A chattering-free sliding mode control method with pulse random disturbance

Abstract

The present disclosure provides a chattering-free sliding mode control method, device, electronic equipment and readable storage medium with pulse random disturbance. First, a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty is established; a sliding surface is designed for the dynamic model to make the system meet the expected stability once it reaches the sliding surface; based on the sliding surface and the dynamic model, a sliding mode dynamic equation is determined; based on the sliding mode dynamic equation, a judgment condition for ensuring the exponential stability of the sliding mode dynamic in the mean square sense and a sliding surface parameter matrix are obtained; a hyperbolic tangent function is introduced as a continuous smooth approximation of the switching function, and a chattering-free sliding mode controller is constructed using the sliding surface parameter matrix to realize the control of the pulse random time delay system. Using the present invention can solve the problem that the existing sliding mode control method cannot simultaneously process pulse, environmental noise, time delay and uncertainty, so that the external disturbance has a great impact on the controlled output of the system, resulting in low sliding mode control precision.

Description

Technical Field

[0001] This invention relates to the field of control and information technology, and specifically to a jitter-free sliding mode control method, apparatus, electronic device, and readable storage medium with pulse random disturbances. Background Technology

[0002] A stochastic system is a system whose dynamic behavior is influenced by random factors, which may originate from internal uncertainties or random disturbances in the external environment. In modern engineering practice, stochastic systems are widespread across various fields. Examples include stock price fluctuations in financial systems, noise interference in communication systems, and wind shear and airflow disturbances in aircraft guidance processes—all typical manifestations of stochasticity. These random factors make the system's state difficult to predict and control accurately, posing significant challenges to engineering practice.

[0003] Impulse stochastic systems are a special type of stochastic system characterized by instantaneous changes in their state at certain moments. These changes can be caused by sudden shifts in the external environment or internal system faults. These instantaneous state changes significantly complicate system stability and control. For example, in power systems, lightning strikes or equipment failures can cause instantaneous changes in current or voltage, threatening the stable operation of the power system. Impulse stochastic systems affected by uncertainty and time delays are even more complex. Uncertainty may stem from unknown or time-varying system parameters, while time delays may be caused by delays in signal transmission or system response. The existence of these factors makes the dynamic behavior of the system even more difficult to predict and control. For instance, in aircraft guidance, due to the uncertainty of target maneuverability and the time delay in guidance command transmission, the aircraft's flight trajectory may deviate from the predetermined path, making precision strikes difficult.

[0004] Sliding mode control is an effective nonlinear control method that, by designing a specific sliding surface and control law, enables the system state to converge rapidly to the desired equilibrium point along the sliding surface when subjected to external disturbances or parameter perturbations. Currently, sliding mode control has been applied to stochastic systems, such as nonlinear uncertain stochastic systems, discrete stochastic systems, stochastic Takagi-Sugeno fuzzy time-delay systems, and Markov jump systems. However, traditional sliding mode control methods have some problems when dealing with stochastic and impulsive stochastic systems, such as chattering and insufficient robustness. Chattering is caused by high-frequency switching of the system state near the sliding surface, which can lead to system instability and a decrease in control accuracy.

[0005] To address this issue, a hyperbolic tangent function can be introduced, combined with adaptive control and sliding mode control theory. By designing suitable sliding surfaces and control laws, the system state can maintain stability and control accuracy even under random disturbances. However, for impulsive stochastic systems affected by uncertainties and time delays, existing sliding mode control methods still face some challenges and require further research and improvement.

[0006] Therefore, a sliding mode control method needs to be designed for pulse random systems to avoid chattering, improve system stability and control accuracy, and effectively cope with various random disturbances, sudden events, time delays and uncertainties, providing strong technical support for engineering practice. Summary of the Invention

[0007] In view of this, the present invention provides a jitter-free sliding mode control method, apparatus, electronic device and readable storage medium with pulse random disturbances, to solve the problem that existing sliding mode control methods cannot simultaneously handle pulses, environmental noise, time delay and uncertainty, so that external disturbances have a large impact on the controlled output of the system, resulting in low sliding mode control accuracy.

[0008] The first aspect of the present invention provides a chatter-free sliding mode control method with pulse random disturbances, comprising:

[0009] Step 1: Considering the time delay in information transmission and processing, and the fluctuation of system parameters with environmental changes, establish a dynamic model of an impulsive random time delay system with bounded state time delay and uncertainty. Step 2: For the dynamic model, design a sliding surface so that the system satisfies the desired stability once it reaches the sliding surface; based on the sliding surface and the dynamic model, determine the sliding mode equations; Step 3: Based on the aforementioned sliding mode equations, the criteria for ensuring exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix are obtained through Lyapunov stability theory and the mean residence time method. ; Step 4: Introduce the hyperbolic tangent function As a continuous and smooth approximation of the switching function, the sliding surface parameter matrix is ​​used. A chatter-free sliding mode controller is constructed to control a pulse random time-delay system.

[0010] According to a second aspect of the present invention, a chatter-free sliding mode control device with pulse random disturbance is provided, comprising a dynamic model establishment module, a sliding mode equation determination module, a decision condition and sliding surface parameter matrix determination module, a chatter-free sliding mode controller construction module, and a control module; The dynamic model building module is used to consider the time delay in information transmission and processing, the fluctuation of system parameters with environmental changes, and to build a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty. The sliding mode equation determination module is used to design a sliding surface for the dynamic model so that the system satisfies the desired stability once it reaches the sliding surface; and to determine the sliding mode equations based on the sliding surface and the dynamic model. The module for determining the criteria and sliding surface parameter matrix is ​​used to obtain, based on the sliding mode equations, the criteria for ensuring exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix, using Lyapunov stability theory and the mean residence time method. ; A chatter-free sliding mode controller building block is used to introduce the hyperbolic tangent function. As a continuous and smooth approximation of the switching function, the sliding surface parameter matrix is ​​used. Construct a chatter-free sliding mode controller; The control module is used to control the pulse random time delay system using the jitter-free sliding mode controller.

[0011] According to a third aspect of the present invention, an electronic device is provided, comprising: a processor and a memory, the memory storing a program or instructions executable on the processor, wherein the program or instructions, when executed by the processor, implement the steps of the jitter-free sliding mode control method with pulse random perturbation as described in any one of the first aspects.

[0012] According to a third aspect of the invention, a readable storage medium is provided having a program or instructions stored thereon, which, when executed by a processor, implement the steps of the jitter-free sliding mode control method with pulse random perturbation as described in any one of the first aspects.

[0013] Beneficial effects: (1) This invention is the first to simultaneously consider the combined effects of random nonlinear disturbances with uncertain occurrence probabilities, impulse effects, bounded state time delays, and system uncertainties on stability. By constructing a suitable Lyapunov function, sufficient conditions for ensuring synchronization between the two networks are established. Compared with existing stochastic system control methods, the sliding mode control strategy proposed in this invention has significant advantages: it can uniformly handle impulses, random disturbances, time delays, and uncertainties, effectively addressing the challenges these factors pose to the stability of the impulse control system. More importantly, this method successfully overcomes the chattering problem in traditional sliding mode control. By deriving a controller design method based on linear matrix inequalities (LMI), efficient suppression of parameter perturbations, random nonlinear disturbances, and time delay effects is achieved.

[0014] (2) By introducing the hyperbolic tangent function, the chattering phenomenon inherent in sliding mode control is effectively suppressed. This method is particularly suitable for stabilization problems of impulsive random systems with complex structures and multiple mixed disturbances.

[0015] (3) The present invention achieves exponential stability of the system in the mean square sense, and at the same time completely solves the chattering problem. Attached Figure Description

[0016] Figure 1 A flowchart of a chatter-free sliding mode control method with pulse random disturbances provided in an embodiment of the present invention; Figure 2 The figure shows the trajectory of the system state over time without the application of a sliding mode controller. It is the state of an impulse random system; Figure 3 The figure shows the trajectory of the system's state change over time under the action of the constructed sliding mode controller. It is the state of a pulse random system; Figure 4 To switch functions under the action of the constructed sliding mode controller The trajectory of change over time; Figure 5 The trajectory of the gain change of the designed adaptive control law; Figure 6 This is a block diagram of a jitter-free sliding mode control device with pulse random disturbance provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the hardware structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] The present invention describes the specific implementation process of a chatter-free sliding mode control method based on pulse random disturbances. It includes the following steps: Step 1: Considering that information transmission and processing often involve time delays, and system parameters may fluctuate with environmental changes, a dynamic model of an impulsive stochastic system with bounded state time delays and uncertainties is established. The specific process is as follows: Define a complete probability space , in It is the sample space, containing all possible random outcomes. It is a subset of the sample space Algebra is The set of subsets of defines measurable events. Denotes the probability measure, as Each event in the dataset is assigned a probability value. Represented as a probability measure Find the average value of the random variable. On this probability space, construct a dynamic model of an impulsive stochastic system with bounded state delays and uncertainties: (1) in, It is the system state vector, containing the information needed to describe the system dynamics. Individual variables, such as displacement, velocity, temperature, voltage, etc.; Let be a set of time-delayed states, representing Before the moment It is its upper bound and is a positive constant; It is the control input vector, with dimension . m . Assuming the system input matrix is ​​of full column rank, describe the control input. How does it affect the state derivative? Given a system parameter matrix, each parameter describes the current state of the system. and time delay state Contributions to the deterministic dynamics and random diffusion terms. Given a known random noise input matrix (usually full column rank), describing Brownian motion. How does it affect the state? It is a one-dimensional Brownian motion, a standard Gaussian white noise source driving random disturbances in the system, satisfying... [ ]=0, [ ]= ; For external disturbances that are time- and system state-dependent, it is assumed that the disturbances are bounded, i.e., there exist normal numbers. , making . Represents the real number field.

[0019] , It is a time-varying uncertainty matrix, representing unknown disturbances or parameter changes in system modeling, satisfying...

[0020]

[0021] in, All of them are known real matrices with appropriate dimensions, and , Let be an unknown, time-varying, Lebesgue-measurable matrix function that satisfies:

[0022] in It is an identity matrix of appropriate dimension.

[0023] For discrete pulse occurrence times, ; at these moments System status A momentary jump occurs due to the influence of the pulse. Describe the pulse moment The state of mind just moments before; It is an invertible matrix, describing the state at the pulse moment. How does the state change? These are the initial conditions, providing the system's initial conditions. 0 Previous status history.

[0024] Step 2: For the dynamic model of the impulsive random time-delay system with bounded state time delay and uncertainty established in Step 1, design a sliding mode surface so that the system satisfies the desired stability once it reaches the sliding mode surface, and derive the corresponding sliding mode equation.

[0025] The specific process for this step is as follows: Step 21: To smoothly handle the impact of pulse transitions on the sliding surface and ensure the continuity of the sliding surface at the pulse moment ( And it is smooth within the interval. =0), define the following piecewise function. :

[0026] in Indicates the first The length of the pulse interval. The degree is the minimum value of the pulse interval length. It represents the set of natural numbers. This represents the maximum value of the pulse interval length; , for interval A specific point in time within, lie in Minimum pulse interval length afterwards

[0027] Next, we define the following integral-type switching function. : (2) in, The parameter matrix of the sliding surface to be designed is the core object of the control design in this invention. It must satisfy: It is non-singular and satisfies To decouple noise, so that Dynamics are only affected by deterministic control. In implementation, let... , ,satisfy ; The feedback gain matrix is ​​a constant. This is required during the design phase. It is a Hurwitz matrix (i.e., all its eigenvalues ​​have negative real parts). Clearly... when The state-space trajectory when =0 is called the sliding surface. Defined The dimension switching function. The goal of the controller is to drive and maintain the system state on this sliding surface.

[0028] Step 22: Describe the system state trajectory once it reaches the sliding surface ( =0) and remain on the sliding surface (d The dynamic behavior when =0) is called sliding mode dynamics.

[0029] make According to the sliding surface 0, achieving equivalent control Substituting into equation (1), we obtain the sliding mode equation as follows: (3) in, and These represent the minimum and maximum values ​​of the pulse interval length, respectively; matrix , The sliding mode equation (3) describes the closed-loop dynamics of the system under ideal sliding mode.

[0030] Step 3: Based on the sliding mode equations obtained in Step 2, the criteria for ensuring exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix are obtained through Lyapunov stability theory and the mean residence time method. .

[0031] The specific process for this step is as follows: Step 31: Determine the stability condition of the mean square exponent.

[0032] set up System state vector At any moment The mean square value (the square of the expected Euclidean norm) measures the average "energy" of a state or the degree of deviation from equilibrium. This indicates the initial state within the historical time window. , The supremum of the upper mean square norm represents the "magnitude" of the initial perturbation.

[0033] If positive numbers exist , Make the system adaptable to any initial conditions All of them have: , Then the stochastic system is exponentially stable in the mean-square sense.

[0034] Step 32: Obtain the criteria for ensuring exponential stability of the sliding mode under the mean square sense by using Lyapunov stability theory and the average residence time method.

[0035] Lyapunov's stability theory states that: ; ,

[0036] in Normal values; pulse jump coefficient It is a positive number; For Lyapunov functions, Represents Lyapunov functions The expectation of the upper right derivative along the system trajectory; express .

[0037] Next, the criterion for exponential stability of the sliding mode equation in the mean square sense is obtained as follows: (4) (5) (6) In the formula,

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] In the formula, The block matrix in the first row and first column of the judgment condition. The block matrix in the first row and second column of the judgment condition. This is the block matrix in the second row and first column of the decision condition. The symmetric part of the block matrix express The transpose of the matrix, Let be the positive definite matrix to be found. ; Pulse jump coefficient The upper bound (i.e., for all) , ). >0 is the lower bound for the average dwell time. It is a constant used to relax the requirements for the average dwell time condition in the initial time period. This represents the system's own ability to maintain composure.

[0048] Formula (5) is equivalent to: (7) This is the parameter matrix for designing the sliding surface. Key constraints applied at the time D The equivalent form of 0.

[0049] In the formula The decision condition then becomes: find the smallest value that satisfies conditions (4), (6), and (7). .

[0050] prove: First, prove the stability of the system.

[0051] Give the Lyapunov function They respectively proved that at non-pulse moments About time The derivative is: , At the pulse moment, there is , , , Then the convergence of the system is given.

[0052] Give the Lyapunov function Comparison functions: ,

[0053] , For matrix The largest eigenvalue, Let be any positive integer.

[0054] Based on the principle of comparison, we obtain... , .

[0055] Using the constant variation formula and proof by contradiction, we can obtain , , ; It is an equation - + b =0 is the root. Therefore, we get: . Step 4: Traditional sliding mode control uses symbolic functions This can lead to high-frequency switching, generating harmful high-frequency oscillations—chickening. The method of this invention introduces a hyperbolic tangent function. As a continuous and smooth approximation of the switching function, the parameter matrix obtained in step three is used. A chatter-free sliding mode controller is constructed to achieve effective control of pulse random time-delay systems.

[0056] The specific process for this step is as follows: Step 41: Design a chatter-free sliding mode controller as follows: (8)

[0057] In the formula For switching gain coefficient, These are adaptive parameters, and their function is to adaptively estimate and compensate for system uncertainties. , and external disturbances The upper bound information. It is the Euclidean norm. The hyperbolic tangent function acts on the switching function vector This is the key innovation in achieving chatter-free sliding mode control.

[0058] Step 42, Adaptive Control Law Designed as follows: (9) Step 43, the conditions for reaching the sliding surface are: (10) in, The derivative of the switching function, >0 is a constant. constant The reciprocal, For adaptive parameters The derivative of is given by the adaptive law (9).

[0059] Example 1: Simulation was performed using the method of this invention: In a spring-mass damper system, the state variable Displacement representing mass, control input to the dynamic model of an impulsive stochastic system. This represents the system's controller. In real-world scenarios, systems are often affected by impulse factors. For example, when a car experiences a severe impact, the car's buffer is described by a spring-mass damper system with impulses. Furthermore, it is affected by various external disturbances such as airflow and temperature. Therefore, in a spring-mass damper system, environmental noise and modeling errors need to be considered. , Time lag And other phenomena. By using variable substitution, the spring-mass damper system is represented as a random impulse system (1). Displacement representing mass The velocity representing mass is used to obtain the system matrix parameters. , , The specific selection of all parameters involved in this system is shown below.

[0060] System parameters:

[0061]

[0062]

[0063] , , Assume a mass of 6, a stiffness of 40, and a damping coefficient of 20. The parameter matrix for feasible solution sliding mode surface control is obtained as follows: . Consider non-uniform pulse signal sequences ,

[0064] The effect of the constructed sliding mode controller: Figure 2 The state trajectory of an impulse random system without a controller Under the influence of impulse, time delay and uncertainty, the impulse random system exhibits an unstable state. Figure 3 The state trajectory of an impulsive random system is influenced by the constructed impulse, time delay, and uncertainty. .according to Figure 2 and Figure 3 It can be seen that even if the system is affected by pulses, time delays and uncertainties, the system will quickly stabilize after applying a chatter-free sliding mode controller. Figure 4 The switching function is implemented under the control of the constructed sliding mode controller. The trajectory can be observed to show that the trajectory of the system's switching function remains on the sliding surface from the initial moment. Figure 5 This is the gain of the designed adaptive control law. As shown in the figure, the gain gradually converges to a constant. Figures 2 to 5 It is evident that, for impulsive random systems with time delays and uncertainties, the invented sliding mode controller method can effectively suppress the influence of interference on the controlled output, achieve exponential asymptotic stability of the system, and overcome the chattering problem of traditional sliding mode controllers.

[0065] Based on the above method, the present invention also provides a jitter-free sliding mode control device with pulse random disturbance, such as... Figure 6 As shown, the device includes a dynamic model establishment module, a sliding mode equation determination module, a judgment condition and sliding surface parameter matrix determination module, a chatter-free sliding mode controller construction module, and a control module.

[0066] The dynamic model building module is used to consider the time delay in information transmission and processing, and the fluctuation of system parameters with environmental changes, to build a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty.

[0067] The sliding mode equation determination module is used to design a sliding surface for the dynamic model so that the system satisfies the desired stability once it reaches the sliding surface; and to determine the sliding mode equation based on the sliding surface and the dynamic model.

[0068] The module for determining the criteria and sliding surface parameter matrix is ​​used to obtain, based on the sliding mode equations, the criteria for ensuring exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix, using Lyapunov stability theory and the mean residence time method. .

[0069] A chatter-free sliding mode controller building block is used to introduce the hyperbolic tangent function. As a continuous and smooth approximation of the switching function, the sliding surface parameter matrix is ​​used. Construct a chatter-free sliding mode controller.

[0070] The control module is used to control the pulse random time delay system using the jitter-free sliding mode controller.

[0071] Furthermore, the jitter-free sliding mode control method with pulse random disturbances in the embodiments of this application can all be implemented by a computer device. Figure 7 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of this application. Figure 7 As shown, the device may include a processor 201 and a memory 202 storing computer program instructions.

[0072] Specifically, the processor 201 may include a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0073] The memory 202 may include a large-capacity memory for data or instructions. For example, and not limitingly, the memory 202 may include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), flash memory, an optical disk drive, a magneto-optical disk drive, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 202 may include removable or non-removable (or fixed) media. Where appropriate, the memory 202 may be internal or external to a data processing device. In a particular embodiment, the memory 202 is non-volatile memory. In a particular embodiment, the memory 202 includes read-only memory (ROM) and random access memory (RAM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable read-only memory (PROM), an erasable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), an electrically alterable read-only memory (EAROM), or flash memory, or a combination of two or more of these. Where appropriate, the RAM can be Static Random-Access Memory (SRAM) or Dynamic Random-Access Memory (DRAM). DRAM can be Fast Page Mode Dynamic Random-Access Memory (FPMDRAM), Extended Data Out Dynamic Random-Access Memory (EDODRAM), Synchronous Dynamic Random-Access Memory (SDRAM), etc.

[0074] The memory 202 can be used to store or cache various data files that need to be processed and / or communicated, as well as possible computer program instructions executed by the processor 201.

[0075] The processor 201 reads and executes computer program instructions stored in the memory 202 to implement any of the jitter-free sliding mode control methods with pulse random disturbances in the above embodiments.

[0076] In some embodiments, the computer device may further include a communication interface 203 and a bus 200. For example, Figure 7 As shown, the processor 201, memory 202, and communication interface 203 are connected through bus 200 and complete communication with each other.

[0077] The communication interface 203 is used to enable communication between the various modules, devices, units, and / or equipment in the embodiments of this application. The communication interface 203 can also enable data communication with other components such as external devices, image / data acquisition devices, databases, external storage, and image / data processing workstations.

[0078] Bus 200 includes hardware, software, or both, that couples components of a computer device together. Bus 200 includes, but is not limited to, at least one of the following: data bus, address bus, control bus, expansion bus, and local bus. For example, and not as a limitation, bus 200 may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand interconnect, a Low Pin Count (LPC) bus, a memory bus, a MicroChannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local Bus (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, bus 200 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnection is contemplated herein.

[0079] The computer device can execute the jitter-free sliding mode control method with pulse random disturbances in the embodiments of this application, thereby realizing the jitter-free sliding mode control method with pulse random disturbances described in this application.

[0080] Furthermore, in conjunction with the jitter-free sliding mode control method with pulse random perturbation in the above embodiments, this application embodiment can provide a computer-readable storage medium for implementation. This computer-readable storage medium stores computer program instructions; when executed by a processor, these computer program instructions implement any of the jitter-free sliding mode control methods with pulse random perturbation in the above embodiments.

[0081] It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. In addition, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0082] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A chatter-free sliding mode control method with pulse random disturbances, characterized in that, include: Step 1: Considering the time delay in information transmission and processing, and the fluctuation of system parameters with environmental changes, establish a dynamic model of an impulsive random time delay system with bounded state time delay and uncertainty. Step 2: For the dynamic model, design a sliding surface so that the system satisfies the desired stability once it reaches the sliding surface; based on the sliding surface and the dynamic model, determine the sliding mode equations; Step 3: Based on the aforementioned sliding mode equations, the criteria for ensuring exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix are obtained through Lyapunov stability theory and the mean residence time method. ; Step 4: Introduce the hyperbolic tangent function As a continuous and smooth approximation of the switching function, the sliding surface parameter matrix is ​​used. Construct a jitter-free sliding mode controller; The aforementioned jitter-free sliding mode controller is used to control the pulse random time-delay system; The dynamic model of the pulse random time-delay system with bounded state delay and uncertainty established in step 1 is as follows: (1) in, yes t The system state at any given time includes descriptions of the system's dynamics. One variable; Let be a set of time-delayed states, representing the state at time delay. Before the moment It is the upper bound of time-varying time delay; It is a control input; Given the system input matrix, assuming it is of full column rank, describe the control input. How does it affect the system state derivative? ; , Given a system parameter matrix, each parameter describes the current system state. and time delay state Contributions to the deterministic dynamics and random diffusion terms; Given a known random noise input matrix, describing Brownian motion. How does it affect the state? It is a one-dimensional Brownian motion, and a standard Gaussian white noise source that drives random disturbances in the system; For external disturbances that are time- and system state-dependent, it is assumed that the disturbances are bounded, i.e., there exist normal numbers. , making ; ， It is a time-varying uncertainty matrix, representing unknown disturbances or parameter changes in system modeling, satisfying: in, It is a known real matrix. , Let be an unknown, time-varying, Lebesgue-measurable matrix function that satisfies: , It is the identity matrix; For the pulse moment, ;exist System status at all times A transient jump occurs due to the influence of the pulse; Describe the pulse moment The state of mind just moments before; It is an invertible matrix, describing the state at the pulse moment. How does the state change? These are the initial conditions, providing the system's initial conditions. 0 Previous status history; Step two specifically involves: Step 21: Define the piecewise function To smoothly handle the impact of pulse transitions on the sliding surface and ensure that the sliding surface is continuous at the pulse moment and smooth within the interval between two pulses, the piecewise function is expressed as follows: in Indicates the first Pulse interval length, ; This is the minimum value of the pulse interval length. The set of natural numbers; This represents the maximum value of the pulse interval length; For interval A specific point in time within, lie in Minimum pulse interval length afterwards Define an integral switching function : (2) in, Here is the parameter matrix of the sliding surface to be designed. M Must meet: It is non-singular and satisfies To decouple noise, so that Dynamics are only affected by deterministic control; let ,satisfy ; The function is piecewise, and the compensation pulse transition makes the switching function continuous; Given a constant feedback gain matrix, it is required that... It is a Hurwitz matrix, meaning that all its eigenvalues ​​have negative real parts; obviously when The state-space trajectory at that time is called the sliding surface; It is the identity matrix; Defined The dimension switching function; the goal of the controller is to drive and maintain the system state on this sliding surface; Step 22: Describe the dynamic behavior of the system state trajectory once it reaches the sliding surface and remains on the sliding surface; this is called sliding dynamics. make Based on the derivative of the switching function while maintaining on the sliding surface Equivalent control is obtained Substituting into equation (1), we obtain the sliding mode equation as follows: (3) in, and These represent the minimum and maximum values ​​of the pulse interval length, respectively; matrix , ; The sliding mode equation (3) describes the closed-loop dynamics of the system in the ideal sliding mode; Step four specifically involves: Introducing the hyperbolic tangent function As a continuous and smooth approximation of the switching function, the sliding surface parameter matrix is ​​used. The construction of a chatter-free sliding mode controller is as follows: (8) In the formula This is the switching gain coefficient; As an adaptive parameter, its function is to adaptively estimate and compensate for system uncertainties. 、 and external disturbances The upper bound information; It is the Euclidean norm; Represents the hyperbolic tangent function Apply to switching function ; Adaptive control law Designed as follows: (9) The conditions for reaching the sliding surface are: (10) in, The derivative of the switching function, >0 is a constant. constant The reciprocal, For adaptive parameters The derivative of is given by the adaptive law (9).

2. The chatter-free sliding mode control method with pulse random disturbance as described in claim 1, characterized in that, Step three specifically involves: Step 31: Determine the mean square exponent stability condition: set up System status At any moment The mean square value measures the average energy of a state or the degree of deviation from the equilibrium point; This indicates the initial state within the historical time window. , The supremum of the upper mean square norm represents the magnitude of the initial perturbation; If positive numbers exist Make the system adaptable to any initial conditions All of them are: ， Then the stochastic system is exponentially stable in the mean-square sense; Step 32: Obtain the criteria for ensuring exponential stability of the sliding mode under the mean square sense using Lyapunov stability theory and the mean residence time method: The Lyapunov stability theory is as follows: At the pulse moment, we have: ， ； in Normal values; pulse jump coefficient It is a positive constant; For Lyapunov functions, Represents Lyapunov functions The expectation of the upper right derivative along the system trajectory; express ; The criterion for determining the exponential stability of the sliding mode equations in the mean square sense is: （4） （5） （6） In the formula, In the formula, The block matrix in the first row and first column of the judgment condition. This refers to the block matrix in the first row and second column of the decision condition. This refers to the block matrix in the second row and first column of the decision criteria; The symmetric part of the block matrix express The transpose of the matrix, Let be the positive definite matrix to be found. ; Pulse jump coefficient The upper bound, that is, for all , ; >0 This represents the lower bound of the average length of stay. It is a constant used to relax the requirements for the average dwell time condition in the initial time period; This represents the system's inherent calming ability and is a positive constant. , , , , All are positive numbers; It is a real positive definite matrix; Formula (5) is equivalent to: (7) This is the parameter matrix for designing the sliding surface. Key constraints applied at time The equivalent form; In the formula The decision condition is then transformed into finding the minimum value that satisfies conditions (4), (6), and (7). .

3. A jitter-free sliding mode control device with pulse random disturbance, characterized in that, The device for implementing the chatter-free sliding mode control method with pulse random disturbance as described in any one of claims 1-2 includes: a dynamic model establishment module, a sliding mode equation determination module, a decision condition and sliding surface parameter matrix determination module, a chatter-free sliding mode controller construction module, and a control module; The dynamic model building module is used to consider the time delay in information transmission and processing, the fluctuation of system parameters with environmental changes, and to build a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty. The sliding mode equation determination module is used to design a sliding surface for the dynamic model so that the system satisfies the desired stability once it reaches the sliding surface; and to determine the sliding mode equations based on the sliding surface and the dynamic model. The module for determining the criteria and sliding surface parameter matrix is ​​used to obtain, based on the sliding mode equations, the criteria for ensuring exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix, using Lyapunov stability theory and the mean residence time method. ; A chatter-free sliding mode controller building block is used to introduce the hyperbolic tangent function. As a continuous and smooth approximation of the switching function, the sliding surface parameter matrix is ​​used. Construct a jitter-free sliding mode controller; The control module is used to control the pulse random time delay system using the jitter-free sliding mode controller.

4. An electronic device, characterized in that, include: A processor and a memory, wherein the memory stores a program or instructions that can run on the processor, and when the program or instructions are executed by the processor, implement the steps of the chatter-free sliding mode control method with pulse random perturbation as described in any one of claims 1 to 2.

5. A readable storage medium, characterized in that, It stores a program or instructions that, when executed by a processor, implement the steps of the jitter-free sliding mode control method with pulse random disturbance as described in any one of claims 1 to 2.

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