CN114326398A - Control method and control system of linear switching system with unstable mode - Google Patents

Control method and control system of linear switching system with unstable mode Download PDF

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CN114326398A
CN114326398A CN202111612522.3A CN202111612522A CN114326398A CN 114326398 A CN114326398 A CN 114326398A CN 202111612522 A CN202111612522 A CN 202111612522A CN 114326398 A CN114326398 A CN 114326398A
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switching system
unstable
mode
linear switching
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CN114326398B (en
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王燕舞
曾泽宏
刘智伟
刘骁康
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Huazhong University of Science and Technology
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Abstract

The invention discloses a control method and a control system of a linear switching system with an unstable mode, which comprises the following steps: constructing a linear switching system model with interference terms:
Figure DDA0003435442040000011
Figure DDA0003435442040000012
constructing a controller model:
Figure DDA0003435442040000013
Figure DDA0003435442040000014
Uj≤μiUi，Ui>0, i, j belongs to gamma, i is not equal to j; initialization model setting parameter mui>1，
Figure DDA0003435442040000015
Solving the controller model to obtain the gain
Figure DDA0003435442040000016
Collecting the current sampling time tkInner system state x (t)k) And the mode σ (t) activatedk) Updating the input signal according to the sampling information
Figure DDA0003435442040000017
Wherein the content of the first and second substances,
Figure DDA0003435442040000018
is the gain KiNeutralization of the activated modality σ (t)k) The corresponding gain. But this application is through considering steady mode and unstable mode simultaneously when the model is founded, solves the gain of controller model, updates switching system's control data according to the gain of solving, in this application, through setting up reasonable controller, can improve the stability of system input state.

Description

Control method and control system of linear switching system with unstable mode
Technical Field
The invention belongs to the technical field of linear switching system control, and particularly relates to a control method and a control system of a linear switching system with an unstable mode.
Background
Due to the particularity of the switching systems, many switching systems have unstable modes, and due to the rapid development of networks, the control of the switching systems through network connection controllers is a current hotspot method. However, due to the instability of the network and the complexity of the switching, the input state of the switching system may be unstable, and especially when the system is under a denial of service attack, it is difficult for the system to maintain the input state stable.
Disclosure of Invention
In view of the above drawbacks and needs of the prior art, the present invention provides a control method and a control system for a linear switching system with unstable mode, which aims to improve the stability of the input signal of the linear switching system with unstable mode.
To achieve the above object, according to an aspect of the present invention, there is provided a control method of a linear switching system with unstable mode, comprising:
construction beltLinear switching system model with interference term:
Figure BDA0003435442020000011
Figure BDA0003435442020000012
where x (t) is the system state, u (t) is the input signal, d (t) is the unknown bounded interference, σ (t) is the mode activated at time t, Aσ(t)、Bσ(t)、Dσ(t)Are respectively a weighting matrix Ai、Bi、DiIn the weighting matrix corresponding to the activated mode σ (t), i ∈ Γ ═ { 1., N }, N is the total number of modes of the system, where r stable modes are ΓsR, N-r unstable modes are Γu＝{r,...N}；
Constructing a controller model:
Figure BDA0003435442020000021
Uj≤μiUi，Ui＞0，i,j∈Γ,i≠j，Ui、Tifor the model to be parameterized, λi、μiSetting parameters for the model;
initialization model setting parameter mui＞1，
Figure BDA0003435442020000022
Solving the controller model to obtain a gain Ki＝TiPi，
Figure BDA0003435442020000023
Collecting the current sampling time tkSystem state x (t)k) And the mode σ (t) activatedk) Updating the input signal according to the sampling information
Figure BDA0003435442020000024
Wherein the content of the first and second substances,
Figure BDA0003435442020000025
is the gain KiNeutralization of the activated modality σ (t)k) The corresponding gain.
In one embodiment, the control method further includes optimally selecting a sampling interval Δ:
Figure BDA0003435442020000026
wherein the content of the first and second substances,
Figure BDA0003435442020000027
Figure BDA0003435442020000028
is a matrix AiLogarithmic norm of;
Figure BDA0003435442020000029
satisfies the following conditions:
Figure BDA00034354420200000210
κi＝max{||Ai+BiKi||,||Di||}，κij＝max{||Aj+BjKi||,||Dj| l }, ε satisfies:
Figure BDA00034354420200000211
wherein ω is1i＝λiλmin(Pi)，ω2i＝||2PiBiKi||。
In one embodiment, the control method further comprises optimizing the switching signal:
constructing a switching model:
Figure BDA0003435442020000031
Figure BDA0003435442020000032
wherein n isi(T, T) is the ith mode at [ T, T]Number of activations, Ti(T, T) is the ith mode at [ T, T]Total duration of inner, τaiIs the modality-dependent mean residence time, T, of the ith modality+(T, T) is all unstable modes in [ T, T ]]Total duration of inner, τ+Is that all unstable modes have a duration of [ T, T ]]Mean time of day, τ+＞1，n0iAnd χ is a compensation parameter;
constructing a switching constraint condition:
Figure BDA0003435442020000033
wherein the content of the first and second substances,
Figure BDA0003435442020000034
Figure BDA0003435442020000035
Figure BDA0003435442020000036
Figure BDA0003435442020000037
obtaining tau in switching model according to switching constraint condition+And τaiAnd determining a switching signal.
In one embodiment, the control method further comprises evaluating the stability of the system according to the maximum blocking rate that the linear switching system can tolerate and the blocking rate suffered by the current linear switching system:
constructing a denial of service attack model:
Figure BDA0003435442020000041
Figure BDA0003435442020000042
wherein n (T, T) is a denial of service attack at [ T, T]Inner number of activations, | xi (T, T) | is denial of service attack [ T, T |)]Total duration of inner, τDIs the average residence time, T, of a denial of service attack*Is a denial of service attack at T, T]Mean time ratio of (T)*Greater than 1, eta and kappa are compensation parameters;
calculating the maximum blocking rate which can be tolerated by the linear switching system:
Figure BDA0003435442020000043
wherein the content of the first and second substances,
Figure BDA0003435442020000044
Figure BDA0003435442020000045
calculating the blocking rate suffered by the current linear switching system
Figure BDA0003435442020000046
Judging whether the blocking rate F' suffered by the current linear switching system is smaller than the maximum blocking rate F which can be tolerated by the linear switching system, if so, indicating that the input state of the current linear switching system is stable, and if not, indicating that the input state of the current linear switching system is unstable.
In one embodiment, it is determined whether the current blocking rate F' suffered by the linear switching system is less than the maximum blocking rate F that the linear switching system can tolerate, and if not, the system parameters are adjusted in a reverse direction to increase the maximum blocking rate F that the linear switching system can tolerate.
In one embodiment, χ ≧ 0, η ≧ 0, κ ≧ 0.
In one embodiment, the controller model is solved by the matlab toolbox.
According to another aspect of the present invention, there is provided a control architecture for a linear switching system with unstable modes, comprising:
the switching system is used for switching different modes according to the switching signal, and the switching system is provided with a stable mode and an unstable mode;
a sampler for acquiring a current sampling time t according to a sampling sequencekSystem state x (t)k) And the mode σ (t) activatedk) And transmitted to the controller through the communication network;
a controller for acquiring the sampling signal of the sampler and processing to obtain a control signal
Figure BDA0003435442020000051
And transmits the control signal to the holder through a communication network, wherein,
Figure BDA0003435442020000052
a gain determined for the control method according to the linear switching system with unstable mode described above;
the retainer is used for acquiring a control signal of the controller and continuously outputting the control signal to the actuator;
and the actuator is used for acquiring the control signal of the retainer and inputting the control signal into the switching system to update the system input signal.
In one embodiment, the sampler is set with a sampling interval Δ, which is determined according to the control method of the linear switching system with unstable mode described above.
In one embodiment, the switching signal is a switching signal determined according to the control method of the linear switching system with unstable mode described above.
This application is through constructing linear switching system model to construct the controller model based on linear switching system model, but consider steady mode and unstability mode simultaneously when constructing the model, and set for different initialization parameters to different modes, solve the gain of controller model, update switching system's control data according to the gain of solving, in this application, through setting up reasonable controller, can improve system input state's stability. Furthermore, on the basis of setting a reasonable controller, the sampling time interval and the switching signal are further optimized, and the stability of the input state of the system can be further improved by setting the reasonable controller, the sampling time interval and the switching signal. Furthermore, considering the denial of service attack, a denial of service attack model is constructed, the blocking rate suffered by the system and the maximum blocking rate which can be tolerated by the system are compared, the stability of the system can be evaluated, meanwhile, the maximum blocking rate which can be tolerated by the system can be improved by adjusting system parameters, and the stability of the input state of the system is further improved.
Drawings
FIG. 1 is a block diagram of a control architecture of a switching system according to an embodiment of the present application;
FIG. 2 is a flow chart illustrating the steps of a method for controlling a linear switching system with unstable modes according to an embodiment of the present application;
fig. 3 is a flowchart illustrating steps of a method for controlling a linear switching system with unstable mode according to another embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In order to facilitate understanding of the present invention, a linear switching system control system is first operatedAnd (4) explanation. Fig. 1 is a schematic diagram of a switching system control system in an embodiment, which includes a switching system, a sampler, a controller, a keeper and an actuator forming a closed-loop control, wherein the switching system has N modes, and a set of the modes is denoted as Γ ═ 1.·, N }, wherein a part of the modes is a stable mode and a part of the modes is an unstable mode, for example, r stable modes, N-r unstable modes, and a set of the stable modes is denoted as ΓsR, the unstable mode is denoted as ΓuN }. When the switching system is determined, the modality is determined. During the operation of the system, the switching system switches from one mode to another mode according to the set switching signal, and the mode which is successfully switched is activated, namely an activation mode sigma (t)k)，σ(tk) E Γ ═ { 1.·, N }, operated by the activation mode. During the period, the sampler samples the switching system according to the set sampling sequence to obtain the current sampling time tkSystem state x (t)k) And the mode σ (t) activatedk) And transmitted to the controller through the communication network, wherein, a fixed sampling interval is arranged between two adjacent samplings. The controller receives the sampling information of the sampler through the communication network and processes the sampling information to obtain a control signal
Figure BDA0003435442020000061
Wherein the content of the first and second substances,
Figure BDA0003435442020000062
for the controller with the current active mode σ (t)k) The corresponding gain factor. The controller transmits the control signal to the retainer through the communication network, and the retainer continuously outputs the control signal to the actuator within a preset time length. After the actuator receives the control signal, the control signal is input into the switching system to update the input signal of the system.
In the control system, the design of the controller, the selection of the sampling time interval and the setting of the switching signal can all influence the stability of the input signal of the switching system, and because the controller is accessed into the system through a communication network, the stability of the input signal of the switching system can also be influenced by network attack.
Based on this, the present application provides a control method for a linear switching system with unstable mode, as shown in fig. 2, in an embodiment, the control method includes:
step S100: and optimizing the design of the controller.
Specifically, the design process of the optimization controller is as follows:
step S110: constructing a linear switching system model with interference terms:
Figure BDA0003435442020000071
Figure BDA0003435442020000072
where x (t) is the system state, u (t) is the input signal, and d (t) is the unknown bounded interference. Wherein, the parameter representing the system state can be flexibly selected according to the requirement. σ (t) is the modality activated at time t, Aσ(t)、Bσ(t)、Dσ(t)Are respectively a weighting matrix Ai、Bi、DiIn a weighting matrix corresponding to the activated modality σ (t), Ai、Bi、DiIs a weighting matrix of the ith mode, i is equal to Γ ═ 1.. and N is the total mode number of the system, wherein r stable modes are ΓsR, N-r unstable modes are ΓuN }. Wherein the weighting matrix Ai、Bi、DiAfter the switching system is determined, the switching system can be determined according to the system parameters and is a known parameter. In model proposal, it is assumed that the state of the system does not jump at all switching moments.
Step S120: constructing a controller model:
Figure BDA0003435442020000073
Uj≤μiUi，Ui＞0，i,j∈Γ,i≠j，Ui、Tifor the model to be parameterized, λi、μiParameters are set for the model.
Wherein the content of the first and second substances,
Figure BDA0003435442020000074
respectively, represent transpose matrices of the corresponding matrices.
Step S130: initialization model setting parameter mui＞1，
Figure BDA0003435442020000075
Solving the controller model to obtain a gain Ki＝TiPi，
Figure BDA0003435442020000076
Wherein the content of the first and second substances,
Figure BDA0003435442020000077
representation matrix UiThe inverse matrix of (c).
Figure BDA0003435442020000078
Denotes when i e rsWhen is lambdai＞0，
Figure BDA0003435442020000081
Denotes when i e ruWhen is lambdai＜0。
Specifically, the initialization model setting parameters are set according to certain conditions, and the model setting parameters can be flexibly set as long as the constraint conditions are met. In the application, when the setting parameters are initialized, the different modes correspond to the setting parameters with different conditions, and the two situations of a stable state and an unstable state are comprehensively considered during the design of the controller, so that the stability of the input signals of the switching system can be improved. It is understood that the range of solutions can be obtained by solving the inequality, and one solution can be arbitrarily selected from the range. Specifically, the matlab toolbox can be used for solving the model by the gain KiAnd when the matlab tool box is used for solving, an optimal solution can be automatically output.
Step S140: collecting the current sampling time tkSystem state x (t)k) And the mode σ (t) activatedk) Updating the input according to the sampling informationIncoming signal
Figure BDA0003435442020000082
Wherein the content of the first and second substances,
Figure BDA0003435442020000083
is a gain KiNeutralization of the activated modality σ (t)k) The corresponding gain.
Determining a sampling sequence of a system
Figure BDA0003435442020000084
Where k denotes the sample number, N0Denotes the number of samples, where t 00. It will be appreciated that the sample sequence has a fixed sampling interval delta.
Specifically, the switching system may be sampled by a sampler to collect the current sampling time tkSystem state x (t)k) And the mode σ (t) activatedk) And transmitted to the controller via the communication network, and the controller calculates the control signal according to the sampling information
Figure BDA0003435442020000085
And feeds back to the switching system through the communication network to update the input signal of the switching system. Wherein the content of the first and second substances,
Figure BDA0003435442020000086
in a mode σ (t) with activationk) Corresponding gain, e.g. the activated mode being the 7 th mode, from which gain K is selected7As a calculated gain.
In the application, for a linear switching system with an unstable mode, the controller is designed by the method, and the stable state and the unstable state are comprehensively considered, so that the stability of signal input of the switching system can be improved.
In an embodiment, as shown in fig. 3, on the basis of designing the controller based on the above method, the method further includes:
step S200: the sampling time interval delta is optimized.
Specifically, step S200 includes:
step S210: constructing a sampling interval constraint condition:
Figure BDA0003435442020000091
Figure BDA0003435442020000092
Figure BDA0003435442020000093
wherein the content of the first and second substances,
Figure BDA0003435442020000094
is a matrix AiThe log-norm of (a) of (b),
Figure BDA0003435442020000095
κi＝max{||Ai+BiKi||,||Di||}，κij＝max{||Aj+BjKi||,||Dj| l | }, wherein | a | | | represents the spectral norm of a;
ε satisfies:
Figure BDA0003435442020000096
wherein ω is1i＝λiλmin(Pi)，ω2i＝||2PiBiKiL | where λmin(Pi) Representation matrix PiThe minimum eigenvalue of (c).
Step S220: and solving the sampling interval delta according to the sampling interval constraint condition.
It should be noted that, the solution range of the sampling time interval Δ is determined by the above method, and one solution may be arbitrarily selected from the solution range as the sampling time interval.
In an embodiment, as shown in fig. 3, on the basis of designing the controller and the sampling time interval, the switching signal is further optimized according to the following method, that is, the control method further includes:
step S300: the switching signal is optimized.
Specifically, step S300 includes:
step S310: constructing a switching model:
Figure BDA0003435442020000101
Figure BDA0003435442020000102
is provided with
Figure BDA0003435442020000103
For systematic switching sequences in which any two successive switching instants slAnd sl+1Satisfies sl+1-sl≥τd，τdIs the dwell time of the switching signal.
Wherein T, T ∈ R≥0，T≥t，ni(T, T) is the ith mode at [ T, T]Number of activations, Ti(T, T) is the ith mode at [ T, T]Total duration of inner, τaiIs the mode-dependent mean residence time of the ith mode, and satisfies tauai≥τd。T+(T, T) is unstable mode in [ T, T ]]In which T, T ∈ R≥0，T≥t，χ∈R≥0，τ+＞R＞1，τ+Is the average time fraction of the unstable mode. R≥aRepresenting a real number greater than or equal to a.
Step S320: constructing a switching constraint condition:
Figure BDA0003435442020000104
wherein the content of the first and second substances,
Figure BDA0003435442020000105
Figure BDA0003435442020000106
Figure BDA0003435442020000107
Figure BDA0003435442020000108
step S330: obtaining tau in switching model according to switching constraint condition+And τaiAnd determining a switching signal.
In this embodiment, different constraints are also set according to different modalities, and when a sampling interval is determined, multiple wakefulness states of a stable modality and an unstable modality are comprehensively considered, so that the stability of the input signal of the switching system is further improved.
In an embodiment, as shown in fig. 3, the control method further considers the influence of the network suffering from the denial of service attack, and comprehensively evaluates the stability of the current handover system, that is, the method includes:
step S400: and evaluating the stability of the system according to the maximum blocking rate which can be tolerated by the linear switching system and the blocking rate suffered by the current linear switching system.
The method comprises the following steps:
step S410: constructing a denial of service attack model:
Figure BDA0003435442020000111
Figure BDA0003435442020000112
wherein n (T, T) is a denial of service attack at [ T, T]Inner number of activations, | xi (T, T) | is denial of service attack [ T, T |)]Total duration of inner, τDIs to rejectAverage residence time of service attack, T*Is a denial of service attack at T, T]Mean time ratio of the components, eta and kappa as compensation parameters, T, T ∈ R≥0，T≥t，η,κ∈R≥0，τD＞R≥Δ，T*＞R＞1。
Step S420: calculating the maximum blocking rate which can be tolerated by the linear switching system:
Figure BDA0003435442020000113
wherein the content of the first and second substances,
Figure BDA0003435442020000114
Figure BDA0003435442020000115
step S430: calculating the blocking rate suffered by the current linear switching system
Figure BDA0003435442020000116
Step S440: judging whether the blocking rate F' suffered by the current linear switching system is smaller than the maximum blocking rate F which can be tolerated by the linear switching system, if so, indicating that the input state of the current linear switching system is stable, and if not, indicating that the input state of the current linear switching system is unstable.
Wherein, the blocking rate is represented as the frequency of the controller suffering from the denial of service attack in a signal interactive manner through a communication network. In this embodiment, the maximum blocking rate that the system can tolerate is derived according to the system parameters, and compared with the blocking rate actually suffered by the switching system in the current network, the stability of the current system in the current network is sequentially evaluated. By
Figure BDA0003435442020000121
It can be seen that the mean time ratio τ of the different unstable modes is chosen+The maximum blocking rate that the system can tolerate is different, illustrating the present controlThe method represents a trade-off between the mean-time ratio of unstable modes and the resilience of the system against denial-of-service attacks. Therefore, the system-related parameters can be adjusted reversely according to the blocking rate F' suffered by the current linear switching system, and the tolerable maximum blocking rate F can be increased appropriately, so as to further improve the stability of the system.
It is to be understood that the order of the steps mentioned in the above embodiments is not limited to the order in the above embodiments, and the execution order of the steps can be flexibly adjusted as long as the method can be implemented.
Accordingly, the present application also proposes a control architecture with a linear switching system with unstable mode, as shown in fig. 1, the system includes:
the switching system is used for switching different modes according to the switching signal, and the switching system is provided with a stable mode and an unstable mode;
a sampler for acquiring a current sampling time t according to a sampling sequencekSystem state x (t)k) And the mode σ (t) activatedk) And transmitted to the controller through the communication network;
a controller for acquiring the sampling signal of the sampler and processing to obtain a control signal
Figure BDA0003435442020000122
Figure BDA0003435442020000123
And transmits the control signal to the holder through a communication network, wherein,
Figure BDA0003435442020000124
the gain determined for the control method above;
the retainer is used for acquiring a control signal of the controller and continuously outputting the control signal to the actuator;
and the actuator is used for acquiring the control signal of the retainer and inputting the control signal into the switching system to update the system input signal.
In an embodiment, the sampler is set with a sampling interval Δ, which is the sampling interval Δ determined according to the control method above.
In an embodiment, the switching signal is a switching signal determined according to the above control method.
Specifically, the control system has been described above, and is not described herein again.
It is emphasized that, in the above control method, each model, the construction of the constraint condition and the expression of the tolerable maximum blocking rate are obtained by a great deal of deductive analysis of the applicant. In the application, the stability of the input state of the system can be improved by arranging a reasonable controller. Furthermore, on the basis of setting a reasonable controller, the sampling time interval and the switching signal are further optimized, and the stability of the input state of the system can be further improved by setting the reasonable controller, the sampling time interval and the switching signal. Furthermore, considering the denial of service attack, a denial of service attack model is constructed, the blocking rate suffered by the system and the maximum blocking rate which can be tolerated by the system are compared, the stability of the system can be evaluated, meanwhile, the maximum blocking rate which can be tolerated by the system can be improved by adjusting system parameters, and the stability of the input state of the system is further improved.
It will be understood by those skilled in the art that the foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included within the scope of the present invention.

Claims (10)

1. A method of controlling a linear switching system with unstable modes, comprising:
constructing a linear switching system model with interference terms:
Figure FDA0003435442010000011
Figure FDA0003435442010000012
wherein, x (t)) For system state, u (t) is the input signal, d (t) is the unknown bounded interference, σ (t) is the mode activated at time t, Aσ(t)、Bσ(t)、Dσ(t)Are respectively a weighting matrix Ai、Bi、DiIn the weighting matrix corresponding to the activated mode σ (t), i ∈ Γ ═ { 1., N }, N is the total number of modes of the system, where r stable modes are ΓsR, N-r unstable modes are Γu＝{r,...N}；
Constructing a controller model:
Figure FDA0003435442010000013
Uj≤μiUi，Ui>0，i,j∈Г,i≠j，Ui、Tifor the model to be parameterized, λi、μiSetting parameters for the model;
initialization model setting parameter mui>1，
Figure FDA0003435442010000014
Solving the controller model to obtain a gain Ki＝TiPi，
Figure FDA0003435442010000015
Collecting the current sampling time tkSystem state x (t)k) And the mode σ (t) activatedk) Updating the input signal according to the sampling information
Figure FDA0003435442010000016
Wherein the content of the first and second substances,
Figure FDA0003435442010000017
is the gain KiNeutralization of the activated modality σ (t)k) The corresponding gain.
2. The method of controlling a linear switching system with unstable mode according to claim 1, further comprising optimally selecting a sampling interval Δ:
Figure FDA0003435442010000018
wherein the content of the first and second substances,
Figure FDA0003435442010000019
Figure FDA00034354420100000110
is a matrix AiLogarithmic norm of;
Figure FDA0003435442010000021
satisfies the following conditions:
Figure FDA0003435442010000022
κi＝max{||Ai+BiKi||,||Di||}，κij＝max{||Aj+BjKi||,||Dj| l }, ε satisfies:
Figure FDA0003435442010000023
wherein ω is1i＝λiλmin(Pi)，ω2i＝||2PiBiKi||。
3. The method of controlling a linear switching system with unstable mode according to claim 2, further comprising optimizing the switching signal:
constructing a switching model:
Figure FDA0003435442010000024
Figure FDA0003435442010000025
wherein n isi(T, T) is the ith mode at [ T, T]Number of activations, Ti(T, T) is the ith mode at [ T, T]Total duration of inner, τaiIs the modality-dependent mean residence time, T, of the ith modality+(T, T) is all unstable modes in [ T, T ]]Total duration of inner, τ+Is that all unstable modes have a duration of [ T, T ]]Mean time of day, τ+＞1，n0iAnd χ is a compensation parameter;
constructing a switching constraint condition:
Figure FDA0003435442010000026
wherein the content of the first and second substances,
Figure FDA0003435442010000031
Figure FDA0003435442010000032
Figure FDA0003435442010000033
Figure FDA0003435442010000034
obtaining tau in switching model according to switching constraint condition+And τaiAnd determining a switching signal.
4. A control method for a linear switching system with unstable mode according to claim 3, characterized in that the control method further comprises evaluating the stability of the system according to the maximum blocking rate that the linear switching system can tolerate and the blocking rate that the current linear switching system suffers:
constructing a denial of service attack model:
Figure FDA0003435442010000035
Figure FDA0003435442010000036
wherein n (T, T) is a denial of service attack at [ T, T]Inner number of activations, | xi (T, T) | is denial of service attack [ T, T |)]Total duration of inner, τDIs the average residence time, T, of a denial of service attack*Is a denial of service attack at T, T]Mean time ratio of (T)*Greater than 1, eta and kappa are compensation parameters;
calculating the maximum blocking rate which can be tolerated by the linear switching system:
Figure FDA0003435442010000037
wherein the content of the first and second substances,
Figure FDA0003435442010000038
Figure FDA0003435442010000039
calculating the blocking rate suffered by the current linear switching system
Figure FDA00034354420100000310
Judging whether the blocking rate F' suffered by the current linear switching system is smaller than the maximum blocking rate F which can be tolerated by the linear switching system, if so, indicating that the input state of the current linear switching system is stable, and if not, indicating that the input state of the current linear switching system is unstable.
5. The method according to claim 4, wherein the method determines whether a current blocking rate F' suffered by the linear switching system is less than a maximum blocking rate F that can be tolerated by the linear switching system, and if not, the system parameters are adjusted in a reverse direction to increase the maximum blocking rate F that can be tolerated by the linear switching system.
6. The method of claim 4, wherein χ ≧ 0, η ≧ 0, and κ ≧ 0.
7. The method of claim 1, wherein the controller model is solved by matlab toolbox.
8. A control architecture for a linear switching system with unstable modes, comprising:
the switching system is used for switching different modes according to the switching signal, and the switching system is provided with a stable mode and an unstable mode;
a sampler for acquiring a current sampling time t according to a sampling sequencekSystem state x (t)k) And the mode σ (t) activatedk) And transmitted to the controller through the communication network;
a controller for acquiring the sampling signal of the sampler and processing to obtain a control signal
Figure FDA0003435442010000041
And transmits the control signal to the holder through a communication network, wherein,
Figure FDA0003435442010000042
is based onGain determined by the control method for a linear switching system with unstable mode according to claim 1;
the retainer is used for acquiring a control signal of the controller and continuously outputting the control signal to the actuator;
and the actuator is used for acquiring the control signal of the retainer and inputting the control signal into the switching system to update the system input signal.
9. The control architecture of a linear switching system with unstable mode according to claim 8, characterized in that the sampler is set with a sampling interval Δ determined according to the control method of a linear switching system with unstable mode according to claim 2.
10. The control architecture of a linear switching system with unstable mode according to claim 8, characterized in that said switching signal is a switching signal determined according to the control method of a linear switching system with unstable mode according to claim 3.
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