Asynchronous undisturbed switching control method for safe operation of sewage treatment system

Abstract

The invention relates to an asynchronous undisturbed switching control method for safe operation of a sewage treatment system. The asynchronous undisturbed switching control method comprises the following steps: establishing a random semi-Markov jump state space model of the sewage treatment system; constructing a sewage treatment system mode and control mode asynchronous hopping framework; according to the semi-Markov jump state space model and the asynchronous jump framework, designing an asynchronous undisturbed switching control scheme under safe operation of the sewage treatment system; constructing a closed-loop system of the sewage treatment system by combining the established model and the designed asynchronous undisturbed switching control scheme; and based on the asynchronous hopping framework and the closed-loop system, determining asynchronous undisturbed switching controller parameters for safe operation of the sewage treatment system, and controlling the sewage treatment system by using the controller. Compared with the prior art, the method can effectively solve the undisturbed switching finite time control problem when the system mode and the controller mode are asynchronous under the complex working condition of the sewage treatment system, and the safe operation problem under the network attack.

Description

Technical Field

[0001] The present invention relates to the field of sewage treatment in smart cities, and in particular to an asynchronous disturbance-free switching control method for safe operation of a sewage treatment system. Background Art

[0002] Since the beginning of the 21st century, my country's urbanization and industrialization have achieved unprecedented development, which has not only significantly improved people's living standards, but also brought some new problems to people's living environment, such as traffic congestion, air pollution and water pollution. Among these challenges, the effectiveness of urban sewage treatment is particularly critical. It is not only related to the sustainable development of the city, but also an important indicator for measuring the level of urban management. Therefore, exploring and implementing efficient urban sewage treatment strategies is an issue that needs to be urgently addressed.

[0003] Sewage mainly comes from living, production and industrial facilities, including domestic sewage generated by toilets, kitchens, bathrooms, etc., and some areas also include industrial sewage, medical sewage and agricultural sewage. Water pollution not only affects industrial production, increases equipment corrosion, affects product quality, and even makes production impossible, but also affects people's lives and the ecological environment, directly endangers human health, and causes irreparable losses. Therefore, exploring sewage treatment technology has very important social and economic value. At present, 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 eutrophication (mainly nitrogen and phosphorus compounds) in water, and 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 purifications can meet the standards of drinking water and can be used for drinking again.

[0004] During the sewage treatment process, the amount of water flowing into the sewage treatment pool changes with the water use situation of each water user, which makes it difficult for a single model to analyze and characterize the sewage treatment process and thus difficult to ensure the effective treatment of sewage. For this reason, a sewage treatment system model with multiple modes that satisfies the random semi-Markov jump process is often established based on the "peak" and "off-peak" characteristics of the water demand of each water user. Among them, sewage treatment systems with different modes adopt different control execution policies to achieve the best control effect. When the modes of the sewage treatment system are frequently switched, it is easy to cause the actuators of the sewage treatment system to vibrate significantly, which may accelerate the wear of the actuators at the least and cause the sewage treatment system to collapse at the worst. In response to this problem, some scholars have proposed non-disturbance control methods, but how to apply non-disturbance control technology to solve the problem of stable operation of sewage treatment systems with multiple modes has not been fully considered.

[0005] In addition, network technology has been gradually applied to many advanced production and manufacturing scenarios such as chemical production, automobile manufacturing, and sewage treatment. The openness of the network environment has promoted the improvement of production efficiency on the one hand, but it has also brought many new challenges to data security and safe production during data transmission on the other hand. For example, actuators and sensors in an open network environment are vulnerable to network attacks. If the actuator executes the wrong execution instruction, it will be difficult to achieve precise control goals at best, and it will cause equipment damage or even production accidents at worst. How to achieve the safe and stable operation of a multi-modal sewage treatment system in an open network environment is of great significance. Summary of the invention

[0006] The purpose of the present invention is to provide an asynchronous undisturbed switching control method for the 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 undisturbed control technology, safety control technology and asynchronous control technology.

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

[0008] An asynchronous disturbance-free switching control method for safe operation of a sewage treatment system comprises 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, construct the asynchronous jump framework of the sewage treatment system mode and control mode;

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

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

[0013] Step 5: Based on the constructed asynchronous jump framework and closed-loop system, determine the parameters of the asynchronous undisturbed switching controller for safe operation of the sewage treatment system, and use 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] in, They represent the water level of the treatment tank in the sewage treatment system at time t, the valve opening, and the nonlinear interference signal in the system operation. Represents the random noise in the sewage treatment process, which satisfies Brownian motion; and They represent n-dimensional, m-dimensional, p-dimensional, and q-dimensional vector spaces respectively, n represents the number of sewage treatment tanks in the sewage treatment system, m represents the number of valves that can control the water level of the sewage treatment tank, p represents the number of complex nonlinear interferences in the sewage treatment process, and q represents the number of random factors that affect the water level of the sewage treatment tank during the sewage treatment process; the function r(t) is a jump signal that can automatically switch the operating mode of the sewage treatment system according to the actual working conditions during the operation of the system, and its value range is a finite set N represents the Nth operating mode of the sewage treatment system; and is the system matrix of the r(t)th operating mode, which is obtained from the water flow change equation of the sewage treatment tank during the sewage treatment process; therefore, when r(t) = i, A is abbreviated 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, based on the semi-Markov jump process theory, the jump signal r(t) of the system operation mode is modeled and its transition probability is determined;

[0019] Step 2.2, combined with the hidden semi-Markov jump theory, the observed signal σ(t) of the modeling system operating mode jump signal r(t) is modeled in a finite set The internal value is taken, and its emission probability and disturbance probability are determined, where M represents the number of observation signals that can realize the observation of the original sewage treatment system modal signal r(t) based on the hidden semi-Markov jump process; σ(t) = M represents that the Mth observation signal realizes the observation of the original sewage treatment system modal signal r(t);

[0020] Step 2.3, according to step 2.1 and step 2.2, the double jump process is obtained And determine its transition probability.

[0021] In step 2.1, the jump signal r(t) of the system operation mode obeys the following transition probability:

[0022]

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

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

[0025]

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

[0027] The perturbation probability 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 channel from the sensor to the controller in the sewage treatment system may be subject to random spoofing attacks, the signal received by the controller is modeled as:

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

[0036] Among them, K σ(t) is the control gain matrix of the σ(t)th observation mode to be designed; γ1(t) is a random variable that obeys the Bernoulli distribution, which is used to characterize the random deception attack on the channel from the sensor to the controller. 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 ; Indicates the sewage level in the sewage treatment tank;

[0037] In step 3.2, consider a random spoofing attack on the channel from the controller to the actuator, and model the actuator input as:

[0038]

[0039] Among them, ξ(t) = -u(t) + ω2(x(t)) is the deceptive signal initiated by the attacker, ω2(x(t)) is a bounded nonlinear signal and 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 jump of the controller and the impact of the attack signal lead to Indicates The gain matrix of the observed modes is, Indicates The gain matrix of the observed modes;

[0041] In order to make the controller jump as smooth as possible, the following disturbance-free switching performance indicators 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 * represents the desired control gain matrix, and for bumpless switching performance levels.

[0044] When γ1(t) = 0, the bumpless switching performance index is rewritten as:

[0045]

[0046] When γ1(t) = 1, the bumpless switching performance index is rewritten as:

[0047]

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

[0049]

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

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

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

[0053]

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

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

[0056] In step 5, the parameters of the asynchronous undisturbed switching controller for safe operation of the sewage treatment system are determined as follows:

[0057] Set the 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 matrix Positive definite matrix For any and So that the following inequality holds,

[0058]

[0059]

[0060]

[0061]

[0062] in,

[0063]

[0064]

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

[0066] The specific design of the controller gain parameter is:

[0067]

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

[0069] The present invention 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, and proposes an asynchronous disturbance-free switching control method for safe operation of the sewage treatment system, which avoids controller vibration and solves the safety control problem of the sewage treatment system under conditions such as network attacks and asynchronous system modes and controller modes, ensuring that the sewage treatment system can operate stably, efficiently and safely under complex conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a schematic diagram of the treatment process of the sewage treatment system;

[0071] Figure 2 A flow chart of the asynchronous disturbance-free switching control method for safe operation of the sewage treatment system of the present invention;

[0072] Figure 3 Schematic diagram of asynchronous disturbance-free switching control architecture for safe operation of the sewage treatment system of the present invention. DETAILED DESCRIPTION

[0073] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0074] The present invention aims at the security control problem of a sewage treatment system with multiple modes under network attacks and proposes an asynchronous disturbance-free switching control method for the safe operation of the sewage treatment system. Figure 1It is a sewage treatment process, including primary treatment, secondary treatment and tertiary treatment. In the primary treatment, the sewage flows through the filter and then settles to remove suspended matter and some suspended pollutants in the sewage, such as dead tree branches, suspended particles and most other particles with a particle size of more than 100 microns; in the secondary treatment, appropriate aeration is introduced, and the microorganisms in the activated sludge and biofilter are used to further treat the sewage from the primary treatment, and then appropriate flocculants are added to remove inorganic suspended matter and colloidal particles or low concentrations of organic matter in the sewage. Secondary treatment is mainly used to fully remove the biological content in human excrement, food waste, soapy water and washing water, and can initially meet the emission standards. Tertiary treatment, also known as deep sewage treatment, includes the removal of nutrients and disinfection of sewage by chlorination, ultraviolet radiation or ozone technology. The water after tertiary treatment can be sent to the reclaimed waterway as a water source for flushing toilets, spraying streets, watering green belts, industrial water, fire prevention, etc. Select such as Figure 1 The key indicators of sewage treatment such as the liquid level, nitrogen and phosphorus content in the primary sedimentation tank, the secondary sedimentation tank, and the tertiary sedimentation tank are state variables of the sewage treatment system, which can be detected by the sensor network. Considering that the sewage treatment process is affected by factors such as the sewage inflow and ambient temperature of each sedimentation tank, the sewage treatment system is modeled as N dynamic models according to the temperature and sewage generation in different time periods, so as to better characterize the actual sewage treatment process. Furthermore, considering that the number of actuators in each sedimentation tank and aeration tank in sewage treatment is certain, the opening and closing of each actuator will have different effects on the state quantity of the sewage treatment system, so the controller mode of the modeling system is M. Through the communication network, a sewage treatment dynamic system consisting of sewage treatment objects, controllers, actuators and sensors is formed. Since the communication network is an open environment, it is susceptible to interference and attack from external network attack signals. In order to better analyze the sewage treatment system, the sewage treatment dynamic system is modeled and analyzed based on the hidden semi-Markov theory.

[0075] Specifically, Figure 2 As shown, an asynchronous disturbance-free switching control method for safe operation of a sewage treatment system of the present invention comprises the following steps:

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

[0077] Collect sewage treatment process data and establish a random semi-Markov jump state space model of the sewage treatment system, which is in the following form:

[0078]

[0079] in, They represent the water level of the treatment tank in the sewage treatment system at time t, the valve opening, and the nonlinear interference signal in the system operation. Represents the random noise in the sewage treatment process, which satisfies Brownian motion; and They represent n-dimensional, m-dimensional, p-dimensional, and q-dimensional vector spaces respectively, n represents the number of sewage treatment tanks in the sewage treatment system, m represents the number of valves that can control the water level of the sewage treatment tank, p represents the number of complex nonlinear interferences in the sewage treatment process, and q represents the number of random factors that affect the water level of the sewage treatment tank during the sewage treatment process; the function r(t) is a jump signal that can automatically switch the operating mode of the sewage treatment system according to the actual working conditions during the operation of the system, and its value range is a finite set N represents the Nth operating mode of the sewage treatment system; and is the system matrix of the r(t)th operating mode, which is obtained from the water flow change equation of the sewage treatment pool during the sewage treatment process; therefore, when r(t) = i, A is abbreviated 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 jump framework for the sewage treatment system mode and control mode.

[0081] The specific process is as follows:

[0082] Step 2.1, based on the semi-Markov jump process theory, the jump signal r(t) of the system operation mode is modeled, which obeys the following transition probability:

[0083]

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

[0085] Step 2.2, considering that it is difficult to accurately obtain the system operation mode jump process r(t) in the actual process, the observation of the system operation mode jump signal r(t) can be realized based on the hidden semi-Markov model. Therefore, the observation signal σ(t) of the modeling system operation mode jump signal r(t) is in the finite set The value is taken within, and its emission probability and disturbance probability are determined, where 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 jump 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, is a known probability constant that satisfies and

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

[0090]

[0091] in,

[0092] Step 2.3, according to step 2.1 and step 2.2, the double jump process is obtained And determine its transition probability:

[0093]

[0094] Among them, the transfer rate

[0095] Step 3: Based on the established semi-Markov jump state space model and the determined asynchronous jump framework, an asynchronous disturbance-free switching control scheme for safe operation of the sewage treatment system is designed. Figure 3 shown.

[0096] The specific process is as follows:

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

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

[0099] Among them, K σ(t)is the control gain matrix of the σ(t)th observation mode to be designed; γ1(t) is a random variable that obeys the Bernoulli distribution, which is used to characterize the random deception attack on the channel from the sensor to the controller. 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 ; Indicates the sewage level in the sewage treatment tank.

[0100] In step 3.2, consider a random spoofing attack on the channel from the controller to the actuator, and model the actuator input as:

[0101]

[0102] Among them, ξ(t) = -u(t) + ω2(x(t)) is the deceptive signal initiated by the attacker, ω2(x(t)) is a bounded nonlinear signal and 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 jump of the controller and the impact of the attack signal lead to Indicates The gain matrix of the observed modes is, Indicates The gain matrix of the observed modes;

[0104] In order to make the controller jump as smooth as possible, the following disturbance-free switching performance indicators 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 * represents the desired control gain matrix, and for bumpless switching performance levels.

[0107] When γ1(t) = 0, the bumpless switching performance index can be rewritten as:

[0108]

[0109] When γ1(t) = 1, the bumpless switching performance index can be rewritten as:

[0110]

[0111] Step 4: Combining the established model with the designed asynchronous disturbance-free switching control scheme, a closed-loop system of the sewage treatment system is constructed, and its expression is:

[0112]

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

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

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

[0116]

[0117] Among them, ε1 and ε2 are positive constants and satisfy 0<ε1<ε2, is a positive definite matrix, T f is a given time constant;

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

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

[0120] The parameters of the asynchronous undisturbed switching controller that determine the safe operation of the sewage treatment system are as follows:

[0121] Set the 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 matrix Positive definite matrix For any and So that the following inequality holds,

[0122]

[0123]

[0124]

[0125]

[0126] in,

[0127]

[0128]

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

[0130] The specific design of the controller gain parameter is:

[0131]

[0132] The verification process of the asynchronous undisturbed switching controller parameters for safe operation of the sewage treatment system to ensure bounded stability and meet the undisturbed performance is as follows:

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

[0134]

[0135] Furthermore, we can get the infinitesimal operator of the random process (x(t), (r(t), σ(t))) as:

[0136]

[0137] Where E is the mathematical expectation. Combined with the conditions in step 5, we can get:

[0138]

[0139] Furthermore, multiply both sides of the above equation by e -μt , and using Dynkin's lemma we can get:

[0140]

[0141] definition We can get:

[0142]

[0143] According to the conditions in step 5, we can get It can be concluded that the sewage treatment closed-loop system is stable for a finite time.

[0144] In addition, according to the conditions in step 5, we get:

[0145]

[0146]

[0147] Therefore, the disturbance-free switching performance constraint of the sewage treatment system is satisfied, and the level is

[0148]

[0149] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. An asynchronous disturbance-free switching control method for safe operation of a sewage treatment system, characterized in that: The steps include: Step 1, establishing a random semi-Markov jump state space model of the sewage treatment system; Step 2, using the hidden semi-Markov principle, construct the asynchronous jump framework of the sewage treatment system mode and control mode; Step 3, designing an asynchronous disturbance-free switching control scheme for safe operation of the sewage treatment system according to the established semi-Markov jump state space model and the determined asynchronous jump framework; Step 4, combining the established model and the designed asynchronous disturbance-free switching control scheme to construct a closed-loop system of the sewage treatment system; Step 5: Based on the constructed asynchronous jump framework and closed-loop system, determine the parameters of the asynchronous undisturbed switching controller for safe operation of the sewage treatment system, and use the controller to control the sewage treatment system.

2. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 1 is characterized in that: The random semi-Markov jump state space model of the sewage treatment system established in step 1 is as follows: in, They represent the water level of the treatment tank in the sewage treatment system at time t, the valve opening, and the nonlinear interference signal in the system operation. Represents the random noise in the sewage treatment process, which satisfies Brownian motion; and They represent n-dimensional, m-dimensional, p-dimensional, and q-dimensional vector spaces respectively, n represents the number of sewage treatment tanks in the sewage treatment system, m represents the number of valves that can control the water level of the sewage treatment tank, p represents the number of complex nonlinear interferences in the sewage treatment process, and q represents the number of random factors that affect the water level of the sewage treatment tank during the sewage treatment process; the function r(t) is a jump signal that can automatically switch the operating mode of the sewage treatment system according to the actual working conditions during the operation of the system, and its value range is a finite set N represents the Nth operating mode of the sewage treatment system; and is the system matrix of the r(t)th operating mode, which is obtained from the water flow change equation of the sewage treatment pool during the sewage treatment process; therefore, when r(t) = i, A is abbreviated 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.

3. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 1 is characterized in that: The specific process of step 2 is as follows: Step 2.1, based on the semi-Markov jump process theory, the jump signal r(t) of the system operation mode is modeled and its transition probability is determined; Step 2.2, combined with the hidden semi-Markov jump theory, the observed signal σ(t) of the modeling system operating mode jump signal r(t) is modeled in a finite set The internal value is taken, and its emission probability and disturbance probability are determined, where M represents the number of observation signals that can realize the observation of the original sewage treatment system modal signal r(t) based on the hidden semi-Markov jump process; σ(t) = M represents that the Mth observation signal realizes the observation of the original sewage treatment system modal signal r(t); Step 2.3, according to step 2.1 and step 2.2, the double jump process is obtained And determine its transition probability.

4. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 3 is characterized in that: In step 2.1, the jump signal r(t) of the system operation mode obeys the following transition probability: in, Δ represents a small increment in time, ο(Δ) represents a high-order infinitesimal of Δ; τ represents the residence time of two freely jumpable operating modes and satisfies τ>0; λ ij (τ) is the transfer rate from mode i to mode j, and satisfies λ ij (τ) ≥ 0 (i ≠ j) and N represents the number of modes of the original system.

5. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 4 is characterized in that: In step 2.2, the emission probability of the observation signal σ(t) is: in, is a known probability constant that satisfies and The perturbation probability of the observed signal σ(t) is: in, 6. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 5 is characterized in that: In step 2.3, the transition probability of the double jump process is: Among them, the transfer rate 7. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 2 is characterized in that: The specific process of step 3 is as follows: Step 3.1, considering that the channel from the sensor to the controller in the sewage treatment system may be subject to random spoofing attacks, the signal received by the controller is modeled as: u(t)=K σ(t) ((1-γ1(t))x(t)+γ1(t)ω1(x(t))) Among them, K σ(t) is the control gain matrix of the σ(t)th observation mode to be designed; γ1(t) is a random variable that obeys the Bernoulli distribution, which is used to characterize the random deception attack on the channel from the sensor to the controller. 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 ≤φ1||x(t)|| 2 ; Indicates the sewage level in the sewage treatment tank; In step 3.2, consider a random spoofing attack on the channel from the controller to the actuator, and model the actuator input as: Among them, ξ(t)=-u(t)+ω2(x(t)) is the deceptive signal initiated by the attacker, ω2(x(t)) is a bounded nonlinear signal and satisfies ||ω1(x(t))|| 2 ≤φ1||x(t)|| 2 , φ1 represents a known scaling constant; γ2(t) is a random Bernoulli variable independent of γ1(t), Step 3.3, the asynchronous jump of the controller and the impact of the attack signal lead to K l ((1-γ1(t))x(t)+γ1(t)ω1(x(t)))≠K j ((1-γ1(t))x(t)+γ1(t)K j ω1(x(t))), K l represents the gain matrix of the lth observed mode, K j represents the gain matrix of the jth observed mode; In order to make the controller jump as smooth as possible, the following disturbance-free switching performance indicators are introduced: Among them, u * (t) = K * ((1-γ1(t))x(t)+γ1(t)ω1(x(t))) is the reference control input, K * represents the desired control gain matrix, and for bumpless switching performance levels.

8. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 7, characterized in that: When γ1(t) = 0, the bumpless switching performance index is rewritten as: When γ1(t) = 1, the bumpless switching performance index is rewritten as:

9. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 7, characterized in that: The closed-loop system expression of the sewage treatment system constructed in step 4 is: in, K σ(t) is the control gain matrix of the σ(t)th observation mode to be designed, so that (i) The constructed closed-loop system is stochastically stable; (ii) The constructed closed-loop system satisfies the finite-time boundedness condition: Among them, ε1 and ε2 are positive constants and satisfy 0<ε1<ε2, Q il is a positive definite matrix, T f is a given time constant; (iii) The constructed closed-loop system meets the disturbance-free switching performance index.

10. The asynchronous non-disturbance switching control method for safe operation of a sewage treatment system according to claim 9, characterized in that: In step 5, the parameters of the asynchronous undisturbed switching controller for safe operation of the sewage treatment system are determined as follows: Set the 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 * , Y ι , a non-singular matrix Z ι , a positive definite matrix X iι , for any and So that the following inequality holds, in, * represents the matrix block obtained by the symmetry of the matrix, and I represents the identity matrix; The specific design of the controller gain parameter is:

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