Non-buffeting sliding mode control method with pulse random disturbance

Abstract

The invention provides a buffeting-free sliding mode control method and device with pulse random disturbance, electronic equipment and a readable storage medium. The method comprises the following steps: firstly, establishing a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty; a sliding mode surface is designed for the dynamic model, so that the system meets the expected stability once reaching the sliding mode surface; determining a sliding mode dynamic equation based on a sliding mode surface in combination with the dynamic model; based on the sliding mode equation, obtaining a judgment condition and a sliding mode surface parameter matrix for ensuring the index stability under the dynamic mean square significance of the sliding mode; and introducing a hyperbolic tangent function as continuous smooth approximation of a switching function, and constructing a buffeting-free sliding mode controller by using a sliding mode surface parameter matrix to realize control of a pulse random time delay system. By using the sliding mode control method, the problem that the sliding mode control precision is low due to the fact that an existing sliding mode control method cannot process pulses, environmental noise, time lag and uncertainty at the same time and the influence of external disturbance on the controlled output of the system is large can be solved.

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.

[0010] 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 dynamic equations.

[0011] Step 3: Based on the sliding mode equation, obtain the criteria for ensuring the exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix M, through Lyapunov stability theory and the average dwell time method.

[0012] Step 4: Introduce the hyperbolic tangent function tanh as a continuous and smooth approximation of the switching function, and use the sliding mode surface parameter matrix M to construct a chatter-free sliding mode controller to realize the control of the pulse random time delay system.

[0013] 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 dynamic equation determination module, a judgment condition and sliding mode surface parameter matrix determination module, a chatter-free sliding mode controller construction module, and a control module;

[0014] 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.

[0015] The sliding mode dynamic 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 dynamic equation based on the sliding surface and the dynamic model.

[0016] The module for determining the judgment conditions and the sliding surface parameter matrix is ​​used to obtain the judgment conditions for ensuring the exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix M, based on the sliding mode equation, through Lyapunov stability theory and the average dwell time method.

[0017] A chatter-free sliding mode controller construction module is used to introduce the hyperbolic tangent function tanh as a continuous and smooth approximation of the switching function, and to construct a chatter-free sliding mode controller using the sliding mode surface parameter matrix M.

[0018] The control module is used to control the pulse random time delay system using the chatter-free sliding mode controller.

[0019] 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.

[0020] 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.

[0021] Beneficial effects:

[0022] (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 impulse control systems. 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.

[0023] (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.

[0024] (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

[0025] Figure 1 A flowchart of a chatter-free sliding mode control method with pulse random disturbances provided in an embodiment of the present invention;

[0026] Figure 2 The figure shows the trajectory of the system state over time without the application of a sliding mode controller, x. i(t) i = 1, 2 are the states of the impulse random system;

[0027] Figure 3 The figure shows the trajectory of the system's state change over time under the action of the constructed sliding mode controller, with x as an example. i(t) i = 1, 2 are the states of the impulse random system;

[0028] Figure 4 The trajectory of the switching function S(t) over time under the action of the constructed sliding mode controller;

[0029] Figure 5 The trajectory of the gain change of the designed adaptive control law;

[0030] 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;

[0031] 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

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0033] 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:

[0034] 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:

[0035] Define a complete probability space Where Ω is the sample space, containing all possible random outcomes. It is the σ-algebra of a subset of the sample space, and is the set of subsets of Ω, defining measurable events. Denotes the probability measure, as Each event in the algorithm is assigned a probability value. E represents the 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:

[0036]

[0037] in, It is the system state vector, which contains n variables required to describe the system dynamics, such as displacement, velocity, temperature, voltage, etc. Let be the set of time-delay states, representing the historical states within the time interval (t-τ(t), t) before time t, where τ(t) is the time-varying time delay. It is its upper bound and is a positive constant; It is the control input vector with dimension m. Given a system input matrix, assuming it is full column rank, describe how the control input u(t) affects the state derivative. Given the system parameter matrix, which describes the current system state x(t) and the time-delay state x, respectively. t Contributions to the deterministic dynamics and random diffusion terms. Let be a known random noise input matrix (usually full column rank) describing how the Brownian motion dw(t) affects the state. w(t) is a one-dimensional Brownian motion, a standard Gaussian white noise source driving the random perturbation of the system, satisfying E[dw(t)] = 0, E[(dw(t))] = 0. 2 ]=dt;f(x(t),t) is an external disturbance related to time and system state. It is assumed that the disturbance is bounded, that is, there exists a positive constant ζ such that f(x(t),t)≤ζ. Represents the real number field.

[0038] ΔA(t), ΔG(t), It is a time-varying uncertainty matrix, representing unknown disturbances or parameter changes in system modeling, satisfying...

[0039]

[0040] [ΔG(t) ΔG(t)]=E2F2(t)[H3 H4];

[0041] in, Both are known real matrices of appropriate dimension, while F1(t) and F2(t) are unknown, time-varying, Lebesgue measurable matrix functions that satisfy:

[0042]

[0043] Where I is an identity matrix of appropriate dimension.

[0044] t k For discrete pulse occurrence times, k = 1, 2, ...; at these times t k The system state x(t) undergoes a transient change due to the pulse. x(t) at time t k Left limit of time Describe the pulse time t k The state of mind just moments before; It is an invertible matrix that describes the state at pulse time t. k How the state transitions; φ(θ) is the initial condition, giving the state history of the system before the initial time t=0.

[0045] 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 dynamic equations.

[0046] The specific process for this step is as follows:

[0047] 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 Define the following piecewise function

[0048]

[0049] Where T k =t k+1 -t k This represents the length of the interval between the k-th pulses, t0 = 0. The degree is the minimum value of the pulse interval length. It represents the set of natural numbers. t' is the maximum value of the pulse interval length; k =t k +α, for the interval [t] k , t k+1 A specific point in time within ) located at t k Then at the minimum pulse interval length α.

[0050] Next, we define the integral switching function S(t) as follows:

[0051]

[0052] in, The sliding surface parameter matrix to be designed is the core object of the control design in this invention. It must satisfy the following conditions: MB is non-singular and MD = 0, to decouple noise and ensure that the dynamics of S(t) are only affected by deterministic control. In implementation, let M = B. T X is a positive definite matrix to be found, satisfying rank(B) = rank(B). T ) = rank(B T X); Let A+BK be a constant feedback gain matrix. The design requires A+BK to be a Hurwitz matrix (i.e., all its eigenvalues ​​have negative real parts). Clearly, S(0) = 0. The state-space trajectory when S(t) = 0 is called the sliding surface. S(t) defines an m-dimensional switching function. The goal of the controller is to drive and maintain the system state on this sliding surface.

[0053] Step 22: Describe the dynamic behavior of the system state trajectory once it reaches the sliding surface (S(t)=0) and remains on the sliding surface (dS(t) / dt=0), which is called sliding dynamics.

[0054] make x(t k )=x(t-τ1(t)),τ1(t)=tt k According to the sliding surface The equivalent control u(t) is obtained. Substituting it into equation (1), the sliding mode equation is obtained as follows:

[0055]

[0056] Where α and These represent the minimum and maximum values ​​of the pulse interval length, respectively; matrix Θ = IB(MB) -1 M, The sliding mode equation (3) describes the closed-loop dynamics of the system under ideal sliding mode.

[0057] Step 3: Based on the sliding mode equations obtained in Step 2, the criteria for ensuring the exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix M are obtained through Lyapunov stability theory and the mean residence time method.

[0058] The specific process for this step is as follows:

[0059] Step 31: Determine the stability condition of the mean square exponent.

[0060] Let E||x(t)|| 2The mean square value (the square of the expected Euclidean norm) of the system state vector x(t) at time t measures the average "energy" of the 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.

[0061] If there exist positive constants λ and C such that the system adapts to any initial conditions All of them are:

[0062]

[0063] Then the stochastic system is exponentially stable in the mean-square sense.

[0064] 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.

[0065] Lyapunov's stability theory states that:

[0066]

[0067] Where β1, β2, and β3 are positive constants; the pulse jump coefficient ρ k It is a positive number; For Lyapunov functions, Represents Lyapunov functions The expectation of the upper right derivative along the system trajectory; express In t k The left limit at time.

[0068] Next, the criterion for making the sliding mode dynamic equation exponentially stable in the mean square sense is obtained as follows:

[0069]

[0070] B T XD=0, (5)

[0071]

[0072] In the formula,

[0073]

[0074]

[0075] In the formula, Ψ1 is the block matrix in the first row and first column of the decision condition, Ψ2 is the block matrix in the first row and second column of the decision condition, and Ψ3 is the block matrix in the second row and first column of the decision condition. X and Q are real positive definite matrices, * represents the symmetric part of the block matrix, and B... T Let M denote the transpose of B, X be the positive definite matrix to be found, and M = B. T X; ρ≥1 is the pulse jump coefficient ρ k The upper bound (i.e., for all k, ρ) k ≤ρ). This represents the lower bound of the average residence time. N0≥0 is a constant used to relax the requirements of the average residence time condition in the initial time period. β1 represents the system's own stabilization capability.

[0076] Formula (5) is equivalent to:

[0077]

[0078] This is the design sliding surface parameter matrix M=B T The equivalent form of the critical constraint MD=0 applied at time X.

[0079] If δ>0, then the judgment condition is transformed into: find the minimum δ that satisfies conditions (4), (6), and (7).

[0080] prove:

[0081] First, prove the stability of the system.

[0082] Give the Lyapunov function They respectively proved that the non-pulse time The derivative of with respect to time t is:

[0083]

[0084] At the pulse moment, there is

[0085]

[0086] Then the convergence of the system is given.

[0087] Give the Lyapunov function Comparison functions:

[0088]

[0089] U(θ)=-σ||φ(θ)||, σ is the largest eigenvalue of matrix Q, and ∈ is any positive constant.

[0090] Based on the principle of comparison, we obtain... t≥0.

[0091] Using the constant variation formula and proof by contradiction, we can obtain It is an equation The root. Therefore, we obtain:

[0092]

[0093] Step 4: Traditional sliding mode control using the sign function (sign) leads to high-frequency switching and generates harmful high-frequency oscillations—chattering. The method of this invention introduces the hyperbolic tangent function (tanh) as a continuous and smooth approximation of the switching function. Using the parameter matrix M obtained in Step 3, a chatter-free sliding mode controller is constructed to achieve effective control of the pulse random time-delay system.

[0094] The specific process for this step is as follows:

[0095] Step 41: Design a chatter-free sliding mode controller as follows:

[0096]

[0097] In the formula, μ>0 is the switching gain coefficient. As an adaptive parameter, its function is to adaptively estimate and compensate for the system uncertainty ΔA(t). The upper bound information of the external disturbance f. ||·|| is the Euclidean norm. tanh(S(t)) is the hyperbolic tangent function acting on the switching function vector S(t). This is the key innovation in realizing chatter-free sliding mode control.

[0098] Step 42, Adaptive Control Law Designed as follows:

[0099]

[0100] Step 43, the conditions for reaching the sliding surface are:

[0101]

[0102] in, Let h be the derivative of the switching function, h>0 be a constant, and h -1 It is the reciprocal of the constant h. For adaptive parameters The derivative of is given by the adaptive law (9).

[0103] Example 1:

[0104] Simulation was performed using the method of this invention:

[0105] In a spring-mass damper system, the state variable *x* represents the displacement of the mass, and the control input *u(t)* in the dynamic model of the impulse stochastic system 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 also affected by various external disturbances such as airflow and temperature. Therefore, in a spring-mass damper system, environmental noise and modeling errors ΔA(t) need to be considered. ΔG(t), Phenomena such as time delay τ(t). By using variable substitution, the spring-mass damper system is represented as a random pulse system (1), where x1 represents the displacement of the mass and x2 represents the velocity of the mass, thus obtaining the system matrix parameters A. B,G, D,ΔA(t), ΔG(t), The specific selection of all parameters involved in this system is shown below.

[0106] System parameters:

[0107]

[0108] f = 0.3(0, tanh(||x(t)||)) T B = (10.5, -5) T D = 0.5I²

[0109] E1 = (0,1) T E2 = (1,1) T F1 = cos(2t),

[0110]

[0111] Assuming a mass of 6, stiffness of 40, damping coefficient of 20, a1 = 2, a2 ​​= -5, a3 = -2, a4 = -2, Given λ1=λ2=0.5, τ(t)=0.5-0.5sin(t), the parameter matrix for feasible solution of sliding mode surface control is obtained as follows.

[0112] ε=0.95, ε1=7.00, ε2=0.11,

[0113] Consider a non-uniform pulse signal sequence {t} k},

[0114]

[0115] The effect of the constructed sliding mode controller:

[0116] Figure 2 The state trajectory x of an impulse random system without a controller i (t), i=1,2; Under the influence of impulse, time delay and uncertainty, the impulse random system exhibits an unstable state. Figure 3 The state trajectory x of the impulsive random system under the influence of constructed impulses, time delays, and uncertainties. i (t), i = 1, 2. 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 trajectory of the switching function S(t) under the action of the constructed sliding mode controller is observed to be maintained 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.

[0117] 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 dynamic equation determination module, a judgment condition and sliding mode surface parameter matrix determination module, a chatter-free sliding mode controller construction module, and a control module.

[0118] 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.

[0119] The sliding mode dynamic 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 dynamic equation based on the sliding surface and the dynamic model.

[0120] The module for determining the judgment conditions and the sliding surface parameter matrix is ​​used to obtain the judgment conditions for ensuring the exponential stability of the sliding mode in the dynamic mean square sense, and the sliding surface parameter matrix M, based on the sliding mode equation, through Lyapunov stability theory and the average dwell time method.

[0121] A chatter-free sliding mode controller construction module is used to introduce the hyperbolic tangent function tanh as a continuous smooth approximation of the switching function, and to construct a chatter-free sliding mode controller using the sliding mode surface parameter matrix M.

[0122] The control module is used to control the pulse random time delay system using the chatter-free sliding mode controller.

[0123] 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.

[0124] 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.

[0125] 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 ROM (EPROM), an electrically erasable read-only ROM (EEPROM), an electrically alterable read-only ROM (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.

[0126] 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.

[0127] 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.

[0128] 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.

[0129] 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.

[0130] 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.

[0131] 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.

[0132] 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.

[0133] 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.

[0134] 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 chattering-free sliding mode control method with pulse random perturbation, characterized by, The method comprises the following steps: Step 1, considering the time delay existing in the information transmission and processing process and the fluctuation of system parameters with the change of environment, a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty is established; Step 2, for the dynamic model, a sliding mode surface is designed to make the system meet the expected stability once reaching the sliding mode surface; based on the sliding mode surface and the dynamic model, a sliding mode dynamic equation is determined; Step 3, based on the sliding mode dynamic equation, a judging condition for ensuring the exponential stability of the sliding mode dynamic in the mean square sense and a sliding mode surface parameter matrix M are obtained by using the Lyapunov stability theory and the average dwell time method; Step 4, a hyperbolic tangent function tanh is introduced as a continuous smooth approximation of the switching function, a chattering-free sliding mode controller is constructed by using the sliding mode surface parameter matrix M, and the control of the pulse random time delay system is realized by using the chattering-free sliding mode controller.

2. The chattering-free sliding mode control method with pulse random disturbance according to claim 1, wherein, The dynamic model of the pulse random time delay system with bounded state time delay and uncertainty established in the step 1 is as follows: where x(t) is the system state at time t, containing n variables that describe the system dynamics; is the set of delayed states, representing the history of the system state in the time period (t-τ(t), t) before time t, where τ(t) is the time-varying delay, is the upper bound of the time-varying delay; u(t) is the control input; B is the system input matrix, which is assumed to be column full rank, describing how the control input u(t) affects the system state derivative dx(t) / dt; A, G, is the known system parameter matrix, describing the system current system state x(t) and the delayed state x t the contribution in the deterministic part and the stochastic diffusion term; D is the known stochastic noise input matrix, describing how the Brownian motion dw(t) affects the state; w(t) is a one-dimensional Brownian motion, which is a standard Gaussian white noise source driving the stochastic disturbance of the system; f(x(t), t) is the external disturbance related to time and system state, which is assumed to be bounded, i.e., there exists a positive number ζ such that f(x(t), t)≤ζ; ΔA(t), ΔG(t), is the time-varying uncertainty matrix, representing the unknown disturbance or parameter variation in the system modeling, which satisfies: [Delta G(t) Delta G(t)] = E2F2(t)[H3 H4]; where E1, E2, H1, H2, H3, H4 are known real matrices, F1(t), F2(t) are unknown, time-varying, Lebesgue measurable matrix functions satisfying: I is the identity matrix; t k is the impulse time, k = 1,2,... ; at the impulse time the system state x(t) undergoes an instantaneous jump; x(t) has a left limit k at the impulse time t k describes the state at the instant just before the impulse time t k ; φ(θ) is the initial condition giving the state history of the system before the initial time t = 0. is a reversible matrix describing how the state jumps at the impulse time t k ; φ(θ) is the initial condition giving the state history of the system before the initial time t = 0.​ 3. The chattering-free sliding mode control method with pulse random perturbation of claim 2, wherein, The step 2 is specifically as follows: Step 21: Define piecewise function To smooth the influence of pulse jump on the sliding surface, ensure the continuity of the sliding surface at the pulse moment and smoothness in the interval between two pulses, the piecewise function is expressed as follows: wherein T k = t k+1 -t k denotes the length of the kth pulse interval, t0= 0; is the minimum value of the pulse interval length, is the set of natural numbers; is the maximum value of the pulse interval length; t k = t k + a is a specific point in time within the interval [t k , t k+1 ) which lies a minimum pulse interval length a after t k . An integral-type switching function S(t) is defined: Where M is the sliding mode surface parameter matrix to be designed, M needs to satisfy: MB is non-singular, and satisfies MD=0, to decouple the noise, so that S(t) dynamics is only affected by deterministic control; Let M=B T X, X is the positive definite matrix to be solved, satisfying rank(B) = rank(B T ) = rank(B T X); is a piecewise function, which compensates for the pulse jump to make the switching function continuous; K is a constant feedback gain matrix, and A+BK is required to be a Hurwitz matrix, that is, the eigenvalues of A+BK all have negative real parts; obviously, S(0) = 0, and the state space trajectory when S(t) = 0 is called a sliding mode surface; I is a unit matrix; S(t) defines a switching function of m dimensions; the objective of the controller is to drive and maintain the system state on the sliding mode surface; Step 22: the dynamic behavior when the system state trajectory reaches and maintains on the sliding mode surface is described, and is called a sliding mode dynamic; Let x(t k )=x(t-τ1(t)),τ1(t)=t-t k , the derivative of the switching function u(t) is obtained, and substituted into (1) to obtain the sliding mode equation: where a and are the minimum and maximum values of the pulse interval length, respectively; the matrix Θ = I - B(MB) -1 M, The sliding mode equation (3) characterizes the closed-loop dynamics of the system in the ideal sliding mode.

4. The chattering-free sliding mode control method with pulse random disturbance according to claim 3, wherein, The step 3 is specifically as follows: Step 31, a mean square exponential stability condition is determined: Let E||x(t)| 2 is the mean square value of the system state x(t) at time t, which measures the average energy of the state or the degree of deviation from the equilibrium point; denotes the upper bound of the upper mean square norm of the initial state in the history time window the upper bound of the upper mean square norm, representing the size of the initial disturbance; If there exist normal numbers lambda and C such that the system has the following condition for any initial condition phi(theta): Then the random system is exponentially stable in the mean square sense. Step 32, a judging condition for ensuring the exponential stability of the sliding mode dynamic in the mean square sense is obtained by using the Lyapunov stability theory and the average dwell time method: The Lyapunov stability theory is as follows: At the pulse time, the following condition is met: where β1, β2, β3are normal numbers; pulse jump coefficient ρ k are normal numbers; is a Lyapunov function, denotes a Lyapunov function the desired upper right derivative along the system trajectory; denotes the left limit at time t k ; The judging condition for ensuring the exponential stability of the sliding mode dynamic equation in the mean square sense is obtained as follows: B T XD = 0, (5) In the formula, delta>0, and then the judging condition is converted into finding the minimum delta that meets the conditions (4), (6) and (7). In the formula, Ψ1 is the block matrix of the first column in the first row of the decision condition, Ψ2 is the block matrix of the second column in the first row of the decision condition, and Ψ3 is the block matrix of the first column in the second row of the decision condition; * is the symmetric part of the block matrix, B T denotes the transpose matrix of B, X is the positive definite matrix to be solved, and M = B T X; ρ ≥ 1 is the pulse jump coefficient ρ k the upper bound of ρ, that is, for all k, ρ k ≤ ρ; is the lower bound of the average residence time; N0 ≥ 0 is a constant, which is used to relax the requirement of the average residence time condition in the initial time period; β1 represents the stabilization ability of the system itself, which is a normal number; ε1, ε2, ε, λ1, λ2 are all normal numbers; and Q is a real positive definite matrix. The step 4 is specifically as follows: This is the design of the sliding mode surface parameter matrix M = B T X when the key constraints MD = 0 is applied equivalent form; The hyperbolic tangent function tanh is introduced as a continuous smooth approximation of the switching function, and a chattering-free sliding mode controller is constructed by using the sliding mode surface parameter matrix M as follows:

5. The chattering-free sliding mode control method with pulse random perturbation of claim 4, wherein, The reaching condition of the sliding mode surface is as follows: The method comprises the following steps: where μ > 0 is a switching gain coefficient; is an adaptive parameter, which is used to adaptively estimate and compensate the upper bound information of system uncertainty ΔA(t), and external disturbance f; || · || is the Euclidean norm; tanh(S(t)) represents the hyperbolic tangent function tanh acting on the switching function S(t); Adaptive control law Designed to: A dynamic model establishing module, a sliding mode dynamic equation determining module, a judging condition and a sliding mode surface parameter matrix determining module, a chattering-free sliding mode controller constructing module and a control module are comprised. where is the derivative of the switching function, h > 0 is a constant, h -1 is the inverse of the constant h, is the derivative of the adaptive parameter is given by the adaptation law (9).

6. A device for chattering-free sliding mode control with pulse random perturbation, characterized by, The dynamic model establishing module is used for considering the time delay existing in the information transmission and processing process and the fluctuation of system parameters with the change of environment, and establishing a dynamic model of a pulse random time delay system with bounded state time delay and uncertainty. ​ ​ a sliding mode dynamic equation determination module, configured to design a sliding surface for the dynamic model, so that the system meets the expected stability once reaching the sliding surface; and determine a sliding mode dynamic equation based on the sliding surface and the dynamic model; a determination condition and sliding surface parameter matrix determination module, configured to obtain a determination condition for ensuring exponential stability of the sliding mode dynamic equation in the mean square sense and a sliding surface parameter matrix M based on the sliding mode dynamic equation, Lyapunov stability theory and the average dwell time method; a chattering-free sliding mode controller construction module, configured to introduce a hyperbolic tangent function tanh as a continuous smooth approximation of a switching function, and construct a chattering-free sliding mode controller using the sliding surface parameter matrix M; a control module, configured to implement control over the pulse random time delay system using the chattering-free sliding mode controller.

7. An electronic device, comprising: comprise: a processor and a memory, the memory storing programs or instructions executable on the processor, the programs or instructions being executed by the processor to implement the steps of the chattering-free sliding mode control method with pulse random disturbance according to any one of claims 1 to 5.

8. A readable storage medium, characterized by, a processor and a memory, the memory storing programs or instructions executable on the processor, the programs or instructions being executed by the processor to implement the steps of the chattering-free sliding mode control method with pulse random disturbance according to any one of claims 1 to 5.

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