in situation of embodiment of the present invention II two aircraft in the controlling party proposed by the present invention based on fuzzy theory
Control input curve under method effect.
Specific embodiment
Referring to Fig.1-7.The present invention is based on how autonomous the ocean navigation device system distributed control method of fuzzy theory be specific
Steps are as follows:
Step 1: more ocean navigation device kinematics and dynamic system are configured to by a series of using fuzzy system theory
The fuzzy system of fuzzy logic composition, establishes more aircraft kinematics and kinetic model:
In formula,Indicate the position vector of aircraft under inertial coodinate system, xiAnd yiRespectively indicate transverse and longitudinal axis
The position in direction, ψiIndicate yaw angle；uiExpression acts on the control input quantity (being provided by propeller and propeller) of aircraft；
vi=[ρi υi ri]TIndicate the velocity vector under aircraft body coordinate system, ρiFor course speed, υiFor lateral velocity, riIt is inclined
Navigate angular speed；Ω(ψi) indicate state-transition matrix between inertial coodinate system and aircraft body coordinate system；M indicates the moment of inertia
Battle array, D indicate damping matrix；Subscript i indicates that i-th of aircraft, N indicate the total number of aircraft.In addition, M, D, Ω (ψi)
Expression formula difference is as follows:
In formula, m11、m22、m23、m33For inertial matrix parameter, d11、d22、d23、d33For damping matrix parameter, sin (ψi) and
cos(ψi) be yaw angle sine and cosine value.Enable A=-M-1D, B=M-1, so that more aircraft power models is turned into following form:
Define ξi=[xi yi ψi ρi υi ri]T, more aircraft kinematics and dynamic (dynamical) overall model are turned into as follows
Form:
In formula,
Using fuzzy system criterion, nonlinear system shown in formula (4) is turned into following fuzzy system:
System ambiguous rule miIf: ξi1It isAnd ... and ξi6It isSo
Wherein,The fuzzy set of expression system, miIndicate miA fuzzy rule, ξi1,...,ξi6It indicates
Vector ξi6 components,Indicate miThe corresponding state parameter matrix of a fuzzy rule, r indicate the total number of fuzzy rule.
Using the weighted average of each linear subsystem, available whole fuzzy system as follows:
In formula,
Step 2: obtaining closed loop fuzzy for fuzzy system formula (6) the design distributed director constructed in step 1
The system is carried out conversion of equal value, obtains one group of fuzzy system of equal value for being more easily performed stability analysis by system.It designs first
Following distributed director:
Wherein K is control gain matrix to be solved, aijIndicate the communication state weight between each aircraft, aiiIt indicates
Acquisition capability of i-th of aircraft to oneself state information.Formula (7) is updated in formula (6), as follows close can be obtained
Loop system:
In formula, ζ=[ξ1 T,...,ξN T]T；Indicate that i-th of diagonal variable matrix isRemaining matrix element is 0
Matrix；The corresponding Laplacian Matrix of communication topological structure between aircraft.Since the structure of formula (8) is complex,
It is difficult to carry out stability analysis to it, it is therefore desirable to carry out equivalence transformation to it.Utilize FUZZY WEIGHTED itemProperty, can
It is following form by formula (8) equivalence transformation:
In formula,
Step 3: designing distributed AC servo system algorithm for the fuzzy system formula (9) of equal value being converted in step 2, obtaining
Closed-loop system is provided the adequate condition for guaranteeing that closed-loop system is stable using Lyapunov stability theory, and utilizes algebra multitude
Riccati equation optimizes control gain parameter, guarantees that control input is optimal.For the fuzzy system formula after equivalence transformation
(9), liapunov function V=ζ is chosenTP ζ, whereinP2For positive definite symmetric matrices, INIndicate N rank unit square
Battle array.It can be obtained using Lyapunov stability theory and infinite horizon optimal control theory, when following Algebraic Riccati equations
When having feasible solution:
Systematic (9) asymptotically stability, and following performance indicator is minimum (i.e. Infinite Time optimal problem has optimal solution):
In formula, U=[u1 T,...,uN T]T,Wherein R2And Q2It is the symmetrical square of positive definite
Battle array, and the minimum value for having performance indicator J is Jmin=V (0), and V (0) indicates liapunov function V in the initial value of zero moment.
Step 4: being increased based on adequate condition obtained in step 3 using linear matrix inequality approach simplified control device
Beneficial parametric solution process.Lemma is mended using the Shu Er in linear matrix inequality approach, formula (10) can be equivalent to such as lower linear
The form of MATRIX INEQUALITIES:
In formula,Wherein ε is sufficiently small positive number, I6Indicate 6 ranks list
Bit matrix.In addition, recycling following two groups of linear matrix inequality to limit the value of (0) V, guarantee V (0)≤δ, wherein δ is one
A positive number:
-δ+αφ≤0, (13)
Wherein φ is scalar, α >=ζT(0) (0) ζ, ζ (0) indicate ζ in the initial value of zero moment.It recycles under constraint condition
Method for optimally controlling solves and guarantees inequality (12), (13), (14) while the minimum δ set up.Due in MATLAB
There is the highly developed tool box for being used to solve linear matrix inequality, therefore is mentioned compared to the algebra multitude card provided in formula (10)
Equation, the linear matrix inequality provided in formula (12) are easier to solve, in addition, there are two matrix R in formula (10)2And Q2It needs
Designer manually adjusts, and matrix only one R for needing designer to manually adjust in formula (12)2, therefore adjusting difficulty is lower,
It is easier to obtain optimal solution.
Beneficial effects of the present invention are verified using following embodiment:
1) situation I: assuming that there are two aircraft in system, and two aircraft can obtain itself status information, because
This communicates topologically corresponding Laplacian Matrix
It takes inertial matrix and damping matrix is respectively
Choose sin (ψi)=0, cos (ψi)=1；sin(ψi)=0,sin(ψi)=1/2, cos (ψi)
=1；sin(ψi)=1/2,As 4 groups of operating points of fuzzy system formula (6), then it can obtain four groups and obscure
Rule, and the corresponding coefficient matrix of every group of fuzzy rule is
Choose R2=200I3, α=3000 utilize three groups of linear matrix inequality (12), (13), (14) and MATLAB
In optimal solver, the smallest δ and corresponding control gain matrix K can be found out, it is as follows:
In addition, providing Nonlinear compensation control as follows using the principle of traditional Nonlinear compensation control method
Device:
K=0.15 is taken, then chooses the state initial value of two aircraft and is respectively
ξ1(0)=[50 50 0.5 11 0.1]T,
ξ2(0)=[- 20-20 0.2 11 0.1]T.
Two aircraft can be obtained in Nonlinear compensation control algorithms (15) and based on the control algolithm of fuzzy theory
State error curve and control input curve under formula (7) effect.By simulation curve it is found that two kinds of control algolithms can protect
The state error curve of card aircraft converged to zero at 40 seconds.However, when using existing Nonlinear compensation control algorithm, two
The maximum control input of aircraft is 55N and 13N；And when using algorithm provided by the invention, the maximum value for controlling input only has
12N and 8N.Therefore, compared to Nonlinear compensation control algorithm, the control algolithm based on fuzzy theory that the present invention designs can
Identical state error convergence rate is realized with smaller control force.
1) situation II: it will again be assumed that there are two aircraft in system, but only first aircraft can obtain oneself state
Information, therefore communicate topologically corresponding Laplacian Matrix and be
It takes inertial matrix and damping matrix is respectively
Still choose sin (ψi)=0, cos (ψi)=1；sin(ψi)=0,sin(ψi)=1/2, cos
(ψi)=1；sin(ψi)=1/2,As 4 groups of operating points of fuzzy system formula (6), then four groups can be obtained
Fuzzy rule, the corresponding coefficient matrix of every group of fuzzy rule are
Choose R2=10I3, α=1000, using in three groups of linear matrix inequality (12), (13), (14) and MATLAB
Optimal solver, the smallest δ and corresponding control gain matrix K can be found out, it is as follows:
The state initial value for choosing two aircraft is respectively
ξ1(0)=[20 20 0.2 11 0.1]T,
ξ2(0)=[- 20-20 0.2 11 0.1]T.
Can obtain two aircraft the lower state error curve of control algolithm formula (7) effect based on fuzzy theory with
Control input curve.By simulation curve it is found that the control aircraft based on fuzzy theory that the present invention designs is applicable to only
There is a case where aircraft can obtain itself status information.However, for Nonlinear compensation control algorithms (15), due to
Contain nonlinear compensation item-B in control input-1[Ω(ψi)vi+Avi], this means that the oneself state information pair of each aircraft
It is all essential information for control algolithm, therefore traditional Nonlinear compensation control algorithm can not be suitable for only one
A aircraft can obtain the case where itself status information.
Content (such as graph theory, Lyapunov stability theory, Algebraic Riccati equations, the line that the present invention is not discussed in detail
Property MATRIX INEQUALITIES) belong to the public common sense in this field.
Claims (1)
1. a kind of how autonomous ocean navigation device system distributed control method based on fuzzy theory, it is characterised in that including following
Step:
Step 1: more ocean navigation device kinematics and dynamic system are configured to by a series of fuzzy using fuzzy system theory
The fuzzy system of logic composition, establishes more aircraft kinematics and kinetic model:
In formula,Indicate the position vector of aircraft under inertial coodinate system, ψiIndicate yaw angle；uiExpression effect
In the control input quantity of aircraft；vi=[ρiυi ri]TIndicate the velocity vector under aircraft body coordinate system, ρiFor course speed
Degree, υiFor lateral velocity, riFor yaw rate；Ω(ψi) indicate shape between inertial coodinate system and aircraft body coordinate system
State transfer matrix；M indicates that inertial matrix, D indicate damping matrix；Subscript i indicates that i-th of aircraft, N indicate the total of aircraft
Number；M,D,Ω(ψi) expression formula difference it is as follows:
In formula, m11、m22、m23、m33For inertial matrix parameter, d11、d22、d23、d33For damping matrix parameter, sin (ψi) and cos
(ψi) be yaw angle sine and cosine value；Enable A=-M-1D, B=M-1, so that more aircraft power models is turned into following form:
Define ξi=[xi yi ψi ρi υi ri]T, more aircraft kinematics and dynamic (dynamical) overall model are turned into following form:
In formula,
Using fuzzy system criterion, nonlinear system shown in formula (4) is turned into following fuzzy system:
System ambiguous rule miIf: ξi1It isAnd ... and ξi6It isSo
Wherein,The fuzzy set of expression system, miIndicate miA fuzzy rule, ξi1,...,ξi6Indicate vector
ξi6 components,Indicate miThe corresponding state parameter matrix of a fuzzy rule, r indicate the total number of fuzzy rule；It utilizes
The weighted average of each linear subsystem obtains whole fuzzy system as follows:
In formula,
Step 2: obtaining closed loop fuzzy for whole fuzzy system formula (6) the design distributed director constructed in step 1
The system is carried out conversion of equal value, obtains one group of fuzzy system of equal value for being more easily performed stability analysis by system；It designs first
Following distributed director:
Wherein, K is control gain matrix to be solved, aijIndicate the communication state weight between each aircraft, aiiIt indicates i-th
Acquisition capability of the aircraft to oneself state information；Formula (7) is updated in formula (6), closed-loop system as follows is obtained:
In formula, ζ=[ξ1 T,...,ξN T]T；Indicate that i-th of diagonal variable matrix isRemaining matrix element is 0 matrix；The corresponding Laplacian Matrix of communication topological structure between aircraft；Since the structure of formula (8) is complex, it is difficult to right
It carries out stability analysis, therefore utilizes FUZZY WEIGHTED itemProperty, by formula (8) equivalence transformation be following form:
In formula,
Step 3: designing distributed AC servo system algorithm for the fuzzy system formula (9) of equal value being converted in step 2, obtaining closed loop
System is provided the adequate condition for guaranteeing that closed-loop system is stable using Lyapunov stability theory, and is mentioned using algebra multitude card
Equation optimizes control gain parameter, guarantees that control input is optimal；For the fuzzy system formula (9) after equivalence transformation,
Choose liapunov function V=ζTP ζ, whereinP2For positive definite symmetric matrices, INIndicate N rank unit matrix；Benefit
Obtained with Lyapunov stability theory and infinite horizon optimal control theory, when following Algebraic Riccati equations have it is feasible
Xie Shi:
Systematic (9) asymptotically stability, and following performance indicator is minimum:
In formula, U=[u1 T,...,uN T]T,Wherein R2And Q2It is positive definite symmetric matrices, and
The minimum value for having performance indicator J is Jmin=V (0), and V (0) indicates liapunov function V in the initial value of zero moment；
Step 4: being joined based on adequate condition obtained in step 3 using linear matrix inequality approach simplified control device gain
Number solution procedure；Lemma is mended using the Shu Er in linear matrix inequality approach, formula (10) is equivalent to following linear matrix not
The form of equation:
In formula,Wherein ε is sufficiently small positive number, I6Indicate 6 rank unit squares
Battle array；In addition, recycling following two groups of linear matrix inequality to limit the value of (0) V, guarantee V (0)≤δ, wherein δ be one just
Number:
(13)
-δ+αφ≤0,
Wherein, φ is scalar, α >=ζT(0) (0) ζ, ζ (0) indicate ζ in the initial value of zero moment；It recycles optimal under constraint condition
Control method solves and guarantees inequality (12), (13), (14) while the minimum δ set up.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110032204A (en) * | 2019-04-24 | 2019-07-19 | 西北工业大学 | More spacecraft Attitude cooperative control methods under input delay |
| CN110032204B (en) * | 2019-04-24 | 2022-07-29 | 西北工业大学 | Multi-spacecraft attitude cooperative control method under input time delay |
| CN110362103A (en) * | 2019-08-19 | 2019-10-22 | 西北工业大学 | Distributed freedom submarine navigation device posture cooperates with optimal control method |
| CN117850249A (en) * | 2024-03-08 | 2024-04-09 | 山东科技大学 | AUV self-adaptive fuzzy control method |
| CN117850249B (en) * | 2024-03-08 | 2024-05-14 | 山东科技大学 | AUV self-adaptive fuzzy control method |
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