CN114326398B - Control method and control system of linear switching system with unstable mode - Google Patents
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Abstract
The invention discloses aA control method and a control system of a linear switching system with an unstable mode comprise the following steps: constructing a linear switching system model with interference terms: constructing a controller model: U j ≤μ i U i ，U i >0, i, j εΓ, i+.j; initializing model setting parameter mu i >1，Solving the controller model to obtain gainCollecting the current sampling time t k System state x (t) k ) The activated modality sigma (t k ) Updating the input signal based on the sampled informationWherein,for the gain K i Medium and activated mode sigma (t k ) Corresponding gain. According to the method and the device, the mode which can be stabilized and the mode which cannot be stabilized are considered simultaneously when the model is built, the gain of the controller model is solved, and the control data of the switching system is updated according to the solved gain.
Description
Technical Field
The invention belongs to the technical field of control of linear switching systems, and particularly relates to a control method and a control system of a linear switching system with an unstable mode.
Background
Because of the specificity of the switching systems, many switching systems have unstable modes, and meanwhile, because of the rapid development of networks, the control of the switching systems through network connection controllers is a current hot spot method. However, because of the instability of the network and the complexity of the switching, the input state of the switching system is unstable, especially when the system is subject to denial of service attack, the system is difficult to maintain the stability of the input state, so it is important to study the control method of the linear switching system with an unstable mode so as to maintain the stability of the input state of the system.
Disclosure of Invention
In order to meet the above defects or improvement demands of the prior art, the invention provides a control method and a control system of a linear switching system with an unstable mode, and aims to improve the stability of an input signal of the linear switching system with the unstable mode.
To achieve the above object, according to one aspect of the present invention, there is provided a control method of a linear switching system with an unstable mode, comprising:
constructing a linear switching system model with interference terms: wherein x (t) is the system state, u (t) is the input signal, d (t) is unknown bounded interference, sigma (t) is the mode activated at time t, A σ(t) 、B σ(t) 、D σ(t) Respectively are weighting matrix A i 、B i 、D i In the weighting matrix corresponding to the activated mode sigma (t), i epsilon gamma = {1, & gt, N }, N is the total mode number of the system, wherein r stable modes are gamma # s = {1,..r }, N-r unstable modes are Γ u ＝{r,...N}；
Constructing a controller model:U j ≤μ i U i ，U i ＞0，i,j∈Γ,i≠j，U i 、T i lambda is the parameter to be solved for the model i 、μ i Setting parameters for the model;
initializing model setting parameter mu i ＞1，Solving the controller model to obtain gain K i ＝T i P i ，/>
Collecting the current sampling time t k System state x (t) k ) The activated modality sigma (t k ) Updating the input signal based on the sampled informationWherein (1)>For the gain K i Medium and activated mode sigma (t k ) Corresponding gain.
In one embodiment, the control method further comprises optimizing the selected sampling interval Δ:
wherein,
as matrix A i Logarithmic norms of (a);
the method meets the following conditions:
κ i ＝max{||A i +B i K i ||,||D i ||}，κ ij ＝max{||A j +B j K i ||,||D j || } ε satisfies:wherein omega 1i ＝λ i λ min (P i )，ω 2i ＝||2P i B i K i ||。
In one embodiment, the control method further comprises optimizing the switching signal:
constructing a switching model:
wherein n is i (T, T) is the ith modality at [ T, T]Number of activations within T i (T, T) is the ith modality at [ T, T]Total duration of time, τ ai Is the mean residence time, T, of the modality dependence of the ith modality + (T, T) is that all unstable modes are in [ T, T]Total duration of time, τ + Is that all unstable modes have duration of [ T, T ]]Average time ratio within τ + ＞1，n 0i And χ is the compensation parameter;
and (3) constructing a switching constraint condition:
wherein,
obtaining tau in the switching model according to the switching constraint condition + And τ ai A switching signal is determined.
In one embodiment, the control method further comprises evaluating the stability of the system based on a maximum blocking rate that the linear switching system can tolerate and a blocking rate that the current linear switching system is subject to:
constructing a denial of service attack model:
where n (T, T) is the denial of service attack at [ T, T]The number of activations in, |xi (T, T) | is the denial of service attack at [ T, T ]]Total duration of time, τ D Is the average residence time of denial of service attacks, T * Is a denial of service attack at [ T, T]Average time duty ratio, T * > 1, η and κ are compensation parameters;
calculating the maximum blocking rate which can be tolerated by the linear switching system:
wherein,
calculating the blocking rate suffered by the current linear switching system
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 blocking rate F' suffered by the current linear switching system is smaller than the maximum blocking rate F tolerated by the linear switching system, and if not, the system parameters are reversely adjusted to increase the maximum blocking rate F tolerated by the linear switching system.
In one embodiment, χ is 0 or greater, η is 0 or greater, and κ is 0 or greater.
In one embodiment, the controller model is solved by a matlab toolbox.
According to another aspect of the present invention there is provided a control system for a linear switching system with an unstable mode, comprising:
the switching system is used for switching different modes according to the switching signals and is provided with a stabilizable mode and an unsteady mode;
the sampler is used for collecting the current sampling time t according to the sampling sequence k System state x (t) k ) The activated modality sigma (t k ) And transmits the data to the controller through a communication network;
a controller forAcquiring the sampling signal of the sampler and processing to obtain a control signalAnd transmitting the control signal to the holder via the communication network, wherein +_>A gain determined according to the control method of the linear switching system with unstable modes described above;
the retainer is used for acquiring the 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 switching system to update the system input signal.
In one embodiment, the sampler is set with a sampling interval Δ determined according to the control method of the linear switching system with unstable modes 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 modes described above.
According to the method, the linear switching system model is built, the controller model is built based on the linear switching system model, the stabile mode and the unsteady mode are considered simultaneously when the model is built, different initialization parameters are set for different modes, the gain of the controller model is solved, the control data of the switching system is updated according to the solved gain, and in the method, the stability of the input state of the system can be improved by setting 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 through setting the reasonable controller, the sampling time interval and the switching signal. Still further, 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 tolerated by the system are compared, the stability of the system can be evaluated, and meanwhile, the maximum blocking rate tolerated by the system can be improved by adjusting the system parameters, so that the stability of the input state of the system is further improved.
Drawings
FIG. 1 is a schematic diagram of a switching system control architecture according to an embodiment of the present application;
FIG. 2 is a flow chart of the steps of a method of controlling a linear switching system with unstable modes in an embodiment of the present application;
fig. 3 is a flow chart of steps of a method of controlling a linear switching system with unstable modes in another embodiment of the present application.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
To facilitate an understanding of the present invention, a linear switching system control architecture will be described first. Fig. 1 is a schematic diagram of an architecture 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, a mode set is denoted as Γ= {1,.. s = {1,..r }, unstable mode is denoted Γ u = { r..n }. When the switching system is determined, the mode is determined. During the system operation, the switching system is switched from one mode to the other mode according to the set switching signal, and the mode which is successfully switched is activated, which is called an activated mode sigma (t k )，σ(t k ) E Γ= {1,..n }, work is performed by the active modality. During this period, the sampler will collect according to the settingSampling the switching system by the sample sequence to obtain the current sampling time t k System state x (t) k ) The activated modality sigma (t k ) And transmitted to the controller through a communication network, wherein a fixed sampling interval is arranged between two adjacent samples. The controller receives the sampling information of the sampler through the communication network and processes the sampling information to obtain a control signalWherein (1)>For the current active mode sigma (t) k ) Corresponding gain coefficients. The controller transmits a control signal to the retainer through the communication network, and the retainer outputs the control signal to the actuator continuously for a preset time period. After receiving the control signal, the actuator inputs the control signal into the switching system to update the input signal of the system.
In the control system, the design of the controller, the selection of sampling time intervals and the setting of switching signals can all influence the stability of the input signals of the switching system, and the controller is connected into the system through a communication network, so that the stability of the input signals of the switching system can be influenced by network attack.
Based on this, the present application proposes a control method of a linear switching system with an unstable mode, as shown in fig. 2, and in an embodiment, the control method includes:
step S100: optimizing the controller design.
Specifically, the design process of the optimization controller is as follows:
step S110: constructing a linear switching system model with interference terms:
wherein x (t) is the system state, u (t) is the input signal, and d (t) isUnknown bounded interference. Wherein, the parameter representing the system state can be flexibly selected according to the requirement. Sigma (t) is the mode activated at time t, A σ(t) 、B σ(t) 、D σ(t) Respectively are weighting matrix A i 、B i 、D i A is a weighting matrix corresponding to the activated mode sigma (t) i 、B i 、D i For the weighting matrix of the ith mode, i e Γ= {1,..once, N }, where N is the total mode number of the system, and r stable modes are Γ s = {1,..r }, N-r unstable modes are Γ u = { r..n }. Wherein, the weighting matrix A i 、B i 、D i After the switching system is determined, the switching system can be determined according to the system parameters and is a known parameter. At the time of model suggestion, it is assumed that at all the switching moments, the state of the system does not jump.
Step S120: constructing a controller model:U j ≤μ i U i ，U i ＞0，i,j∈Γ,i≠j，U i 、T i lambda is the parameter to be solved for the model i 、μ i Parameters are set for the model.
Wherein,respectively representing transpose matrices of the corresponding matrices.
Step S130: initializing model setting parameter mu i ＞1，Solving the controller model to obtain gain K i ＝T i P i ，/>
Wherein,representation matrix U i Is a matrix of inverse of (a). />Indicating that when i is E f s Lambda is at the time i ＞0，Indicating that when i is E f u Lambda is at the time i ＜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 method, when the set parameters are initialized, the set parameters with different conditions corresponding to different modes are comprehensively considered in the design of the controller, and the stability of the input signals of the switching system can be improved. It will be appreciated that solving the inequality results in a range of solutions, and that a solution may be arbitrarily selected from the range. Specifically, the matlab tool box can be used to solve the model for the gain K i When solving through the matlab tool box, an optimal solution can be automatically output.
Step S140: collecting the current sampling time t k System state x (t) k ) The activated modality sigma (t k ) Updating the input signal based on the sampled informationWherein (1)>Is gain K i Medium and activated mode sigma (t k ) Corresponding gain.
Determining a sampling sequence of a systemWhere k represents the sampling number, N 0 Represents the number of samplings, where t 0 =0. It will be appreciated that the sampling sequence has a fixed sampling interval delta.
Specifically, the switching system can be sampled by a sampler, and the sampling is performedCurrent sampling time t k System state x (t) k ) The activated modality sigma (t k ) And transmitted to the controller through the communication network, the controller calculates control signals according to the sampling informationAnd feeds back to the switching system through the communication network to update the input signal of the switching system. Wherein (1)>Is a mode sigma (t) k ) The corresponding gain, e.g. the mode activated is the 7 th mode, is selected from the gain K 7 As calculated gain.
In the application, for the linear switching system with an unstable mode, the controller is designed by the method, and the stability of signal input of the switching system can be improved by comprehensively considering the steady state and the unsteady state.
In one 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:
wherein,as matrix A i Logarithmic norm of>
κ i ＝max{||A i +B i K i ||,||D i ||}，κ ij ＝max{||A j +B j K i ||,||D j || where || a| represents the spectral norm of a;
ε satisfies:
wherein omega 1i ＝λ i λ min (P i )，ω 2i ＝||2P i B i K i I, wherein λ min (P i ) Representation matrix P i Is a minimum feature value of (a).
Step S220: and solving the sampling interval delta according to the sampling interval constraint condition.
It should be noted that, by determining the solution range of the sampling time interval Δ by the above method, one solution may be arbitrarily selected from the 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:
is provided withFor a switching sequence of the system, in which any two successive switching moments s l Sum s l+1 Satisfy s l+1 -s l ≥τ d ，τ d Is the dwell time of the switching signal.
Wherein T, t.epsilon.R ≥0 ，T≥t，n i (T, T) is the ith modality at [ T, T]Number of activations within T i (T, T) is the ith modality at [ T, T]Total duration of time, τ ai Is the average residence time of the mode dependence of the ith mode, satisfies tau ai ≥τ d 。T + (T, T) is an unstable mode in [ T, T]Total duration of time in T, t.epsilon.R ≥0 ，T≥t，χ∈R ≥0 ，τ + ＞R ＞1 ，τ + Is the average time duty cycle of the unstable mode. R is R ≥a Representing a real number greater than or equal to a.
Step S320: and (3) constructing a switching constraint condition:
wherein,
step S330: obtaining tau in the switching model according to the switching constraint condition + And τ ai A switching signal is determined.
In this embodiment, different constraint conditions are set according to different modes, and when determining the sampling interval, multiple wakefulness of the stabile mode and the unsteady mode is 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 denial of service attack on the network, and comprehensively evaluates the stability of the current switching system, namely, the control method includes:
step S400: the stability of the system is assessed based on the maximum blocking rate that the linear switching system can tolerate and the blocking rate that the current linear switching system is subject to.
The method comprises the following steps:
step S410: constructing a denial of service attack model:
where n (T, T) is the denial of service attack at [ T, T]The number of activations in, |xi (T, T) | is the denial of service attack at [ T, T ]]Total duration of time, τ D Is the average residence time of denial of service attacks, T * Is a denial of service attack at [ T, T]The average time duty ratio, eta and kappa are compensation parameters, T, T E R ≥0 ，T≥t，η,κ∈R ≥0 ，τ D ＞R ≥Δ ，T * ＞R ＞1 。
Step S420: calculating the maximum blocking rate which can be tolerated by the linear switching system:
wherein,
step S430: calculating the blocking rate suffered by the current linear switching system
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.
The blocking rate is expressed as the frequency of the controller signal interactive through the communication network and is subject to denial of service attack. In this embodiment, by deriving the maximum blocking rate that the system can tolerate according to the system parameters, the stability of the current system under the current network is sequentially evaluated compared with the blocking rate that the switching system actually suffers under the current network. From the following componentsIt can be seen that the average time duty ratio τ of the different unstable modes is selected + The maximum blocking rate that the system can tolerate is also different, which illustrates that the control method embodies a trade-off between the average time duty cycle of the unstable mode and the elasticity of the system against denial of service attacks. Therefore, the relevant parameters of the system can be reversely adjusted according to the blocking rate F' suffered by the current linear switching system, and the tolerable maximum blocking rate F can be properly increased, so that the stability of the system is further improved.
It will be appreciated 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 may be flexibly adjusted, so long as the method can be implemented.
Correspondingly, the application also proposes a control system of a linear switching system with an unstable mode, as shown in fig. 1, the system comprises:
the switching system is used for switching different modes according to the switching signals and is provided with a stabilizable mode and an unsteady mode;
the sampler is used for collecting the current sampling time t according to the sampling sequence k System state x (t) k ) The activated modality sigma (t k ) And transmits the data to the controller through a communication network;
a controller for acquiring the sampling signal of the sampler and processing to obtain a control signal And transmitting the control signal to the holder via the communication network, wherein +_>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 delta, which is determined according to the control method above.
In an embodiment, the switching signal is a switching signal determined according to the control method above.
Specifically, the control system is specifically described above, and will not be described again.
It should be emphasized that in the above control method, the construction of each model, constraint condition and expression of the tolerable maximum occlusion rate are all obtained by the applicant through a large number of deduction analyses. 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 through setting the reasonable controller, the sampling time interval and the switching signal. Still further, 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 tolerated by the system are compared, the stability of the system can be evaluated, and meanwhile, the maximum blocking rate tolerated by the system can be improved by adjusting the system parameters, so that the stability of the input state of the system is further improved.
It will be readily appreciated by those skilled in the art that the foregoing is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. A method of controlling a linear switching system with an unstable mode, comprising:
constructing a linear switching system model with interference terms: wherein x (t) is the system state, u (t) is the input signal, d (t) is unknown bounded interference, sigma (t) is the mode activated at time t, A σ(t) 、B σ(t) 、D σ(t) Respectively are weighting matrix A i 、B i 、D i In the weighting matrix corresponding to the activated mode sigma (t), i epsilon gamma = {1, & gt, N }, N is the total mode number of the system, wherein r stable modes are gamma # s = {1,..r }, N-r unstable modes are Γ u ＝{r，…N}；
Constructing a controller model:U j ≤μ i U i ，U i ＞0，i，j∈Γ，i≠j，U i 、T i the parameters to be solved for the model are,λ i 、μ i setting parameters for the model;
initializing model setting parameter mu i ＞1，Solving the controller model to obtain gain K i ＝T i P i ，/>
Collecting the current sampling time t k System state x (t) k ) The activated modality sigma (t k ) Updating the input signal based on the sampled informationWherein (1)>For the gain K i Medium and activated mode sigma (t k ) Corresponding gain.
2. The method of controlling a linear switching system with unstable modes according to claim 1, wherein the method further comprises optimizing the selection of sampling intervals Δ:
wherein,
as matrix A i Logarithmic norms of (a);
the method meets the following conditions:
κ i ＝max{||A i +B i K i ||，||D i ||}，κ ij ＝max{||A j +B j K i ||，||D j || } ε satisfies:
wherein omega 1i ＝λ i λ min (P i )，ω 2i ＝||2P i B i K i ||。
3. The method of controlling a linear switching system with unstable modes according to claim 2, wherein the method of controlling further comprises optimizing the switching signal:
constructing a switching model:
wherein n is i (T, T) is the ith modality at [ T, T]Number of activations within T i (T, T) is the ith modality at [ T, T]Total duration of time, τ ai Is the mean residence time, T, of the modality dependence of the ith modality + (T, T) is that all unstable modes are in [ T, T]Total duration of time, τ + Is that all unstable modes have duration of [ T, T ]]Average time ratio within τ + ＞1，n oi And χ is the compensation parameter;
and (3) constructing a switching constraint condition:
wherein,
obtaining tau in the switching model according to the switching constraint condition + And τ ai A switching signal is determined.
4. A method of controlling a linear switching system with an unstable mode according to claim 3, wherein the method further comprises assessing the stability of the system based on the maximum blocking rate tolerated by the linear switching system and the blocking rate suffered by the current linear switching system:
constructing a denial of service attack model:
where n (T, T) is the denial of service attack at [ T, T]The number of activations in, |xi (T, T) | is the denial of service attack at [ T, T ]]Total duration of time, τ D Is the average residence time of denial of service attacks, T * Is a denial of service attack at [ T, T]The average time-to-time ratio within the time frame,T * > 1, η and κ are compensation parameters;
calculating the maximum blocking rate which can be tolerated by the linear switching system:
wherein,
calculating the blocking rate suffered by the current linear switching system
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 of claim 4, wherein determining whether the current blocking rate F' of the linear switching system is less than the maximum blocking rate F tolerated by the linear switching system, and if not, reversely adjusting the system parameters to increase the maximum blocking rate F tolerated by the linear switching system.
6. The method of claim 4, wherein χ is equal to or greater than 0, η is equal to or greater than 0, and κ is equal to or greater than 0.
7. The method of controlling a linear switching system with unstable modes according to claim 1, wherein the controller model is solved by a matlab toolbox.
8. A control system for a linear switching system with an unstable mode, comprising:
the switching system is used for switching different modes according to the switching signals and is provided with a stabilizable mode and an unsteady mode;
the sampler is used for collecting the current sampling time t according to the sampling sequence k System state x (t) k ) The activated modality sigma (t k ) And transmits the data to the controller through a communication network;
a controller for acquiring the sampling signal of the sampler and processing to obtain a control signalAnd transmitting the control signal to the holder via the communication network, wherein +_>A gain determined for the control method of a linear switching system with unstable modes according to claim 1;
the retainer is used for acquiring the 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 switching system to update the system input signal.
9. The control system of a linear switching system with an unstable mode according to claim 8, wherein the sampler is set with a sampling interval Δ determined by the control method of a linear switching system with an unstable mode according to claim 2.
10. A control system of a linear switching system with an unstable mode according to claim 8, wherein the switching signal is a switching signal determined according to the control method of a linear switching system with an unstable mode according to claim 3.
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| CN112859605A (en) * | 2021-01-12 | 2021-05-28 | 哈尔滨工业大学 | Switching system control method with control quantity anti-shake and interference suppression performance |
| CN113093539A (en) * | 2021-03-29 | 2021-07-09 | 西北工业大学 | Wide-area flight robust self-adaptive switching control method based on multi-mode division |
| CN113406930A (en) * | 2021-05-24 | 2021-09-17 | 杭州电子科技大学 | Finite time control method of state saturation networked industrial system |
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| 基于输出采样数据的非线性切换系统网络化同步;潘睿;周磊;;现代电子技术;20180703(第13期);全文 * |
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