A dynamic self-triggered filtering method under incomplete semi-markov kernel information

Abstract

The application discloses a dynamic self-triggering filtering method under incomplete semi-Markov kernel information, relates to the technical field of automatic control and signal processing, and aims at the problems of difficult acquisition of semi-Markov kernel information, heavy communication burden and insufficient peak value control. The semi-Markov information known / unknown set is classified, the known parameters and the lower bound are utilized, a self-triggering mechanism containing dynamic variables is designed to determine the data transmission time, a modal dependent filter is constructed, the Lyapunov theory and the linear matrix inequality technology are combined to verify the mean square exponential stability and the robust performance of the filtering error system, and the problems of high conservativeness and resource waste of the existing method are solved.

Description

Technical Field

[0001] This invention relates to the fields of automatic control and signal processing technology, and in particular to a dynamic self-triggered filtering method under incomplete semi-Markov kernel information. Background Technology

[0002] Semi-Markov transition systems, as an important class of stochastic switching systems, exhibit mode switching that depends not only on the current mode but also on the dwell time in that mode, making them more general and practical than traditional Markov transition systems. However, in real-world applications, due to difficulties in data acquisition and uncertainties in statistical characteristics, the semi-Markov kernel information of the system is often incomplete, posing challenges to system stability analysis and filter design.

[0003] In the field of state estimation (filtering) for semi-Markov jump systems, the energy peak l2-l ∞ Performance is a key indicator because it can constrain the impact of external disturbances on the system's maximum output (e.g., limiting grid voltage fluctuations and peak vibrations in mechanical systems). In existing research, event-triggered mechanisms reduce communication burden by "on-demand transmission," but traditional static event-triggered mechanisms require continuous monitoring of system output, increasing hardware costs; dynamic event-triggered mechanisms introduce dynamic variables to optimize triggering conditions, but have not been extended to self-triggered scenarios; static self-triggered mechanisms, while not requiring real-time monitoring, result in excessively high communication frequencies due to amplified triggering errors.

[0004] Existing filtering techniques based on incomplete semi-Markov kernels still have the following problems:

[0005] 1. Insufficient utilization of semi-Markov kernel information: In real-world scenarios, semi-Markov kernels (which describe the joint probability of dwell time and mode transition) often exhibit "incomplete" characteristics due to data acquisition limitations and parameter uncertainties (the dwell time probability density function or transition probability of some modes is unknown). Existing methods usually discard some known semi-Markov kernel information directly, resulting in overly conservative filtering designs.

[0006] 2. Waste of communication resources and physical components: Event-triggered mechanisms require external devices for continuous monitoring of system output, leading to complex system structure and increased usage costs. Furthermore, while static self-triggered mechanisms do not require constant monitoring of the output signal, they lack dynamic adjustment mechanisms, making triggering conditions easily met and failing to achieve the goal of reducing communication frequency.

[0007] 3. High complexity of filter design: Traditional filter design requires finding the "strictly decreasing" Lyapunov function, which can easily lead to coupling problems between the system matrix and the noise matrix, increasing the difficulty of solving the problem and resulting in excessive conservatism in the filter design.

[0008] To address the aforementioned issues, there is an urgent need for a filtering method that can cope with the lack of semi-Markov kernel information in complex environments, alleviate communication pressure, reduce conservatism, and has performance constraints, so as to meet the requirements of actual industrial production for state estimation. Summary of the Invention

[0009] To address the above technical problems, this invention provides a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, comprising the following steps:

[0010] S1. Construct a semi-Markov transition system and a filtering error system; classify the semi-Markov kernel information; design a mode-dependent filter and use the measurement output sent by the dynamic self-triggering mechanism to update the state;

[0011] S2. The trigger function based on the dynamic event triggering mechanism is obtained by amplifying the norm boundary of the triggering error; the update law of the time-varying triggering threshold is designed.

[0012] Classify the semi-Markov kernel information, defining the mode after the nth transition as 'a', the mode after the (n+1)th transition as 'b', and the mode transition probability as . , where r n and r n+1 Let ρ represent the modes of the nth and (n+1)th transitions of the system, respectively; define the dwell time of the system between the nth and (n+1)th transitions as τ, and the dwell time probability distribution as ρ. ab (τ)=Pr(t n+1 -t n =τ|r n+1 =b,r n =a), where t n and t n+1 Let these represent the times of the nth and (n+1)th transitions of the system, respectively; Indicates a semi-Markov nucleus. ;

[0013] S3, Analyze the stability of the filtering error system and l2-l ∞ performance;

[0014] S4. Solve for the filter gain.

[0015] The technical solution further defined in this invention is:

[0016] Furthermore, in step S1, a semi-Markov transition system model is defined, and the mode set of the semi-Markov transition system is set as follows: The state equation in discrete time is:

[0017]

[0018] Where M represents the total number of modes, Indicates the system status. Indicates the measurement output. Let ω(k) ∈ l2[0,∞) represent the signal to be estimated; let v(k) ∈ l2[0,∞) represent the external disturbance; and let v(k) ∈ l2[0,∞) represent the measurement noise. A is a semi-Markov process, representing the system modes; A a B a C a D a E a This represents the known parameter matrix for mode a.

[0019] As described above, in a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, step S1 involves... Due to the incomplete nature of the information, the semi-Markov kernel information set of mode a is defined as follows: express A fully known set of modes; express An incomplete set of known modalities; Representing π ab Given that ρ ab (τ) An unknown set of modes; Representing π ab Unknown and ρ ab (τ) is a known set of modes; Representing π ab Unknown and ρ ab (τ) An unknown set of modes;

[0020] For ρ ab (τ) Unknown situation ,set up The unknown residence time distribution ρ of the system in mode a is represented. ab The lower bound of the probability of (τ), ,in This represents the upper bound of the system's residence time in mode a.

[0021] As described above, in a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, step S1 involves designing a mode-dependent filter ∑ f The measurement output y(k) is sent using a dynamic self-triggering mechanism. m Update status:

[0022]

[0023] Where, k m Indicates the trigger time. Indicates the filtering state. This represents the filtered output; for k∈[t]n ,t n+1 -1],d(k)=kt n Represents the dwell time count; for s(k)=a, d(k)=ι, A fa (ι), B fa (ι), C fa (ι) represents the filter gain to be designed.

[0024] As described above, in a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, step S1 defines the augmented state. ,error disturbance And the triggering error g(k) = y(k) - y(k) m Derive the filtering error system for:

[0025]

[0026] in,

[0027] .

[0028] As described above, in a dynamic self-triggering filtering method based on incomplete semi-Markov kernel information, step S2 involves a triggering function based on a dynamic event triggering mechanism. δ∈[0,1] represents the trigger threshold coefficient. By amplifying the norm boundary of the trigger error g(k), the trigger function of the dynamic self-triggering mechanism is obtained. ;

[0029] First, the system matrix properties are used to derive the following...

[0030]

[0031] in, , , ω M and v M These represent the peak values ​​of the external disturbance ω(k) and the measurement noise v(k), respectively.

[0032] Therefore, the triggering condition for the dynamic self-triggering mechanism is:

[0033]

[0034] in, α>0 represents the adjustment coefficient, and η(k) represents the time-varying trigger threshold.

[0035] As described above, in a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, step S2 involves designing the update law for the time-varying trigger threshold η(k):

[0036]

[0037] Where β>0 and λ>0 represent adjustment coefficients, with an initial value η(0)≥0; when αβ-λ>0, η(k)≥0 is guaranteed.

[0038] As described above, in a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, step S3 introduces a symmetric matrix P. a (ι)>0 and relaxation matrix G a , where the symmetric matrix P a (ι) represents the Lyapunov matrix and relaxation matrix G under mode a and residence time ι. a Used to handle nonlinear couplings present in matrix elements;

[0039] Let l a and h a The Lyapunov function energy attenuation parameter is represented; the filter gain must satisfy the following linear matrix inequality: there exists l a >0 and h a >0, satisfies

[0040]

[0041]

[0042]

[0043]

[0044] in, It is a symmetric matrix, and its non-zero elements are:

[0045] , , ,

[0046] , , ,

[0047] , ,

[0048] ,

[0049] , ;

[0050] The final performance index is ,in

[0051]

[0052] .

[0053] As described above, in a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, step S4 involves solving the linear matrix inequality constraints from step S3 to obtain the symmetric matrix P. a (ι), Relaxation matrix G a and filter gain:

[0054] , and .

[0055] The beneficial effects of this invention are:

[0056] (1) In this invention, the incomplete semi-Markov kernel information is fully utilized to reduce conservatism; by classifying the next mode according to the known / unknown semi-Markov kernel, and combining the transition probability π of the known part, ab Conditional probability ρ of dwell time ab (τ) and unknown ρ ab The lower bound of (τ) The invention derives non-conservative stability conditions, avoiding performance redundancy caused by discarding known portions of semi-Markov kernel information in existing technologies. In the same RLC circuit example, the average mean square error of the invention is reduced from 0.0209 to 0.0036, improving the estimation accuracy by approximately 83%.

[0057] (2) In this invention, the dynamic self-triggering mechanism optimizes communication resources; it does not require continuous monitoring of the system measurement output y(k), but only relies on the current triggering time k. m Based on the system model parameters, determine the next triggering time k. m+1 Furthermore, by adaptively updating the triggering conditions through the dynamic variable η(k), the number of communications and filtering errors are balanced. In the RLC circuit example with 50 sampling experiments, only 23 data transmissions are required (49 transmissions are required for the static self-triggering mechanism), reducing the communication burden by about 53% and without significant increase in error, making it suitable for bandwidth-constrained networked control systems.

[0058] (3) In this invention, the peak output control requirements are met, and it is suitable for engineering scenarios; l2-l is adopted. ∞ The (energy-peak) performance index can strictly suppress the influence of external disturbances and measurement noise on the peak output of the system, and solve the defect that traditional H∞ filters cannot control the peak value; for example, in RLC circuits, it can control the peak fluctuation of inductor current within ±0.05A, which meets the safety operation constraints of power electronic equipment.

[0059] (4) In this invention, the stability is guaranteed to be reliable and adaptable to random switching. By constructing a non-monotonic decreasing Lyapunov function with dynamic variable η(k), the mean square exponential stability of the filtering error system is rigorously proven. Even in the scenario where the semi-Markov kernel information is incomplete and the mode is randomly switched, the state estimation error can still be guaranteed to converge to a small range, ensuring the long-term reliable operation of the system. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0061] Figure 2 This is a comparison diagram of the trajectory of the system output and the filter estimation output under complete semi-Markov kernel information in an embodiment of the present invention;

[0062] Figure 3 This is a comparison diagram of the trajectory of the system output and the filter estimation output under incomplete semi-Markov kernel information in an embodiment of the present invention.

[0063] Figure 4 This is a comparison chart of filtering errors under complete and incomplete semi-Markov kernel information in the embodiments of the present invention;

[0064] Figure 5 This is a comparison chart of the filtering errors of the method of the present invention and existing filtering methods under incomplete semi-Markov kernel information;

[0065] Figure 6 This is a comparison chart of filtering errors under the dynamic self-triggering mechanism and the static self-triggering mechanism in an embodiment of the present invention. Detailed Implementation

[0066] This embodiment provides a dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, such as... Figure 1 As shown, it includes the following steps:

[0067] S1. Construct a semi-Markov transition system and a filtering error system; classify the semi-Markov kernel information; design a mode-dependent filter and use the measurement output sent by the dynamic self-triggering mechanism to update the state.

[0068] Definition of a semi-Markov jumping system model: Let the mode set of a semi-Markov jumping system be... The state equation in discrete time is:

[0069]

[0070] Where M represents the total number of modes, Indicates the system status. Indicates the measurement output. Let ω(k) ∈ l2[0,∞) represent the signal to be estimated; let v(k) ∈ l2[0,∞) represent the external disturbance; and let v(k) ∈ l2[0,∞) represent the measurement noise. A is a semi-Markov process, representing the system modes; A a B a C a D a E a This represents the known parameter matrix for mode a.

[0071] Semi-Markov kernel information classification: Define the mode after the nth transition of the system as a, and the mode after the (n+1)th transition as b. Then the mode transition probability of the system is... , where r n and r n+1 These represent the modes of the system's nth and (n+1)th transitions, respectively.

[0072] Let τ be the dwell time of the system between the nth and (n+1)th transitions. Then the dwell time probability distribution is ρ. ab (τ)=Pr(t n+1 -t n =τ|r n+1 =b,r n =a), where t n and t n+1 Let these represent the times of the nth and (n+1)th transitions of the system, respectively; Indicates a semi-Markov nucleus. .

[0073] Targeting the semi-Markov nucleus Due to the incomplete nature of the information, the semi-Markov kernel information set of mode a is defined as follows:

[0074] express A fully known set of modes;

[0075] express An incomplete set of known modalities;

[0076] Representing π ab Given that ρ ab (τ) An unknown set of modes;

[0077] Representing π ab Unknown and ρ ab (τ) is a known set of modes;

[0078] Representing π ab Unknown and ρ ab (τ) An unknown set of modes;

[0079] For ρ ab (τ) Unknown situation ,set up The unknown residence time distribution ρ of the system in mode a is represented. ab The lower bound of the probability of (τ), ,in This represents the upper bound of the system's residence time in mode a.

[0080] Filtering error system construction: Design of mode-dependent filter ∑ f The measurement output y(k) is sent using a dynamic self-triggering mechanism. m Update status:

[0081]

[0082] Where, k m Indicates the trigger time. Indicates the filtering state. This represents the filtered output; for k∈[t] n ,t n+1 -1],d(k)=kt n Represents the dwell time count; for s(k)=a, d(k)=ι, A fa (ι), B fa (ι), C fa (ι) represents the filter gain to be designed.

[0083] Define augmented state ,error disturbance And the triggering error g(k) = y(k) - y(k) m Derive the filtering error system for:

[0084]

[0085] in,

[0086] .

[0087] S2. The trigger function based on the dynamic event triggering mechanism is obtained by amplifying the norm boundary of the triggering error; the update law of the time-varying triggering threshold is designed.

[0088] Trigger condition derivation: Trigger function based on dynamic event triggering mechanism δ∈[0,1] represents the trigger threshold coefficient. By amplifying the norm boundary of the trigger error g(k), the trigger function of the dynamic self-triggering mechanism is obtained. .

[0089] The specific process involves deriving the following using the properties of the system matrix:

[0090]

[0091] in, , , ω M and v M These represent the peak values ​​of the external disturbance ω(k) and the measurement noise v(k), respectively.

[0092] Therefore, the triggering condition for the dynamic self-triggering mechanism can be obtained as follows:

[0093]

[0094] in, α>0 represents the adjustment coefficient, and η(k) represents the time-varying trigger threshold.

[0095] Trigger threshold update law: Design an update law for the time-varying trigger threshold η(k) to counteract the frequent triggering caused by the amplification of ‖g(k)‖.

[0096]

[0097] Where β>0 and λ>0 represent adjustment coefficients, with an initial value η(0)≥0; when αβ-λ>0, η(k)≥0 can be guaranteed.

[0098] S3, Analyze the stability of the filtering error system and l2-l ∞ performance.

[0099] To solve the mean square exponential stability and l2-l of the filtering error system ∞ Performance constraints, introducing a symmetric matrix P a (ι)>0 (Lyapunov matrix at mode a and residence time ι) and relaxation matrix G a (Handling nonlinear couplings in matrix elements).

[0100] Let l a and h a Represent the Lyapunov function energy attenuation parameter; the design of the filter gain must satisfy the following linear matrix inequality: there exists l a >0 and h a >0, satisfies

[0101]

[0102]

[0103]

[0104] .

[0105] in, It is a symmetric matrix, and its non-zero elements are:

[0106] , , ,

[0107] , , ,

[0108] , ,

[0109] ,

[0110] , .

[0111] The final performance index is ,in

[0112]

[0113] .

[0114] S4. Solve for the filter gain: Solve the linear matrix inequality constraints in step S3 using the toolbox to obtain the symmetric matrix P. a (ι), Relaxation matrix G a and filter gain:

[0115] , and .

[0116] The system in this embodiment includes the following functional modules:

[0117] 1. Semi-Markov Jumping System Modeling Module: Used to establish the state-space model of a semi-Markov jumping system with incomplete semi-Markov kernel information, defining the modal space, system matrix, and semi-Markov kernel classification. .

[0118] 2. Dynamic self-triggering module: Used to implement the dynamic self-triggering mechanism and calculate the triggering error boundary. Update the dynamic variable η(k) and determine the trigger time k. m The output of the measured trigger time is y(k). m ).

[0119] 3. Data Interaction Module: Used for triggered data transmission between the sensor and the filter, only at k m Transmit y(k) in real time m This reduces the communication burden.

[0120] 4. Filter Design Module: Used to construct mode-dependent l2-l ∞ Filter, based on y(k) m Output estimated state With estimated signal .

[0121] 5. Stability and Performance Verification Module: Used to verify the mean square exponential stability and l²-l² of the filtering error system through Lyapunov functions and linear matrix inequalities. ∞ Performance, the output filter gain that meets the conditions.

[0122] In this embodiment, taking an RLC circuit system (3 operating modes) as an example, the circuit has 3 operating modes (mode 1: full load, mode 2: light load, mode 3: half load) due to component aging (such as resistance value drift) and load switching.

[0123] The objective of this embodiment is to realize the inductor current (i) in an RLC circuit. L ), capacitor voltage (U) C The accurate estimation reduces the number of communications between the sensor and the filter, while keeping peak output fluctuations within a safe range.

[0124] The following is the actual implementation process of the method in this embodiment:

[0125] State of RLC circuit The system model is obtained based on Kirchhoff's laws; the state matrix is... ,in , , These represent resistance, inductance, and capacitance, respectively.

[0126] Configure the parameters of the RLC circuit: , , , , , , .

[0127] System matrix settings: To facilitate computer control, a sampling period of 0.5s is set to obtain the discrete system state matrix parameters; in addition, other system matrix parameters are as follows: C a=I, E1=[1 1], E2=[1 -1], E3=[-1 1], a=1,2,3; I represents an identity matrix with appropriate dimensions.

[0128] Semi-Markov kernel parameter settings: Upper bound of dwell time is , , .

[0129] In the first case, the information of the semi-Markov kernel is completely known;

[0130] The transition probability matrix is:

[0131] ;

[0132] Conditional probability ρ of dwell time ab (τ):

[0133] , ,

[0134] , ,

[0135] , .

[0136] In the second case, the information of the semi-Markov kernel is not fully known, where ρ 13 (τ), ρ 32 (τ), π 31 π 32 unknown; .

[0137] Dynamic self-triggering and filtering parameter settings: the triggering parameters are δ=1, α=1, β=1.1, λ=0.2, η(0)=15; the Lyapunov parameters are l1=0.6, l2=0.5, l3=0.6, h1=1.1, h2=1.2, h3=1.1; the disturbance and noise are ω(k)=2exp(-10k)sin(k) and v(k)=5exp(-2k).

[0138] First, the semi-Markov transition system is modeled: the above parameters are input through the semi-Markov transition system modeling module to generate a system state-space model, and the model is classified according to the known and unknown semi-Markov kernel information.

[0139] Then, dynamic self-triggering: the dynamic self-triggering module calculates in real time. With η(k), 23 trigger times k are determined from 50 samples. m Only 23 measurement signals y(k) were transmitted. m ).

[0140] Next, the linear matrix inequality constraints are solved: the stability and performance verification module calls the MATLAB toolbox to solve the linear matrix inequality constraints to obtain the filter gain and l2-l. ∞ The performance index γ = 9.2936.

[0141] Ultimately, filter verification: The filter design module is loaded with gain, and the output z(k) is... The simulation results show that:

[0142] (1) Under the fully semi-Markov kernel information, the method of this embodiment estimates the system as follows: Figure 2 As shown, the filtering error e(k) converges to below 0.01.

[0143] (2) Under incomplete semi-Markov kernel information, the method in this embodiment estimates the system as follows: Figure 3 As shown, although the error is slightly higher than that of the case with complete semi-Markov kernel information, it still converges stably; the estimation errors under complete / incomplete semi-Markov kernel information are as follows: Figure 4 As shown; the error comparison between the method in this embodiment and existing methods is as follows. Figure 5 As shown, the performance is significantly lower than existing filtering methods based on incomplete semi-Markov kernel information.

[0144] (3) The dynamic self-triggered mechanism reduces the number of communication calls by 53% compared to the static self-triggered mechanism, with no significant increase in error. The estimation errors under the two different triggering mechanisms are as follows: Figure 6 As shown.

[0145] This embodiment verifies that in an RLC circuit system, the method described in this embodiment can still ensure the stability of the mean square exponent of the filtering error system under incomplete semi-Markov kernel information, satisfying l2-l. ∞ It improves performance while significantly reducing communication overhead, making it suitable for scenarios such as power electronics and circuit control that require random switching of system state estimation.

[0146] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A dynamic self-triggered filtering method based on incomplete semi-Markov kernel information, characterized in that: Includes the following steps: S1. Construct a semi-Markov jump system and a filtering error system; Classify the semi-Markov kernel information; design a mode-dependent filter and use the measurement output sent by the dynamic self-triggering mechanism to update the state; Targeting the semi-Markov nucleus Due to the incomplete nature of the information, the semi-Markov kernel information set of mode a is defined as follows: express A fully known set of modes; express An incomplete set of known modalities; Representing π ab Given that ρ ab (τ) An unknown set of modes; Representing π ab Unknown and ρ ab (τ) is a known set of modes; Representing π ab Unknown and ρ ab (τ) An unknown set of modes; For ρ ab (τ) Unknown situation ,set up The unknown residence time distribution ρ of the system in mode a is represented. ab The lower bound of the probability of (τ), ,in This represents the upper bound of the system's residence time in mode a; Design a mode-dependent filter ∑ f The measurement output y(k) is sent using a dynamic self-triggering mechanism. m Update status: Where, k m Indicates the trigger time. Indicates the filtering state. This represents the filtered output; for k∈[t] n ,t n+1 -1],d(k)=kt n Represents the dwell time count; for s(k)=a, d(k)=ι, A fa (ι), B fa (ι), C fa (ι) represents the filter gain to be designed; S2. The trigger function based on the dynamic event triggering mechanism is obtained by amplifying the norm boundary of the triggering error; the update law of the time-varying triggering threshold is designed. Trigger function based on dynamic event triggering mechanism δ∈[0,1] represents the trigger threshold coefficient. By amplifying the norm boundary of the trigger error g(k), the trigger function of the dynamic self-triggering mechanism is obtained. ; First, the system matrix properties are used to derive the following... in, , , ω M and v M These represent the peak values ​​of the external disturbance ω(k) and the measurement noise v(k), respectively. Therefore, the triggering condition for the dynamic self-triggering mechanism is: in, α>0 represents the adjustment coefficient, and η(k) represents the time-varying trigger threshold; Classify the semi-Markov kernel information, defining the mode after the nth transition as 'a', the mode after the (n+1)th transition as 'b', and the mode transition probability as . , where r n and r n+1 Let ρ represent the modes of the nth and (n+1)th transitions of the system, respectively; define the dwell time of the system between the nth and (n+1)th transitions as τ, and the dwell time probability distribution as ρ. ab (τ)=Pr(t n+1 -t n =τ|r n+1 =b,r n =a), where t n and t n+1 Let these represent the times of the nth and (n+1)th transitions of the system, respectively; Indicates a semi-Markov nucleus. ; S3, Analyze the stability of the filtering error system and l2-l ∞ performance; S4. Solve for the filter gain.

2. The dynamic self-triggered filtering method under incomplete semi-Markov kernel information according to claim 1, characterized in that: In step S1, a semi-Markov transition system model is defined, and the mode set of the semi-Markov transition system is set as follows. The state equation in discrete time is: Where M represents the total number of modes, Indicates the system status. Indicates the measurement output. Let ω(k) ∈ l2[0,∞) represent the signal to be estimated; let v(k) ∈ l2[0,∞) represent the external disturbance; and let v(k) ∈ l2[0,∞) represent the measurement noise. A is a semi-Markov process, representing the system modes; A a B a C a D a E a This represents the known parameter matrix for mode a.

3. The dynamic self-triggered filtering method under incomplete semi-Markov kernel information according to claim 2, characterized in that: In step S1, the augmented state is defined. ,error disturbance And the triggering error g(k) = y(k) - y(k) m Derive the filtering error system for: in, 。 4. The dynamic self-triggered filtering method under incomplete semi-Markov kernel information according to claim 3, characterized in that: In step S2, the update law for the time-varying trigger threshold η(k) is designed: Where β>0 and λ>0 represent adjustment coefficients, with an initial value η(0)≥0; when αβ-λ>0, η(k)≥0 is guaranteed.

5. The dynamic self-triggered filtering method under incomplete semi-Markov kernel information according to claim 4, characterized in that: In step S3, a symmetric matrix P is introduced. a (ι)>0 and relaxation matrix G a , where the symmetric matrix P a (ι) represents the Lyapunov matrix and relaxation matrix G under mode a and residence time ι. a Used to handle nonlinear couplings present in matrix elements; Let l a and h a The Lyapunov function energy attenuation parameter is represented; the filter gain must satisfy the following linear matrix inequality: there exists l a >0 and h a >0, satisfies in, It is a symmetric matrix, and its non-zero elements are: ， ， ， ， ， ， ， ， ， ， ； The final performance index is ,in 。 6. The dynamic self-triggered filtering method under incomplete semi-Markov kernel information according to claim 5, characterized in that: In step S4, the linear matrix inequality constraints in step S3 are solved to obtain the symmetric matrix P. a (ι), Relaxation matrix G a and filter gain: , and .

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