CN113419429A - Dredging control method for port ship bearing capacity saturation - Google Patents

Dredging control method for port ship bearing capacity saturation Download PDF

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CN113419429A
CN113419429A CN202110800428.4A CN202110800428A CN113419429A CN 113419429 A CN113419429 A CN 113419429A CN 202110800428 A CN202110800428 A CN 202110800428A CN 113419429 A CN113419429 A CN 113419429A
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following
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焦晨旭
张俊锋
张石涛
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Hangzhou Dianzi University
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Abstract

The invention belongs to the field of automation technology and modern control, and discloses a control method for port ship bearing capacity saturation. The invention establishes a port ship distribution control method through means of data acquisition, modeling, optimization control and the like, and the method can effectively solve the problem of congestion in a port caused by natural conditions and the limitation of outburst events in the port. A port ship distribution control system based on a direct switching system modeling with random state saturation designs a class of event trigger controllers to control distribution of port ships in real time and ensure safe and efficient operation of ports.

Description

Dredging control method for port ship bearing capacity saturation
Technical Field
The invention belongs to the field of automation technology and modern control, and particularly relates to a method for controlling distribution of port ship bearing capacity saturation.
Background
Ocean transportation is the most prominent mode of transportation in international logistics, which transports cargo between ports in different countries and regions by using ships. The main technical equipment of marine transportation comprises ships, channels, harbors, communication facilities, navigation facilities and the like, wherein harbors are used as important transportation infrastructures for marine transportation, are transport hubs with land and water intermodal equipment and conditions for safe entering, exiting and berthing of ships, and are gathering points of marine transportation tools. In recent years, the situation of high-speed development of marine transportation in China is continuously kept, and more large ships and ultra-large ships are put into use. With the trend of large-scale ships and the increasing year by year of port cargo throughput, the number of ships needing to enter ports is continuously increased, but many ports are not enough to meet the requirements of ship berthing and operation simultaneously due to the limited berth capacity of a wharf. Therefore, in order to prevent the occurrence of the situations that the ships are excessively concentrated in the channel and the port and exceed the port berth capacity, the ships entering and exiting the port need to be managed and controlled in time, so that the congestion of a large number of ships in the port is avoided, and the port operation efficiency is improved.
The invention mainly dynamically obtains the flow value of ships entering and leaving a port, dynamically dispatches the ships at the port according to the change trend of the navigation environment and the ship flow on the premise of ensuring the navigation safety, provides a reliable port ship distribution control method, and adopts necessary control measures for the ships entering and leaving the port so as to ensure that the port has a complete and smooth collection distribution system.
The capacity of berths in ports and the number of ships entering and leaving ports are all non-negative, and in this case, non-negative variables can be used to describe the ship flow in ports. Furthermore, it is reasonable to model the port ship distribution control system with a positive system. While taking into account the effectiveness of the switching system in modeling a multi-mode system, it is more appropriate to describe such a multi-dock port vessel distribution control system with a switching system. FIG. 1 is a schematic diagram of the process of transmitting and controlling the ship entering and exiting information in a port, wherein the port is only illustrated as A, B wharfs; FIG. 2 is a schematic diagram of an event-triggered control framework of a direct switching system based on random state saturation for system modeling in the invention. Because part of ports are restricted by natural conditions or the construction cost of the channel is considered, the width and the water depth of the channel in the port are limited, the ship is easy to collide, run aground and other accidents in a narrow channel, the limiting factors can cause serious ship waiting conditions, the non-operation time of the ship in the port is prolonged, and the ship congestion in the port is further caused. As in the case of the seaport, the efficiency of port operations is reduced due to uncertain bad weather, a large number of ships stay in the port, some ships cannot sail away in time in the port, and the port berth capacity is limited, so that the number of ships arriving at the port is increased continuously, thereby causing severe port congestion. Because port congestion caused by various uncertain factors has randomness, at the moment, the problem that the number of ships in the port is saturated randomly can be effectively solved by designing event trigger conditions. An event-triggered control strategy is a real-time control method based on events. When the berth capacity in the port is about to be saturated, an event trigger control strategy is adopted, measures such as reasonably dispatching ships in the port, slowing the ships entering the port and the like can be quickly taken, and the port has the capacity of efficient operation all the time. The port ship distribution control system based on the event trigger mechanism can effectively distribute ships, so that the problem of berth capacity limitation is solved, and port congestion is prevented. Therefore, the method aims to adopt a random state saturation tangent switching system to model a port ship distribution control system, and a control method of the system based on an event trigger mechanism is designed to control the flow of a port ship in real time, so that safe and efficient operation of the port is ensured.
Disclosure of Invention
The invention aims to provide a method for controlling distribution of port ship with saturated bearing capacity, so as to solve the technical problem.
In order to solve the technical problems, the specific technical scheme of the dredging control method for the saturated bearing capacity of the port ship is as follows:
a method for controlling distribution of saturated bearing capacity of ships in a port comprises the following steps:
step 1, establishing a state space model of a port ship distribution control system with random state saturation;
step 2, constructing event trigger control conditions of port ship congestion;
step 3, designing a controller of the port ship distribution control system;
step 4, verifying the positive performance of the constructed port ship distribution control system under the controller;
and 5, verifying the stability of the constructed port ship distribution control system under the controller.
Further, the step 1 comprises the following specific steps:
step 1.1: firstly, collecting the ship flow of a port, and establishing a state space model of a port ship distribution control system by using collected data, wherein the form is as follows:
x(k+1)＝ασ(k)(k)sat(Aσ(k)x(k)+Bσ(k)u(k)) +(1-ασ(k)(k))sat(Aσ(k)x(k)+Bσ(k)u(k)),
wherein the content of the first and second substances,
Figure BDA0003164473270000021
representing the number of vessels in the port at the kth sampling time, n representing the number of berths in the port,
Figure BDA0003164473270000022
for the control signal of the port ship flow, m represents the number of port wharfs, and the function sat (-) is:
Figure BDA0003164473270000023
is a standard saturation function of vector values, defined as sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T，sat(ui(k))＝sgn(ui(k))min{1,|ui(k) I ∈ m, σ (k) is a switching signal, whose value is in a finite set S ∈ {1,2, …, J }, J ∈ Z+，
Figure BDA0003164473270000024
And
Figure BDA0003164473270000025
is a known system matrix, for σ (k) i, i ∈ S, there are
Figure BDA0003164473270000031
Step 1.2: the randomly occurring actuators are saturated with a random variable α (k) which satisfies the following condition:
Figure BDA0003164473270000032
wherein the content of the first and second substances,
Figure BDA0003164473270000033
further, the step 2 comprises the following specific steps:
establishing event triggering conditions of port ship congestion:
‖e(k)‖1＞δ‖x(k)‖1,
wherein, delta is more than 0,
Figure BDA0003164473270000034
is the error in the sampling of the signal,
Figure BDA0003164473270000035
represents the sampling state | · |1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all the elements in the vector.
Further, the step 3 comprises the following specific steps:
step 3.1: a symmetrical polyhedron L (H)i) Is defined as:
Figure BDA0003164473270000036
wherein the content of the first and second substances,
Figure BDA0003164473270000037
Hipis a matrix HiRow p of (1);
introducing a cone domain, which is as follows:
Figure BDA0003164473270000038
wherein T represents a transposed symbol,
Figure BDA0003164473270000039
is an n-dimensional real column vector, and
Figure BDA00031644732700000310
i.e. vector viEach element is a positive number;
step 3.2: the port ship distribution control system is analyzed by adopting a state saturation method, wherein a saturation function meets the following requirements:
Figure BDA00031644732700000311
wherein u ═ u1(k),u2(k),…,um(k)]T,v＝[v1(k),v2(k),…,vm(k)]TAnd | vj|≤1,j＝1,2,…,m,
Figure BDA00031644732700000316
Is a diagonal matrix of m x m, whose diagonal elements are 0 or 1,
Figure BDA00031644732700000312
step 3.3: the event trigger control law is designed as follows:
Figure BDA00031644732700000313
wherein the content of the first and second substances,
Figure BDA00031644732700000314
is a controller gain matrix, and
Figure BDA00031644732700000315
the concrete form is as follows:
Figure BDA0003164473270000041
wherein 1 ismA column vector in which all elements of m-dimension are 1,
Figure BDA0003164473270000042
denotes that the iota element is 1 and the rest elementsAn m-dimensional column vector of 0 in each case,
Figure BDA0003164473270000043
is an n-dimensional column vector;
step 3.4: from step 3.2, it can be obtained:
Figure BDA0003164473270000044
wherein the content of the first and second substances,
Figure BDA0003164473270000045
further:
Figure BDA0003164473270000046
wherein HiIs a controller auxiliary gain matrix, an
Figure BDA0003164473270000047
The concrete form is as follows:
Figure BDA0003164473270000048
step 3.5, the constraint conditions of the port ship distribution control system with random state saturation for stable operation under the event trigger mechanism are designed as follows:
design constant ρ1＞0,ρ2＞0,η1＞0,η2> 0, ζ > 0, λ > 1, if n-dimensional vectors are present
Figure BDA0003164473270000049
Figure BDA00031644732700000410
Such that the following inequality:
Figure BDA0003164473270000051
Figure BDA0003164473270000052
Figure BDA0003164473270000053
Figure BDA0003164473270000054
Figure BDA0003164473270000055
Figure BDA0003164473270000056
Figure BDA0003164473270000057
Figure BDA0003164473270000058
Figure BDA0003164473270000059
Figure BDA00031644732700000510
Figure BDA00031644732700000511
Figure BDA00031644732700000512
if true, then the control rate is triggered at the event
Figure BDA00031644732700000513
And controller auxiliary gain matrix HiThe lower closed loop system is positive and stable, and the average residence time condition satisfies τ*≥-lnλ/lnμ；
Wherein, theta1＝I-δ1n×n,Θ2＝I+δ1n×n,
Figure BDA00031644732700000514
For N00 from
Figure BDA00031644732700000515
The starting system state will remain at bound
Figure BDA00031644732700000516
And (4) the following steps.
Further, the step 4 comprises the following specific steps:
step 4.1: according to step 1, step 3.3 and step 3.4, there are:
Figure BDA00031644732700000517
step 4.2: according to the event triggering condition in step 2, the following can be obtained:
Figure BDA00031644732700000518
wherein 1 isn×nAn n × n matrix representing elements all 1;
step 4.3, in combination with step 4.1 and step 4.2, yields the following inequality:
Figure BDA0003164473270000061
in combination with the positive constraint in step 3.5, when
Figure BDA0003164473270000062
When there is
Figure BDA0003164473270000063
The following are obtained by a recursive method: for an arbitrary initial state
Figure BDA0003164473270000064
Is provided with
Figure BDA0003164473270000065
I.e. the closed loop system is positive.
Further, the step 5 comprises the following specific steps:
step 5.1: designing a linear complementary Li ya Punuo function:
Vi(k)＝xT(k)vi,
the mathematical expectation of its difference is:
Figure BDA0003164473270000066
combining the step 4.2, the following can be obtained:
Figure BDA0003164473270000067
step 5.2: according to step 3.4 and step 3.5:
Figure BDA0003164473270000068
step 5.3: case 1: consider a matrix
Figure BDA00031644732700000615
When there is
Figure BDA0003164473270000069
The method comprises the following steps of 5.2:
Figure BDA00031644732700000610
thus, E { Δ V in step 5.1i(k) Can be converted into:
Figure BDA00031644732700000611
case 2: consider a matrix
Figure BDA00031644732700000614
When it is, then
Figure BDA00031644732700000612
The method comprises the following steps of 3.4 and 3.5:
Figure BDA00031644732700000613
combining step 5.1 yields:
Figure BDA0003164473270000071
case 3: consider a matrix
Figure BDA00031644732700000714
And is
Figure BDA00031644732700000715
Then, according to case 2 in step 3.5, step 5.2 and step 5.3, it can be obtained:
Figure BDA0003164473270000072
step 5.4, case 3 according to step 5.1 and step 5.3 has:
Figure BDA0003164473270000073
e { Δ V in three cases to be considered in step 5.3i(k) Combining the conditions in the step 3.5, the following inequality is obtained:
E{ΔVi(k)}≤-(1-μ)Vi(k).
thus, it is possible to provide
Figure BDA0003164473270000074
Step 5.5: suppose that
Figure BDA0003164473270000075
Is the switching time sequence of σ (k) within the interval [0, k), according to the switching conditions in step 3.5, there are:
Figure BDA0003164473270000076
further, the method can be used for preparing a novel material
Figure BDA0003164473270000077
Wherein the content of the first and second substances,
Figure BDA0003164473270000078
χ1hexix-2Are each vi,
Figure BDA0003164473270000079
The smallest and largest elements; from the average residence time condition, one can derive: phi is more than 0 and less than 1.
Further, the step 5 further comprises the following steps for proving the invariance of the system state under the designed controller:
for the
Figure BDA00031644732700000710
Has xT(k)viLess than or equal to 1, i.e.
Figure BDA00031644732700000711
Further, from step 3.5,
Figure BDA00031644732700000712
therefore, the temperature of the molten metal is controlled,
Figure BDA00031644732700000716
namely, it is
Figure BDA00031644732700000713
The dredging control method for port ship bearing capacity saturation has the following advantages:
aiming at the problems of the current port ship capacity limitation and ship operation conflict, a state space model of a port ship distribution control system is established by utilizing the modern control theory technology, and an event trigger controller is designed to effectively control ships entering and leaving the port, so that the ships in the port are prevented from being blocked, and safe and effective operation and passage of the ships in the port are ensured.
Drawings
Fig. 1 is a schematic diagram of the process of transmitting and controlling the ship entering and leaving a port in the present invention.
FIG. 2 is a schematic diagram of an event-triggered control framework for a system modeling a random state saturation-based positive switching system.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, the following will describe a method for controlling distribution of saturated carrying capacity of a port ship in detail with reference to the accompanying drawings.
As shown in fig. 2, the method for controlling the distribution of the saturated carrying capacity of the port ship comprises the following specific steps:
step 1, firstly, collecting the ship flow of a port, and establishing a state space model of a port ship distribution control system by using collected data, wherein the form is as follows:
x(k+1)＝ασ(k)(k)sat(Aσ(k)x(k)+Bσ(k)u(k))
+(1-ασ(k)(k))sat(Aσ(k)x(k)+Bσ(k)u(k)),
wherein the content of the first and second substances,
Figure BDA0003164473270000081
representing the number of vessels in the port at the kth sampling time, n representing the number of berths in the port,
Figure BDA0003164473270000082
for the control signal of the port ship flow, m represents the number of port terminals, and the function sat (·):
Figure BDA0003164473270000083
is a standard saturation function of vector values, defined as sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T，sat(ui(k))＝sgn(ui(k))min{1,|ui(k) I ∈ m, σ (k) is a switching signal, whose value is in a finite set S ∈ {1,2, …, J }, J ∈ Z+，
Figure BDA0003164473270000084
And
Figure BDA0003164473270000085
is a known system matrix, for σ (k) i, i ∈ S, there are
Figure BDA0003164473270000086
The randomly occurring actuators are saturated with a random variable α (k) which satisfies the following condition:
Figure BDA0003164473270000087
wherein the content of the first and second substances,
Figure BDA0003164473270000088
step 2, establishing event triggering conditions of port ship congestion:
‖e(k)‖1＞δ‖x(k)‖1,
wherein, delta is more than 0,
Figure BDA0003164473270000089
is the error in the sampling of the signal,
Figure BDA00031644732700000810
represents the sampling state | · |1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all the elements in the vector.
Step 3, designing an event trigger controller of the port ship distribution control system, wherein the construction form is as follows:
step 3.1, a symmetrical polyhedron L (H)i) Is defined as:
Figure BDA00031644732700000811
wherein the content of the first and second substances,
Figure BDA0003164473270000091
Hipis a matrix HiRow p.
Further, in consideration of the capacity limit of the berth number of the port and the wharf, a cone domain is introduced, and the specific steps are as follows:
Figure BDA0003164473270000092
wherein T represents a transposed symbol,
Figure BDA0003164473270000093
is an n-dimensional real column vector, and
Figure BDA0003164473270000094
i.e. vector viEach element being a positive number。
Step 3.2, the port ship distribution control system adopts a state saturation method for analysis, wherein a saturation function is satisfied:
Figure BDA0003164473270000095
wherein u ═ u1(k),u2(k),…,um(k)]T,v＝[v1(k),v2(k),…,vm(k)]TAnd | vj|≤1,j＝1,2,…,m, DlIs a diagonal matrix of m x m, whose diagonal elements are 0 or 1,
Figure RE-GDA0003222597230000096
step 3.3, designing an event trigger control law as follows:
Figure BDA0003164473270000098
wherein the content of the first and second substances,
Figure BDA0003164473270000099
is a controller gain matrix, and
Figure BDA00031644732700000910
the concrete form is as follows:
Figure BDA00031644732700000911
wherein 1 ismA column vector in which all elements of m-dimension are 1,
Figure BDA00031644732700000912
an m-dimensional column vector representing that the iota-th element is 1 and the remaining elements are 0,
Figure BDA00031644732700000913
is an n-dimensional column vector.
Step 3.4, from step 3.2, can be obtained:
Figure BDA00031644732700000914
wherein the content of the first and second substances,
Figure BDA00031644732700000915
further:
Figure BDA00031644732700000916
wherein HiIs a controller auxiliary gain matrix, an
Figure BDA00031644732700000917
The concrete form is as follows:
Figure BDA00031644732700000918
step 3.5, the constraint conditions of the port ship distribution control system with random state saturation for stable operation under the event trigger mechanism are designed as follows:
design constant ρ1＞0,ρ2＞0,η1＞0,η2> 0, ζ > 0, λ > 1, if n-dimensional vectors are present
Figure BDA00031644732700000919
Figure BDA0003164473270000101
Such that the following inequality:
Figure BDA0003164473270000102
Figure BDA0003164473270000103
Figure BDA0003164473270000104
Figure BDA0003164473270000105
Figure BDA0003164473270000106
Figure BDA0003164473270000107
Figure BDA0003164473270000108
Figure BDA0003164473270000109
Figure BDA00031644732700001010
Figure BDA00031644732700001011
Figure BDA00031644732700001012
Figure BDA00031644732700001013
i ≠ j, iota ≠ 1,2, …, m holds, then the control rate is triggered at event
Figure BDA00031644732700001014
And controller auxiliary gain matrix HiThe lower closed loop system is positive and stable, and the average residence time condition satisfies τ*≥-lnλlnμ。
Wherein, theta1＝I-δ1n×n,Θ2＝I+δ1n×n,
Figure BDA00031644732700001015
Furthermore, for N00 from
Figure BDA00031644732700001016
The starting system state will remain at bound
Figure BDA00031644732700001017
And (4) the following steps.
Further, the step 4 of verifying the positivity of the constructed ship evacuation control system under the event triggering condition comprises the following steps:
step 4.1, according to step 1, step 3.3 and step 3.4, there is:
Figure BDA00031644732700001018
step 4.2, according to the event triggering condition formula in step 2, obtaining:
Figure BDA00031644732700001019
wherein 1 isn×nAn n × n matrix with elements all 1 is shown.
Step 4.3, in combination with step 4.1 and step 4.2, yields the following inequality:
Figure BDA0003164473270000111
in combination with the positive constraint in step 3.5, when
Figure BDA0003164473270000112
When there is
Figure BDA0003164473270000113
It can then be derived by a recursive method: for an arbitrary initial state
Figure BDA0003164473270000114
Is provided with
Figure BDA0003164473270000115
I.e. the closed loop system is positive.
And 5, verifying the stability of the constructed port ship distribution control system under the controller, wherein the verification process is as follows:
step 5.1, designing a linear complementary Li Jacobov function:
Vi(k)＝xT(k)vi,
the mathematical expectation of its difference is:
Figure BDA0003164473270000116
combining the step 4.2, the following can be obtained:
Figure BDA0003164473270000117
step 5.2, according to step 3.4 and step 3.5, has:
Figure BDA0003164473270000118
step 5.3, case 1: consider a matrix
Figure BDA00031644732700001114
When there is
Figure BDA0003164473270000119
The method comprises the following steps of 5.2:
Figure BDA00031644732700001110
thus, E { Δ V in step 5.1i(k) Can be converted into:
Figure BDA00031644732700001111
case 2: consider a matrix
Figure BDA00031644732700001115
When it is, then
Figure BDA00031644732700001112
The method comprises the following steps of 3.4 and 3.5:
Figure BDA00031644732700001113
combining step 5.1 yields:
Figure BDA0003164473270000121
case 3: consider a matrix
Figure BDA00031644732700001214
And is
Figure BDA00031644732700001215
Then, according to case 2 in step 3.5, step 5.2 and step 5.3, one can obtain:
Figure BDA0003164473270000122
step 5.4, case 3 according to step 5.1 and step 5.3 has:
Figure BDA0003164473270000123
e { Δ V in three cases to be considered in step 5.3i(k) Combining the conditions in step 3.5, the following inequality can be obtained:
E{ΔVi(k)}≤-(1-μ)Vi(k).
thus, it is possible to provide
Figure BDA0003164473270000124
Step 5.5, suppose
Figure BDA0003164473270000125
Is the switching time sequence of σ (k) within the interval [0, k), according to the switching conditions in step 3.5, there are:
Figure BDA0003164473270000126
further, the method can be used for preparing a novel material
Figure BDA0003164473270000127
Wherein the content of the first and second substances,
Figure BDA0003164473270000128
Φ＝e(lnμ+(lnλ)/τ),χ1hexix-2Are each vi,
Figure BDA0003164473270000129
The smallest and largest elements.
From the average residence time condition, one can derive: 0 < Φ < 1, so the closed loop system is stable.
Further, the method comprises the following steps for proving invariance of the system state under the designed controller:
for the
Figure BDA00031644732700001210
Has xT(k)viLess than or equal to 1, i.e.
Figure BDA00031644732700001211
Further, from step 3.5,
Figure BDA00031644732700001212
therefore, the temperature of the molten metal is controlled,
Figure BDA00031644732700001216
namely, it is
Figure BDA00031644732700001213
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (7)

1. A method for controlling distribution of saturated bearing capacity of ships in a port is characterized by comprising the following steps:
step 1, establishing a state space model of a port ship distribution control system with random state saturation;
step 2, constructing event trigger control conditions of port ship congestion;
step 3, designing a controller of the port ship distribution control system;
step 4, verifying the positive performance of the constructed port ship distribution control system under the controller;
and 5, verifying the stability of the constructed port ship distribution control system under the controller.
2. The method for controlling the distribution of the saturated carrying capacity of the port ship according to claim 1, wherein the step 1 comprises the following specific steps:
step 1.1: firstly, collecting the ship flow of a port, and establishing a state space model of a port ship distribution control system by using collected data, wherein the form is as follows:
x(k+1)＝ασ(k)(k)sat(Aσ(k)x(k)+Bσ(k)u(k))+(1-ασ(k)(k))sat(Aσ(k)x(k)+Bσ(k)u(k)),
wherein the content of the first and second substances,
Figure FDA0003164473260000011
representing the number of vessels in the port at the kth sampling time, n representing the number of berths in the port,
Figure FDA0003164473260000012
for the control signal of the port ship flow, m represents the number of port terminals, and the function sat (·):
Figure FDA0003164473260000013
is a standard saturation function of vector values, defined as sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T，sat(ui(k))＝sgn(ui(k))min{1,|ui(k) I ∈ m, σ (k) is a switching signal, whose value is in a finite set S ∈ {1,2, …, J }, J ∈ Z+，
Figure FDA0003164473260000014
And
Figure FDA0003164473260000015
is a known system matrix, for σ (k) i, i ∈ S, there are
Figure FDA00031644732600000110
Step 1.2: the randomly occurring actuators are saturated with a random variable α (k) which satisfies the following condition:
Figure FDA0003164473260000016
wherein the content of the first and second substances,
Figure FDA0003164473260000017
3. the method for controlling the distribution of the saturated carrying capacity of the port ship according to claim 2, wherein the step 2 comprises the following specific steps:
establishing event triggering conditions of port ship congestion:
‖e(k)‖1＞δ‖x(k)‖1,
wherein, delta is more than 0,
Figure FDA0003164473260000018
is the error in the sampling of the signal,
Figure FDA0003164473260000019
represents the sampling state | · |1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all the elements in the vector.
4. The method for controlling the distribution of the saturated carrying capacity of the port ship according to claim 3, wherein the step 3 comprises the following specific steps:
step 3.1: a symmetrical polyhedron L (H)i) Is defined as:
Figure FDA0003164473260000021
wherein the content of the first and second substances,
Figure FDA0003164473260000022
Hipis a matrix HiRow p of (1);
introducing a cone domain, which is as follows:
Figure FDA0003164473260000023
wherein T represents a transposed symbol,
Figure FDA0003164473260000024
is an n-dimensional real column vector, and
Figure FDA00031644732600000216
i.e. vector viEach element is a positive number;
step 3.2: the port ship distribution control system is analyzed by adopting a state saturation method, wherein a saturation function meets the following requirements:
Figure FDA0003164473260000025
wherein u ═ u1(k),u2(k),…,um(k)]T,v＝[v1(k),v2(k),…,vm(k)]TAnd | vj|≤1,j＝1,2,…,m,DlIs a diagonal matrix of m x m, whose diagonal elements are 0 or 1,
Figure FDA0003164473260000026
step 3.3: the event trigger control law is designed as follows:
Figure FDA0003164473260000027
wherein the content of the first and second substances,
Figure FDA0003164473260000028
is a controller gain matrix, and
Figure FDA0003164473260000029
the concrete form is as follows:
Figure FDA00031644732600000210
wherein 1 ismA column vector in which all elements of m-dimension are 1,
Figure FDA00031644732600000211
an m-dimensional column vector representing that the iota-th element is 1 and the remaining elements are 0,
Figure FDA00031644732600000212
is an n-dimensional column vector;
step 3.4: from step 3.2, it can be obtained:
Figure FDA00031644732600000213
wherein the content of the first and second substances,
Figure FDA00031644732600000214
further:
Figure FDA00031644732600000215
wherein HiIs a controller auxiliary gain matrix, an
Figure FDA0003164473260000031
The concrete form is as follows:
Figure FDA0003164473260000032
step 3.5: the constraint condition that the port ship distribution control system with random state saturation runs stably under an event trigger mechanism is designed as follows:
design constant ρ1＞0,ρ2＞0,η1＞0,η2> 0, ζ > 0, λ > 1, if n-dimensional vectors are present
Figure FDA0003164473260000033
Figure FDA0003164473260000034
Such that the following inequality:
Figure FDA0003164473260000035
Figure FDA0003164473260000036
Figure FDA0003164473260000037
Figure FDA0003164473260000038
Figure FDA0003164473260000039
Figure FDA00031644732600000310
Figure FDA00031644732600000311
Figure FDA00031644732600000312
Figure FDA00031644732600000313
Figure FDA00031644732600000314
Figure FDA00031644732600000315
Figure FDA00031644732600000316
if true, then the control rate is triggered at the event
Figure FDA00031644732600000317
And controller auxiliary gain matrix HiThe lower closed loop system is positive and stable, and the average residence time condition satisfies τ*≥-lnλ/lnμ；
Wherein, theta1＝I-δ1n×n,Θ2＝I+δ1n×n,
Figure FDA00031644732600000318
For N00 from
Figure FDA00031644732600000319
The starting system state will remain at bound
Figure FDA00031644732600000320
And (4) the following steps.
5. The method for controlling the distribution of the saturated carrying capacity of the harbor ship according to claim 4, wherein the step 4 comprises the following steps:
step 4.1: according to step 1, step 3.3 and step 3.4, there are:
Figure FDA0003164473260000041
step 4.2: according to the event triggering condition in step 2, the following can be obtained:
Figure FDA0003164473260000042
wherein 1 isn×nAn n × n matrix representing elements all 1;
step 4.3, in combination with step 4.1 and step 4.2, yields the following inequality:
Figure FDA0003164473260000043
in combination with the positive constraint in step 3.5, when
Figure FDA0003164473260000044
When there is
Figure FDA0003164473260000045
The following are obtained by a recursive method: for an arbitrary initial state
Figure FDA0003164473260000046
Is provided with
Figure FDA0003164473260000047
I.e. the closed loop system is positive.
6. The method for controlling the distribution of the saturated carrying capacity of the harbor ship according to claim 5, wherein said step 5 comprises the following steps:
step 5.1: designing a linear complementary Li ya Punuo function:
Vi(k)＝xT(k)vi,
the mathematical expectation of its difference is:
Figure FDA0003164473260000048
combining the step 4.2, the following can be obtained:
Figure FDA0003164473260000049
step 5.2: according to step 3.4 and step 3.5:
Figure FDA00031644732600000410
step 5.3: case 1: consider matrix DilWhen I, there is
Figure FDA0003164473260000051
The method comprises the following steps of 5.2:
Figure FDA0003164473260000052
thus, E { Δ V in step 5.1i(k) Can be converted into:
Figure FDA0003164473260000053
case 2: consider matrix DilWhen equal to 0, then
Figure FDA0003164473260000054
The method comprises the following steps of 3.4 and 3.5:
Figure FDA0003164473260000055
combining step 5.1 yields:
Figure FDA0003164473260000056
case 3: consider matrix DilNot equal to 0 and DilWhen not equal to I, it is possible to obtain, according to case 2 in step 3.5, step 5.2 and step 5.3:
Figure FDA0003164473260000057
Figure FDA0003164473260000058
step 5.4: according to step 5.1 and step 5.3 case 3 has:
Figure FDA0003164473260000059
e { Δ V in three cases to be considered in step 5.3i(k) Combining the conditions in the step 3.5, the following inequality is obtained:
E{ΔVi(k)}≤-(1-μ)Vi(k),
thus, it is possible to provide
Figure FDA00031644732600000510
Step 5.5: suppose that
Figure FDA00031644732600000511
Is the switching time sequence of σ (k) within the interval [0, k), according to the switching conditions in step 3.5, there are:
Figure FDA00031644732600000512
further, the method can be used for preparing a novel material
Figure FDA00031644732600000513
Wherein the content of the first and second substances,
Figure FDA0003164473260000061
Φ＝e(lnμ+(lnλ)/τ),χ1hexix-2Are respectively
Figure FDA0003164473260000062
The smallest and largest elements;
from the average residence time condition, one can derive: phi is more than 0 and less than 1.
7. The method for controlling the distribution of the saturated load of the harbor ship according to claim 6, wherein said step 5 further comprises the following steps for proving the invariance of the system state under the designed controller:
for the
Figure FDA0003164473260000063
Has xT(k)viLess than or equal to 1, i.e.
Figure FDA0003164473260000064
Further, from step 3.5,
Figure FDA0003164473260000065
therefore, -1. ltoreq.Hijx (k) is less than or equal to 1, i.e
Figure FDA0003164473260000066
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