Method and device for stabilizing networked linear random system under continuous data packet loss

Abstract

The invention discloses a method and device for stabilizing a networked linear stochastic system under continuous data packet loss, and the method comprises the steps: constructing a linear stochastic dynamic model of a networked control system with continuous data packet loss based on an Italian linear stochastic system; considering control input with sampling holding and substituting the control input into the linear random dynamic model to obtain a continuous time closed-loop system model with time-varying and time-lag; in order to process time-varying and time-lag in the continuous-time closed-loop system model, a packet loss probability model is constructed by jointly representing double indexes of the maximum continuous packet loss frequency and the packet loss probability; a Halanay inequality is popularized to a multiple time delay type; and on the basis of the packet loss probability model, the multiple time-delay Halanay inequality and the Lyapunov stability theory, obtaining specific parameter conditions of global asymptotic mean square stability of the networked control system so as to enable a balance point of a continuous time closed-loop system model to be global asymptotic mean square stability. According to the method, the problem of system instability of the networked linear random system under continuous packet loss is solved.

Description

Technical Field

[0001] The present invention relates to the field of networked control systems and network security technology, and in particular to a method, apparatus, terminal equipment, computer-readable storage medium, and computer program product for stabilizing a networked linear random system under continuous data packet loss. Background Art

[0002] Networked control systems, with their advantages of low wiring costs, high flexibility, and high scalability, play an irreplaceable role in a wide range of fields, from industrial automation to smart grids. However, their reliance on communication networks also presents challenges such as latency, quantization errors, and packet loss. Packet loss, in particular, can disrupt control signal transmission, leading to system performance degradation and even instability, and has become a critical issue that needs to be addressed urgently.

[0003] Due to the inherent unreliability of communication networks, packet loss is an unavoidable phenomenon in networked control systems. Existing methods for handling packet loss in control systems can be mainly divided into three categories: asynchronous dynamic system methods, switching system methods, and Markov jump system methods. However, these methods are mainly oriented towards discrete-time systems and have difficulty accurately describing the dynamics of continuous-time systems with time-varying delays and random perturbations. This limitation highlights the need for alternative methods that can directly address the challenges posed by packet loss in continuous-time systems. Furthermore, existing research has mostly focused on deterministic systems and stochastic systems with additive noise, leaving a gap in the analysis of Ito-type stochastic systems with continuous packet loss. Summary of the Invention

[0004] In view of this, the present invention provides a method, apparatus, terminal device, computer-readable storage medium and computer program product for stabilizing a networked linear stochastic system under continuous packet loss, aiming to solve the problem of system instability of a networked linear stochastic system under continuous packet loss.

[0005] The first object of the present invention is to provide a method for stabilizing a networked linear stochastic system under continuous data packet loss.

[0006] A second object of the present invention is to provide a stabilization device for a networked linear random system under continuous data packet loss.

[0007] The third object of the present invention is to provide a terminal device.

[0008] A fourth object of the present invention is to provide a computer-readable storage medium.

[0009] A fifth object of the present invention is to provide a computer program product.

[0010] The first object of the present invention can be achieved by adopting the following technical solutions:

[0011] A stabilization method for a networked linear stochastic system under continuous packet loss, the method comprising:

[0012] Based on an Itô-type linear stochastic system, construct a linear stochastic dynamic model of a networked control system with continuous packet loss;

[0013] Consider a control input with sample and hold and substitute it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying delay;

[0014] To handle the time-varying delay in the continuous-time closed-loop system model, construct a packet loss probability model by jointly characterizing a dual index of the maximum number of consecutive packet losses and the packet loss rate;

[0015] Generalize the Halanay inequality to a multi-delay type Halanay inequality;

[0016] Based on the packet loss probability model, the multi-delay type Halanay inequality, and the Lyapunov stability theory, obtain the specific parameter conditions for the globally asymptotically mean-square stability of the networked control system, so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

[0017] Furthermore, let the linear matrix equation be:

[0018] (A + BK) T P + P(A + BK) + G T PG = -Q

[0019] Wherein, and respectively represent coefficient matrices related to the system state and the control input; K represents the gain matrix to be designed; represents a given positive definite symmetric matrix, represents the symmetric solution existing in the linear matrix equation;

[0020] The specific parameter conditions for the globally asymptotically mean-square stability of the obtained networked control system are:

[0021] If for a given positive definite matrix the linear matrix equation has a positive solution such that

[0022]

[0023] Wherein, a0 = ||A||, a1 = ||BK||, ||·|| represents the Euclidean norm of the matrix; λ m = λ min (P) represents the minimum eigenvalue of the matrix P, λ M = λmax (P) represents the maximum eigenvalue of matrix P, and a = λ min (Q) / λ M , h represents the sampling period; represents the upper bound of the possible number of consecutive packet losses that may occur in an interval.

[0024] Furthermore, the process of constructing the packet loss probability model includes:

[0025] Considering the packet loss on the sampler-to-controller channel, assume the packet loss rate is ρ (0 ≤ ρ < 1); the upper bound of the possible number of consecutive packet losses δ j , t j+1 ) that may occur in the interval is j where δ and δ j , is the set of non-negative integers;

[0026] Introduce a random variable to partition the time-delay interval as:

[0027]

[0028] where, τ(t) is a random variable that includes τ j (t), and τ j (t) is a time-varying delay;

[0029] The obtained packet loss probability model is:

[0030]

[0031] where, represents the event occurrence probability.

[0032] Furthermore, considering the system is periodic sampling, let the sampling period be h, and the control input u(t) generated by the zero-order hold is expressed as:

[0033] u(t) = Kx(t j ) = Kx(t - τ j (t))

[0034] where, t ∈ [t j , t j+1 ), represents the discrete sampling time sequence of successful data packet transmission from the sampler to the controller channel, τ j (t) is a time-varying delay, and K is the gain matrix to be designed.

[0035] Furthermore, the linear stochastic dynamic model of the networked control system with continuous packet losses constructed is:

[0036] dx(t) = (Ax(t) + Bu(t))dt + Gx(t)dw(t)

[0037] wherein, represents the state of the system, represents the control input of the system; and respectively represent coefficient matrices related to the system state and control input; the stochastic perturbation w(t) is a one-dimensional standard Wiener process defined on the complete probability space of

[0038] Furthermore, the generalization of the Halanay inequality to the multiple time-delay type Halanay inequality includes:

[0039] Let positive constants a, b i , satisfy If the function satisfies the differential inequality:

[0040]

[0041] where t ∈ [t0, +∞), then there is:

[0042]

[0043] where:

[0044] |v t |( i+1)h = sup θ∈[-(i+1)h，0] v(t + θ), γ > 0 is the unique positive root of the transcendental equation ; represents the continuous function space from the set of positive real numbers to the set of positive real numbers ; represents all continuous functions defined on taking values in and with the norm ; represents the interval

[0045] The second object of the present invention can be achieved by adopting the following technical solutions:

[0046] A stabilizing device for a networked linear stochastic system under continuous packet loss, the device includes:

[0047] The first construction module is used to construct a linear stochastic dynamic model of a networked control system with continuous packet loss based on an Itô-type linear stochastic system;

[0048] The second construction module is used to consider a control input with sample and hold and substitute it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying time delay;

[0049] The third construction module is used to construct a packet loss probability model by jointly characterizing a dual index of the maximum number of consecutive packet losses and the packet loss rate for dealing with the time-varying time delay in the continuous-time closed-loop system model;

[0050] The generalization module is used to generalize the Halanay inequality to the multi-time-delay type Halanay inequality;

[0051] The stabilization module is used to obtain specific parametric conditions for the global asymptotic mean-square stability of the networked control system based on the packet loss probability model, the multi-time-delay type Halanay inequality, and the Lyapunov stability theory, so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

[0052] The third objective of the present invention can be achieved by adopting the following technical solutions:

[0053] A terminal device includes a processor and a memory for storing programs executable by the processor. When the processor executes the programs stored in the memory, the method for stabilizing a networked linear stochastic system under continuous packet loss as described above is implemented.

[0054] The fourth objective of the present invention can be achieved by adopting the following technical solutions:

[0055] A computer-readable storage medium stores a program, and when the program is executed by a processor, the method for stabilizing a networked linear stochastic system under continuous packet loss as described above is implemented.

[0056] The fifth objective of the present invention can be achieved by adopting the following technical solutions:

[0057] A computer program product includes a computer program, and when the computer program is executed by a processor, the method for stabilizing a networked linear stochastic system under continuous packet loss as described above is implemented.

[0058] The present invention has the following beneficial effects compared with the prior art:

[0059] 1. The present invention for the first time obtains a global asymptotic mean-square stability criterion for a networked control system under continuous packet loss based on the multi-time-delay type Halanay inequality combined with the Lyapunov function method, which has low conservativeness.

[0060] 2. By jointly characterizing the dual indices of the maximum consecutive packet loss count and the packet loss rate, the present invention constructs a packet loss probability model, decomposes the time-varying time delay in the continuous-time closed-loop system into multiple time-invariant time delay intervals, and further transforms the random packet loss process into the sum of multiple deterministic probability events. Compared with the traditional Bernoulli distribution assumption for the packet loss process, the packet loss probability model proposed by the present invention is closer to the engineering reality.

[0061] 3. The present invention studies the stabilization problem of a class of Itô-type linear stochastic systems under continuous packet loss. Compared with modeling networked control systems as deterministic systems or stochastic systems with additive noise in traditional technologies, the Itô-type linear stochastic system is more in line with the actual object. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0063] Figure 1 It is a flowchart of the stabilization method for a networked linear stochastic system under continuous packet loss in Embodiment 1 of the present invention;

[0064] Figure 2 It is a network packet loss simulation diagram in Embodiment 1 of the present invention;

[0065] Figure 3 It is the state trajectory of the closed-loop system using the controller K in Embodiment 1 of the present invention: the single simulation experiment condition is the sampling period h = 0.04;

[0066] Figure 4 It is the mean-square trajectory of the closed-loop system using the controller K in Embodiment 1 of the present invention: the single simulation experiment condition is the sampling period h = 0.04;

[0067] Figure 5 It is a structural block diagram of the stabilization device for a networked linear stochastic system under continuous packet loss in Embodiment 2 of the present invention;

[0068] Figure 6 It is a structural block diagram of the terminal device in Embodiment 3 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0069] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. It should be understood that the specific embodiments described are only used to explain the present application and are not used to limit the present application.

[0070] Embodiment 1:

[0071] To overcome the influence of continuous packet loss on networked control systems, this embodiment provides a stabilization method for networked linear stochastic systems under continuous packet loss, which can be referred to Figure 1 , and specifically includes the following steps:

[0072] S101. Based on Itô-type linear stochastic systems, construct a linear stochastic dynamic model of a networked control system with continuous packet loss.

[0073] The linear stochastic dynamic model of the networked control system with continuous packet loss is:

[0074] dx(t) = (Ax(t) + Bu(t))dt + Gx(t)dw(t) (1)

[0075] Wherein, represents the state of the system, represents the control input of the system; and respectively represent coefficient matrices related to the system state and control input; the random perturbation w(t) is a one-dimensional standard Wiener process defined on the complete probability space .

[0076] S102. Consider the control input with sample and hold and substitute it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying time delay.

[0077] This embodiment considers that the system adopts periodic sampling with a sampling period of h. The control input u(t) generated by the zero-order hold can be expressed as:

[0078] u(t) = Kx(t j ) = Kx(t - τ j (t)) (2)

[0079] Wherein, t ∈ [t j , t j+1 )), is the discrete sampling time sequence for successful transmission of data packets from the sampler to the controller channel, τj (t) is a time-varying time delay, and K is the gain matrix to be designed.

[0080] Substituting equation (2) into equation (1), the closed-loop networked control system model is obtained as:

[0081] dx(t) = (Ax(t) + BKx(t - τ j (t)))dt + Gx(t)dw(t)

[0082] where t ∈ [t j , t j+1 ).

[0083] Over the entire time period, the above equation can be written as:

[0084] dx(t) = (Ax(t) + BKx(t - τ(t)))dt + Gx(t)dw(t) (3)

[0085] where τ(t) is a random variable including τ j (t).

[0086] S103. To handle the time-varying time delay in the continuous-time closed-loop system, a packet loss probability model is constructed by jointly characterizing the dual indices of the maximum continuous packet loss times and the packet loss rate.

[0087] In this embodiment, the packet loss on the channel from the sampler to the controller is considered. Assuming the packet loss rate is ρ (0 ≤ ρ < 1), the upper bound of the possible continuous packet loss times δ j on the interval [t j+1 is j where δ , j , is the set of non-negative integers. The following random variable is introduced to partition the time delay interval:

[0088]

[0089] where

[0090] Thus, the packet loss probability model is obtained as follows:

[0091]

[0092] where represents the event occurrence probability.

[0093] S104. Generalize the Halanay inequality to the multi-time-delay type.

[0094] In this embodiment, the Halanay inequality is generalized to the multi-time-delay type:

[0095] Let \(a\) and \(b\) be positive constants i , satisfy If the function satisfies the differential inequality:

[0096]

[0097] where \(t\in[t_0,+\infty)\).

[0098] Then there is:

[0099]

[0100] where \(t\in[t_0,+\infty)\); \(\vert v\vert\) t \(\vert\) (i+1)h \(=\sup\) θ∈[-(i+1)h，0] \(v(t + \theta)\), \(\gamma>0\) is the unique positive root of the transcendental equation ; denotes the space of continuous functions from the set of positive real numbers to the set of positive real numbers ; denotes all functions defined on with values in and with norm ]>; denotes the interval

[0101] S105. Based on the packet loss probability model, the multiple time-delay type Halanay inequality, and the Lyapunov stability theory, specific parameter conditions are obtained to make the equilibrium point of the continuous-time closed-loop system model with time-varying time delay globally asymptotically mean-square stable.

[0102] Given a positive definite symmetric matrix For the following linear matrix equation, there exists a symmetric solution

[0103] (A + BK) T P+P(A + BK)+G T PG=-Q (4)

[0104] Define \(a_0=\vert\vert A\vert\vert\), \(a_1=\vert\vert BK\vert\vert\), \(\vert\vert\cdot\vert\vert\) represents the Euclidean norm of the matrix; \(\lambda\) m \(=\lambda\) min (P) represents the minimum eigenvalue of the matrix P, \(\lambda\) M \(=\lambda\) max (P) represents the maximum eigenvalue of the matrix P, \(a = \lambda\) min (Q) / \lambda M ,

[0105] If for a given positive definite matrix the linear matrix equation (4) has a positive definite solution \(P\) such that then the equilibrium point of the system (3) is globally asymptotically mean square stable.

[0106] Proof: For any given initial time the system (3) can be rewritten as:

[0107] \(dx(t)=((A + BK)x(t)+BK(x(t-\tau(t))-x(t)))dt+Gx(t)dw(t)\ (5)\)

[0108] where \(t\in[t_0,+\infty)\).

[0109] To achieve global asymptotic mean square stability, construct the following Lyapunov function:

[0110] \(V(t,x(t))=x(t)\) T \(Px(t)\)

[0111] Thus, the infinitesimal generator can be obtained:

[0112]

[0113] where \(\zeta(t,x(t)) = 2x\) T (t)PBK(x(t-\tau(t))-x(t)).

[0114] [[ID=C40]]According to equation (5), we have:

[0115]

[0116] where guaranteeing when \(t-\tau(t)\geq0\).

[0117] Furthermore, \(\zeta(t,x(t))\) can be decomposed into \(\zeta\) a (t,x(t))+\(\zeta\) w (t,x(t)), where:

[0118] It is easy to know that and according to the packet loss probability model, it can be estimated that:

[0119] According to equations (4) and (6), we have:

[0120]

[0121] where \(|\cdot|\) represents the supremum norm.

[0122] make Then there is Further application of the multiple-delay Halanay inequality yields Furthermore, based on the existing stability theory, it can be proved that the equilibrium point of system (3) is globally asymptotically stable.

[0123] The following simulation experiments verify the technical effects obtained by the method provided in this embodiment:

[0124] This embodiment considers a networked control system, assuming that the network packet loss rate ρ = 0.1, the maximum number of consecutive packet losses The packet loss process simulation diagram is shown in Figure 2 . Consider the system parameters are set as follows:

[0125]

[0126] First, consider the linear algebra Riccati equation A T P+PA-PBR -1 B T P=-Q1; if ||G T PG||≤λ min (Q1), which guarantees A T P+PA+G T PG-PBR -1 B T The existence of positive solutions for P=-Q; given parameters R=[1] 1×1 , the positive definite solution can be obtained by Matlab After calculation, we get ||G T PG||=0.0867,λ min (Q1)=1.9, satisfying ||G T PG||≤λ min (Q1), and then we get a=0.8373; when the sampling period is selected as h=0.04, we can calculate Given the initial time t0 = 0, the initial state x0 = [2 1] T , using the control gain matrix K = -R -1 B T P=[-1.7397 -0.8510]. The state response curve and mean square trajectory of system (3) are respectively as follows: Figure 3 and Figure 4 As shown in the figure, it can be seen that the system state can be stabilized quickly under the stabilization method provided by this embodiment, which shows its effectiveness and feasibility.

[0127] Those skilled in the art can understand that all or part of the steps in the methods of the above embodiments can be completed by a program instructing relevant hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0128] It should be noted that although the method operations of the above embodiments are described in a specific order in the drawings, this does not require or imply that these operations must be performed in that specific order, or that all the shown operations must be performed to achieve the desired result. On the contrary, the depicted steps can be executed in a changed order. Additionally or alternatively, certain steps can be omitted, multiple steps can be combined into one step for execution, and / or one step can be decomposed into multiple steps for execution.

[0129] Embodiment 2:

[0130] As Figure 5 shown, this embodiment provides a stabilization device for a networked linear stochastic system under continuous packet loss. The device includes a first construction module 501, a second construction module 502, a third construction module 503, a generalization module 504, and a stabilization module 505, where:

[0131] The first construction module 501 is used to construct a linear stochastic dynamic model of a networked control system with continuous packet loss based on an Itô-type linear stochastic system;

[0132] The second construction module 502 is used to consider a control input with sample and hold and substitute it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying time delay;

[0133] The third construction module 503 is used to construct a packet loss probability model by jointly characterizing a dual index of the maximum continuous packet loss times and the packet loss rate for dealing with the time-varying time delay in the continuous-time closed-loop system model;

[0134] The generalization module 504 is used to generalize the Halanay inequality to a multi-time-delay type Halanay inequality;

[0135] The stabilization module 505 is used to obtain specific parameter conditions for the globally asymptotically mean-square stability of the networked control system based on the packet loss probability model, the multi-time-delay type Halanay inequality, and the Lyapunov stability theory, so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

[0136] For the specific implementation of each module in this embodiment, reference can be made to Embodiment 1 above, which will not be elaborated here one by one. It should be noted that the device provided in this embodiment is only exemplified by the above division of each functional module. In practical applications, the above functions can be allocated to different functional modules as needed, that is, the internal structure is divided into different functional modules to complete all or part of the functions described above.

[0137] Embodiment 3:

[0138] This embodiment provides a terminal device, which can be a computer, such as Figure 6 shown, which is connected by a system bus 601 to a processor 602, a memory, an input device 603, a display 604, and a network interface 605. The processor is used to provide computing and control capabilities. The memory includes a non-volatile storage medium 606 and an internal memory 607. The non-volatile storage medium 606 stores an operating system, a computer program, and a database. The internal memory 607 provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. When the processor 602 executes the computer program stored in the memory, the method for stabilizing a networked linear stochastic system under continuous packet loss in Embodiment 1 above is implemented as follows:

[0139] Based on the Itô-type linear stochastic system, construct a linear stochastic dynamic model of a networked control system with continuous packet loss;

[0140] Consider a control input with sample and hold and substitute it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying time delay;

[0141] To handle the time-varying time delay in the continuous-time closed-loop system model, construct a packet loss probability model by jointly characterizing a dual index of the maximum number of consecutive packet losses and the packet loss rate;

[0142] Generalize the Halanay inequality to the multi-time-delay type Halanay inequality;

[0143] Based on the packet loss probability model, the multi-time-delay type Halanay inequality, and the Lyapunov stability theory, obtain the specific parametric conditions for the global asymptotic mean-square stability of the networked control system, so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

[0144] Embodiment 4:

[0145] This embodiment provides a computer-readable storage medium that stores a computer program. When the computer program is executed by a processor, the method for stabilizing a networked linear stochastic system under continuous packet loss in Embodiment 1 above is implemented as follows:

[0146] Based on Itô-type linear stochastic systems, a linear stochastic dynamic model of a networked control system with consecutive packet losses is constructed;

[0147] Considering the control input with sample-and-hold and substituting it into the linear stochastic dynamic model, a continuous-time closed-loop system model with time-varying delay is obtained;

[0148] To handle the time-varying delay in the continuous-time closed-loop system model, a packet loss probability model is constructed by jointly characterizing the dual indices of the maximum consecutive packet loss number and the packet loss rate;

[0149] The Halanay inequality is extended to the multi-delay-type Halanay inequality;

[0150] Based on the packet loss probability model, the multi-delay-type Halanay inequality, and the Lyapunov stability theory, specific parametric conditions for the globally asymptotically mean-square stability of the networked control system are obtained, so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

[0151] It should be noted that the computer-readable storage medium of this embodiment can be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0152] Embodiment 5:

[0153] This embodiment provides a computer program product, including a computer program, which when executed by a processor implements the stabilization method of the networked linear stochastic system under continuous packet loss in the above Embodiment 1, as follows:

[0154] Based on Itô-type linear stochastic systems, a linear stochastic dynamic model of a networked control system with consecutive packet losses is constructed;

[0155] Considering the control input with sample-and-hold and substituting it into the linear stochastic dynamic model, a continuous-time closed-loop system model with time-varying delay is obtained;

[0156] To handle the time-varying delay in the continuous-time closed-loop system model, a packet loss probability model is constructed by jointly characterizing the dual indices of the maximum consecutive packet loss number and the packet loss rate;

[0157] Generalize the Halanay inequality to the multiple time-delay type Halanay inequality;

[0158] Based on the packet loss probability model, the multiple time-delay type Halanay inequality, and the Lyapunov stability theory, specific parametric conditions for the globally asymptotically mean-square stability of the networked control system are obtained, so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

[0159] As mentioned above, it is only a preferred embodiment of the present invention patent, but the protection scope of the present invention patent is not limited thereto. Any person skilled in the art within the scope disclosed by the present invention patent, according to the technical solution and inventive concept of the present invention patent, makes equivalent substitutions or changes, and all belong to the protection scope of the present invention patent.

Claims

1. A method for stabilizing a networked linear stochastic system under continuous packet loss, characterized in that, The method includes: Based on the Itô-type linear stochastic system, constructing a linear stochastic dynamic model of a networked control system with consecutive packet losses; Considering the control input with sample and hold and substituting it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying delays; To handle the time-varying delays in the continuous-time closed-loop system model, constructing a packet loss probability model by jointly characterizing the dual indices of the maximum consecutive packet loss number and the packet loss rate; Generalizing the Halanay inequality to the multi-delay-type Halanay inequality; Based on the packet loss probability model, the multi-delay-type Halanay inequality, and the Lyapunov stability theory, obtaining the specific parametric conditions for the globally asymptotically mean-square stability of the networked control system so that the equilibrium point of the continuous-time closed-loop system model is globally asymptotically mean-square stable.

2. The calming method according to claim 1, wherein Let the linear matrix equation be: (A + BK) T P + P(A + BK)+G T PG = -Q Among them, and respectively represent coefficient matrices related to the system state and control input; K represents the gain matrix to be designed; represents a given positive definite symmetric matrix, represents the symmetric solution existing for the linear matrix equation; The specific parametric conditions for the globally asymptotically mean-square stability of the obtained networked control system are: If for a given positive definite matrix the linear matrix equation has a positive solution such that where \(a_0 = \|A\|\), \(a_1=\|BK\|\), and \(\|\cdot\|\) represents the Euclidean norm of a matrix; \(\lambda\) m =\(\lambda\) min \((P)\) represents the minimum eigenvalue of matrix \(P\), \(\lambda\) M =\(\lambda\) max \((P)\) represents the maximum eigenvalue of matrix \(P\), \(a = \lambda\) min (Q) / \(\lambda\) M , where \(h\) represents the sampling period; represents the upper bound of the possible number of consecutive packet losses that may occur in an interval.

3. The calming method according to claim 1, characterized in that, The process of constructing the packet loss probability model includes: Consider packet loss on the sampler-to-controller channel, assuming a packet loss rate of ρ (0 ≤ ρ < 1); in the interval [t j , t j+1 ) The possible number of consecutive packet losses δ that may occur j has an upper bound of where δ j , is the set of non-negative integers; Introducing random variables to partition the delay intervals as: Among them, τ(t) is a random variable that includes τ j (t), and τ j (t) is a time-varying delay; The obtained packet loss probability model is: Among them, represents the probability of an event occurring.

4. The calming method according to claim 1, characterized in that, Considering that the system is periodic sampling, let the sampling period be h, and the control input u(t) generated by the zero-order hold is expressed as: u(t) = Kx(t j ) = Kx(t - τ j (t)) where \(t\in[t j ,t j+1 )\), denotes the sequence of discrete sampling instants at which data packets are successfully transmitted from the sampler to the controller channel, \(\tau j (t)\) is the time-varying time delay, and \(K\) is the gain matrix to be designed.

5. The calming method according to any one of claims 1 to 4, characterized in that, The constructed linear stochastic dynamic model of the networked control system with consecutive packet losses is: dx(t) = (Ax(t) + Bu(t))dt + Gx(t)dw(t) Among them, represents the state of the system, represents the control input of the system; and represent coefficient matrices related to the system state and control input respectively; the random perturbation w(t) is a one-dimensional standard Wiener process defined on the complete probability space .

6. The calming method according to any one of claims 1 to 4, characterized in that, The generalization of the Halanay inequality to the multi-delay-type Halanay inequality includes: Let the positive constant satisfy If the function satisfies the differential inequality: Where, t ∈ [t0, +∞), then there is: Where: |v t | (i+1)h =sup θ∈[-(i+1)h，0] v(t + θ), γ > 0 is the unique positive root of the transcendental equation ; denotes the continuous function space from the set of positive real numbers to the set of positive real numbers ; denotes all functions defined on with values in and with norm ; denotes the interval 7. A stabilizing device for a networked linear stochastic system under continuous packet loss, characterized in that, The device includes: The first construction module for constructing a linear stochastic dynamic model of a networked control system with consecutive packet losses based on the Itô-type linear stochastic system; The second construction module for considering the control input with sample and hold and substituting it into the linear stochastic dynamic model to obtain a continuous-time closed-loop system model with time-varying delays; The third construction module for constructing a packet loss probability model by jointly characterizing the dual indices of the maximum consecutive packet loss number and the packet loss rate to handle the time-varying delays in the continuous-time closed-loop system model; The generalization module for generalizing the Halanay inequality to the multi-delay-type Halanay inequality; ​ 8. A terminal device, comprising a processor and a memory for storing processor-executable programs, characterized in that, ​ 9. A computer-readable storage medium having a computer program stored thereon, characterized in that, ​ 10. A computer program product, characterized in that, ​

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