Quantized dynamic event-triggered h-infinity control method, device and system based on interval 2-type t-s fuzzy markov jump system

Abstract

The application relates to a kind of quantization dynamic event trigger control mode, device and system based on interval 2 type T-S fuzzy Markov jump system, the system includes N control links, each control link includes: step S1: the interval 2 type T-S fuzzy Markov jump system with partially unknown transition probability and random occurrence coupling delay is constructed;Step S2: the model of Markov jump system target node is constructed;Step S3: according to the step S1 and S2, the synchronous error system is established according to the set synchronous error;Step S4: according to the measurement output of step S1 output, the controller is designed, acts on step S5;Step S5: design quantization dynamic event trigger mechanism;Step S6: system reaches synchronization, output error;Step S7: using mode related Lyapunov function ensures the system finite time synchronization problem.Compared with the existing event trigger mechanism, the bandwidth utilization is further optimized, the data communication overhead is reduced, the data update frequency is kept low, and the time required for the system to reach stability is shortened.

Description

Technical Field

[0001] This invention belongs to the field of Markov jump system control, specifically relating to a quantitative dynamic event triggering control method, device and system based on a two-class TS fuzzy Markov jump system. Background Technology

[0002] Markov jump systems are versatile hybrid systems used for structural simulation or parameter mutations, with wide applications in aerospace, industrial manufacturing, and robotics. Throughout operation, the system continuously jumps between different modes based on internal or external disturbances, component failures, structural disconnections, and other factors. It is well known that communication congestion can lead to long delays, increased packet loss, and reduced throughput, inevitably degrading system stability, performance, and reliability. By establishing a robust connection between sampling and control and system measurements, the frequency of data transmission is effectively reduced, alleviating communication burden.

[0003] In practical applications, the main focus is on addressing coupling delays, whether constant or time-varying. Due to factors such as component failures, network attacks, and external noise, random system disturbances and node communication delays may occur in real-world scenarios. The literature (Sakthivel R, Alzahrani F, Selvaraj P, et al. Synchronization of complex dynamical networks with random coupling delay and actuator faults[J]. ISAtransactions, 2019, 94: 57-69.) studies the synchronization problem of neutral complex networks in Markov jump systems, considering coupling time delays and actuator faults. The literature (Ren Y, Jiang H, Li J, et al. Finite-timesynchronization of stochastic complex networks with random coupling delay via quantized aperiodically intermittent control[J]. Neurocomputing, 2021, 420:337-348.) considers the topic of hybrid time-varying and delayed stochastic complex networks, with the authors focusing on the finite-time synchronization problem using improved quantized aperiodically intermittent control techniques.

[0004] In addition, many scholars have confirmed that event-triggered mechanisms are one of the methods to reduce resource waste. The literature (Zhang L, Liang H, Sun Y, et al. Adaptive event-triggered fault detection scheme for semi-Markovian jump systems with output quantization[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 51(4): 2370-2381.) introduces a new DETM that has confirmed the quantization of output in hidden Markov jump systems. Practicality of performance. Reference (Zhang Tingting, Gao Jinfeng, Li Jiahao. Event Triggering of Discrete Markov Jump Systems) Quantization Output Feedback Control. Computer Measurement & Control [J]. 2019, 27(03), 72-78.) This paper studies the dissipative control model of discrete Markov jump systems and designs a fuzzy asynchronous quantization controller. It is evident that improving communication efficiency is of great significance in practical applications. Summary of the Invention

[0005] The following is an overview of the subject matter described in detail herein. This overview is not intended to limit the scope of the claims.

[0006] This invention relates to a quantization dynamic event triggering based on a two-class TS fuzzy Markov transition system in an interval. Control methods, devices, and systems to further optimize bandwidth utilization, reduce data communication overhead, and maintain a low data update frequency.

[0007] In a first aspect, the present invention relates to a quantized dynamic event triggering based on an interval-type TS fuzzy Markov transition system. The control method includes the following steps:

[0008] Step S1: Construct a range-2 type TS fuzzy Markov jump system with partially unknown transition probabilities and randomly occurring coupling delays;

[0009] Step S2: Construct a model of the target node in the Markov transition system;

[0010] Step S3: Based on the synchronization error set in steps S1 and S2, establish a synchronization error system;

[0011] Step S4: Based on the measurement output from step S1, design a fuzzy logic circuit with random faults. The controller acts on step S5;

[0012] Step S5: Design a dynamic event triggering mechanism by combining a hysteresis uniform quantizer with a dynamic event triggering scheme;

[0013] Step S6: Output error. If the output error is not 0, return to step S4; otherwise, end the process. The system has reached its target. synchronous;

[0014] Step S7: The modally dependent Lyapunov function ensures the finite-time operation of the system. Synchronization issues.

[0015] 2. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0016] Step S1: Consider a class of interval-based 2-type TS fuzzy Markov jump systems consisting of N nodes, with partially unknown transition probabilities and randomly occurring coupling delays. The i-th fuzzy rule of this model can be expressed as:

[0017] Fuzzy rule i: If yes , yes ,…,and yes ,but

[0018]

[0019] in Represents the state vector; and These represent the measurement output and control output, respectively. Describe the control inputs when the actuator fails. It is a disturbance input. satisfy Instantaneous variable delay. The external coupling configuration matrices for both time-delayed and non-time-delayed models are respectively derived from... and This indicates that both are symmetric matrices. and It is an internal coupling matrix. Random variable. Its characteristic is that it has a Bernoulli distribution (when delayed information exchange occurs). It equals 1 when there is no delayed information exchange. (equal to 0). , , , , , and It is a constant matrix with known dimensions. Is it a membership function? Connected intervals, class 2 TS fuzzy fuzzy sets. This indicates the system switching mode of the Markov chain.

[0020] Furthermore, the transition probability matrix Corresponding to:

[0021] In other words, only matrices Some elements are known, as shown in the case of a 3 × 3 matrix:

[0022]

[0023] The "?" represents an unspecified element. Continuing, this leads to a finite set. It can be used To describe it in order to conduct subsequent analysis:

[0024]

[0025] 3. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0026] Step S2: Construct a model of the target node in the Markov transition system;

[0027] The target node network of a class 2 TS fuzzy Markov transition system with partially unknown transition probabilities and randomly occurring coupling delays can be described as follows:

[0028]

[0029] in This corresponds to the state trajectory of the target node in a type 2 TS fuzzy Markov transition system. The controlled output and measurement output of the target node are determined by... and express.

[0030] 4. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0031] Step S3: Based on the synchronization error set in steps S1 and S2, establish a synchronization error system;

[0032] Based on the above system and target node system, the following error system is generated:

[0033]

[0034] in It is a synchronization error unique to the interval type 2 TS fuzzy Markov jump system. and .

[0035] 5. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0036] Step S4: Based on the measurement output from step S1, design a fuzzy logic circuit with random faults. The controller acts on step S5;

[0037] To address the fault tolerance issues between the system and the controller, this paper designs an IT2 fuzzy controller that relies on the quantized output signal.

[0038] Controller rule j: If yes , yes ,...,and yes ,So:

[0039]

[0040] in This represents the gain matrix that needs to be designed. It is a Hidden Markov Chain, with a conditional probability matrix. Partially unknown. The IT2 fuzzy set of rule j, denoted as... AND function Actuators are prone to failure due to aging or prolonged operation. This article considers the following failure modes:

[0041]

[0042] in Is with An irrelevant constant that follows a Bernoulli distribution. =1 indicates that the actuator is working normally. =0 indicates that the actuator cannot work. This indicates a partial failure in the actuator. A more comprehensive description is as follows: .

[0043] 6. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0044] Step S5: Design a dynamic event triggering mechanism by combining a hysteresis uniform quantizer with a dynamic event triggering scheme;

[0045] To optimize network resource utilization and reduce data transmission frequency, an adaptive QDETM is introduced. Based on the quantization Q(y(k)), the quantization event triggering conditions are determined as follows:

[0046]

[0047] in , To dynamically adjust variables, and > 0. and It is considered a weight matrix and has positive definite properties. , This represents the quantized value recorded at the last trigger moment. It is an adaptive threshold parameter:

[0048]

[0049] in < 1 and Adjust parameters Adjustable The sensitivity. acot(·) is the arccot ​​function. Update the criterion on the next triggered event.

[0050] 7. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0051] Step S6: Output error. If the output error is not 0, return to step S4; otherwise, end the process. The system has reached its target. synchronous;

[0052] Based on steps S3 and S4, a closed-loop interval type 2 TS fuzzy Markov transition system can be realized:

[0053]

[0054] in .

[0055]

[0056] in ,

[0057] 8. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by comprising the following steps:

[0058] Step S7: The modally dependent Lyapunov function ensures the finite-time operation of the system. Synchronization issues.

[0059] Set scalar and positive definite matrix If a symmetric positive definite matrix exists... Scalar If the following linear matrix inequality conditions are satisfied, then the interval type 2 TS fuzzy Markov jump system maintains finite-time boundedness. .

[0060]

[0061] in,

[0062]

[0063] Secondly, embodiments of the present invention also provide a quantization dynamic event triggering control device based on a range-2 type TS fuzzy Markov transition system, mainly comprising:

[0064] First module (step S1): Construct an interval 2-class TS fuzzy Markov jump system with partially unknown transition probabilities and random coupling delays. The system includes N control links. Each control link includes a sensor, a controller model, a quantized dynamic event trigger, etc., connected in sequence. The sensor is connected to the object under test.

[0065] The second module (step S2): Construct a model of the target node of the Markov jump system to prepare for solving the error in step S3;

[0066] Third module (step S3): Based on steps S1 and S2, the synchronization error system is obtained;

[0067] Fourth Module (Step S4): Based on the measurement output from Step S1 and the synchronization error from Step S3, design a fuzzy logic circuit with random faults. The controller acts on step S5;

[0068] Fifth module (step S5): Apply the Q(y(k)) and e(k) obtained by quantizing the dynamic event triggering mechanism with the hysteresis uniform quantizer and the dynamic event triggering scheme to step S4;

[0069] Module 6 (Step S6): Output system error.

[0070] Thirdly, embodiments of the present invention also provide a quantization dynamic event triggering control system based on a two-class interval TS fuzzy Markov jump system, comprising: a controlled object, a sensor, a zero-order hold, a quantization event trigger, and a controller.

[0071] A computer program that can run on a processor, wherein when the processor executes the computer program, it implements the quantization dynamic event triggering control method based on a range-2 type TS fuzzy Markov jump system as described in the first aspect.

[0072] This invention offers the following advantages: Inspired by the aforementioned insights, this invention considers finite-time H∞ synchronization control for a class of discrete-time type 2 fuzzy Markov jump systems, including partially unknown transition probabilities, randomly occurring coupling delays, and controllers with random faults. A quantized dynamic event triggering mechanism is proposed by combining a hysteresis uniform quantizer with a dynamic event triggering scheme to further reduce data communication overhead. The asymptotic finite-time H∞ synchronization problem of FMJS is investigated in depth from a mean-square perspective using modal-dependent Lyapunov functions.

[0073] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims, and drawings. Attached Figure Description

[0074] The accompanying drawings are provided to further illustrate the present invention and form part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention, but do not constitute a limitation on the technical solutions of the present invention.

[0075] Figure 1 This is a flowchart of the quantitative dynamic event triggering control method based on the interval 2-class TS fuzzy Markov jump system of the present invention;

[0076] Figure 2 This is a schematic diagram of the quantization dynamic event triggering control device based on the interval 2-class TS fuzzy Markov jump system of the present invention;

[0077] Figure 3This is a schematic diagram of the quantization dynamic event triggering control system based on the interval 2-type TS fuzzy Markov jump system of the present invention;

[0078] Figure 4 This is a graph showing the change of system error over time according to an embodiment of the present invention;

[0079] Figure 5 This is a graph showing the change of the system controller over time according to an embodiment of the present invention;

[0080] Figure 6 This is a line graph comparing the error between the Quantized Dynamic Event Triggering Mechanism (QDETM) provided in one embodiment of the present invention and existing triggering mechanisms (Static Event Triggering Mechanism (SETM), Adaptive Static Event Triggering Mechanism (ASETM), and Dynamic Time Triggering Mechanism (DETM)).

[0081] Figure 7 This is a timing diagram of a quantized dynamic event triggering mechanism provided in one embodiment of the present invention;

[0082] Figure 8 This is a graph showing the change of adaptive parameters over time in a quantized dynamic event triggering mechanism provided by an embodiment of the present invention. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0084] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, or the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0085] like Figure 1 As shown, this invention provides a quantized dynamic event triggering control method based on a two-class TS fuzzy Markov jump system in an interval. The method includes the following steps:

[0086] Step S1: Consider a class of interval-based 2-type TS fuzzy Markov jump systems consisting of N nodes, with partially unknown transition probabilities and randomly occurring coupling delays. The i-th fuzzy rule of this model can be expressed as:

[0087] Fuzzy rule i: If yes , yes ,…,and yes ,but

[0088]

[0089] in Represents the state vector; and These represent the measurement output and control output, respectively. Describe the control inputs when the actuator fails. It is a disturbance input. satisfy Instantaneous variable delay. The external coupling configuration matrices for both time-delayed and non-time-delayed models are respectively derived from... and This indicates that both are symmetric matrices. and It is an internal coupling matrix. Random variable. Its characteristic is that it has a Bernoulli distribution (when delayed information exchange occurs). It equals 1 when there is no delayed information exchange. (equal to 0). , , , , , and It is a constant matrix with known dimensions. Is it a membership function? Connected intervals, class 2 TS fuzzy fuzzy sets. This indicates the system switching mode of the Markov chain.

[0090] Furthermore, the transition probability matrix Corresponding to:

[0091] In other words, only matrices Some elements are known, as shown in the case of a 3 × 3 matrix:

[0092]

[0093] The "?" represents an unspecified element. Continuing, this leads to a finite set. It can be used To describe it in order to conduct subsequent analysis:

[0094]

[0095] Step S2: Construct a model of the target node in the Markov transition system;

[0096] The target node network of a class 2 TS fuzzy Markov transition system with partially unknown transition probabilities and randomly occurring coupling delays can be described as follows:

[0097]

[0098] in This corresponds to the state trajectory of the target node in a type 2 TS fuzzy Markov transition system. The controlled output and measurement output of the target node are determined by... and express.

[0099] Step S3: Based on the synchronization error set in steps S1 and S2, establish a synchronization error system;

[0100] Based on the above system and target node system, the following error system is generated:

[0101]

[0102] in It is a synchronization error unique to the interval type 2 TS fuzzy Markov jump system. and .

[0103] Step S4: Based on the measurement output from step S1, design a fuzzy logic circuit with random faults. The controller acts on step S5;

[0104] To address the fault tolerance issues between the system and the controller, this paper designs an IT2 fuzzy controller that relies on the quantized output signal.

[0105] Controller rule j: If yes , yes ,...,and yes ,So:

[0106]

[0107] in This represents the gain matrix that needs to be designed. It is a Hidden Markov Chain, with a conditional probability matrix. Partially unknown. The IT2 fuzzy set of rule j, denoted as... AND function Actuators are prone to failure due to aging or prolonged operation. This article considers the following failure modes:

[0108]

[0109] in Is with An irrelevant constant that follows a Bernoulli distribution. =1 indicates that the actuator is working normally. =0 indicates that the actuator cannot work. This indicates a partial failure in the actuator. A more comprehensive description is as follows: .

[0110] Step S5: Design a dynamic event triggering mechanism by combining a hysteresis uniform quantizer with a dynamic event triggering scheme;

[0111] To optimize network resource utilization and reduce data transmission frequency, an adaptive QDETM is introduced. Based on the quantization Q(y(k)), the quantization event triggering conditions are determined as follows:

[0112]

[0113] in , To dynamically adjust variables, and > 0. and It is considered a weight matrix and has positive definite properties. , This represents the quantized value recorded at the last trigger moment. It is an adaptive threshold parameter:

[0114]

[0115] in < 1 and Adjust parameters Adjustable The sensitivity. acot(·) is the arccot ​​function. Update the criterion on the next triggered event.

[0116] Step S6: Output error. If the output error is not 0, return to step S4; otherwise, end the process. The system has reached its target. synchronous;

[0117] Based on steps S3 and S4, a closed-loop interval type 2 TS fuzzy Markov transition system can be realized:

[0118]

[0119] in .

[0120]

[0121] in ,

[0122] Step S7: The modally dependent Lyapunov function ensures the finite-time operation of the system. Synchronization issues.

[0123] Set scalar and positive definite matrix If a symmetric positive definite matrix exists... Scalar If the following linear matrix inequality conditions are satisfied, then the interval type 2 TS fuzzy Markov jump system maintains finite-time boundedness. .

[0124]

[0125] in

[0126]

[0127] like Figure 2 As shown, the present invention provides a quantization dynamic event triggering control device based on a range-2 type TS fuzzy Markov jump system, the device comprising the following steps:

[0128] First module (step S1): Construct an interval 2-class TS fuzzy Markov jump system with partially unknown transition probabilities and random coupling delays. The system includes N control links. Each control link includes a sensor, a controller model, a quantized dynamic event trigger, etc., connected in sequence. The sensor is connected to the object under test.

[0129] The second module (step S2): Construct a model of the target node of the Markov jump system to prepare for solving the error in step S3;

[0130] Third module (step S3): Based on steps S1 and S2, the synchronization error system is obtained;

[0131] Fourth Module (Step S4): Based on the measurement output from Step S1 and the synchronization error from Step S3, design a fuzzy logic circuit with random faults. The controller acts on step S5;

[0132] Fifth module (step S5): Apply the Q(y(k)) and e(k) obtained by quantizing the dynamic event triggering mechanism with the hysteresis uniform quantizer and the dynamic event triggering scheme to step S4;

[0133] Module 6 (Step S6): Output system error.

[0134] like Figure 3As shown, the present invention provides a quantization dynamic event triggering control system based on a two-class TS fuzzy Markov jump system. The system includes: a controlled object, a sensor, a zero-order hold, a quantization event trigger, a controller, and a computer program that can run on a processor. When the processor executes the computer program, it implements the quantization dynamic event triggering control method based on a two-class TS fuzzy Markov jump system as described in the first aspect.

[0135] Example verification of the design of quantitative dynamic event triggering control:

[0136] Consider the following interval 2-type TS fuzzy Markov transition system:

[0137] Consider a discrete-time interval 2-class TS fuzzy Markov jump system consisting of five identical nodes. The coefficient matrix is ​​detailed in Table I.

[0138] Table I: Coefficient matrices for different modes

[0139]

[0140] In addition, the coupling matrix is ​​set as follows:

[0141] External disturbances and time-varying delays can be expressed as: and The initial value of the network node is... , and The controller gain is set to:

[0142]

[0143] Using the controller gain, it is clear that the synchronization error and control input of the discrete-time interval type 2 TS fuzzy Markov jump system both converge to zero, such as... Figure 4 and 5 As shown. By combining the system model with various popular event-triggered mechanisms (Static Event Triggered Mechanism (SETM), Adaptive Static Event Triggered Mechanism (ASETM), and Dynamic Event Triggered Mechanism (DETM)), this invention demonstrates the superiority of the proposed method in terms of control performance and average TF. Clearly, compared to SETM, ASETM, and DETM, the Quantized Dynamic Event Triggered Mechanism (QDETM) maintains a lower data update frequency while shortening the time to reach stability. The system performance of the quantized output is significantly improved, effectively reducing communication resource consumption. Under the same conditions, QAETM... It converges to zero faster, thus achieving superior control performance, such as... Figure 6 As shown. Figure 7The event triggering times of two types of TS fuzzy Markov jump systems in discrete time intervals were depicted, with an average triggering rate of 9.33% across six nodes. As the error decreases, the adaptive threshold... Approaching zero, such as Figure 8 As shown. In summary, QDETM outperforms other triggering mechanisms in terms of low resource consumption and significant control improvements.

[0144] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A quantization dynamic event triggering method based on interval-2 type TS fuzzy Markov jump system The control method is characterized by, Includes the following steps: Step S1: Construct a range-2 type TS fuzzy Markov jump system with partially unknown transition probabilities and randomly occurring coupling delays; Step S2: Construct a model of the target node in the Markov transition system; Step S3: Based on the synchronization error set in steps S1 and S2, establish a synchronization error system; Step S4: Based on the measurement output from step S1, design a fuzzy logic circuit with random faults. The controller acts on step S5; Step S5: Design a dynamic event triggering mechanism by combining a hysteresis uniform quantizer with a dynamic event triggering scheme; Step S6: Output error. If the output error is not 0, return to step S4; otherwise, end the process. The system has reached its target. synchronous; Step S7: The modally dependent Lyapunov function ensures the finite-time operation of the system. Synchronization issues.

2. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 1. The control method is characterized by, Includes the following steps: Step S1: Consider a class of interval-based 2-type TS fuzzy Markov jump systems consisting of N nodes, with partially unknown transition probabilities and randomly occurring coupling delays. The i-th fuzzy rule of this model can be expressed as: Fuzzy rule i: If yes , yes ,…,and yes ,but in Represents the state vector; and These represent the measurement output and control output, respectively. Describe the control inputs when the actuator fails; It is a disturbance input; satisfy Instantaneous variable delay; the external coupling configuration matrices for time-delayed and non-time-delayed systems are respectively composed of... and This indicates that both are symmetric matrices; and It is an internally coupled matrix; random variables Its characteristic is that it has a Bernoulli distribution (when delayed information exchange occurs). It equals 1 when there is no delayed information exchange. (equal to 0); , , , , , and It is a constant matrix with known dimensions; Is it a membership function? Connected intervals, type 2 TS fuzzy sets; This indicates the system switching mode of the Markov chain; Furthermore, the transition probability matrix Corresponding to: In other words, only matrices Some elements are known, as shown in the case of a 3 × 3 matrix: Here, "?" represents an unspecified element; continuing on, the finite set... It can be used To describe it in order to conduct subsequent analysis: 。 3. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 2. The control method is characterized by, Includes the following steps: Step S2: Construct a model of the target node in the Markov transition system; The target node network of a class 2 TS fuzzy Markov transition system with partially unknown transition probabilities and randomly occurring coupling delays can be described as follows: in The state trajectory of the target node corresponds to the second type of TS fuzzy Markov jump system in the interval; the controlled output and measured output of the target node are determined by... and express.

4. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 3. The control method is characterized by, Includes the following steps: Step S3: Based on the synchronization error set in steps S1 and S2, establish a synchronization error system; Based on the above system and target node system, the following error system is generated: in It is a synchronization error unique to the interval type 2 TS fuzzy Markov jump system; and .

5. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 4. The control method is characterized by, Includes the following steps: Step S4: Based on the measurement output from step S1, design a fuzzy logic circuit with random faults. The controller acts on step S5; To address the fault tolerance issue between the system and the controller, this paper designs an IT2 fuzzy controller that relies on the quantized output signal; Controller rule j: If yes , yes ,...,and yes ,So: in This represents the gain matrix that needs to be designed; It is a Hidden Markov Chain, with a conditional probability matrix. Partially unknown; the IT2 fuzzy set of rule j, labeled as AND function Due to aging or prolonged operation, actuators are prone to failure; this paper considers the following failure modes: in Is with An irrelevant constant that follows a Bernoulli distribution; =1 indicates that the actuator is working normally. =0 indicates that the actuator cannot work. This indicates a partial failure in the actuator; It can be described more comprehensively as follows: .

6. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 5. The control method is characterized by, Includes the following steps: Step S5: Design a dynamic event triggering mechanism by combining a hysteresis uniform quantizer with a dynamic event triggering scheme; To optimize network resource utilization and reduce data transmission frequency, an adaptive QDETM is introduced; based on the quantization Q(y(k)), the quantization event triggering conditions are determined as follows: in , To dynamically adjust variables, and > 0; and It is considered a weight matrix and has positive definite properties; , This represents the quantized value recorded at the last trigger moment; It is an adaptive threshold parameter: in < 1 and Adjust parameters Adjustable The sensitivity; acot(·) is the arccot ​​function; update the criterion on the next triggered event.

7. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 6. The control method is characterized by, Includes the following steps: Step S6: Output error. If the output error is not 0, return to step S4; otherwise, end the process. The system has reached its target. synchronous; Based on steps S3 and S4, a closed-loop interval type 2 TS fuzzy Markov transition system can be realized: in , in , 8. A quantization dynamic event triggering method based on a two-class TS fuzzy Markov transition system according to claim 7. The control method is characterized by, Includes the following steps: Step S7: The modally dependent Lyapunov function ensures the finite-time operation of the system. Synchronization issues; Set scalar and positive definite matrix ; If a symmetric positive definite matrix exists Scalar If the following linear matrix inequality conditions are satisfied, then the interval type 2 TS fuzzy Markov jump system maintains finite-time boundedness. , in

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