CN114055463B - Fuzzy sliding mode control method of networked mechanical arm system - Google Patents

Fuzzy sliding mode control method of networked mechanical arm system Download PDF

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CN114055463B
CN114055463B CN202111132089.3A CN202111132089A CN114055463B CN 114055463 B CN114055463 B CN 114055463B CN 202111132089 A CN202111132089 A CN 202111132089A CN 114055463 B CN114055463 B CN 114055463B
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mechanical arm
networked
mode control
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sliding
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CN114055463A (en
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齐文海
夏梦圆
宗广灯
吕彩玉
曹佃国
孙海滨
杨东
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Qufu Normal University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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Abstract

A fuzzy sliding mode control method of a networked mechanical arm system comprises the following steps: establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system; establishing an actuator fault model and a deception attack model; deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has actuator faults; constructing a public sliding mode switching surface; designing a sliding mode control law; carrying out stability analysis on a system adopting the sliding mode control law, and solving controller parameters; and determining the conditions which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state. Aiming at the conditions that the mechanical arm system is subjected to randomly generated deception attack and actuator faults, the fuzzy sliding mode control method of the networked mechanical arm system is provided, and the anti-interference control problem of the system under the condition of limited data transmission is solved.

Description

Fuzzy sliding mode control method of networked mechanical arm system
Technical Field
The invention relates to the technical field of mechanical arm system control, in particular to a fuzzy sliding mode control method of a networked mechanical arm system.
Background
In the single-link mechanical arm, the rigidity of a link structure is reduced due to the design of a slender link, but the single-link mechanical arm also brings a plurality of difficulties which are difficult to solve and brings a plurality of problems to the fields of dynamic modeling, control and the like. Since the network links between the single-link robot arm sensors, the controller, and the actuators are open, they are vulnerable to network attacks. Spoofing attacks are an important type of network attack, also known as spurious data injection attacks. A typical spoofing attack may trap a sensor node, inject malicious code or modify a program with its unauthorized privileges, thereby degrading or even worsening system performance.
The markov switching system has become an important research branch in the control field due to its modeling stability in a physical system with a sudden change in structure. For a markov handover system, the continuous probability distribution function of residence time follows an exponential distribution. More generally, the dwell time follows some other non-exponential probability distribution, in which case the corresponding switching system is referred to as a semi-markov switching system. In recent years, stability of semi-markov switching systems, sliding mode control, and event triggering schemes have yielded many significant results.
The natural behavior of physical systems is usually described by nonlinear models, and the T-S fuzzy strategy provides a powerful and popular tool for nonlinear systems, which can accurately approximate smooth nonlinear terms by using the 'IF-THEN' rule.
The sliding mode control is used as an effective robust control strategy, and has the advantages of fast response, simple design process, stronger robustness on parameter uncertainty, input nonlinearity and matching interference and the like.
In summary, it is a problem to be solved urgently to research a sliding mode control method of a manipulator system under deception attack and actuator failure, and establish a controller to enable the manipulator system to stably operate under deception attack and actuator failure, and the method has important research significance.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the conditions that the mechanical arm system is subjected to random deception attack and actuator faults, the fuzzy sliding mode control method of the networked mechanical arm system is provided, and the anti-interference control problem of the system under the condition that data transmission is limited is solved.
The technical scheme adopted by the method for solving the problems is as follows: a fuzzy sliding mode control method of a networked mechanical arm system comprises the following steps:
the method comprises the following steps: establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system;
step two: establishing an actuator fault model and a deception attack model;
step three: deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has an actuator fault;
step four: constructing a public sliding mode switching surface;
step five: designing a sliding mode control law;
step six: carrying out stability analysis on the system established by adopting the steps and solving the parameters of the controller;
step seven: and determining the condition which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state.
Further, the uncertain fuzzy networked semi-markov switching system model is defined as follows:
fuzzy rule i if theta 1 (t) is M i1 ,θ 2 (t) is M i2 ,...,θ p (t) is M ip Then, then
Figure GDA0003315456140000021
Wherein M is ij (i =1,2.,. R, j =1,2.,. P) is a fuzzy set, θ 1 (t),θ 2 (t),...,θ r (t) is a precondition, x (t) is ∈ R n 、u(t)∈R m Respectively representing system state, control inputs. { r t T is not less than 0, is a continuous time semi-Markov process, values are taken in S = {1,2,.. Multidot., S }, and the transition probability satisfies:
Figure GDA0003315456140000022
wherein
Figure GDA0003315456140000023
When the transfer rate is not equal to the value omega, the transfer mode is changed from the mode omega at the time t to the mode tau at the time t + h, and the mode is changed into the value tau and the value tau is judged>
Figure GDA0003315456140000024
o (h) is not less than 0 and satisfies lim h→0 o(h)/h＝0。
Taking into account the probability of a general uncertain transition, p ωτ (h) The following two cases are satisfied: (1) Rho ωτ (h) Is completely unknown; (2) Rho ωτ (h) Is known, i.e. the upper and lower bounds of
Figure GDA0003315456140000025
Whereinρ ωτ And &>
Figure GDA0003315456140000026
Respectively represent rho ωτ (h) Lower and upper bounds. Define >>
Figure GDA0003315456140000027
And->
Figure GDA0003315456140000028
∣Δρ ωτ (h)∣≤π ωτ ，/>
Figure GDA0003315456140000029
Thus, the transition probability matrix is:
Figure GDA0003315456140000031
wherein? Representing the unknown transition probabilities.
Definition I ω ＝I ω,k ∪I ω,uk Wherein
Figure GDA0003315456140000032
Figure GDA0003315456140000033
A i (r t )，B i (r t ) Is a system matrix. Delta A i (r t ) Is norm-bounded and satisfies Δ A i (r t )＝L(r t )F i (r t )H(r t )，L(r t )，H(r t ) Is a known real matrix, F i (r t ) Satisfy the requirement of
Figure GDA0003315456140000034
And I is an identity matrix. For convenience, let r t If "= ω, then for any ω ∈ S, there is ^ based on>
Figure GDA0003315456140000035
Here, suppose B i,ω ＝B ω ，i＝1,2,...,r，ω＝1,2,...,s。
Further, the actuator fault model is defined as:
u A (t)＝(I m -σ)u B (t)，
wherein I m Is an m-order identity matrix, σ k Represents the efficiency loss of the kth actuator, σ = diag { σ } 1 ,σ 2 ,...,σ m }, satisfy
Figure GDA0003315456140000036
k =1,2. Definition of
Figure GDA0003315456140000037
Further, the spoofing attack model is defined as:
u B (t)＝u(t)+ζ(t)Q ω (t)Ψ(x(t),t,ω),
wherein psi (x (t), t, omega) is a nonlinear function, and satisfies | | | psi (x (t), t, omega) | < ψ (x (t), t, omega), Q ω (t) represents the mode of attack, satisfying | | Q ω (t)||≤q ω Constant q ω The function psi (x (t), t, omega) > 0 is known, and zeta (t) follows the exponential distribution of the switching, satisfying
Figure GDA0003315456140000038
Figure GDA0003315456140000039
Are known constants.
Further, in combination with the actuator fault model and the spoofing attack model, the uncertain fuzzy networked half-markov switching system model of the mechanical arm system subjected to spoofing attack and having the actuator fault is as follows:
Figure GDA0003315456140000041
wherein θ (t) = [ θ = 1 (t),θ 2 (t),...,θ p (t),] T ，h i (θ (t)) is a membership function of the form:
Figure GDA0003315456140000042
wherein mu ij (θ j (t)) is θ j (t) in μ ij The membership degree in (1) is more than or equal to 0 for all t and h i (theta) is not less than 0, and
Figure GDA0003315456140000043
further, in order to avoid instability caused by repeated jumping of the sliding mode surface, the function of the common sliding mode surface is selected as follows:
s(t)＝Gx(t),
wherein
Figure GDA0003315456140000044
Further, considering the situations of deception attack and the existence of actuator faults, fuzzy sliding mode control is selected, and the state track is driven to the specified sliding mode surface. The sliding mode control law is designed as follows:
Figure GDA0003315456140000045
wherein P is ω Is non-singular, χ ω Is greater than 0. The closed-loop system model adopting the sliding mode control law can be rewritten as follows:
Figure GDA0003315456140000046
further, stability analysis is performed on the system established by the steps, and the solving process of the controller parameters is as follows:
there is a symmetric positive definite matrix W ωτ ＞0，Z ωτ ＞0，P ω 0,X > 0 and scalar rho > 0, epsilon 1 ＞0,ε 2 ＞0,β＞0,α ω > 0, the following linear matrix inequality is satisfied:
Figure GDA0003315456140000051
case 1: omega epsilon is I ω,k ,
Figure GDA0003315456140000052
1≤o1≤s,/>
Figure GDA0003315456140000053
Case 2: omega belongs to I ω,uk ，
Figure GDA0003315456140000054
1≤o2≤s,
Figure GDA0003315456140000055
Wherein
Figure GDA0003315456140000056
Figure GDA0003315456140000057
Figure GDA0003315456140000058
Figure GDA0003315456140000059
Figure GDA00033154561400000510
Wherein,
Figure GDA00033154561400000511
1. Ltoreq. O1. Ltoreq. S, for
Figure GDA00033154561400000512
Meaning is the same as>
Figure GDA00033154561400000513
Further, if the system satisfies accessibility of the sliding state, the sliding mode control law should satisfy the following conditions:
Figure GDA00033154561400000514
wherein oa is > 0.
Through analysis, when the deception attack randomly occurs and the actuator fault exists, the sliding mode dynamic can be driven to a preassigned sliding domain and keeps moving on the preassigned sliding domain.
A storage medium for receiving a user input program, the stored computer program causing an electronic device to perform steps comprising:
the method comprises the following steps: establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system;
step two: establishing an actuator fault model and a deception attack model;
step three: deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has actuator faults;
step four: constructing a public sliding mode switching surface;
step five: designing a sliding mode control law;
step six: carrying out stability analysis on the system established by adopting the steps and solving the parameters of the controller;
step seven: and determining the condition which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state.
The invention has the beneficial effects that: the fuzzy half Markov model is used for describing a mechanical arm system model under deception attack and actuator failure, has strong mixing and randomness, and can better describe the dynamic characteristics of the mechanical arm system model. Secondly, the method designs a proper sliding mode control law by utilizing the probability information of the occurrence of the deception attack and the actuator fault information, and can ensure the stability of the system track in the sliding stage and the accessibility of the system track in the reaching stage.
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The aspects and advantages of the present application will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention.
In the drawings:
FIG. 1 is a schematic flow chart of a fuzzy sliding mode control method of a networked mechanical arm system according to the present invention;
FIG. 2 is a simulation result diagram of a sliding mode switching surface;
FIG. 3 is a diagram of a simulation result of a control input to the robotic arm system;
fig. 4 is a diagram showing a simulation result of a state trajectory of the robot system.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. It should be noted that these embodiments are provided so that this disclosure can be more completely understood and fully conveyed to those skilled in the art, and the present disclosure may be implemented in various forms without being limited to the embodiments set forth herein.
Example 1
Referring to fig. 1, fig. 1 is a schematic flow chart of a fuzzy sliding mode control method of a networked mechanical arm system according to the present invention, where the fuzzy sliding mode control method of the networked mechanical arm system includes the following steps:
s101: establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system;
s102: establishing an actuator fault model and a deception attack model;
s103: deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has an actuator fault;
s104: constructing a public sliding mode switching surface;
s105: designing a sliding mode control law;
s106: carrying out stability analysis on the system established by adopting the steps, and solving the parameters of the controller;
s107: and determining the condition which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state.
Firstly, in S101, the uncertain fuzzy networked half-markov switching system model is defined as follows:
fuzzy rule i if theta 1 (t) is M i1 ,θ 2 (t) is M i2 ,...,θ p (t) is M ip Then, then
Figure GDA0003315456140000071
Wherein M is ij (i =1,2.,. R, j =1,2.,. P) is a fuzzy set, θ 1 (t),θ 2 (t),...,θ r (t) is a precondition, x (t) is ∈ R n 、u(t)∈R m Respectively representing system state, control inputs. { r t T is not less than 0, is a continuous time semi-Markov process, values are taken in S = {1,2,.. Multidot., S }, and the transition probability satisfies:
Figure GDA0003315456140000072
wherein
Figure GDA0003315456140000073
When the transfer rate is not equal to the value omega, the transfer mode is changed from the mode omega at the time t to the mode tau at the time t + h, and the mode is changed into the value tau and the value tau is judged>
Figure GDA0003315456140000074
o (h) is not less than 0 and satisfies lim h→0 o(h)/h＝0。
Taking into account the general probability of uncertain transitions, p ωτ (h) The following two cases are satisfied: (1) Rho ωτ (h) Is completely unknown; (2) ρ is a unit of a gradient ωτ (h) Is known, i.e. the upper and lower bounds of
Figure GDA0003315456140000075
Whereinρ ωτ And &>
Figure GDA0003315456140000076
Respectively represent rho ωτ (h) Lower and upper bounds. Define >>
Figure GDA0003315456140000077
And->
Figure GDA0003315456140000078
∣Δρ ωτ (h)∣≤π ωτ ，/>
Figure GDA0003315456140000079
Thus, the transition probability matrix is:
Figure GDA0003315456140000081
wherein? Representing the unknown transition probabilities.
Definition I ω ＝I ω,k ∪I ω,uk Wherein
Figure GDA0003315456140000082
Figure GDA0003315456140000083
A i (r t )，B i (r t ) Is a system matrix. Delta A i (r t ) Is norm-bounded and satisfies Δ A i (r t )＝L(r t )F i (r t )H(r t )，L(r t )，H(r t ) Is a known real matrix, F i (r t ) Satisfies F i T (r t )F i (r t ) Less than or equal to I. And I is an identity matrix. For convenience, let r t If (= ω), then for any ω ∈ S, there are
Figure GDA0003315456140000084
Here, suppose B i,ω ＝B ω ，i＝1,2,...,r，ω＝1,2,...,s。
In order to establish the uncertain fuzzy networked half-markov switching system model of the mechanical arm system in the step S101, in this embodiment, a single-link mechanical arm system is selected, and a dynamic model of the single-link mechanical arm system is established, so that the model is converted into the uncertain fuzzy networked half-markov switching system model of the mechanical arm system in the step S101. The dynamic model of the single-link mechanical arm system is as follows:
Figure GDA0003315456140000085
where θ (t) is the angular position of the arm, u A (t) is the control input, W (t) is the coefficient of uncertainty of viscous friction, M (r) t )，J(r t ) L respectively represents load mass, moment of inertia and arm length, g represents gravity acceleration, and g =9.81, L =2.5, D (t) = D) are selected 0 ＝10，M(r t ) And J (r) t ) There are three different modes, M 1 ＝1，J 1 ＝1；M 2 ＝1.5，J 2 ＝2；M 3 ＝2，J 3 ＝2.5。
Let x 1 (t)＝θ(t)，
Figure GDA0003315456140000086
Sin (x) 1 (t)) may be represented as
sin(x 1 (t))＝h 1 (x 1 (t))x 1 (t)+δh 2 (x 1 (t))x 1 (t),
Wherein delta = 0.01/pi, h 1 (x 1 (t))，h 2 (x 1 (t))∈[0,1]And h is a 1 (x 1 (t))+h 2 (x 1 (t)) =1. Can obtain
Figure GDA0003315456140000091
Figure GDA0003315456140000092
From the above membership functions, if x 1 (t) is about 0 radians, then h 1 (x 1 (t)) =1. If x 1 (t) is about pi radians or about-pi radians, then h 2 (x 1 (t)) =0. Therefore, the uncertainty fuzzy networked half-markov switching system model established according to the mechanical arm system in the embodiment is described as follows:
fuzzy rule 1: if x 1 (t) is "about 0 radians", then
Figure GDA0003315456140000093
Fuzzy rule 2: if x 1 (t) is "about pi radians" or "about-pi radians", then
Figure GDA0003315456140000094
Wherein
Figure GDA0003315456140000095
Selecting
Figure GDA0003315456140000096
Figure GDA0003315456140000097
Figure GDA0003315456140000098
H i,1 ＝[0.1 -0.1],H i,2 ＝[-0.1 0.2],H i,3 ＝[0 0.1],(i∈{1,2})。
The transition probability matrix is selected as:
Figure GDA0003315456140000099
in S102 provided in this embodiment, the actuator fault model is defined as:
u A (t)＝(I m -σ)u B (t)，
wherein I m Is an m-order identity matrix, σ k Represents the efficiency loss of the kth actuator, σ = diag { σ } 1 ,σ 2 ,...,σ m Is satisfied with
Figure GDA0003315456140000101
k =1,2. Definition of
Figure GDA0003315456140000102
Specifically, in the present embodiment, the actuator fault model parameter σ =0.5.
Further, the spoofing attack model is defined as:
u B (t)＝u(t)+ζ(t)Q ω (t)Ψ(x(t),t,ω),
wherein psi (x (t), t, omega) is a nonlinear function, and satisfies | | | psi (x (t), t, omega) | < ψ (x (t), t, omega), Q ω (t) represents the mode of attack, satisfying | | Q ω (t)||≤q ω Constant q ω The function psi (x (t), t, omega) > 0 is known, and zeta (t) follows the exponential distribution of the switching, satisfying
Figure GDA0003315456140000103
Figure GDA0003315456140000104
Is a known constant.
Specifically, in this embodiment, the parameters of the spoofing attack model are:
Figure GDA0003315456140000105
Q 2 (t)＝0.5sin(t),Q 3 (t)＝0.5,/>
Figure GDA0003315456140000106
Figure GDA0003315456140000107
further, in S103 provided by this embodiment, in combination with the actuator fault model and the spoofing attack model in S102, an uncertain fuzzy networked half markov switching system model of the mechanical arm system which is subjected to the spoofing attack and has the actuator fault is derived as follows:
Figure GDA0003315456140000108
wherein θ (t) = [ θ = 1 (t),θ 2 (t),...,θ p (t),] T ，h i (θ (t)) is a membership function of the form:
Figure GDA0003315456140000109
wherein mu ij (θ j (t)) is θ j (t) in μ ij The membership degree in (1) is more than or equal to 0 for all t and h i (θ) ≥ 0, and
Figure GDA00033154561400001010
in S104 provided in this embodiment, to avoid instability caused by repeated jump of the sliding mode surface, the function of the common sliding mode surface is selected as follows:
s(t)＝Gx(t),
wherein
Figure GDA0003315456140000111
In S105 provided in this embodiment, in consideration of the situations of spoofing attack and actuator failure, fuzzy sliding mode control is selected, and the state trajectory is driven to a specified sliding mode surface. The sliding mode control law is designed as follows:
Figure GDA0003315456140000112
wherein P is ω Is non-singular, χ ω Is greater than 0. The closed-loop system model adopting the sliding mode control law can be rewritten as follows:
Figure GDA0003315456140000113
in S106 provided in this embodiment, stability analysis is performed on the single link arm system established by using the above steps in this embodiment, and a solving process of the controller parameters is as follows:
there is a symmetric positive definite matrix W ωτ ＞0，Z ωτ ＞0，P ω 0,X > 0 and scalar ρ > 0, ε 1 ＞0,ε 2 ＞0,β＞0,α ω > 0, the following linear matrix inequality is satisfied:
Figure GDA0003315456140000114
case 1: omega epsilon is I ω,k ,
Figure GDA0003315456140000115
1≤o1≤s,/>
Figure GDA0003315456140000116
Case 2: omega epsilon is I ω,uk ，
Figure GDA0003315456140000117
1≤o2≤s,
Figure GDA0003315456140000118
Wherein
Figure GDA0003315456140000121
Figure GDA0003315456140000122
Figure GDA0003315456140000123
Figure GDA0003315456140000124
Figure GDA0003315456140000125
Wherein,
Figure GDA0003315456140000126
1. Ltoreq. O1. Ltoreq. S for
Figure GDA0003315456140000127
Meaning is the same as>
Figure GDA0003315456140000128
The controller parameters can be solved:
Figure GDA0003315456140000129
in S107 provided in this embodiment, if the system satisfies the reachability of the sliding state, the sliding mode control law should satisfy the following condition:
Figure GDA00033154561400001210
wherein oa is > 0.
Through analysis, when the deception attack randomly occurs and the actuator fault exists, the sliding mode dynamic can be driven to a preassigned sliding domain and keeps moving on the preassigned sliding domain.
To clearly demonstrate the limited time accessibility in S107, partial data traces are plotted in fig. 2-4, with the axis of abscissa representing time and the axis of ordinate representing a particular quantity:
FIG. 2 depicts a sliding mode switching surface, achieving limited time accessibility;
FIG. 3 depicts control inputs that converge to an origin under an actuator failure and spoofing attack;
fig. 4 depicts the state trajectory of the robotic arm system to the equilibrium point under sliding mode control.
As can be seen from fig. 2 to 4, the method of the present invention can effectively suppress the influence of the actuator failure and the deception attack on the mechanical arm system, solve the sliding mode control problem of the mechanical arm system, and improve the safety of the mechanical arm system. The fuzzy half Markov model is used for describing a mechanical arm system model under deception attack and actuator failure, has strong clutter and randomness, and can better describe the dynamic characteristics of the mechanical arm system model. Secondly, the method designs a proper sliding mode control law by utilizing the probability information of the occurrence of the deception attack and the actuator fault information, and can ensure the stability of the system track in the sliding stage and the accessibility of the system track in the reaching stage.
A storage medium for receiving a user input program, the stored computer program being capable of causing an electronic device to perform the steps of:
s101: establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system;
s102: establishing an actuator fault model and a deception attack model;
s103: deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has actuator faults;
s104: constructing a public sliding mode switching surface;
s105: designing a sliding mode control law;
s106: carrying out stability analysis on the system established by adopting the steps, and solving the parameters of the controller;
s107: and determining the condition which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or additions or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are also included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (9)

1. A fuzzy sliding mode control method of a networked mechanical arm system is characterized by comprising the following steps of:
establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system;
the uncertain fuzzy networked half Markov switching system model is defined as follows:
fuzzy rule i if theta 1 (t) is M i1 ,θ 2 (t) is M i2 ,...,θ p (t) is M ip Then, then
Figure FDA0004131859290000011
Wherein M is ij (i =1,2.., r, j =1,2., p) is a fuzzy set, θ 1 (t),θ 2 (t),...,θ r (t) is a precondition variable, x (t) is E.R n 、u(t)∈R m Respectively represent system status, control input, { r } t T is not less than 0, is a continuous time semi-Markov process, values are taken in S = {1,2,.. Multidot., S }, and the transition probability satisfies:
Figure FDA0004131859290000012
where ρ is ωτ (h) More than or equal to 0 represents that when the transfer rate is omega is not equal to tau, the mode is transferred from the mode omega at the time t to the mode tau at the time t + h,
Figure FDA0004131859290000013
satisfy lim h→0 o(h)/h＝0，
Taking into account the probability of a general uncertain transition, p ωτ (h) The following two cases are satisfied: (1) Rho ωτ (h) Is completely unknown; (2) ρ is a unit of a gradient ωτ (h) Are known, i.e. the upper and lower bounds of
Figure FDA0004131859290000014
Where ρ is ωτ And &>
Figure FDA0004131859290000015
Respectively represent ρ ωτ (h) Lower and upper bound of (c), define +>
Figure FDA0004131859290000016
And->
Figure FDA0004131859290000017
∣Δρ ωτ (h)∣≤π ωτ ，/>
Figure FDA0004131859290000018
Thus, the transition probability matrix is:
Figure FDA0004131859290000019
wherein? Representing the probability of a transition that is not known,
definition I ω ＝I ω,k ∪I ω,uk In which
Figure FDA00041318592900000110
Figure FDA00041318592900000111
A i (r t )，B i (r t ) Is a system matrix, Δ A i (r t ) Is norm-bounded and satisfies Δ A i (r t )＝L(r t )F i (r t )H(r t )，L(r t )，H(r t ) Is a known real matrix, F i (r t ) Satisfies F i T (r t )F i (r t ) I is less than or equal to I, I is a unit matrix, and r is made as a convenient order t If ω is not greater than ω, then for any ω ∈ S, there is
Figure FDA0004131859290000021
Here, suppose B i,ω ＝B ω ，i＝1,2,...,r，ω＝1,2,...,s；
Establishing an actuator fault model and a deception attack model;
deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has an actuator fault;
constructing a public sliding mode switching surface;
designing a sliding mode control law;
carrying out stability analysis on a system adopting the sliding mode control law, and solving controller parameters;
and determining the condition which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state.
2. The fuzzy sliding-mode control method of the networked mechanical arm system according to claim 1, wherein the actuator fault model is defined as:
u A (t)＝(I m -σ)u B (t),
wherein I m Is an m-th order identity matrix, σ k Represents the efficiency loss of the kth actuator, σ = diag { σ } 1 ,σ 2 ,...,σ m Is satisfied with
Figure FDA0004131859290000022
Definition of
Figure FDA0004131859290000023
3. The fuzzy sliding-mode control method of the networked mechanical arm system according to claim 2, wherein the spoofing attack model is defined as:
u B (t)＝u(t)+ζ(t)Q ω (t)Ψ(x(t),t,ω),
wherein psi (x (t), t, omega) is a nonlinear function, and satisfies | | | psi (x (t), t, omega) | < ψ (x (t), t, omega), Q ω (t) represents the mode of attack, satisfying | | Q ω (t)||≤q ω Constant q ω The function psi (x (t), t, omega) > 0 is known, and zeta (t) follows the exponential distribution of the switching, satisfying
Figure FDA0004131859290000024
Figure FDA0004131859290000025
Figure FDA0004131859290000026
Are known constants.
4. The fuzzy sliding-mode control method of the networked mechanical arm system according to claim 3, wherein the uncertain fuzzy networked half-Markov switching system model of the mechanical arm system which is subjected to the spoofing attack and has an actuator fault is as follows:
Figure FDA0004131859290000031
wherein θ (t) = [ θ = 1 (t),θ 2 (t),...,θ p (t),] T ，h i (θ (t)) is a membership function of the form:
Figure FDA0004131859290000032
wherein mu ij (θ j (t)) is θ j (t) in μ ij The membership degree in (1) is more than or equal to 0 for all t and h i (theta) is not less than 0, and
Figure FDA0004131859290000033
5. the fuzzy sliding-mode control method of the networked mechanical arm system according to claim 1, wherein the common sliding-mode surface function is selected as:
s(t)＝Gx(t),
wherein
Figure FDA0004131859290000034
6. The fuzzy sliding-mode control method of the networked mechanical arm system according to claim 1, wherein the sliding-mode control law is designed as follows:
Figure FDA0004131859290000035
wherein P is ω Is non-singular, χ ω And if the sliding mode control law is adopted, the system model can be rewritten as follows:
Figure FDA0004131859290000036
/>
7. the fuzzy sliding-mode control method of the networked mechanical arm system according to claim 6, wherein the solving process of the controller parameters is as follows:
there is a symmetric positive definite matrix W ωτ ＞0，Z ωτ ＞0，P ω 0,X > 0 and scalar ρ > 0, ε 1 ＞0,ε 2 ＞0,β＞0,α ω > 0, the following linear matrix inequality is satisfied:
Figure FDA0004131859290000041
case 1:
Figure FDA0004131859290000042
Figure FDA0004131859290000043
case 2:
Figure FDA0004131859290000044
Figure FDA0004131859290000045
Figure FDA0004131859290000046
Figure FDA0004131859290000047
Figure FDA0004131859290000048
Figure FDA0004131859290000049
Figure FDA00041318592900000410
wherein,
Figure FDA00041318592900000411
1. Ltoreq. O1. Ltoreq. S, for
Figure FDA00041318592900000412
Means together with>
Figure FDA00041318592900000413
8. The fuzzy sliding-mode control method of the networked mechanical arm system according to claim 1, wherein if the system satisfies accessibility of a sliding state, the sliding-mode control law should satisfy the following condition:
Figure FDA00041318592900000414
wherein
Figure FDA00041318592900000415
9. A storage medium for receiving a user input program, the stored computer program causing an electronic device to perform the steps of any one of claims 1 to 8, comprising:
the method comprises the following steps: establishing an uncertain fuzzy networked half Markov switching system model for the mechanical arm system;
step two: establishing an actuator fault model and a deception attack model;
step three: deducing an uncertain fuzzy networked half Markov switching system model of the mechanical arm system which is subjected to deception attack and has actuator faults;
step four: constructing a public sliding mode switching surface;
step five: designing a sliding mode control law;
step six: carrying out stability analysis on the system established by adopting the steps and solving the parameters of the controller;
step seven: and determining the conditions which should be met by the sliding mode control law so that the system can meet the accessibility of the sliding state.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108972560A (en) * 2018-08-23 2018-12-11 北京邮电大学 A kind of activation lacking mechanical arm Hierarchical sliding mode control method based on fuzzy optimization
CN110213115A (en) * 2019-06-25 2019-09-06 南京财经大学 A kind of Multi net voting attacks the method for controlling security of lower event-driven network control system
CN111258223A (en) * 2020-03-12 2020-06-09 电子科技大学 Sliding mode-based switching networked control system safety control method
CN111872934A (en) * 2020-06-19 2020-11-03 南京邮电大学 Mechanical arm control method and system based on hidden semi-Markov model
WO2021069129A1 (en) * 2019-10-07 2021-04-15 Robert Bosch Gmbh Device and method for controlling a robot device
CN113341724A (en) * 2021-06-18 2021-09-03 曲阜师范大学 Asynchronous sliding mode control method of multi-mode mechanical arm

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108972560A (en) * 2018-08-23 2018-12-11 北京邮电大学 A kind of activation lacking mechanical arm Hierarchical sliding mode control method based on fuzzy optimization
CN110213115A (en) * 2019-06-25 2019-09-06 南京财经大学 A kind of Multi net voting attacks the method for controlling security of lower event-driven network control system
WO2021069129A1 (en) * 2019-10-07 2021-04-15 Robert Bosch Gmbh Device and method for controlling a robot device
CN111258223A (en) * 2020-03-12 2020-06-09 电子科技大学 Sliding mode-based switching networked control system safety control method
CN111872934A (en) * 2020-06-19 2020-11-03 南京邮电大学 Mechanical arm control method and system based on hidden semi-Markov model
CN113341724A (en) * 2021-06-18 2021-09-03 曲阜师范大学 Asynchronous sliding mode control method of multi-mode mechanical arm

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
马跃超，李欢.观测器基于自适应滑模控制的半马尔科夫跳变***.自动化与仪器仪表.2021,(第第2期期),9-16页. *

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