An asynchronous undisturbed switching control method for safe operation of a sewage treatment system

Abstract

The present application relates to a kind of wastewater treatment system safe operation asynchronous disturbance-free switching control method, comprising the following steps: establishing the random semi-markov jump state space model of wastewater treatment system;Modal and control modal asynchronous jump framework of wastewater treatment system are constructed;According to semi-markov jump state space model and asynchronous jump framework, design wastewater treatment system safe operation under asynchronous disturbance-free switching control scheme;Combining the model established and the asynchronous disturbance-free switching control scheme designed, the closed-loop system of wastewater treatment system is constructed;Based on asynchronous jump framework and closed-loop system, the parameter of wastewater treatment system safe operation asynchronous disturbance-free switching controller is determined, and wastewater treatment system is controlled using controller.Compared with prior art, the present application can effectively solve the problem of disturbance-free switching finite time control of wastewater treatment system under complex working conditions, and the safe operation problem under network attack when system modal and controller modal are asynchronous.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of sewage treatment in smart city, and particularly relates to an asynchronous undisturbed switching control method for safe operation of a sewage treatment system. BACKGROUND

[0002] Since the 21st century, the level of urbanization and industrialization in China has developed unprecedentedly, which not only significantly improves people's living standards, but also brings some new problems to people's living environment, such as traffic congestion, air pollution and water pollution, etc. Among these challenges, the effectiveness of urban sewage treatment is particularly critical, which not only relates to the sustainable development of the city, but also is an important indicator to measure the level of urban management. Therefore, exploring and implementing efficient urban sewage treatment strategies is a problem that needs to be solved urgently.

[0003] Sewage mainly comes from life, production and industrial facilities, including domestic sewage generated by toilets, kitchens, bathrooms, etc., and in some areas, it also includes industrial sewage, medical sewage and agricultural sewage. Water pollution not only affects industrial production, increases equipment corrosion, affects product quality, and even makes production unable to continue, but also affects people's life and ecological environment, directly endangers human health and causes irreparable loss. Therefore, exploring sewage treatment technology has very important social and economic value. Currently, sewage treatment often uses physical, biological and chemical methods to treat domestic sewage and industrial wastewater to separate solid pollutants in water and reduce organic pollutants and nutrients (mainly nitrogen and phosphorus compounds) in water, so as to obtain environmentally friendly liquid waste streams (or treated sewage) and solid waste (or sludge treatment), thereby reducing the pollution of sewage to the environment, and even the water after multiple purification can reach the standard of drinking water and can be used for drinking.

[0004] In the sewage treatment process, the amount of inflow sewage treatment tank varies with the water use of each water end, which makes it difficult for a single model to analyze and depict the sewage treatment process and thus to ensure effective sewage treatment. Therefore, according to the "peak period" and "non-peak period" characteristics of the water demand of each water end, multiple modal sewage treatment system models satisfying the random semi-Markov jump process are established. Different modal sewage treatment systems adopt different control execution guidelines to achieve the best control effect. When the modal of the sewage treatment system frequently switches, it is easy to cause the execution device of the sewage treatment system to vibrate greatly, which may speed up the wear of the execution device, or even cause the collapse of the sewage treatment system. In view of this problem, some scholars have proposed undisturbed control methods, but how to apply the undisturbed control technology to solve the stable operation problem of the sewage treatment system with multiple modes has not been fully considered.

[0005] In addition, network technology is gradually applied to chemical production, automobile manufacturing, sewage treatment and many other advanced production and manufacturing scenes. The openness of the network environment on the one hand promotes the improvement of production efficiency, and on the other hand brings many new challenges to data security and safe production in the data transmission process, such as the vulnerability of actuators and sensors in an open network environment to network attacks. If the actuator executes the wrong execution instruction, it is difficult to achieve accurate control goals, or even cause equipment damage and production accidents. It is of great significance to realize the safe and stable operation of the sewage treatment system with multiple modes under the open network environment. SUMMARY

[0006] The purpose of the present application is to provide an asynchronous disturbance-free switching control method for safe operation of a sewage treatment system, which solves the safety control problem of a sewage treatment system with multiple modes under network attacks based on disturbance-free control technology, safety control technology and asynchronous control technology.

[0007] The purpose of the present application can be achieved by the following technical solutions:

[0008] An asynchronous disturbance-free switching control method for safe operation of a sewage treatment system, comprising the following steps:

[0009] Step 1, establishing a random semi-Markov jump state space model of the sewage treatment system;

[0010] Step 2, using the hidden semi-Markov principle, constructing an asynchronous jump framework of the sewage treatment system mode and the control mode;

[0011] Step 3, according to the established semi-Markov jump state space model and the determined asynchronous jump framework, designing an asynchronous disturbance-free switching control scheme for safe operation of the sewage treatment system;

[0012] Step 4, combining the established model and the designed asynchronous disturbance-free switching control scheme, constructing a closed-loop system of the sewage treatment system;

[0013] Step 5, based on the constructed asynchronous jump framework and closed-loop system, determining the parameters of the asynchronous disturbance-free switching controller for safe operation of the sewage treatment system, and using the controller to control the sewage treatment system.

[0014] The random semi-Markov jump state space model of the sewage treatment system established in step 1 is as follows:

[0015]

[0016] wherein, respectively represent the water level of the treatment tank, the opening of the valve and the nonlinear disturbance signal in the system operation in the sewage treatment system at time t, This represents random noise in the wastewater treatment process, which follows Brownian motion. and Let represent n-dimensional, m-dimensional, p-dimensional, and q-dimensional vector spaces, respectively. Here, n represents the number of wastewater treatment tanks in the wastewater treatment system, m represents the number of valves controlling the water level in the tanks, p represents the number of complex nonlinear disturbances encountered during wastewater treatment, and q represents the number of random factors affecting the water level in the tanks. The function r(t) is a transition signal that automatically switches the operating mode of the wastewater treatment system based on actual operating conditions during system operation; its value range is a finite set. N represents the Nth operating mode of the wastewater treatment system; and The system matrix for the r(t)th operating mode is obtained from the equation governing the change in water flow in the wastewater treatment tank during the wastewater treatment process; therefore, when r(t) = i, it is simply denoted as A. i =A r(t) B i =B r(t) D i =D r(t) E i =E r(t) ; and They represent n×n, n×m, n×p, and n×q dimensional Euclidean matrix spaces, respectively.

[0017] The specific process of step 2 is as follows:

[0018] Step 2.1: Model the transition signal r(t) of the system's operating mode based on the semi-Markov transition process theory, and determine its transition probability;

[0019] Step 2.2, combining the hidden semi-Markov transition theory, model the observed signal σ(t) of the system's operating mode transition signal r(t), which is in a finite set. The values ​​are selected from the inner values, and their transmission probability and perturbation probability are determined. Here, M represents the number of observation signals that can be used to observe the modal signal r(t) of the original sewage treatment system based on the hidden semi-Markov transition process; σ(t) = M represents that the Mth observation signal can be used to observe the modal signal r(t) of the original sewage treatment system.

[0020] Step 2.3: Based on steps 2.1 and 2.2, obtain the double-jump transition process. And determine its transition probability.

[0021] In step 2.1, the transition signal r(t) of the system operating mode follows the following transition probabilities:

[0022]

[0023] in, Δ represents a small time increment, and ο(Δ) represents a higher-order infinitesimal of Δ; τ represents the dwell time of two freely transitioning operating modes, satisfying τ>0; λ ij (τ) is the transition rate from mode i to mode j, and satisfies λ ij (τ)≥0(i≠j) and N represents the number of modes in the original system.

[0024] In step 2.2, the transmission probability of the observed signal σ(t) is:

[0025]

[0026] in, It is a known probability constant that satisfies and

[0027] The probability of perturbation of the observed signal σ(t) is:

[0028]

[0029] in,

[0030] In step 2.3, the transition probability of the double-jump process is:

[0031]

[0032] Among them, the transfer rate

[0033] The specific process of step 3 is as follows:

[0034] Step 3.1, considering that the sensor-to-controller channel in the wastewater treatment system may be subject to random spoofing attacks, the signal received by the controller is modeled as follows:

[0035] u(t) = K σ(t) ((1-γ1(t))x(t)+γ1(t)ω1(x(t)))

[0036] Among them, K σ(t) γ1(t) is the control gain matrix of the σ(t)th observation mode to be designed; γ1(t) is a random variable that follows a Bernoulli distribution and is used to characterize a spoofing attack that occurs randomly on the sensor-to-controller channel. When γ1(t) = 1, the attack occurs; when γ1(t) = 0, the signal is transmitted normally. Where E{} represents the mathematical expectation; the attack signal ω1(x(t)) is an unknown and bounded nonlinear function that satisfies ω1(x(t)). 2 ≤φ1x(t)2 ; This indicates the sewage level in the sewage treatment tank;

[0037] Step 3.2, considering a random spoofing attack occurring on the controller-to-actuator channel, the actuator input is modeled as follows:

[0038]

[0039] Where ξ(t)=-u(t)+ω2(x(t)) is the deception signal initiated by the attacker, and ω2(x(t)) is a bounded nonlinear signal that satisfies ω1(x(t)). 2 ≤φ1x(t) 2 φ1 represents a known scaling constant; γ2(t) is a random Bernoulli variable independent of γ1(t).

[0040] Step 3.3, the asynchronous switching of the controller and the impact of attack signals lead to Indicates the first The gain matrix of each observation mode. Indicates the first Gain matrix of each observation mode;

[0041] To ensure the controller transitions are as smooth as possible, the following bumpless switching performance metrics are introduced:

[0042]

[0043] Among them, u * (t)=K * ((1-γ1(t))x(t)+γ1(t)ω1(x(t))) is the reference control input, K * This represents the desired control gain matrix. and This represents the performance level for seamless switching.

[0044] When γ1(t) = 0, the disturbance-free handover performance index is rewritten as:

[0045]

[0046] When γ1(t) = 1, the disturbance-free handover performance index is rewritten as:

[0047]

[0048] The closed-loop system expression of the wastewater treatment system constructed in step 4 is as follows:

[0049]

[0050] in, K σ(t) It is the control gain matrix of the σ(t)th observation mode to be designed, such that

[0051] (i) The constructed closed-loop system is stochastically stable;

[0052] (ii) The constructed closed-loop system satisfies the condition of finite-time boundedness:

[0053]

[0054] Where ε1 and ε2 are positive constants and satisfy 0 < ε1 < ε2, Q il T is a positive definite matrix. f Given a time constant;

[0055] (iii) The constructed closed-loop system meets the performance index of disturbance-free switching.

[0056] In step 5, the parameters for determining the asynchronous, non-disruptive switching controller for the safe operation of the wastewater treatment system are as follows:

[0057] Set constant T f >0, 0<ε1<ε2, φ0>0, φ1>0, φ2>0, δ0>0, δ1>0, δ2>0, μ > 0, υ > 0, Matrix K * , Non-singular matrices Positive definite matrix For any and This makes the following inequality hold.

[0058]

[0059]

[0060]

[0061]

[0062] in,

[0063]

[0064]

[0065] * denotes a matrix block obtained by the symmetry of the matrix, and I denotes the identity matrix;

[0066] The controller gain parameters are specifically designed as follows:

[0067]

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] This invention addresses the security control problem of multimodal wastewater treatment systems under network attacks based on disturbance-free control technology, security control technology, and asynchronous control technology. It proposes an asynchronous disturbance-free switching control method for the safe operation of wastewater treatment systems, avoiding controller flutter and solving the security control problem of wastewater treatment systems under network attacks and asynchronous system and controller modes, ensuring that wastewater treatment systems can operate stably, efficiently, and safely even under complex conditions. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the wastewater treatment process.

[0071] Figure 2 This is a flowchart of the asynchronous, non-disruptive switching control method for the safe operation of a wastewater treatment system according to the present invention.

[0072] Figure 3 This is a schematic diagram of the asynchronous, non-disruptive switching control architecture for the safe operation of the wastewater treatment system of the present invention. Detailed Implementation

[0073] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0074] This invention addresses the security control problem of multimodal wastewater treatment systems under network attacks, and proposes an asynchronous, non-disruptive switching control method for the safe operation of wastewater treatment systems. Figure 1This refers to a wastewater treatment process, including primary, secondary, and tertiary treatment. In primary treatment, wastewater flows through filters and undergoes sedimentation to remove suspended solids and some suspended pollutants, such as debris from dead branches and suspended particles, most of which are larger than 100 micrometers. In secondary treatment, appropriate aeration is introduced, and activated sludge and microorganisms in biological filters further treat the wastewater from primary treatment. Appropriate flocculants are then added to remove inorganic suspended solids, colloidal particles, or low-concentration organic matter. Secondary treatment primarily removes the biological content of human excrement, food waste, soapy water, and washing water, achieving preliminary compliance with discharge standards. Tertiary treatment, also known as advanced wastewater treatment, includes nutrient removal and disinfection through chlorination, ultraviolet radiation, or ozone technology. The treated water can be sent to reclaimed water systems for use as a source for toilet flushing, street spraying, green belt irrigation, industrial water, and fire prevention. (The text then abruptly shifts to a seemingly unrelated topic: "Selecting...") Figure 1 The key wastewater treatment indicators, such as liquid level and nitrogen and phosphorus content in the primary, secondary, and tertiary sedimentation tanks, are the state variables of the wastewater treatment system, which can be detected by a sensor network. Considering the influence of factors such as the wastewater inflow to each sedimentation tank and ambient temperature on the wastewater treatment process, the wastewater treatment system is modeled into N dynamic models based on temperature and wastewater generation at different time periods to better characterize the actual wastewater treatment process. Furthermore, considering that the number of actuators in each sedimentation tank and aeration tank is fixed, and the opening and closing status of each actuator will have different effects on the state variables of the wastewater treatment system, the controller mode of the modeled system is M. A dynamic wastewater treatment system consisting of the wastewater treatment object, controller, actuators, and sensors is formed through a communication network. Since the communication network is an open environment, it is susceptible to interference and attacks from external network attack signals. To better analyze the wastewater treatment system, the dynamic wastewater treatment system is modeled and analyzed based on hidden semi-Markov theory.

[0075] Specifically, such as Figure 2 As shown, the asynchronous, disturbance-free switching control method for the safe operation of a wastewater treatment system according to the present invention includes the following steps:

[0076] Step 1: Establish a stochastic semi-Markov jump state-space model of the wastewater treatment system.

[0077] Data from the wastewater treatment process are collected, and a stochastic semi-Markov jump state-space model of the wastewater treatment system is established, which takes the following form:

[0078]

[0079] in, These represent the water level in the treatment tank, the valve opening, and the nonlinear interference signal during system operation in the wastewater treatment system at time t, respectively. This represents random noise in the wastewater treatment process, which follows Brownian motion. and Let represent n-dimensional, m-dimensional, p-dimensional, and q-dimensional vector spaces, respectively. Here, n represents the number of wastewater treatment tanks in the wastewater treatment system, m represents the number of valves controlling the water level in the tanks, p represents the number of complex nonlinear disturbances encountered during wastewater treatment, and q represents the number of random factors affecting the water level in the tanks. The function r(t) is a transition signal that automatically switches the operating mode of the wastewater treatment system based on actual operating conditions during system operation; its value range is a finite set. N represents the Nth operating mode of the wastewater treatment system; and The system matrix for the r(t)th operating mode is obtained from the equation governing the change in water flow in the wastewater treatment tank during the wastewater treatment process; therefore, when r(t) = i, it is simply denoted as A. i =A r(t) B i =B r(t) D i =D r(t) E i =E r(t) ; and They represent n×n, n×m, n×p, and n×q dimensional Euclidean matrix spaces, respectively.

[0080] Step 2: Using the hidden semi-Markov principle, construct an asynchronous transition framework for the wastewater treatment system modes and control modes.

[0081] The specific process is as follows:

[0082] Step 2.1: Based on the semi-Markov transition process theory, model the transition signal r(t) of the system's operating mode, which follows the transition probabilities as follows:

[0083]

[0084] in, Δ represents a small time increment, and ο(Δ) represents a higher-order infinitesimal of Δ; τ represents the dwell time of two freely transitioning operating modes, satisfying τ>0; λ ij (τ) is the transition rate from mode i to mode j, and satisfies λ ij (τ)≥0(i≠j) and N represents the number of modes in the original system.

[0085] Step 2.2: Considering the difficulty in accurately obtaining the system's modal transition process r(t) in practice, but the observation of the system's modal transition signal r(t) can be achieved based on a hidden semi-Markov model. Therefore, the observed signal σ(t) of the modeled system's modal transition signal r(t) is within a finite set. The values ​​are taken from the inner value and the emission probability and perturbation probability are determined. M represents the number of observation signals that can be used to observe the modal signal r(t) of the original sewage treatment system based on the hidden semi-Markov transition process; σ(t) = M represents that the Mth observation signal realizes the observation of the modal signal r(t) of the original sewage treatment system.

[0086] The emission probability of the observed signal σ(t) is:

[0087]

[0088] in, It is a known probability constant that satisfies and

[0089] The probability of perturbation of the observed signal σ(t) is:

[0090]

[0091] in,

[0092] Step 2.3: Based on steps 2.1 and 2.2, obtain the double-jump transition process. And determine its transition probability:

[0093]

[0094] Among them, the transfer rate

[0095] Step 3: Based on the established semi-Markov transition state-space model and the determined asynchronous transition framework, design an asynchronous, disturbance-free switching control scheme for the safe operation of the wastewater treatment system. Its architecture is as follows: Figure 3 As shown.

[0096] The specific process is as follows:

[0097] Step 3.1, considering that the sensor-to-controller channel in the wastewater treatment system may be subject to random spoofing attacks, the signal received by the controller is modeled as follows:

[0098] u(t) = K σ(t) ((1-γ1(t))x(t)+γ1(t)ω1(x(t)))

[0099] Among them, K σ(t)γ1(t) is the control gain matrix of the σ(t)th observation mode to be designed; γ1(t) is a random variable that follows a Bernoulli distribution and is used to characterize a spoofing attack that occurs randomly on the sensor-to-controller channel. When γ1(t) = 1, the attack occurs; when γ1(t) = 0, the signal is transmitted normally. Where E{} represents the mathematical expectation; the attack signal ω1(x(t)) is an unknown and bounded nonlinear function that satisfies ω1(x(t)). 2 ≤φ1x(t) 2 ; This indicates the sewage level in the sewage treatment pond.

[0100] Step 3.2, considering a random spoofing attack occurring on the controller-to-actuator channel, the actuator input is modeled as follows:

[0101]

[0102] Where ξ(t)=-u(t)+ω2(x(t)) is the deception signal initiated by the attacker, and ω2(x(t)) is a bounded nonlinear signal that satisfies ω1(x(t)). 2 ≤φ1x(t) 2 φ1 represents a known scaling constant; γ2(t) is a random Bernoulli variable independent of γ1(t).

[0103] Step 3.3, the asynchronous switching of the controller and the impact of attack signals lead to Indicates the first The gain matrix of each observation mode. Indicates the first Gain matrix of each observation mode;

[0104] To ensure the controller transitions are as smooth as possible, the following bumpless switching performance metrics are introduced:

[0105]

[0106] Among them, u * (t)=K * ((1-γ1(t))x(t)+γ1(t)ω1(x(t))) is the reference control input, K * This represents the desired control gain matrix. and This represents the performance level for seamless switching.

[0107] When γ1(t) = 0, the performance index for disturbance-free handover can be rewritten as:

[0108]

[0109] When γ1(t) = 1, the performance index for disturbance-free handover can be rewritten as:

[0110]

[0111] Step 4: Combining the established model and the designed asynchronous, non-disruptive switching control scheme, construct the closed-loop system of the wastewater treatment system, whose expression is:

[0112]

[0113] in, K σ(t) It is the control gain matrix of the σ(t)th observation mode to be designed, such that

[0114] (i) The constructed closed-loop system is stochastically stable;

[0115] (ii) The constructed closed-loop system satisfies the condition of finite-time boundedness:

[0116]

[0117] Where ε1 and ε2 are positive constants and satisfy 0 < ε1 < ε2. T is a positive definite matrix. f Given a time constant;

[0118] (iii) The constructed closed-loop system meets the disturbance-free switching performance index in step 3.3.

[0119] Step 5: Based on the constructed asynchronous switching framework and closed-loop system, determine the asynchronous non-disruptive switching controller parameters for the safe operation of the wastewater treatment system, and use the controller to control the wastewater treatment system.

[0120] The specific parameters for the asynchronous, non-disruptive switching controller used to ensure the safe operation of the wastewater treatment system are as follows:

[0121] Set constant T f >0, 0<ε1<ε2, φ0>0, φ1>0, φ2>0, δ0>0, δ1>0, δ2>0, μ > 0, υ > 0, Matrix K * , Non-singular matrices Positive definite matrix For any and This makes the following inequality hold.

[0122]

[0123]

[0124]

[0125]

[0126] in,

[0127]

[0128]

[0129] * denotes a matrix block obtained by the symmetry of the matrix, and I denotes the identity matrix.

[0130] The controller gain parameters are specifically designed as follows:

[0131]

[0132] The verification process for ensuring the bounded stability and undisrupted performance of the asynchronous non-disruptive switching controller parameters for the safe operation of the wastewater treatment system is as follows:

[0133] Choose the Lyapunov function as in It is a positive definite matrix. Using Taylor expansion and Itō's lemma, we can obtain:

[0134]

[0135] Furthermore, the if infinitesimal operator for the stochastic process (x(t), (r(t), σ(t))) can be obtained as:

[0136]

[0137] Where E is the expected value. Combining this with the conditions in step 5, we can obtain:

[0138]

[0139] Furthermore, multiplying both sides of the above equation by e... -μt And using Dynkin's lemma, we can obtain:

[0140]

[0141] definition We can obtain:

[0142]

[0143] Based on the conditions in step 5, we can obtain Therefore, it can be deduced that the wastewater treatment closed-loop system is stable for a finite time.

[0144] Furthermore, based on the conditions in step 5, we obtain:

[0145]

[0146]

[0147] Therefore, the uninterrupted switching performance constraint of the wastewater treatment system is satisfied, and the level is [value missing].

[0148]

[0149] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An asynchronous, non-disruptive switching control method for the safe operation of a wastewater treatment system, characterized in that, Includes the following steps: Step 1: Establish a stochastic semi-Markov jump state-space model of the wastewater treatment system; Step 2: Using the hidden semi-Markov principle, construct an asynchronous transition framework for the modal and control modes of the wastewater treatment system; Step 3: Based on the established semi-Markov transition state space model and the determined asynchronous transition framework, design an asynchronous, disturbance-free switching control scheme for the safe operation of the wastewater treatment system. Step 4: Combining the established model and the designed asynchronous non-disruptive switching control scheme, construct the closed-loop system of the wastewater treatment system; Step 5: Based on the constructed asynchronous switching framework and closed-loop system, determine the asynchronous non-disruptive switching controller parameters for the safe operation of the wastewater treatment system, and use the controller to control the wastewater treatment system. The stochastic semi-Markov jump state-space model of the wastewater treatment system established in step 1 is as follows: in, , , They represent time. The system monitors the water level in the treatment tank, the valve opening, and nonlinear interference signals during system operation in a constant-time wastewater treatment system. This represents random noise in the wastewater treatment process, which follows Brownian motion. , , ,and Represent dimension, dimension, dimension, 3D vector space, This indicates the number of wastewater treatment tanks in the wastewater treatment system. This indicates the number of valves that can control the water level in the wastewater treatment tank. This indicates the number of complex nonlinear disturbances encountered during the wastewater treatment process. This represents the number of random factors affecting the water level in the wastewater treatment pond during the wastewater treatment process; (function) This is a transition signal that allows the wastewater treatment system to automatically switch operating modes based on actual working conditions during system operation; its value range is a finite set. , The first part of the wastewater treatment system Types of operating modes; , , ,and For the first The system matrix for each operating mode is obtained from the equation governing the change in water flow rate in the wastewater treatment tank during the wastewater treatment process; therefore, when At that time, a brief note , , , ; , , ,and Represent dimension, dimension, peacekeeping 3D Euclidean matrix space; The specific process of step 2 is as follows: Step 2.1: Model the transition signals of the system's operating modes based on the semi-Markov transition process theory. Determine its transition probability; Step 2.2: Using the hidden semi-Markov transition theory, model the system's operating mode transition signals. Observation signal In a finite set The values ​​are taken from the inner range, and the emission probability and perturbation probability are determined, where, This indicates that modal signals of the original wastewater treatment system can be obtained based on hidden semi-Markov transition processes. The number of observed signals; Indicates the first The observation signals enable the analysis of the modal signals of the original wastewater treatment system. Observations; Step 2.3: Based on steps 2.1 and 2.2, obtain the double-jump transition process. And determine its transition probability; In step 2.1, the system operating mode transition signal The transition probabilities are as follows: in, , Indicates a small increment in time. express higher-order infinitesimals; Represents the dwell time of two freely switchable operating modes and satisfies ; From modality Switch to mode The transfer rate, and satisfying and , Indicates the number of modes in the original system; In step 2.2, the observed signal The launch probability is: in, It is a known probability constant that satisfies and ; Observation signal The probability of the disturbance is: in, ; In step 2.3, the transition probability of the double-jump process is: Among them, the transfer rate .

2. The asynchronous, non-disruptive switching control method for safe operation of a wastewater treatment system according to claim 1, characterized in that, The specific process of step 3 is as follows: Step 3.1, considering that the sensor-to-controller channel in the wastewater treatment system may be subject to random spoofing attacks, the signal received by the controller is modeled as follows: in, It is the first one to be designed Control gain matrix for each observation mode; It is a random variable that follows a Bernoulli distribution, used to characterize spoofing attacks that occur randomly on the sensor-to-controller channel. At that time, the attack occurred; when The signal is being transmitted normally. ,in Represents mathematical expectation; attack signal It is an unknown and bounded nonlinear function that satisfies ; This indicates the sewage level in the sewage treatment tank; Step 3.2, considering a random spoofing attack occurring on the controller-to-actuator channel, the actuator input is modeled as follows: in, A deceptive signal initiated by the attacker. It is a bounded nonlinear signal that satisfies , Represents a known scaling constant; To be independent random Bernoulli variables, ; Step 3.3, the asynchronous switching of the controller and the impact of attack signals lead to , Indicates the first The gain matrix of each observation mode. Indicates the first Gain matrix of each observation mode; To ensure the controller transitions are as smooth as possible, the following bumpless switching performance metrics are introduced: in, For reference control input, This represents the desired control gain matrix. and This represents the performance level for seamless switching.

3. The asynchronous, disturbance-free switching control method for safe operation of a wastewater treatment system according to claim 2, characterized in that, when At that time, the performance metrics for bumpless handover are rewritten as follows: when At that time, the performance metrics for bumpless handover are rewritten as follows: 。 4. The asynchronous, disturbance-free switching control method for safe operation of a wastewater treatment system according to claim 2, characterized in that, The closed-loop system expression of the wastewater treatment system constructed in step 4 is as follows: in, ; It is the first one to be designed The control gain matrix of each observation mode makes (i) The constructed closed-loop system is stochastically stable; (ii) The constructed closed-loop system satisfies the condition of finite-time boundedness: in, and A positive constant and satisfying , It is a positive definite matrix. Given a time constant; (iii) The constructed closed-loop system meets the performance index of disturbance-free switching.

5. The asynchronous, disturbance-free switching control method for safe operation of a wastewater treatment system according to claim 4, characterized in that, In step 5, the parameters for determining the asynchronous, non-disruptive switching controller for the safe operation of the wastewater treatment system are as follows: Set constant , , , , , , , , , , , , , , ,matrix , non-singular matrix Positive definite matrix For any and This makes the following inequality true. in, , , , , , , , , , , , , , , This represents a matrix block obtained by the symmetry of the matrix. Represents the identity matrix; The controller gain parameters are specifically designed as follows: 。

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