Adaptive event-triggered tracking control method for complex systems under sensor failures

Abstract

The application discloses a self-adaptive event-triggered tracking control method for a complex system under sensor failure, and belongs to the technical field of event-triggered control. Firstly, an output signal of a controlled object is collected by using a sensor, and a system dynamics and fault mathematical model are established in combination with nonlinear characteristics, external interference, sensor gain variation and measurement error. Based on the model, the nonlinear constraint characteristics are determined, a dynamic gain and a state observer are constructed by using a nonlinear boundary conclusion under sensor failure, and unmeasurable states of the system are estimated in real time. In combination with the estimated states of the dynamic gain and the state observer, a trigger time is determined by using integrated event-triggered judgment logic, a feedback self-adaptive event-triggered control signal is generated, and the signal is output to an actuator. The method can compensate for system nonlinearity, sensor failure and external interference, ensure accurate tracking of a reference signal, guarantee that a closed-loop signal is bounded and free of Zeno phenomenon, and effectively save communication and calculation resources.

Description

Technical Field

[0001] This invention belongs to the field of event-triggered control technology, and particularly relates to an adaptive event-triggered tracking control method for complex systems under sensor failure. Background Technology

[0002] Over the past decade, event-triggered control has received widespread attention due to the proliferation of networks in numerous practical systems. One of its most important characteristics is its ability to significantly save communication and computing resources. It is worth noting that practical systems often exhibit substantial parameter uncertainties, and adaptive event-triggered control has also been studied to some extent. Its main advantage lies in its ability to simultaneously handle system uncertainties and execution errors caused by the event-triggered mechanism, thus eliminating the need for input state stability assumptions regarding execution errors.

[0003] Although some progress has been made in the research of state feedback adaptive event-triggered control, further research is still needed for uncertain nonlinear systems with output feedback. Specifically, most related results require the calculation of continuous control signals to determine the event-triggered control signal, and all assume that the system's output sensors are fault-free. In addition, a few related results that consider sensor faults only consider single sensor faults.

[0004] Therefore, researching an adaptive event-triggered tracking control method for complex systems under sensor failure still has potential application value. Summary of the Invention

[0005] The technical objective of this invention is to propose an output feedback adaptive event-triggered tracking method for a class of nonlinear systems with system nonlinearity, sensor failure, and external interference.

[0006] To achieve the above-mentioned technical objectives, the embodiments of the present invention adopt the following technical solutions.

[0007] This implementation provides an adaptive event-triggered tracking control method for complex systems under sensor failure, including:

[0008] By using sensors to collect the output signal of the controlled object, and combining the nonlinear characteristics of the controlled object, external disturbances, sensor gain changes and measurement errors, a dynamic model of the uncertain nonlinear system and a mathematical model of sensor faults are established.

[0009] Based on the aforementioned dynamic model and sensor fault mathematical model, the constraint characteristics of the system's nonlinear function are clarified, and the derived conclusions on the system's nonlinear boundary under sensor fault are directly applied.

[0010] Based on the aforementioned dynamic model, sensor fault mathematical model, and nonlinear boundary conclusions, a dynamic gain and state observer are constructed, and the unmeasurable state of the system is estimated in real time through the state observer.

[0011] Based on the characteristics of the dynamic model and the sensor fault mathematical model, and combined with the unmeasurable state estimated by the dynamic gain and the state observer, the event trigger judgment logic is applied to determine the event trigger time.

[0012] Based on the event triggering time, dynamic gain, state estimated by the state observer, and the fault compensation requirements of the dynamic model and the sensor fault mathematical model, a feedback adaptive event triggering control signal is generated.

[0013] The control signal is output to the actuator of the controlled object to control the output of the controlled object to accurately track the given reference signal, while ensuring that all signals in the closed-loop system are bounded and free from Zeno phenomenon.

[0014] Furthermore, the event triggering judgment logic is implemented through a threshold function with dynamic gain adjustment; the threshold function is based on dynamic gain and preset positive triggering parameter settings, and is directly applied to the rapid determination of the event triggering time.

[0015] Furthermore, the event triggering judgment logic includes: performing deviation calculation to obtain the superposition value of the observer state deviation and the dynamic gain deviation, and using a preset positive triggering parameter. , And a threshold function for dynamic gain calculation adapted to the current system state and sensor fault conditions. The expression is: ,in, It is a positive constant to be designed. for abbreviation, for Dynamic gain at any given time;

[0016] If the rule that the cumulative deviation value is greater than or equal to the threshold is met, an event is triggered, and the triggering time is determined. The expression is as follows:

[0017] in For the next trigger time, The last time it was triggered. for The state estimated by the observer at time [time]. for The state estimated by the observer at time [time]. for The dynamic gain at time n, where n is the order of the system.

[0018] Furthermore, the dynamic gain is adaptively updated based on preset positive constants, measurable tracking error, observer-estimated state, output characteristics of the uncertain nonlinear system dynamics model, and sensor-measured output signal. It is used to counteract the effects of system nonlinearity, sensor fault, and external interference represented by the dynamics model and sensor fault mathematical model. The measurable tracking error is calculated from the sensor-acquired output signal and a given reference signal.

[0019] Furthermore, the state observer is constructed based on the structural characteristics of the uncertain nonlinear system dynamics model, the output signal of sensor fault measurement, and the measurable tracking error, and is directly applied to the real-time estimation of the unmeasurable state of the system; the measurable tracking error is calculated from the output signal collected by the sensor and the given reference signal.

[0020] Furthermore, ensuring that all signals in the closed-loop system are bounded and free from Zeno's phenomenon specifically involves: based on the stability analysis of the dynamic model and the mathematical model of sensor faults, determining the bounded range of the closed-loop system signals and the positive lower bound of the event triggering time interval, and setting the dynamic gain and triggering parameters to ensure that the system operation satisfies the positive lower bound, thereby avoiding Zeno's phenomenon and achieving accurate tracking of the reference signal.

[0021] It should be understood that the summary section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description.

[0022] Compared with existing technologies, the adaptive event-triggered tracking control method for complex systems under sensor failure provided by this invention has the following beneficial technical effects: In this invention, the system nonlinearity coupled with the unmeasurable state satisfies the polynomial growth condition and non-vanishing characteristics, and simultaneously considers sensor gain changes and additional errors; this invention constructs an integrated triggering condition adjusted by dynamic gain to obtain the trigger values ​​of the observer state and dynamic gain, and uses these trigger values ​​to update the event triggering input at the triggering time. This greatly improves the practicality of the control method and reduces the computational burden of the control system. Under the event-triggered framework proposed in this invention, there is no need to calculate continuous control signals; system nonlinearity, execution errors, sensor failures, and external disturbances can all be effectively canceled out by dynamic gain, and the actual tracking error can converge to a small residual set, further enhancing the practicality of the control method. This invention designs an output feedback adaptive event-triggered tracking control method to compensate for system nonlinearity, sensor failures, execution errors, and external disturbances, thereby effectively saving communication and computing resources, and enabling the system output to track the given reference signal as accurately as possible. Attached Figure Description

[0023] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. Furthermore, the shapes and proportions of the components in the drawings are merely illustrative to aid in understanding the invention and are not intended to specifically limit the shapes and proportions of the components. Those skilled in the art, guided by the teachings of this invention, can select various possible shapes and proportions to implement the invention according to specific circumstances. In the drawings:

[0024] Figure 1 This is a schematic diagram illustrating the principle of an adaptive event-triggered tracking control method for a complex system under sensor failure conditions, provided in an embodiment. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown, the embodiment provides an adaptive event-triggered tracking control method for a complex system under sensor failure, including:

[0028] Step 1: Use sensors to collect the output signal of the controlled object, and combine the nonlinear characteristics of the controlled object, external disturbances, and possible gain changes and measurement errors of the sensors to establish a dynamic model of the uncertain nonlinear system and a mathematical model of sensor faults.

[0029] Step 2: Based on the dynamic model and the mathematical model of sensor fault, clarify the constraint characteristics of the system's nonlinear function, and directly apply the derivation of the nonlinear boundary conclusions of the system under sensor fault.

[0030] Step 3: Based on the dynamic model, the sensor fault mathematical model, and the nonlinear boundary conclusions, construct the dynamic gain and state observer, and estimate the unmeasurable state of the system in real time through the state observer;

[0031] Step 4: Based on the characteristics of the dynamic model and the sensor fault mathematical model, combined with the unmeasurable state estimated by the dynamic gain and the state observer, the integrated event trigger judgment logic is applied to determine the event trigger time;

[0032] Step 5: Based on the event triggering time, dynamic gain, unmeasurable state estimated by the state observer, and fault compensation requirements of the dynamic model and sensor fault mathematical model, generate a feedback adaptive event triggering control signal; output the control signal to the actuator of the controlled object to control the output of the controlled object to accurately track the given reference signal, while ensuring that all signals of the closed-loop system are bounded and free from Zeno phenomenon.

[0033] In this embodiment, in step 1, a dynamic model of an uncertain nonlinear system and a mathematical model of sensor faults are established. The nonlinear system dynamic model is as follows:

[0034] (1)

[0035] in, Let be the state vector of the system. It is the state of the system. The input to the system, i.e., the control signal input to the system. y represents the system output. , It is a real number. For an unknown continuous vector, It is time-varying and confined to an unknown bounded convex set. It is an m-dimensional real space. An unknown continuous function. , , It is an n-dimensional real space; the unknown continuous function satisfies the local Lipschitz condition with respect to all system states. , Represents external disturbance and satisfies ,here It is an unknown positive number.

[0036] Where the context will not cause confusion, the time sign and certain function arguments will be omitted, such as a function It can be represented as or .

[0037] System output Measured by a sensor, and the output at time t is This sensor may malfunction during system operation, and the mathematical model for sensor failure is as follows:

[0038] (2)

[0039] This was the first unknown moment when the sensor malfunction occurred. Represents the gain change of the sensor. ; This represents the sensor's measurement error. It is worth noting... and It is a uniformly differentiable and bounded function. Furthermore, over a time interval... superior, and This indicates that the sensor is fault-free.

[0040] In this embodiment, the following assumptions are made regarding the nonlinear function of the system in step 2:

[0041] Assumption 1: There exists an unknown constant. The nonlinear function of the system satisfies the polynomial growth condition, expressed as:

[0042] (3)

[0043] in It is a positive integer.

[0044] Furthermore, the lemma for the nonlinear function of the system under sensor failure is derived as follows:

[0045] Lemma 1: Let the inequality in formula (3) hold and the signal , The given reference signal.

[0046] Then, there exists a positive constant. Make the function

[0047] The following specific nonlinear boundary conditions must be met:

[0048] (4)

[0049] in It is an unknown positive constant. yes The derivative of .

[0050] Proof: Applying Assumption 1,

[0051] (5)

[0052] Using formula (2), (6)

[0053] Therefore, formula (5) can be rewritten as:

[0054] (7)

[0055] Applying inequalities: (8)

[0056] here , And noticed and Since all numbers are bounded, there must exist a positive constant. Make:

[0057] (9)

[0058] Substituting formula (9) into formula (7) yields formula (4). Q.E.D.

[0059] In this embodiment, the construction of the dynamic gain and state observer in step 3 is as follows:

[0060] First, we introduce the following lemma to determine certain design parameters that will be used to facilitate controller design and stability analysis.

[0061] Lemma 2: For any positive constant... There must exist positive numbers. and Positive definite matrix and ,vector and This makes the following inequality hold:

[0062] (10)

[0063] here Matrix A and vectors b and c are defined as follows:

[0064] (11)

[0065] Next, define the following two variables:

[0066] (12)

[0067] The actual tracking error here Used only for stability analysis, measurable tracking error It was used to construct state observers and dynamic gains so that sensor failures could be taken into account.

[0068] Then, with the help of equations (1), (12) and lemma 2, the state observer and dynamic gain are... It is designed as follows:

[0069] (13)

[0070] in It is the state estimated by the observer.

[0071] (14)

[0072] It is the control signal that needs to be designed, the gain vector It has already been chosen by Lemma 2 and

[0073] (15).

[0074] Meanwhile, dynamic gain (Initial value) The following formula has been updated:

[0075] (16)

[0076] here and It is a preset positive integer. Since... Regarding its independent variable It partially satisfies the Lipschitz condition. It satisfies the following characteristics:

[0077] (17)

[0078] In this embodiment, in step 4, the integrated event trigger judgment logic is implemented through a threshold function with dynamic gain adjustment; the threshold function is based on the nonlinear characteristics of the dynamic model of the uncertain nonlinear system, the fault type of the mathematical model of sensor fault, and the preset positive trigger parameter settings, and is directly applied to the rapid determination of the event trigger time.

[0079] In this embodiment, step 4 designs the integrated event triggering judgment logic (i.e., event triggering condition), as follows: First, assume the event triggering time is... ,Right now:

[0080] (18)

[0081] here ( This will be determined by the event triggering mechanism. This is the initial sampling time.

[0082] Assuming the event is triggered at the time The timing of the next trigger has already been determined by the previous trigger. This will be determined by monitoring the following triggering conditions:

[0083] (19)

[0084] in Indicates dynamic gain exist The value at any given moment. For the next trigger time, The last time it was triggered. for The state estimated by the observer at time [time]. for The state estimated by the observer at time [time]. for The dynamic gain at time n, where n is the order of the system.

[0085] here It is a threshold function and is determined by dynamic gain. Adjustments are made, and the definition is as follows:

[0086] (20)

[0087] in and These are positive trigger parameters that need to be designed.

[0088] As can be seen from formulas (19) and (20), the event trigger judgment logic includes: using formula (19) to calculate the deviation and obtain the superposition value of the observer's estimated state deviation and dynamic gain deviation; using formula (20) to preset the positive trigger parameter. , Calculate the threshold that adapts to the current system state and sensor fault conditions; according to the judgment condition of formula (19), if the rule that the deviation superposition value is ≥ the threshold is met, the event is triggered, and the triggering time is determined.

[0089] In this embodiment, step 5 includes designing an output feedback adaptive event-triggered controller, as detailed below:

[0090] The state observer (Equation (13)), dynamic gain (Equation (16)) and triggering environment (Equation (19)) have been designed above, and then the time period is... The output feedback adaptive event-triggered controller is designed as follows:

[0091] (twenty one)

[0092] in To provide feedback for adaptive event-triggered control signals, the gain vector... It has already been chosen by Lemma 2. From formula (16), we know that... In time period The above is based on the state observer's state. and dynamic gain It is calculated, therefore it is a constant.

[0093] In this embodiment, stability analysis is performed on all signals in the closed-loop system, specifically including:

[0094] Step 5.1, firstly, for the event triggering mechanism, formulas (19) and (20) show that in each time period , It can export:

[0095] (twenty two)

[0096] Therefore, there exists a series of continuously time-varying parameters. , satisfy and , , so that:

[0097] (twenty three)

[0098] Furthermore, since and If this holds true, then we can deduce that:

[0099] (twenty four)

[0100] Therefore, there exists a continuously time-varying parameter. satisfy and , , so that:

[0101] (25)

[0102] Next, the estimation error is defined as follows:

[0103] (26)

[0104] in , and:

[0105] (27)

[0106] Then, consider the following transformation:

[0107] (28)

[0108] Error vector and The dynamics, by applying formulas (1), (13), (21), (23) and (25), satisfy:

[0109] (29)

[0110] here , .

[0111] Therefore, we obtain Theorem 1.

[0112] Theorem 1: The closed-loop system satisfies Assumption 2, and the models for system and sensor faults are given by equations (1) and (2), respectively; the state observer and dynamic gain are given by equations (13) and (16), respectively; and the event-triggered environment and event-triggered control signal are given by equations (19), (20), and (21), respectively. Then, there exists a constant... Such that if the sensor gain change satisfies So:

[0113] ① All signals in the closed-loop system The upper limit is bounded;

[0114] ②Despite the existence of event-triggered mechanisms and sensor malfunctions, the measurable tracking error It can converge to an arbitrarily small compact set;

[0115] ③ Actual tracking error It can converge to a small compact set, and this compact set is only affected by sensor faults. and The impact. In particular, and The closer and , The smaller. If the sensor is fault-free, and It can also converge to an arbitrarily small compact set.

[0116] Proof: For part ①, for the closed-loop system consisting of equations (1), (13), (16), and (21), the local Lipschitz condition is satisfied. Therefore, there exists a certain... So that in the maximum time interval Above, these variables It exists and is unique.

[0117] From Lemma 2, we know that for positive constants satisfying formula (15), the design parameters and matrix... It's already been confirmed. Since... and It is Hurwitz, and the Lyapunov function is selected as follows:

[0118] (30)

[0119] in (31)

[0120] Then, The time derivative, by applying formulas (10) and (29), satisfies:

[0121] (32)

[0122] Next, eliminate the effects of the last two terms caused by the event triggering mechanism in equation (32). Let: (33)

[0123] in Then, apply the inequality. ,have:

[0124] (34)

[0125] application , From Young's inequality, we can derive:

[0126] (35)

[0127] Furthermore, the effects of other terms caused by system nonlinearity are eliminated. The error of the sensor gain variation is defined as follows:

[0128] (36)

[0129] And satisfy:

[0130] (37)

[0131] Using Young's inequalities, we can derive the following three inequalities:

[0132] (38)

[0133] Applying Lemma 1 and coordinate transformation (28), we have:

[0134] (39)

[0135] in It is an unknown positive constant. Then, select the design parameters. and :

[0136] (40)

[0137] Applying formulas (10) and (16), we have:

[0138] (41)

[0139] Finally, substituting formulas (34)-(39) and (41) into formula (32) results in:

[0140] (42)

[0141] in:

[0142] (43)

[0143] It is an unknown positive number.

[0144] By applying formula (42), variables can be proven in a manner similar to that in existing literature. During the maximum time interval All variables are bounded, and the proof process includes proof by contradiction and is relatively mature, so it is omitted here. During the maximum time interval Everything above is bounded, then Therefore, formula (28) shows , and exist The upper limit is bounded. Moreover, since... and If it is bounded, then It is bounded.

[0145] For Part ②, prove the measurable tracking error. It can converge to an arbitrarily small compact set. Clearly, the formula defined in equation (16) is... Regarding its independent variable It is Lipschitz on any compact set. Since exist The above is bounded, and there exists a positive constant. Makes any ,

[0146] (44)

[0147] application Boundedness and The consistency and continuity have It is uniformly continuous, meaning that for any positive constant... There exists a constant Make .so:

[0148] (45)

[0149] Applying formulas (44) and (45), For all Established, that is to say, exist The above is consistent and continuous. At the same time, because... exist Above is bounded, there is Applying Barbalat's lemma, we can obtain:

[0150] (46)

[0151] Then, formula (17) shows that:

[0152] (47)

[0153] Therefore, by applying formula (46), we can obtain:

[0154] (48)

[0155] Therefore, measurable tracking error Able to reduce The value of converges to an arbitrarily small compact set. This concludes the proof in Part ②.

[0156] For part ③, regarding the actual tracking error From formulas (2), (12) and (48), we can obtain:

[0157] (49)

[0158] Therefore, the actual tracking error Mainly due to sensor failure and The impact. In particular, if and The closer and The actual tracking error The smaller. And, if and If the sensor is fault-free, then the actual tracking error is... and measurable tracking error They are equal and can all converge to arbitrarily small compact sets. This completes the proof.

[0159] Step 5.2, analyze whether the system exhibits the Zeno phenomenon, see the following theorem for details:

[0160] Theorem 2: By applying the adaptive event-triggered fault-tolerant control scheme in Theorem 1, there exists a constant. Make:

[0161] (50)

[0162] In other words, internal event time The lower bound is .

[0163] Proof: In order to prove The existence of the triggering environment (Equation (19)) will be investigated. Let:

[0164] (51)

[0165] It can be deduced that:

[0166] (52)

[0167] From formulas (13) and (16), it can be seen that, The following signals are , The function is bounded. Therefore, there must exist a positive constant. Make:

[0168] (53)

[0169] Applying formulas (19) and (20), we can obtain:

[0170] (54)

[0171] now that exist The upper bound is assumed. ,in It is a positive constant. Therefore, we can deduce that:

[0172] (55)

[0173] This allows us to further obtain:

[0174] (56)

[0175] Therefore, formula (50) holds true. In other words, the Zeno phenomenon does not exist.

[0176] This invention proposes an adaptive event-triggered tracking control method for complex systems under sensor failure, wherein the nonlinearity of the controlled system satisfies the polynomial growth condition and non-vanishing characteristics, and the controlled system also exhibits sensor gain variations and measurement errors. This method is more universal than existing methods. Furthermore, this invention considers a more general tracking problem.

[0177] Compared to existing methods utilizing gain adjustment techniques with multiple trigger conditions, this invention requires only one trigger condition, thus eliminating the need for more trigger channels. Furthermore, the control method provided by this invention avoids the Zeno phenomenon by ensuring that the trigger condition is not forcibly suspended.

[0178] The event triggering scheme disclosed in this invention does not require the calculation of continuous control signals to construct the state observer or event triggering conditions, and provides the possibility of event triggering transmission of the observer state, thus further saving transmission and computing resources.

[0179] The above provides a detailed description of the adaptive event-triggered tracking control method for complex systems under sensor failure conditions provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the concept of this invention and should not be construed as limiting the scope of protection of this invention.

Claims

1. An adaptive event-triggered tracking control method for a complex system under sensor failure, characterized in that, This includes: using sensors to collect the output signal of the controlled object, and combining the nonlinear characteristics of the controlled object, external disturbances, sensor gain changes and measurement errors to establish a dynamic model of the uncertain nonlinear system and a mathematical model of sensor faults; Based on the aforementioned dynamic model and sensor fault mathematical model, the constraint characteristics of the system's nonlinear function are clarified, and the derived conclusions of the system's nonlinear boundary under sensor fault are directly applied. Based on the aforementioned dynamic model, sensor fault mathematical model, and nonlinear boundary conclusions, a dynamic gain and state observer are constructed, and the unmeasurable state of the system is estimated in real time through the state observer. Based on the characteristics of the dynamic model and the sensor fault mathematical model, and combined with the dynamic gain and the state estimated by the state observer, the event trigger judgment logic is applied to determine the event trigger time. Based on the event triggering time, dynamic gain, state estimated by the state observer, and the fault compensation requirements of the dynamic model and the sensor fault mathematical model, a feedback adaptive event triggering control signal is generated. The control signal is output to the actuator of the controlled object to control the output of the controlled object to accurately track the given reference signal, while ensuring that all signals in the closed-loop system are bounded and free from Zeno phenomenon. The event triggering judgment logic includes: performing deviation calculation to obtain the superposition value of the observer state deviation and the dynamic gain deviation, and using preset positive trigger parameters. , And a threshold function for dynamic gain calculation adapted to the current system state and sensor fault conditions. The expression is: ,in It is a positive constant to be designed. for abbreviation, for The dynamic gain at any given time; if the rule that the cumulative deviation value is greater than or equal to the threshold is met, an event is triggered, completing the determination of the trigger time, as shown in the expression: ; in For the next trigger time, The last time it was triggered. for The state estimated by the observer at time [time]. for The state estimated by the observer at time [time]. for The dynamic gain at time n, where n is the order of the system; The dynamic gain is based on a preset positive constant, measurable tracking error, the state estimated by the observer, and the output characteristics of the dynamic model of the uncertain nonlinear system and the output signal measured by the sensor. It is adaptively updated to counteract the effects of system nonlinearity, sensor failure and external interference represented by the dynamic model and the mathematical model of sensor failure. The measurable tracking error is calculated from the output signal collected by the sensor and a given reference signal. The state observer is constructed based on the structural characteristics of the dynamic model of the uncertain nonlinear system, the output signal of the sensor fault measurement, and the measurable tracking error, and is directly applied to the real-time estimation of the unmeasurable state of the system; the measurable tracking error is calculated from the output signal collected by the sensor and the given reference signal.

2. The control method according to claim 1, characterized in that, The event triggering judgment logic is implemented through a threshold function with dynamic gain adjustment; the threshold function is based on dynamic gain and preset positive triggering parameter settings, and is directly applied to the rapid determination of the event triggering time.

3. The control method according to claim 1, characterized in that, The guarantee that all signals in the closed-loop system are bounded and free from Zeno's phenomenon is specifically achieved by: based on the stability analysis of the dynamic model and the mathematical model of sensor faults, determining the bounded range of the closed-loop system signals and the positive lower bound of the event triggering time interval, and setting the dynamic gain and triggering parameters to ensure that the system operation meets the positive lower bound, thereby avoiding Zeno's phenomenon and achieving accurate tracking of the reference signal.

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