CN110162039A - A kind of novel integrated ship path trace and rollstabilization optimal control method - Google Patents
A kind of novel integrated ship path trace and rollstabilization optimal control method Download PDFInfo
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- G05D1/02—Control of position or course in two dimensions
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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Abstract
The present invention provides a kind of novel integrated ship path trace and rollstabilization optimal control method, comprising the following steps: being established according to ship motion feature with rudder angle be the ship motion controller model inputted；Choose prediction time domain and control time domain, the future state of forecasting system；It converts the optimization problem for considering that energy consumption is combined with control performance for ship path trace and rollstabilization problem to solve optimization problem in the case where constraining with actuator, and by first element interaction of solution in system；The Ship-Fin-Stabilizer Control model based on sliding-mode method is established, On-line Estimation is carried out to system unknown portions by RBF neural method.The course line that the present invention can make ship tracking set, mitigates the steering burden of crewman, while reducing ship rolling motion, reduces stormy waves to safety of ship, ship equipment, cargo security, the harm of personnel health, it is ensured that the normal operation of ship precision instrument.And the present invention can also reduce the energy consumption of ship, keep ship more economical, environmentally friendly.
Description
Technical field
The present invention relates to ship control technical fields, specifically, more particularly to a kind of novel integrated ship path trace
With rollstabilization optimal control method.
Background technique
When ship rides the sea, by the interference of extraneous stormy waves, can generate it is various rock, these of ship rock and main
It is maximum with the harm of rolling.It is traversing that ship rolling may cause cargo, adversely affects to Ship Structure, or even will affect ship
The stability of oceangoing ship, causes ship to topple.Ship rolling will affect driver's physical condition simultaneously, prevent driver from fulfiling well
Obligation endangers navigation safety.
There is certain research for ship rollstabilization and path trace problem at present, relevant document has: 2009, Li
" the Path following with roll constraints for marine surface vessels in that Z is delivered
The advantages of wave fields " is using MPC-processing restricted problem-is regarded roll angle as output and is limited, and straight line is realized
Path trace and ship rollstabilization.Liu C etc. has delivered " Integrated on " Journal of Ship Research "
line of sight and model predictive control for path following and roll motion
Control using rudder " realizes the tracking of free routing on the basis of Li Z.But both only use rudder progress
Ship rollstabilization and path trace.It is well known that stabilizer subtracts the tool of shaking as specialized ships, subtract the effect shaken is very
Significantly.Fang MC has delivered " Applying the PD controller on the on " Ocean Engineering "
Roll reduction and track keeping for the ship advancing in waves ", combine rudder and
Stabilizer carries out ship rollstabilization, but is confined to that Heading control can only be carried out.
Summary of the invention
According to technical problem set forth above, and provide a kind of novel integrated ship path trace and rollstabilization optimal control
Method.The present invention mainly utilizes a kind of novel integrated ship path trace and rollstabilization optimal control method, comprising the following steps:
S1: according to ship motion feature, establishing with rudder angle is the ship motion controller model inputted；
S2: choosing prediction time domain and control time domain, design a model predictive controller；S3: by ship path trace and subtract cross
The problem of shaking is converted into the optimization problem for considering that energy consumption is combined with control performance, in the case where constraining with actuator, to optimization
Problem is solved, and by first element interaction of solution in system；
S4: the Ship-Fin-Stabilizer Control model based on sliding-mode method is established, by RBF neural method to system unknown portions
Carry out On-line Estimation.
Further, according to ship motion feature, ship motion controller model is established:
Wherein,ut=δ, e indicate path with
Track error,Indicate course error, φ indicates roll angle, and v indicates lateral drift speed, and p indicates that angular velocity in roll, r indicate angle of yaw
Speed, δ indicate rudder angle,
Wherein, a11…a34, b11…b13It can be calculated and be acquired by ship parameter；
By giving the sampling time, by ship motion controller model conversion at discrete model:
X (k+1)=Ax (k)+B δ (k) (21)
Y (k)=Cx (k) (22)
Wherein, x ∈ R6×1, y ∈ R4×1, A ∈ R6×6, B ∈ R6×1, C ∈ R4×6, the shape of x (k) expression kth sampling instant system
State vector matrix, x (k+1) indicate that the state vector matrix of+1 sampling instant system of kth, δ (k) indicate kth sampling instant control
Input matrix, y (k) indicate the output matrix of kth sampling instant system, and matrix A, B, C are respectively At, Bt, CtSquare after discrete
Battle array, k indicate sampling instant.
Further, rudder angle is limited, Controlling model is rewritten as incremental model, formula (2) and formula (3) are carried out
Such as down conversion:
Formula (2) are subjected to differential, can be expressed as:
X (k+1)-x (k)=A (x (k)-x (k-1))+B (δ (k)-δ (k-1)) (23)
For the statement of simplified style (4), such as given a definition:
Δ x (k)=x (k)-x (k-1)
Δ δ (k)=δ (k)-δ (k-1)
Then formula (4) may be expressed as:
Δ x (k+1)=A Δ x (k)+B Δ δ (k) (24)
Similarly, differential is carried out to formula (3), then:
Y (k+1)-y (k)=C (x (k+1)-x (k))=CA Δ x (k)+CB Δ δ (k) (6)
Formula (5) and formula (6) are indicated with augmented matrix are as follows:
Wherein, O6×4Indicate 6 × 4 full null matrix, I indicates 4 × 4 unit matrix；And
Then formula (7) may be expressed as:
Choose the prediction time domain NpWith the control time domain Nc, then in kth sampling instant, the system future is being controlled
Input in time domain may be expressed as: δ (k), δ (k+1), δ (k+2) ..., δ (k+Nc-1)；
State of the system future in prediction time domain may be expressed as:
Output of the system future in prediction time domain may be expressed as: y (k+1 | k), y (k+2 | k), y (k+3 | k) ...,
y(k+NP|k)。y(k+NP| it k) respectively indicates according to kth sampling instantY (k) predicts kth+Np
Sampling instanty(k+Np) value；
In kth sampling instant, by the input in the system future: δ (k), δ (k+1), δ (k+2) ..., δ (k+Nc- 1) it, asks
Obtain Δ δ (k), Δ δ (k+1), Δ δ (k+2) ..., Δ δ (k+Nc- 1), bring into formula (8) obtain system prediction time domain in it is defeated
Out:
Such as given a definition to variable in formula (9):
Δ U=[Δ δ (k) Δ δ (k+1) Δ δ (k+2) ... Δ δ (k+Nc-1)]T∈RNc；
Formula (9) can then be indicated are as follows:
Wherein F and Φ are as follows:
Further, described convert ship path trace and rollstabilization problem to considers energy consumption and control performance phase
In conjunction with optimization problem；It defines cost function are as follows:
J=YTQY+ΔUTRΔU (11)
Wherein, YTQY indicates that the target deviateed control error is adjusted, Δ UTR Δ U indicates the adjusting to energy consumption, Q, R
Respectively indicate weight matrix；
Limit the size and change rate size of input rudder angle δ:
δmin≤δ(k+i)≤δmax, i=0,1 ... Np-1
Δδmin≤Δδ(k+i)≤Δδmax, i=0,1 ... Np-1
Cost function is solved, find out control input δ with the first item of Δ U and is brought into formula (2), system mode, system are acquired
Output successively brings into formula (3) to formula (11), by solving cost function again, new Δ U is found out, with the first of new Δ U
Item finds out new control input δ and brings into formula (2), and repetitive cycling is carried out until reaching setting cycle-index.
Further, the Ship-Fin-Stabilizer Control model based on sliding-mode method is established:
S=c φ+p (12)
Wherein, c indicates that positive design parameter, φ indicate roll angle, and p indicates angular velocity in roll；
Derivation is carried out to formula (12):
In formula, bfIt indicates constant, f is approached by radial basis function neural network methodp,Wherein,It is fpEstimated value,Indicate that neural network adapts to rule, H1(z) basis function vector is indicated.
The control of stabilizer includes: equivalent control part αeqWith switching control part αsw:
α=αeq+αsw (14)
Wherein,
In above formula, η1, k1Indicate positive control design case parameter；
Define Liapunov function:
Wherein, γ indicates positive design parameter,W1 *Indicate that optimal neural network adapts to rule；
By above-mentioned Liapunov function derivation:
In formula,
Wherein, H1(Z) it indicates basis function vector, brings formula (14), (15), (16) and formula (19) into formula (18) abbreviation afterwards
:
By formula (17) and formula (20), stable closed-loop control system is obtained according to Lyapunov theorem judgement.
Compared with the prior art, the invention has the following advantages that
The present invention provides a kind of novel ship automatic control method, by alloing ship to exist in conjunction with stabilizer and rudder
It is navigated by water in stormy waves along set path, while the rolling of ship can be reduced.The present invention may be mounted at the quotient of stabilizer
Supplement on the ships such as ship, ferry boat, pleasure boat, as auto-pilot control system existing on ship.The present invention can make ship tracking
Set course line, mitigates the steering burden of crewman, while reducing ship rolling motion, reduces stormy waves to safety of ship, ship is set
It is standby, cargo security, the harm of personnel health, it is ensured that the normal operation of ship precision instrument.And the present invention can also reduce ship
Energy consumption, make that ship is more economical, environmental protection.
(1) existing patented technology only has simple ship rollstabilization or path following control, and the application can be simultaneously
Carry out ship rollstabilization and path following control.
(2) it is found after more existing patented technology only carries out rollstabilization control with stabilizer, the application is various
Rollstabilization effect in the case of stormy waves wants more obvious, while stabilizer only needs to reach non-using lesser control angle
Often good effect.
(3) it is not that rudder and stabilizer carry out ship path trace respectively and subtract that the rudder of the application type and stabilizer, which jointly control,
Rolling control, but rudder also cooperates stabilizer to carry out the control of ship rollstabilization while carrying out ship path trace, therefore
Rollstabilization effect is more more obvious than rudder or stabilizer is used alone.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to do simply to introduce, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without any creative labor, can be with
It obtains other drawings based on these drawings.
Fig. 1 is overall flow schematic diagram of the present invention.
Specific embodiment
In order to enable those skilled in the art to better understand the solution of the present invention, below in conjunction in the embodiment of the present invention
Attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is only
The embodiment of a part of the invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill people
The model that the present invention protects all should belong in member's every other embodiment obtained without making creative work
It encloses.
It should be noted that description and claims of this specification and term " first " in above-mentioned attached drawing, "
Two " etc. be to be used to distinguish similar objects, without being used to describe a particular order or precedence order.It should be understood that using in this way
Data be interchangeable under appropriate circumstances, so as to the embodiment of the present invention described herein can in addition to illustrating herein or
Sequence other than those of description is implemented.In addition, term " includes " and " having " and their any deformation, it is intended that cover
Cover it is non-exclusive include, for example, the process, method, system, product or equipment for containing a series of steps or units are not necessarily limited to
Step or unit those of is clearly listed, but may include be not clearly listed or for these process, methods, product
Or other step or units that equipment is intrinsic.
As shown in Figure 1, the present invention provides a kind of novel integrated ship path trace and rollstabilization optimal control method, packet
Include following steps: step S1: according to ship motion feature, establishing with rudder angle is the ship motion controller model inputted.Step S2:
Prediction time domain and control time domain are chosen, design a model predictive controller.Step S3: by ship path trace and rollstabilization problem
Be converted into and consider the optimization problem that combines with control performance of energy consumption, in the case where being constrained with actuator, to optimization problem into
Row solves, and by first element interaction of solution in system.Step S4: establishing the Ship-Fin-Stabilizer Control model based on sliding-mode method,
On-line Estimation is carried out to system unknown portions by RBF neural method.
Ship motion controller model is established according to ship motion feature as preferred embodiment:
Wherein,ut=δ, e indicate path with
Track error,Indicate course error, φ indicates roll angle, and v indicates lateral drift speed, and p indicates that angular velocity in roll, r indicate angle of yaw
Speed, δ indicate rudder angle；
Wherein, a11…a34, b11…b13It can be calculated and be acquired by ship parameter；
By giving the sampling time, by ship motion controller model conversion at discrete model:
X (k+1)=Ax (k)+B δ (k) (2)
Y (k)=Cx (k) (3)
Wherein, x ∈ R6×1, y ∈ R4×1, A ∈ R6×6, B ∈ R6×1, C ∈ R4×6, the shape of x (k) expression kth sampling instant system
State vector matrix, x (k+1) indicate that the state vector matrix of+1 sampling instant system of kth, δ (k) indicate kth sampling instant control
Input matrix, y (k) indicate the output matrix of kth sampling instant system, and matrix A, B, C are respectively At, Bt, CtSquare after discrete
Battle array, k indicate sampling instant.
In the present embodiment, rudder angle is limited, Controlling model is rewritten as incremental model, to formula (2) and formula (3)
Carry out such as down conversion:
Formula (2) are subjected to differential, can be expressed as:
X (k+1)-x (k)=A (x (k)-x (k-1))+B (δ (k)-δ (k-1)) (4)
For the statement of simplified style (4), such as given a definition:
Δ x (k)=x (k)-x (k-1)
Δ δ (k)=δ (k)-δ (k-1)
Then formula (4) may be expressed as:
Δ x (k+1)=A Δ x (k)+B Δ δ (k) (5)
Similarly, differential is carried out to formula (3), then:
Y (k+1)-y (k)=C (x (k+1)-x (k))=CA Δ x (k)+CB Δ δ (k) (6)
Formula (5) and formula (6) are indicated with augmented matrix are as follows:
Wherein, O6×4Indicate 6 × 4 full null matrix, I indicates 4 × 4 unit matrix；And
Then formula (7) may be expressed as:
Choose the prediction time domain NpWith the control time domain Nc, then in kth sampling instant, the system future is being controlled
Input in time domain may be expressed as: δ (k), δ (k+1), δ (k+2) ..., δ (k+Nc-1)；The system future is in prediction time domain
State may be expressed as: The system
The following output in prediction time domain of system may be expressed as: y (k+1 | k), y (k+2 | k), y (k+3 | k) ..., y (k+NP|k)。y(k+NP| it k) respectively indicates according to kth sampling instantY (k) predicts kth+NpSampling instanty(k+Np) value；In kth sampling instant, by the input in the system future:: δ (k), δ (k+1), δ (k+
2) ..., δ (k+Nc- 1) Δ δ (k), Δ δ (k+1), Δ δ (k+2) ..., Δ δ (k+N, are acquiredc- 1) it, brings formula (8) into and obtains system
Output in prediction time domain:
Such as given a definition to variable in formula (9):
Δ U=[Δ δ (k) Δ δ (k+1) Δ δ (k+2) ... Δ δ (k+Nc-1)]T∈RNc；
Formula (9) can then be indicated are as follows:
Wherein F and Φ are as follows:
As preferred embodiment, it is described by ship path trace and rollstabilization problem be converted into consider energy consumption with
The optimization problem that control performance combines；It defines cost function are as follows:
J=YTQY+ΔUTRΔU (11)
Wherein, YTQY indicates that the target deviateed control error is adjusted, Δ UTR Δ U indicates the adjusting to energy consumption, Q, R
Respectively indicate weight matrix；
Limit the size and change rate size of input rudder angle δ:
δmin≤δ(k+i)≤δmax, i=0,1 ... Np-1
Δδmin≤Δδ(k+i)≤Δδmax, i=0,1 ... Np-1
Cost function is solved, find out control input δ with the first item of Δ U and is brought into formula (2), system mode, system are acquired
Output successively brings into formula (3) to formula (11), by solving cost function again, new Δ U is found out, with the first of new Δ U
Item finds out new control input δ and brings into formula (2), and repetitive cycling is carried out until reaching setting cycle-index.
Further, the Ship-Fin-Stabilizer Control model based on sliding-mode method is established:
S=c φ+p (12)
Wherein, c indicates that positive design parameter, φ indicate roll angle, and p indicates angular velocity in roll；
Derivation is carried out to formula (12):
In formula, bfIt indicates constant, f is approached by radial basis function neural network methodp,Wherein,It is fpEstimated value,Indicate that neural network adapts to rule, H1(z) basis function vector is indicated.
The control of stabilizer includes: equivalent control part αeqWith switching control part αsw:
α=αeq+αsw (14)
Wherein,
In above formula, η1, k1Indicate positive control design case parameter；
Define Liapunov function:
Wherein, γ indicates positive design parameter,W1 *Indicate that optimal neural network adapts to rule；
By above-mentioned Liapunov function derivation:
In formula,
Wherein, H1(Z) it indicates basis function vector, brings formula (14), (15), (16) and formula (19) into formula (18) abbreviation afterwards
:
By formula (17) and formula (20), stable closed-loop control system is obtained according to Lyapunov theorem judgement.
The serial number of the above embodiments of the invention is only for description, does not represent the advantages or disadvantages of the embodiments.
In the above embodiment of the invention, it all emphasizes particularly on different fields to the description of each embodiment, does not have in some embodiment
The part of detailed description, reference can be made to the related descriptions of other embodiments.
In several embodiments provided herein, it should be understood that disclosed technology contents can pass through others
Mode is realized.Wherein, the apparatus embodiments described above are merely exemplary, such as the division of the unit, Ke Yiwei
A kind of logical function partition, there may be another division manner in actual implementation, for example, multiple units or components can combine or
Person is desirably integrated into another system, or some features can be ignored or not executed.Another point, shown or discussed is mutual
Between coupling, direct-coupling or communication connection can be through some interfaces, the INDIRECT COUPLING or communication link of unit or module
It connects, can be electrical or other forms.
The unit as illustrated by the separation member may or may not be physically separated, aobvious as unit
The component shown may or may not be physical unit, it can and it is in one place, or may be distributed over multiple
On unit.It can some or all of the units may be selected to achieve the purpose of the solution of this embodiment according to the actual needs.
It, can also be in addition, the functional units in various embodiments of the present invention may be integrated into one processing unit
It is that each unit physically exists alone, can also be integrated in one unit with two or more units.Above-mentioned integrated list
Member both can take the form of hardware realization, can also realize in the form of software functional units.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (5)
1. a kind of novel integrated ship path trace and rollstabilization optimal control method, which comprises the following steps:
S1: according to ship motion feature, establishing with rudder angle is the ship motion controller model inputted；
S2: prediction time domain and control time domain are chosen, design a model predictive controller；
S3: the optimization for considering that energy consumption is combined with control performance is converted by ship path trace and rollstabilization problem and is asked
Topic, in the case where constraining with actuator, solves optimization problem, and by first element interaction of solution in system；
S4: establishing the Ship-Fin-Stabilizer Control model based on sliding-mode method, is carried out by RBF neural method to system unknown portions
On-line Estimation.
2. a kind of novel integrated ship path trace according to claim 1 and rollstabilization optimal control method, feature
It also resides in:
According to ship motion feature, ship motion controller model is established:
Wherein,ut=δ, e indicate that path trace misses
Difference,Indicating course error, φ indicates roll angle, and v indicates lateral drift speed, and p indicates that angular velocity in roll, r indicate angular velocity in yaw,
δ indicates rudder angle,
Wherein a11…a34, b11…b13It can be calculated and be acquired by ship parameter；
By giving the sampling time, by ship motion controller model conversion at discrete model:
X (k+1)=Ax (k)+B δ (k) (2)
Y (k)=Cx (k) (3)
Wherein, x ∈ R6×1, y ∈ R4×1, A ∈ R6×6, B ∈ R6×1, C ∈ R4×6, x (k) indicate kth sampling instant system state to
Moment matrix, x (k+1) indicate that the state vector matrix of+1 sampling instant system of kth, δ (k) indicate kth sampling instant control input
Matrix, y (k) indicate the output matrix of kth sampling instant system, and matrix A, B, C are respectively At, Bt, CtMatrix after discrete, k table
Show sampling instant.
3. a kind of novel integrated ship path trace according to claim 1 and rollstabilization optimal control method, feature
It also resides in:
Rudder angle is limited, Controlling model is rewritten as incremental model, such as down conversion is carried out to formula (2) and formula (3):
Formula (2) are subjected to differential, can be expressed as:
X (k+1)-x (k)=A (x (k)-x (k-1))+B (δ (k)-δ (k-1)) (4)
For the statement of simplified style (4), such as given a definition:
Δ x (k)=x (k)-x (k-1)
Δ δ (k)=δ (k)-δ (k-1)
Then formula (4) may be expressed as:
Δ x (k+1)=A Δ x (k)+B Δ δ (k) (5)
Similarly, differential is carried out to formula (3), then:
Y (k+1)-y (k)=C (x (k+1)-x (k))=CA Δ x (k)+CB Δ δ (k) (6)
Formula (5) and formula (6) are indicated with augmented matrix are as follows:
Wherein, O6×4Indicate 6 × 4 full null matrix, I indicates 4 × 4 unit matrix；And
Then formula (7) may be expressed as:
Choose the prediction time domain NpWith the control time domain Nc, then in kth sampling instant, the system future is in control time domain
Interior input may be expressed as: δ (k), δ (k+1), δ (k+2) ..., δ (k+Nc-1)；Shape of the system future in prediction time domain
State may be expressed as:
Output of the system future in prediction time domain may be expressed as: y (k+1 | k), y (k+2 | k), y (k+3 | k) ..., y (k+
NP|k)。y(k+NP| it k) respectively indicates according to kth sampling instantY (k) predicts kth+NpSampling
Momenty(k+Np) value；
In kth sampling instant, by the input in the system future: δ (k), δ (k+1), δ (k+2) ..., δ (k+Nc- 1) Δ δ, is acquired
(k), Δ δ (k+1), Δ δ (k+2) ..., Δ δ (k+Nc- 1) it, brings formula (8) into and obtains output of the system in prediction time domain:
Such as given a definition to variable in formula (9):
Formula (9) can then be indicated are as follows:
Wherein F and Φ are as follows:
4. a kind of novel integrated ship path trace according to claim 1 and rollstabilization optimal control method, feature
It also resides in:
Described convert ship path trace and rollstabilization problem to considers that the optimization that combines with control performance of energy consumption is asked
Topic；It defines cost function are as follows:
J=YTQY+ΔUTRΔU (11)
Wherein, YTQY indicates that the target deviateed control error is adjusted, Δ UTR Δ U indicates the adjusting to energy consumption, Q, R difference
Indicate weight matrix；
Limit the size and change rate size of input rudder angle δ:
δmin≤δ(k+i)≤δmax, i=0,1 ... Np-1
Δδmin≤Δδ(k+i)≤Δδmax, i=0,1 ... Np-1
Cost function is solved, find out control input δ with the first item of Δ U and is brought into formula (2), system mode is acquired, system exports,
It successively brings into formula (3) to formula (11), by solving cost function again, finds out new Δ U, asked with the first item of new Δ U
New control inputs δ and brings into formula (2) out, and repetitive cycling is carried out until reaching setting cycle-index.
5. a kind of novel integrated ship path trace according to claim 1 and rollstabilization optimal control method, feature
It also resides in:
Establish the Ship-Fin-Stabilizer Control model based on sliding-mode method:
S=c φ+p (12)
Wherein, c indicates that positive design parameter, φ indicate roll angle, and p indicates angular velocity in roll；
Derivation is carried out to formula (12):
In formula, bfIt indicates constant, f is approached by radial basis function neural network methodp,Wherein,It is
fpEstimated value,Indicate that neural network adapts to rule, H1(z) basis function vector is indicated.
The control of stabilizer includes: equivalent control part αeqWith switching control part αsw:
α=αeq+αsw (14)
Wherein,
In above formula, η1, k1Indicate positive control design case parameter；
Define Liapunov function:
Wherein, γ indicates positive design parameter,W1 *Indicate that optimal neural network adapts to rule；
By above-mentioned Liapunov function derivation:
In formula,
Wherein, H1(Z) basis function vector is indicated, bringing formula (14), (15), (16) and formula (19) into formula (18), abbreviation obtains afterwards:
By formula (17) and formula (20), stable closed-loop control system is obtained according to Lyapunov theorem judgement.
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| CN111506080A (en) * | 2020-05-14 | 2020-08-07 | 大连海事大学 | Comprehensive ship path tracking and rudder stabilization control method based on neural network optimization |
| CN112256026A (en) * | 2020-10-14 | 2021-01-22 | 中国船舶重工集团公司第七0七研究所九江分部 | Ship course model predictive control algorithm design method under multi-constraint condition |
| CN112596393A (en) * | 2020-12-24 | 2021-04-02 | 武汉理工大学 | Control method, system and storage medium for ship path tracking |
| CN112650233A (en) * | 2020-12-15 | 2021-04-13 | 大连海事大学 | Unmanned ship trajectory tracking optimal control method based on backstepping method and self-adaptive dynamic programming under dead zone limitation |
| CN113359446A (en) * | 2021-06-02 | 2021-09-07 | 武汉理工大学 | Nonlinear ship course control model and control system |
| CN113419422A (en) * | 2021-07-02 | 2021-09-21 | 哈尔滨理工大学 | Marine rudder fin combined anti-rolling control system |
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| CN111506080A (en) * | 2020-05-14 | 2020-08-07 | 大连海事大学 | Comprehensive ship path tracking and rudder stabilization control method based on neural network optimization |
| CN111506080B (en) * | 2020-05-14 | 2023-10-24 | 大连海事大学 | Comprehensive ship path tracking and rudder stabilization control method based on neural network optimization |
| CN112256026A (en) * | 2020-10-14 | 2021-01-22 | 中国船舶重工集团公司第七0七研究所九江分部 | Ship course model predictive control algorithm design method under multi-constraint condition |
| CN112256026B (en) * | 2020-10-14 | 2022-11-29 | 中国船舶重工集团公司第七0七研究所九江分部 | Ship course model predictive control algorithm design method under multi-constraint condition |
| CN112650233A (en) * | 2020-12-15 | 2021-04-13 | 大连海事大学 | Unmanned ship trajectory tracking optimal control method based on backstepping method and self-adaptive dynamic programming under dead zone limitation |
| CN112650233B (en) * | 2020-12-15 | 2023-11-10 | 大连海事大学 | Unmanned ship track tracking optimal control method |
| CN112596393A (en) * | 2020-12-24 | 2021-04-02 | 武汉理工大学 | Control method, system and storage medium for ship path tracking |
| CN112596393B (en) * | 2020-12-24 | 2022-02-22 | 武汉理工大学 | Control method, system and storage medium for ship path tracking |
| CN113359446A (en) * | 2021-06-02 | 2021-09-07 | 武汉理工大学 | Nonlinear ship course control model and control system |
| CN113359446B (en) * | 2021-06-02 | 2022-06-17 | 武汉理工大学 | Nonlinear ship course control method and system |
| CN113419422A (en) * | 2021-07-02 | 2021-09-21 | 哈尔滨理工大学 | Marine rudder fin combined anti-rolling control system |
| CN113419422B (en) * | 2021-07-02 | 2022-01-28 | 哈尔滨理工大学 | Marine rudder fin combined anti-rolling control system |
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