An Adaptive Cooperative Optimal Tracking Control Method for Wastewater Treatment Based on Dynamic Event Triggering

Abstract

This invention belongs to the field of wastewater treatment technology and provides an adaptive collaborative optimal tracking control method for wastewater treatment based on dynamic event triggering. The method includes: simplified dynamic model construction, Lyapunov function construction, optimal controller construction based on execution network construction, evaluation network construction, weight adaptive law construction, dynamic event triggering mechanism setting, and tracking control. This invention selectively updates the parameters of the evaluation network and execution network through the weight adaptive law, reducing the burden of large information communication volume and insufficient computing power in water plants. Through the adaptive controller of the execution network, the set values ​​of dissolved oxygen concentration and nitrate nitrogen concentration can be accurately tracked, and effective and rapid control can be achieved. By optimizing the execution network and controller through the evaluation network, the operating energy consumption of the equipment is effectively reduced while ensuring that the effluent water quality meets the standards.

Description

Technical Field

[0001] This invention relates to the field of wastewater treatment technology, and in particular to an adaptive collaborative optimal tracking control method for wastewater treatment based on dynamic event triggering. Background Technology

[0002] The application of wastewater treatment technologies can significantly reduce pollutant discharge into water bodies and promote the recycling and reuse of water resources. Currently, the activated sludge process is widely used in wastewater treatment, which involves numerous physical and biochemical reactions and exhibits complex time-varying dynamic characteristics. Therefore, there is an urgent need to develop efficient control technologies to effectively reduce equipment operating energy consumption while ensuring that stringent effluent quality standards are met. Extensive research has been conducted on adaptive tracking control for wastewater treatment processes, including methods such as model predictive control, neural network control, and proportional-integral-derivative (PID) control.

[0003] However, the aforementioned methods rely solely on instantaneous tracking errors for iterative parameter updates, which only guarantees effluent quality but cannot reduce equipment operating energy consumption. Due to feedback, reward, and penalty mechanisms, reinforcement learning-based adaptive optimal control methods can interact with the environment over long periods and have been widely researched and applied. However, this technology requires complex computations, which can easily impose a communication burden on real-time control in practical industrial applications. Currently, in wastewater treatment processes at reclaimed water plants, fixed threshold triggering control methods are mostly used, which are prone to delays or over-triggering. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide an adaptive collaborative optimal tracking control method for wastewater treatment based on dynamic event triggering, which solves the problems of excessive communication and computing power burden, untimely concentration tracking, and high power consumption of equipment in order to ensure water quality in conventional tracking control methods.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] An adaptive collaborative optimal tracking control method for wastewater treatment based on dynamic event triggering includes:

[0007] A simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration was constructed;

[0008] Construct the Lyapunov function based on the simplified dynamic model;

[0009] Construct an execution network based on a fuzzy neural network, and construct an optimal controller based on the execution network according to the Lyapunov function;

[0010] Construct a long-term loss function, and construct an evaluation network based on the fuzzy neural network according to the long-term loss function;

[0011] Construct the weight adaptive law for the execution network and the evaluation network;

[0012] Two sets of dynamic trigger thresholds are set, and a dynamic event triggering mechanism is set according to the dynamic trigger thresholds;

[0013] The dynamic event triggering mechanism and the weight adaptive law are updated in the execution network and the evaluation network, and the updated execution network and the evaluation network are used to update the optimal controller of the target device.

[0014] Preferably, a simplified kinetic model is constructed for dissolved oxygen concentration and nitrate nitrogen concentration, including:

[0015] Establish the original dynamic model; the expression of the original dynamic model is:

[0016]

[0017] Among them, S O,4 (t) represents the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank; S O,5 (t) represents the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank; S NO,1 (t) represents the nitrate nitrogen concentration in the first zone of the biochemical reaction tank; S NO,2 (t) represents the nitrate nitrogen concentration in the second zone of the biochemical reaction tank; S NO,5 (t) represents the nitrate nitrogen concentration in the fifth zone of the biochemical reaction tank; S O,S K represents the saturation value of dissolved oxygen concentration. L a5(t) is the operating variable for dissolved oxygen concentration; Q r ψ(t) is the operating variable for nitrate nitrogen concentration; μ(t) is the microbial respiration coefficient; ψ1(t) is the flow rate of the first zone of the bioreactor; ψ2(t) is the flow rate of the second zone of the bioreactor; ψ4(t) is the flow rate of the fourth zone of the bioreactor; ψ5(t) is the flow rate of the fifth zone of the bioreactor; X b,h (t) represents the concentration of heterotrophic biomass; Y h V1 represents heterotrophic biomass; V2 represents the volume of the second section of the biochemical reactor; V5 represents the volume of the fifth section of the biochemical reactor; a1 represents the first constant; a2 represents the second constant.

[0018] Define a first unknown function and a second unknown function; the expression for the first unknown function is:

[0019]

[0020] Wherein, D1(t) represents the unknown dynamic information of the environment when tracking and controlling the dissolved oxygen concentration;

[0021] The expression for the second unknown function is:

[0022]

[0023] Wherein, D2(t) represents the unknown dynamic information of the environment when tracking and controlling the nitrate nitrogen concentration;

[0024] The original dynamic model is simplified using the first unknown function and the second unknown function to obtain the simplified dynamic model; the expression of the simplified dynamic model is:

[0025]

[0026] Where, P1(t)=S O,S -S O,5 (t); P2(t) = S NO,5 (t) / V2; For S O,5 The derivative of (t); P1(t) is the dissolved oxygen saturation value minus the current dissolved oxygen concentration; P2(t) is the current nitrate nitrogen concentration divided by the volume of the second section of the biochemical reaction tank.

[0027] Preferably, constructing the Lyapunov function based on the simplified dynamic model includes:

[0028] Based on the simplified kinetic model, the tracking errors for dissolved oxygen concentration and nitrate nitrogen concentration are set; the expression for the dissolved oxygen concentration tracking error is: e O (t)=S O,5 (t)-S O,set (t); where e O (t) represents the dissolved oxygen concentration tracking error; S O,set (t) represents the dissolved oxygen concentration setpoint; the expression for the nitrate nitrogen concentration tracking error is: e NO (t)=S NO,2 (t)-S NO,set (t); where e NO (t) represents the tracking error of the nitrate nitrogen concentration; S NO,set (t) represents the setpoint for nitrate nitrogen concentration;

[0029] The Lyapunov function is constructed based on the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the Lyapunov function based on the errors is: Among them, V z e(t) is the Lyapunov function based on the error; e(t) is the tracking control error; T represents the transpose operation.

[0030] Preferably, constructing an optimal controller based on the execution network according to the Lyapunov function includes:

[0031] Differentiating the Lyapunov function yields the Lyapunov derivative function;

[0032] Extract the unknown dynamic information portion from the Lyapunov derivative function; the expression for the unknown dynamic information portion is: Where, D(t) = [D1(t), D2(t)] T D(t) is a matrix formed by vertically concatenating D1(t) and D2(t);

[0033] The execution network is constructed based on the unknown portion of the dynamic information; the expression of the execution network based on the fuzzy neural network is:

[0034]

[0035] in, The optimal output weights for the execution network; U a (t) represents the output of the normalized layer of the execution network; θ a (t) represents the estimation error of the execution network; For the input of the execution network; It is the center of the execution network; is the width of the execution network; m is the number of neurons in the input layer; l is the number of neurons in the RBF layer and the normalization layer.

[0036] Preferably, constructing an optimal controller based on the execution network according to the Lyapunov function includes:

[0037] Construct an optimal controller; the expression for the optimal controller is:

[0038]

[0039] Among them, v * ζ is the output of the optimal controller; ζ is the control coefficient vector. This is the transpose of the optimal output weights;

[0040] Construct an actual controller based on the optimal controller; the expression of the actual controller is:

[0041]

[0042] Where v(t) is the output of the actual controller; for The transpose of the current value;

[0043] The actual controller is iteratively updated based on the updated execution network to obtain the updated optimal controller.

[0044] Preferably, constructing a long-term loss function and constructing the evaluation network of the fuzzy neural network based on the long-term loss function includes:

[0045] An instantaneous loss function is constructed based on the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the instantaneous loss function is:

[0046]

[0047] Wherein, R(t) is the output value of the instantaneous loss function;

[0048] Integrating the instantaneous loss function yields the long-term loss function; the expression for the long-term loss function is: in, ι is the output value of the long-term loss function; ι is the integration variable;

[0049] The evaluation network is constructed based on the long-term loss function; the expression of the evaluation network based on the fuzzy neural network is:

[0050]

[0051] in, U represents the optimal output weights of the evaluation network. c (t) represents the output of the normalization layer of the evaluation network; θ c (t) represents the estimation error of the evaluation network; This serves as the input to the evaluation network; The center of the evaluation network; The width of the evaluation network.

[0052] Preferably, constructing the adaptive weight law for the execution network and the evaluation network includes:

[0053] Define a first estimation error for the evaluation network and a second estimation error for the execution network; the expression for the first estimation error is:

[0054]

[0055] Where η1(t) is the first estimation error; ξ is the discounted future cost; The output function of the evaluation network;

[0056] The expression for the second estimation error is:

[0057]

[0058] Wherein, η2(t) is the second estimation error;

[0059] A first cost function for the evaluation network is constructed based on the first estimation error, and a second cost function for the execution network is constructed based on the second estimation error; the expression for the first cost function is: Among them, E c (t) is the first cost function;

[0060] The expression for the second cost function is: Among them, E a (t) is the second cost function;

[0061] The weight adaptation laws for the execution network and the evaluation network are constructed based on the first cost function and the second cost function, respectively; the expressions for the weight adaptation laws include:

[0062]

[0063] in, for The transpose of the current value of β; c This is the first adaptive rate coefficient; for The current value of β; a This is the second adaptive rate coefficient; The rule layer change value of the evaluation network.

[0064] Preferably, a dynamic trigger threshold is set, and a dynamic event triggering mechanism is set according to the dynamic trigger threshold, including:

[0065] Construct the dynamic trigger threshold; the expression for the dynamic trigger threshold includes:

[0066] and

[0067]

[0068] Where τ1 is the first dynamic threshold; δ1 is the first positive definite parameter; λ is the Pushtz constant; τ2 is the second dynamic threshold; δ2 is the second positive definite parameter;

[0069] A dynamic event triggering mechanism is set according to the dynamic triggering threshold; the expression of the dynamic event triggering mechanism is: in, M1 is the first event; This is the second event; For tracking error based on event sampling; This is a long-run cost function.

[0070] The present invention discloses the following technical effects:

[0071] This invention provides an adaptive collaborative optimal tracking control method for wastewater treatment based on dynamic event triggering. By selectively updating the parameters of the evaluation network and the execution network through a weighted adaptive law, it solves the problem of excessive communication and computing power burden in conventional tracking control methods, thereby reducing the information communication volume and computing power burden of the water plant. Through the adaptive controller of the execution network, it solves the problem of untimely concentration tracking in conventional tracking control methods, achieving accurate tracking of the set values ​​of dissolved oxygen concentration and nitrate nitrogen concentration. By optimizing the execution network and controller through the evaluation network, it solves the problem of high equipment power consumption caused by conventional tracking control methods in order to ensure water quality, thereby reducing the operating energy consumption of the equipment while ensuring that the effluent water quality meets the standards. Attached Figure Description

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a schematic diagram of the adaptive collaborative optimal tracking control process for wastewater treatment based on dynamic event triggering, provided in an embodiment of the present invention.

[0074] Figure 2 This is a schematic diagram of comparative simulation results provided for an embodiment of the present invention. Figure 2 (a) is a schematic diagram of the results of dissolved oxygen concentration control; Figure 2 (b) is a schematic diagram showing the results of nitrate nitrogen concentration control;

[0075] Figure 3 The control error curves for the two methods provided in the embodiments of the present invention are as follows. Figure 3 (a) is a schematic diagram of the control error curve for dissolved oxygen. Figure 3 (b) is a schematic diagram of the control error curve for nitrate nitrogen;

[0076] Figure 4 The change curve of the control variable provided in the embodiment of the present invention. Figure 4 (a) is K L A schematic diagram of the change curve of a5(t), Figure 4 (b) is Q r A schematic diagram of the curve of change of (t);

[0077] Figure 5This is a schematic diagram illustrating the parameter update intervals of the dissolved oxygen concentration controller and the nitrate nitrogen concentration controller under two triggering conditions provided in this embodiment of the invention. Figure 5 (a) is a schematic diagram showing the parameter update interval of the dissolved oxygen concentration controller. Figure 5 (b) is a schematic diagram of the parameter update interval of the nitrate nitrogen concentration controller. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] The purpose of this invention is to provide an adaptive collaborative optimal tracking control method for wastewater treatment based on dynamic event triggering, which solves the problems of excessive communication and computing power burden, untimely concentration tracking, and high power consumption of equipment in order to ensure water quality in conventional tracking control methods.

[0080] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0081] Figure 1 This is a schematic diagram of the adaptive collaborative optimal tracking control process for wastewater treatment based on dynamic event triggering provided in an embodiment of the present invention, as shown below. Figure 1 As shown, this invention provides an adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering, comprising:

[0082] Step 100: Construct a simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration;

[0083] Step 200: Construct the Lyapunov function based on the simplified dynamic model;

[0084] Step 300: Construct an execution network based on a fuzzy neural network, and construct an optimal controller based on the execution network according to the Lyapunov function;

[0085] Step 400: Construct a long-term loss function, and construct an evaluation network based on the fuzzy neural network according to the long-term loss function;

[0086] Step 500: Construct the adaptive weight law for the execution network and the evaluation network;

[0087] Step 600: Set two sets of dynamic trigger thresholds, and set a dynamic event triggering mechanism according to the dynamic trigger thresholds;

[0088] Step 700: Update the dynamic event triggering mechanism and the weight adaptive law to the execution network and the evaluation network, and use the updated execution network and the evaluation network to update the optimal controller of the target device.

[0089] Furthermore, simplified kinetic models for dissolved oxygen concentration and nitrate nitrogen concentration are constructed, including:

[0090] Establish the original dynamic model; the expression of the original dynamic model is:

[0091]

[0092] Among them, S O,4 (t) represents the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank; S O,5 (t) represents the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank; S NO,1 (t) represents the nitrate nitrogen concentration in the first zone of the biochemical reaction tank; S NO,2 (t) represents the nitrate nitrogen concentration in the second zone of the biochemical reaction tank; S NO,5 (t) represents the nitrate nitrogen concentration in the fifth zone of the biochemical reaction tank; S O,S K represents the saturation value of dissolved oxygen concentration. L a5(t) is the operating variable for dissolved oxygen concentration; Q r ψ(t) is the operating variable for nitrate nitrogen concentration; μ(t) is the microbial respiration coefficient; ψ1(t) is the flow rate of the first zone of the bioreactor; ψ2(t) is the flow rate of the second zone of the bioreactor; ψ4(t) is the flow rate of the fourth zone of the bioreactor; ψ5(t) is the flow rate of the fifth zone of the bioreactor; X b,h (t) represents the concentration of heterotrophic biomass; Y h V1 represents heterotrophic biomass; V2 represents the volume of the second section of the biochemical reactor; V5 represents the volume of the fifth section of the biochemical reactor; a1 represents the first constant; a2 represents the second constant.

[0093] Define a first unknown function and a second unknown function; the expression for the first unknown function is:

[0094]

[0095] Wherein, D1(t) represents the unknown dynamic information of the environment when tracking and controlling the dissolved oxygen concentration;

[0096] The expression for the second unknown function is:

[0097]

[0098] Wherein, D2(t) represents the unknown dynamic information of the environment when tracking and controlling the nitrate nitrogen concentration;

[0099] The original dynamic model is simplified using the first unknown function and the second unknown function to obtain the simplified dynamic model; the expression of the simplified dynamic model is:

[0100]

[0101] Where, P1(t)=S O,S -S O,5 (t); P2(t) = S NO,5 (t) / V2; For S O,5 The derivative of (t); P1(t) is the dissolved oxygen saturation value minus the current dissolved oxygen concentration; P2(t) is the current nitrate nitrogen concentration divided by the volume of the second section of the biochemical reaction tank.

[0102] Preferably, constructing the Lyapunov function based on the simplified dynamic model includes:

[0103] Based on the simplified kinetic model, the tracking errors for dissolved oxygen concentration and nitrate nitrogen concentration are set; the expression for the dissolved oxygen concentration tracking error is: e O (t)=S O,5 (t)-S O,set (t); where e O (t) represents the dissolved oxygen concentration tracking error; S O,set (t) represents the dissolved oxygen concentration setpoint; the expression for the nitrate nitrogen concentration tracking error is: e NO (t)=S NO,2 (t)-S NO,set (t); where e NO (t) represents the tracking error of the nitrate nitrogen concentration; S NO,set (t) represents the setpoint for nitrate nitrogen concentration;

[0104] The Lyapunov function is constructed based on the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the Lyapunov function based on the errors is: Among them, V z e(t) is the Lyapunov function based on the error; e(t) is the tracking control error; T represents the transpose operation.

[0105] Specifically, constructing an optimal controller based on the execution network according to the Lyapunov function includes:

[0106] Differentiating the Lyapunov function yields the Lyapunov derivative function;

[0107] Extract the unknown dynamic information portion from the Lyapunov derivative function; the expression for the unknown dynamic information portion is: Where, D(t) = [D1(t), D2(t)] T D(t) is a matrix formed by vertically concatenating D1(t) and D2(t);

[0108] The execution network is constructed based on the unknown portion of the dynamic information; the expression of the execution network based on the fuzzy neural network is:

[0109]

[0110] in, The optimal output weights for the execution network; U a (t) represents the output of the normalized layer of the execution network; θ a (t) represents the estimation error of the execution network; For the input of the execution network; It is the center of the execution network; is the width of the execution network; m is the number of neurons in the input layer; l is the number of neurons in the RBF layer and the normalization layer.

[0111] Furthermore, constructing an optimal controller based on the execution network according to the Lyapunov function includes:

[0112] Construct an optimal controller; the expression for the optimal controller is:

[0113]

[0114] Among them, v * ζ is the output of the optimal controller; ζ is the control coefficient vector. This is the transpose of the optimal output weights;

[0115] Construct an actual controller based on the optimal controller; the expression of the actual controller is:

[0116]

[0117] Where v(t) is the output of the actual controller; for The transpose of the current value;

[0118] The actual controller is iteratively updated based on the updated execution network to obtain the updated optimal controller.

[0119] Specifically, constructing a long-term loss function and constructing the evaluation network of the fuzzy neural network based on the long-term loss function includes:

[0120] An instantaneous loss function is constructed based on the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the instantaneous loss function is:

[0121]

[0122] Wherein, R(t) is the output value of the instantaneous loss function;

[0123] Integrating the instantaneous loss function yields the long-term loss function; the expression for the long-term loss function is: in, ι is the output value of the long-term loss function; ι is the integration variable;

[0124] The evaluation network is constructed based on the long-term loss function; the expression of the evaluation network based on the fuzzy neural network is:

[0125]

[0126] in, U represents the optimal output weights of the evaluation network. c (t) represents the output of the normalization layer of the evaluation network; θ c (t) represents the estimation error of the evaluation network; This serves as the input to the evaluation network; The center of the evaluation network; The width of the evaluation network.

[0127] Furthermore, constructing the weight adaptation law for the execution network and the evaluation network includes:

[0128] Define a first estimation error for the evaluation network and a second estimation error for the execution network; the expression for the first estimation error is:

[0129]

[0130] Where η1(t) is the first estimation error; ξ is the discounted future cost; The output function of the evaluation network;

[0131] The expression for the second estimation error is:

[0132]

[0133] Wherein, η2(t) is the second estimation error;

[0134] A first cost function for the evaluation network is constructed based on the first estimation error, and a second cost function for the execution network is constructed based on the second estimation error; the expression for the first cost function is: Among them, E c (t) is the first cost function;

[0135] The expression for the second cost function is: Among them, E a (t) is the second cost function;

[0136] The weight adaptation laws for the execution network and the evaluation network are constructed based on the first cost function and the second cost function, respectively; the expressions for the weight adaptation laws include:

[0137] and

[0138]

[0139] in, for The transpose of the current value of β; c This is the first adaptive rate coefficient; for The current value of β; a This is the second adaptive rate coefficient; The change value of the rule layer of the evaluation network.

[0140] Specifically, a dynamic trigger threshold is set, and a dynamic event triggering mechanism is set according to the dynamic trigger threshold, including:

[0141] Construct the dynamic trigger threshold; the expression for the dynamic trigger threshold includes:

[0142] and

[0143]

[0144] Where τ1 is the first dynamic threshold; δ1 is the first positive definite parameter; λ is the Pushtz constant; τ2 is the second dynamic threshold; δ2 is the second positive definite parameter;

[0145] A dynamic event triggering mechanism is set according to the dynamic triggering threshold; the expression of the dynamic event triggering mechanism is: in, The first event; This is the second event; For tracking error based on event sampling; This is a long-run cost function.

[0146] Specifically, a kinetic model is established for dissolved oxygen concentration and nitrate nitrogen concentration:

[0147]

[0148] Furthermore, for the above dynamic model, the following two unknown functions are defined:

[0149]

[0150]

[0151] Therefore, the dynamic model can be rewritten as:

[0152]

[0153] Preferably, the tracking error for dissolved oxygen concentration and nitrate nitrogen concentration is defined as follows:

[0154] e O (t)=S O,5 (t)-S O,set (t)

[0155] e NO (t)=S NO,2 (t)-S NO,set (t)

[0156] The time derivatives of the tracking errors for dissolved oxygen concentration and nitrate nitrogen concentration are calculated as follows:

[0157]

[0158] in, It is the derivative of the dissolved oxygen concentration setpoint. It is the derivative of the setpoint for nitrate nitrogen concentration.

[0159] Furthermore, the Lyapunov function based on the tracking error is designed as follows:

[0160]

[0161] Differentiating the Lyapunov function yields:

[0162]

[0163] Where, e(t)=[e O (t),e NO (t)] T P(t) = [P1(t), P2(t)] T D(t) = [D1(t), D2(t)] T ,

[0164] Specifically, regarding dynamic information of the wastewater treatment process To address the unknowns, an execution network based on a fuzzy neural network is designed for approximation.

[0165]

[0166] in, It is the optimal output weight. Let Γ(t) represent the input of the fuzzy neural network, γ(t) represent the center of the fuzzy neural network, b(t) represent the width of the fuzzy neural network, and Γ(t) represent the width weights of the fuzzy neural network; m represents the number of neurons in the input layer of the fuzzy neural network, and l represents the number of neurons in the RBF layer and the normalization layer of the fuzzy neural network; U a (t) is the output of the normalization layer of the fuzzy neural network, θ a (t) is the estimation error, and the weight change is: in yes The current value.

[0167] Furthermore, the optimal controller can be designed as follows:

[0168]

[0169] The control coefficient vector is ζ = [ζ1ζ2]. Therefore, the actual controller can be expressed as:

[0170]

[0171] Preferably, based on the current state of the network identification process, the long-term loss function is calculated using the accumulated tracking control error of the wastewater treatment process. The instantaneous loss function is first designed as follows:

[0172]

[0173] Therefore, the long-term loss function can be expressed as follows:

[0174]

[0175] Where ξ>0 represents the discounted future cost.

[0176] A fuzzy neural network-based evaluation network is used to approximate the long-run cost function, and is designed as follows:

[0177]

[0178] in, Γ(t) represents the optimal output weights, x(t) represents the input of the fuzzy neural network, γ(t) represents the center of the fuzzy neural network, b(t) represents the width of the fuzzy neural network, and Γ(t) represents the width weights of the fuzzy neural network; m represents the number of neurons in the input layer of the fuzzy neural network, and l represents the number of neurons in the RBF layer and the normalization layer of the fuzzy neural network; U c (t) is the output of the normalization layer of the fuzzy neural network, θ c (t) is the boundary approximation error. The weight changes are as follows: in yes The current value of . Therefore, the output function of the comment network is

[0179] Furthermore, the estimation error based on the evaluation network and the execution network can be defined as:

[0180]

[0181] Define the cost functions of the evaluation network and the execution network as follows: and Therefore, the adaptive weight law design for the two networks is as follows:

[0182]

[0183] Where, β c >0,β a >0 is the adaptive rate coefficient, and

[0184] Specifically, a dynamic event triggering mechanism is designed: In the absence of event triggers, the final controller is as shown above. The adaptive event-triggered optimized controller is reconstructed using event sampling time.

[0185]

[0186] in, When t∈[t k ,t k+1 When, among them This represents a monotonically increasing sequence of trigger times when events occur. Assume the first event occurs at the initial time.

[0187] The triggering mechanism ET is represented as follows:

[0188]

[0189] Among them, the event and for

[0190]

[0191] Wherein, the dynamic trigger threshold τ1 is defined as τ2 is defined as

[0192]

[0193] Where λ is the known Pushtz constant of the Gaussian function, and δ1 and δ2 are positive definite parameters.

[0194] This event is triggered under the following conditions: 1) If the current error e(t) reaches the threshold τ1, then the weight parameters of both the evaluator network and the actor network are updated simultaneously; 2) If the long-run cost function... If the threshold τ2 is reached, the weight parameters of the evaluator network are updated, and simultaneously... 3) If the above deviation conditions are not met, it means that the current model can meet the control accuracy requirements and no update is needed.

[0195] Specifically, for the tracking and control problem of wastewater treatment processes, a dynamic cooperative optimal controller and parameter adaptive update method are adopted. This not only achieves good transient and steady-state performance but also strictly adheres to... and The boundedness of the system ensures the stability of the wastewater treatment process.

[0196] Furthermore, we introduce the Lyapunov candidate function as follows:

[0197]

[0198] The time derivative of the above function is:

[0199]

[0200] Further results were obtained:

[0201]

[0202] As the reinforcement learning-based iterative process continues, the cost function continuously decreases and eventually converges to the minimum boundary. Therefore, there exists a small constant function. Right now therefore:

[0203]

[0204] in, And ρ(t) is bounded, that is

[0205] According to Young's inequality

[0206]

[0207]

[0208] in, and It is a normal number.

[0209] The previous expression can be further written as:

[0210]

[0211] Therefore, we can conclude that:

[0212]

[0213] in,

[0214]

[0215] exist Based on this, we can further obtain the following:

[0216]

[0217] Therefore, we can conclude that:

[0218] 1) All signals in the wastewater treatment system are bounded:

[0219] Based on the previous equation, the boundedness of V(t) is achieved, which represents the change in weights. and The tracking error e(t) is bounded. Because It is bounded, therefore we can obtain and The boundedness of S. Additionally, S set It is known and bounded. Therefore, S O,5 (t) and S NO,2 The boundedness of υ(t) can be determined from the above analysis and the definition of υ(t). * It is bounded.

[0220] 2) Ensured transient and steady-state tracking performance of dissolved oxygen concentration and nitrate nitrogen concentration:

[0221] The stability analysis above shows that the boundedness of dissolved oxygen concentration, nitrate nitrogen concentration, and tracking error is strictly satisfied, which means that transient performance is effectively maintained. We can conclude that:

[0222]

[0223] By selecting appropriate parameters, the tracking error e(t) is made to converge to a small range, thus achieving accurate tracking of dissolved oxygen concentration and nitrate nitrogen concentration.

[0224] Based on the above theoretical discussion, the stability of the control system has been proven.

[0225] Furthermore, the control effect of the actual controller with optimal parameters is evaluated using the combined square error and the combined absolute error to obtain the evaluation result; the formula for calculating the combined square error is:

[0226]

[0227] The formula for calculating the comprehensive absolute error is as follows:

[0228]

[0229] Wherein, IAE is the combined squared error; ISE is the combined absolute error; The total number of samples.

[0230] Specifically, to demonstrate the superiority of the designed control method, Figure 2 and Figure 3 The simulation results are shown in comparison with proportional-integral-derivative (PID), fuzzy neural network (FNN), and adaptive dynamic programming (ADP) control methods. Figure 2 (a) and Figure 2 (b) The tracking curves for dissolved oxygen concentration and nitrate nitrogen concentration are presented respectively, and the results show that the DECOC control method can achieve the best tracking performance. Figure 3 (a) and Figure 3 (b) Control error curves for both methods were plotted, confirming that the proposed scheme achieves the highest control accuracy. Therefore, it can be concluded that, compared to PID, FNN, and ADP methods, the proposed DECOC achieves the best control accuracy and tracking response speed under stormy weather conditions. Figure 3 (a) and Figure 3 (b) Further, the curves showing the changes in the control variables are presented, and Figure 4 (a) and Figure 4 (b) shows the parameter update intervals for the dissolved oxygen concentration controller and the nitrate nitrogen concentration controller under two triggering conditions. A schematic diagram of the parameter update intervals for the dissolved oxygen concentration controller is provided below. Figure 5 (a) Schematic diagram of parameter update interval for nitrate nitrogen concentration controller (see reference figure) Figure 5 (b)

[0231] The beneficial effects of this invention are as follows:

[0232] This invention selectively updates the parameters of the evaluation network and the execution network through a weighted adaptive law, reducing the burden of large information communication volumes and insufficient computing power in water plants; through the adaptive controller of the execution network, it can accurately track the set values ​​of dissolved oxygen concentration and nitrate nitrogen concentration and achieve effective and rapid control; by optimizing the execution network and controller through the evaluation network, it effectively reduces the operating energy consumption of the equipment while ensuring that the effluent water quality meets the standards.

[0233] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0234] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A wastewater treatment adaptive cooperative optimal tracking control method based on dynamic event triggering, characterized in that, include: A simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration was constructed; Construct the Lyapunov function based on the simplified dynamic model; Construct an execution network based on a fuzzy neural network, and construct an optimal controller based on the execution network according to the Lyapunov function; Construct a long-term loss function, and construct an evaluation network based on the fuzzy neural network according to the long-term loss function; Construct the weight adaptive law for the execution network and the evaluation network; Two sets of dynamic trigger thresholds are set, and a dynamic event triggering mechanism is set according to the dynamic trigger thresholds; The dynamic event triggering mechanism and the weight adaptive law are updated in the execution network and the evaluation network, and the updated execution network and the evaluation network are used to update the optimal controller of the target device; A simplified kinetic model for dissolved oxygen and nitrate nitrogen concentrations was constructed, including: Establish the original dynamic model; the expression of the original dynamic model is: ； in, This refers to the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank. This refers to the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank. The concentration of nitrate nitrogen in the first zone of the biochemical reaction tank; The concentration of nitrate nitrogen in the second zone of the biochemical reaction tank; The concentration of nitrate nitrogen in the fifth zone of the biochemical reaction tank; This represents the saturation value of dissolved oxygen concentration. Dissolved oxygen concentration is the operating variable; The operating variable is the concentration of nitrate nitrogen; Microbial respiration coefficient; The flow rate of the first section of the biochemical reaction tank; The flow rate of the second section of the biochemical reaction tank; The flow rate of the fourth section of the biochemical reaction tank; The flow rate of the fifth section of the biochemical reaction tank; The concentration of heterotrophic biomass; Heterotrophic biomass; This refers to the volume of the second section of the biochemical reaction tank. This refers to the volume of the fifth section of the biochemical reaction tank; It is the first constant; It is the second constant; Define a first unknown function and a second unknown function; the expression for the first unknown function is: ； in, To track and control the unknown dynamic information of the environment when controlling dissolved oxygen concentration; The expression for the second unknown function is: ； in, To track and control unknown environmental dynamics when controlling nitrate nitrogen concentration; The original dynamic model is simplified using the first unknown function and the second unknown function to obtain the simplified dynamic model; the expression of the simplified dynamic model is: ； in, ; ; for The derivative; The result is the dissolved oxygen saturation value minus the current dissolved oxygen concentration; This is the result of dividing the current concentration of nitrate nitrogen by the volume of the second section of the biochemical reaction tank.

2. The adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering as described in claim 1, characterized in that, The Lyapunov function is constructed based on the simplified dynamic model, including: Based on the simplified kinetic model, the tracking errors for dissolved oxygen concentration and nitrate nitrogen concentration are set; the expression for the dissolved oxygen concentration tracking error is: ;in, This refers to the dissolved oxygen concentration tracking error; The setpoint for dissolved oxygen concentration; the expression for the tracking error of nitrate nitrogen concentration is: ;in, This refers to the tracking error of the nitrate nitrogen concentration. Set the nitrate nitrogen concentration value; The Lyapunov function is constructed based on the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the Lyapunov function based on the errors is: ;in, The Lyapunov function is based on the error. To track and control errors; This indicates the transpose operation.

3. The adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering according to claim 2, characterized in that, Constructing an optimal controller based on an execution network using the Lyapunov function includes: Differentiating the Lyapunov function yields the Lyapunov derivative function; Extract the unknown dynamic information portion from the Lyapunov derivative function; the expression for the unknown dynamic information portion is: ;in, ; For the reason and A matrix formed by vertically joining elements; The execution network is constructed based on the unknown portion of the dynamic information; the expression of the execution network based on the fuzzy neural network is: ； in, The optimal output weights for the execution network; The output of the normalization layer of the execution network; The estimation error of the execution network; For the input of the execution network; It is the center of the execution network; The width of the execution network; This represents the number of neurons in the input layer. This represents the number of neurons in the RBF layer and the normalized layer.

4. The adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering according to claim 3, characterized in that, Constructing an optimal controller based on an execution network using the Lyapunov function includes: Construct an optimal controller; the expression for the optimal controller is: ； in, This is the output of the optimal controller; This is a vector of control coefficients; This is the transpose of the optimal output weights; Construct an actual controller based on the optimal controller; the expression of the actual controller is: ； in, This is the output of the actual controller; for The transpose of the current value; The actual controller is iteratively updated based on the updated execution network to obtain the updated optimal controller.

5. The adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering according to claim 4, characterized in that, Constructing a long-term loss function, and constructing the evaluation network of the fuzzy neural network based on the long-term loss function, includes: An instantaneous loss function is constructed based on the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the instantaneous loss function is: ； in, The output value of the instantaneous loss function; Integrating the instantaneous loss function yields the long-term loss function; the expression for the long-term loss function is: ;in, The output value of the long-term loss function; For integration variables; The evaluation network is constructed based on the long-term loss function; the expression of the evaluation network based on the fuzzy neural network is: ； in, The optimal output weights of the evaluation network; The output of the normalization layer of the evaluation network; The estimation error of the evaluation network; This serves as the input to the evaluation network; The center of the evaluation network; The width of the evaluation network.

6. The adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering according to claim 5, characterized in that, Constructing the adaptive weight law for the execution network and the evaluation network includes: Define a first estimation error for the evaluation network and a second estimation error for the execution network; the expression for the first estimation error is: ； in, This is the first estimation error; To discount future costs; The output function of the evaluation network; The expression for the second estimation error is: ； in, This is the second estimation error; A first cost function for the evaluation network is constructed based on the first estimation error, and a second cost function for the execution network is constructed based on the second estimation error; the expression for the first cost function is: ;in, Let the first cost function be used. The expression for the second cost function is: ;in, This is the second cost function; The weight adaptation laws for the execution network and the evaluation network are constructed based on the first cost function and the second cost function, respectively; the expressions for the weight adaptation laws include: and ； in, for The transpose of the current value; This is the first adaptive rate coefficient; for The current value; This is the second adaptive rate coefficient; The change value of the rule layer of the evaluation network.

7. The adaptive cooperative optimal tracking control method for wastewater treatment based on dynamic event triggering according to claim 6, characterized in that, Setting a dynamic trigger threshold and setting a dynamic event triggering mechanism based on the dynamic trigger threshold, including: Construct the dynamic trigger threshold; the expression for the dynamic trigger threshold includes: and ； in, The first dynamic threshold; It is the first positive definite parameter; It is the Pushtz constant; This is the second dynamic threshold; It is the second positive definite parameter; A dynamic event triggering mechanism is set according to the dynamic triggering threshold; the expression of the dynamic event triggering mechanism is: ;in, ; The first event; This is the second event; For tracking error based on event sampling; This is a long-run cost function.

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