An adaptive self-triggered optimal control method for catalytic rod reactor

Abstract

This invention discloses an adaptive self-triggered optimal control method for catalytic rod reactors, specifically comprising: a temperature field model of the catalytic rod reaction process described by a high-dissipation partial differential equation system based on the control input of the cooling material under time triggering, and obtaining a low-order slow subsystem characterizing the high-dissipation partial differential equation system after order reduction processing; constructing a corresponding Hamiltonian function based on the performance index of the low-order slow subsystem, obtaining the optimal control strategy under time triggering control based on the Hamiltonian function, and then obtaining the optimal control strategy under self-triggered control, converting the Hamiltonian function into HJB equations; constructing a self-triggered controller based on an evaluation-execution dual-network structure using data-driven adaptive dynamic programming, and outputting the adaptive self-triggered optimal strategy based on the optimal value function of the HJB equations.

Description

Technical Field

[0001] This invention relates to the field of industrial preparation technology, and specifically to an adaptive self-triggered optimal control method for catalytic rod reactors. Background Technology

[0002] Catalytic rod reactions are a typical type of complex, spatiotemporally coupled dynamic system in industrial manufacturing, widely found in industrial applications such as catalytic combustion, waste gas treatment, and chemical synthesis. In this process, reactants undergo a catalytic reaction on the surface of the catalyst rod, releasing heat. This heat is conducted axially and radially along the rod, while convective heat transfer occurs with the surrounding fluid environment. The temperature distribution inside the rod is determined by both spatial and temporal variables, and its kinetic behavior is typically described by high-dissipation partial differential equations. Because catalytic reactions are infinite-dimensional, nonlinear, and strongly spatiotemporally coupled, and because the process between exothermic and heat dissipation can lead to multiple steady states or even thermal runaway in the temperature distribution, precise control of catalytic rod reactions is crucial for ensuring reaction efficiency, extending catalyst lifespan, and ensuring production safety.

[0003] To address the challenges of designing controllers for complex industrial processes, reinforcement learning methods, such as Adaptive Dynamic Programming (ADP), have demonstrated significant advantages and are widely used. However, traditional time-triggered ADP methods often suffer from high computational costs and low resource utilization, making them unsuitable for real-world industrial processes. This has prompted researchers to explore aperiodic optimization control methods. Currently, aperiodic optimization control methods are mainly divided into two types: event-triggered control methods and self-triggered control methods. Event-triggered control methods aim to continuously optimize control strategies by monitoring system states and identifying triggering conditions, thereby improving resource utilization efficiency and computational flexibility. However, the effectiveness of this method relies on continuous monitoring of system states, which is often difficult to guarantee in the complex environments of real-world industrial processes. Self-triggered control methods effectively overcome this limitation. Based on the system state and control information at the current triggering moment, they calculate and predict the next triggering moment, thus achieving self-adjustment of the control strategy according to changes in the system's internal state. Self-triggered control methods greatly relax the requirements for continuous monitoring of triggering conditions, further reducing the consumption of computational resources and communication bandwidth.

[0004] Currently, research on control methods combining self-triggering mechanisms and ADP in the field of high dissipation partial differential equations is still in its early stages. The main reasons are as follows: First, the research objects of existing self-triggering ADP control methods are concentrated on ordinary differential equation systems, and there are few reports on methods for spatiotemporal processes described by partial differential equations (PDEs). Second, PDE systems have infinite dimensions, nonlinearity, and strong spatiotemporal coupling characteristics, resulting in an extremely complex system structure, making it difficult to establish accurate mechanistic models using traditional methods. Summary of the Invention

[0005] In view of this, the present invention provides an adaptive self-triggering optimal control method for catalytic rod reactors, which at least solves the problems in the prior art that it is difficult to establish an accurate mechanism model for high dissipation partial differential equation systems, and that the existing self-triggering ADP method cannot be directly applied to infinite-dimensional nonlinear spatiotemporal processes.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: An adaptive self-triggered optimal control method for catalytic rod reactors includes the following steps: S1. Control input for cooling material based on time-triggered operation A temperature field model of the catalyst rod reaction process is described by a high-dissipation partial differential equation system, and a low-order slow subsystem characterizing the high-dissipation partial differential equation system is obtained after order reduction, where the time variable... ; S2. Construct the corresponding Hamiltonian function based on the performance indicators of the low-order slow subsystem, and obtain the optimal control strategy under time-triggered control based on the Hamiltonian function. ,based on The optimal control strategy under self-triggered control is then obtained. The Hamiltonian function is transformed into the HJB equation, where Representing the time modes of a low-order slow subsystem ; S3. Construct a data-driven adaptive dynamic programming-based evaluation-execution dual-network self-triggering controller to output the adaptive self-triggering optimal strategy. : S31. Evaluation Network: Using a neural network structure to continuously approximate the optimal value function of the HJB equation. and output The estimated value ; S32. Execution Network: Based on and gradient Building a data-driven And according to the preset self-triggered update mechanism, at the trigger time, Update it, and then send the updated version. Apply to the controlled object.

[0007] Preferably, the temperature field model for the catalyst rod reaction process in S1 is as follows: ; In the formula, The temperature distribution inside the reactor, , Represents the spatial variables inside the reactor. and They are respectively The lower and upper boundaries, and Control inputs and temperature output The matrix, For spatial differential operators, and These are the boundary conditions for the lower and upper boundaries of the temperature state distribution inside the reactor, respectively. for The initial temperature distribution inside the reactor.

[0008] Preferably, in S1, the high-dissipation partial differential equation system is reduced in order based on the spatiotemporal separation method, and then a low-order slow subsystem is obtained from the perspective of separating the fast and slow modes of the system. The low-order slow subsystem is specifically as follows: ; In the formula, Represents the modes of a low-order slow subsystem The derivative, express The initial mode of the low-order slow subsystem at time t, Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation and They are respectively and with space basis functions The input and output matrices of the low-order slow subsystem obtained after the inner product operation are, where Indicates the index of the spatial basis function. and Control inputs and temperature output The matrix, This is the output of the low-order slow subsystem.

[0009] Preferably, the specific content of S2 is as follows: (1) Constructing performance indicators of low-order slow subsystems : ; In the formula, yes The weighted matrix, yes The weighted matrix; (2) Based on the performance indicators of low-order slow subsystems Constructing Hamiltonian functions for high dissipation partial differential equation systems : ; in, Value function The transpose of the gradient, Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation, where Indicates the index of the spatial basis function; (3) Transform the Hamiltonian function into the HJB equation, i.e.: make This refers to the optimal control strategy under time-triggered conditions. Under the influence of the action, the minimum value of the Hamiltonian function is zero, where, For optimal value function The gradient; According to the principle of first-order optimality, for the Hamiltonian function... about By taking the partial derivatives, we obtain the optimal control strategy for a high-dissipation partial differential equation system under time-triggered conditions. ,Right now: ; ; in, for The inverse matrix, for with space basis functions The input matrix of the low-order slow subsystem obtained after the inner product operation, where Indicates the index of the spatial basis function. To control input Matrix; based on Then the optimal control strategy under self-triggered control can be obtained. for: ; in, This represents the gradient of the function representing the optimal value at the trigger moment. Indicates the first A trigger moment, Indicates the trigger time index. The available time modes for the controller are defined as follows: when at the trigger moment, i.e. The controller can use the system's time mode at the current moment, i.e. When it is a non-triggered moment, i.e. The controller can use the system's time mode at the previous trigger moment, i.e. ; Based on The HJB equation is obtained as follows: .

[0010] Preferably, the specific content of S3 includes: In the evaluation network, a neural network structure is introduced to approximate the optimal value function of the HJB equation. Evaluate the estimated value of the network output optimal value function. : ; in, For activation function, weight Estimated value; For execution networks: based on and gradient We obtained the adaptive self-triggering optimal control strategy for a high-dissipation partial differential equation system driven by data. : ; In the formula, yes The weighted matrix, for with space basis functions The input matrix of the low-order slow subsystem obtained after the inner product operation, where Indicates the index of the spatial basis function. To control input The matrix, for The transpose of the gradient, when The weight at the current trigger time As an estimate, i.e. ;when The weight of the previous trigger moment As an estimate, i.e. ; Time-triggered Hamiltonian function Depend on and Composition, self-triggered Hamiltonian function Depend on and Composition, according to and The difference is defined as the residual. And by minimizing the square of the residuals To approximate the true weights of the evaluation network, where ; Constructing an update law for evaluating network weights using gradient descent : ; In the formula, For learning rate, For adaptive parameters, For Lyapunov functions to be radially unbounded, , ; According to the law of renewal The evaluation network parameters were adjusted and iterated multiple times. When the network converges to the optimal value, executing the network will output the optimal value. .

[0011] Preferably, the specific content of obtaining the preset self-triggered update mechanism includes: Modal derivatives of low-order slow subsystems norm Represented as: ; in, It is a number greater than zero; Denotes the Euclidean vector norm; Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation; and They are respectively and with space basis functions The input and output matrices of the low-order slow subsystem obtained after the inner product operation are, where Indicates the index of the spatial basis function. and Control inputs and temperature output Matrix; Based on the adaptive self-triggering optimal control strategy in S3 The Lipschitz conditions are as follows: ; in, for norm, It is a number greater than zero; according to Boundedness, for time Mathematical operations based on the Lipschitz conditions yield the following: ; ; ; ; ; in, Modal error is defined as follows: ; Using the comparison lemma, at the self-triggered moment get: ; ; in, A threshold that includes status and control information; threshold The design is then expressed as the following inequality relationship: ; in, Numbers greater than zero; Let be a positive real number; It is an identity matrix; Through inequality transformations and logarithmic operations, the self-triggered update mechanism is specifically represented as follows: ; in, Represented as based on the current trigger time The next triggering time; and the triggering interval in S32 satisfies .

[0012] As can be seen from the above technical solution, compared with the prior art, the present invention discloses an adaptive self-triggered optimal control method for catalyst rod reactors, which has the following beneficial effects: (1) In view of the problem that it is difficult to obtain the analytical solution of HJB equation in the traditional optimization control of high dissipation partial differential equation system, the present invention proposes an adaptive self-triggering optimization control method based on ADP using a data-driven approach. This method approximates the optimal value function through the evaluation network, without needing to obtain the accurate analytical expression of the nonlinear dynamics of the system in advance, thus bypassing the dependence of the traditional method on the accurate mechanism model; the execution network is only updated non-periodically at the trigger time, which significantly reduces the computation and communication burden and provides an efficient way for the optimization control of the system in complex industrial environments.

[0013] (2) For a class of complex nonlinear systems with high dissipation partial differential equations, traditional periodic control strategies are prone to system instability due to frequent updates. However, the adaptive self-triggering optimal control method proposed in this invention dynamically predicts the next triggering time by using the system's state and control information at the current triggering time. This avoids continuous monitoring of the triggering conditions and significantly reduces the data transmission load and computational burden of the optimization control process of high dissipation partial differential equation systems. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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.

[0015] Figure 1 A flowchart of an adaptive self-triggered optimal control method for a catalyst rod reactor provided by the present invention; Figure 2 This is a schematic diagram of a typical zero-order exothermic catalytic reaction provided in an embodiment of the present invention; Figure 3 These are the two spatial basis functions ultimately selected for this embodiment of the invention, wherein... Figure 3 (a) is , Figure 3 (b) for ; Figure 4 This is an adaptive self-triggering optimal control input curve provided in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the convergence process of the weight norm of the neural network over time, provided in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the characteristics of the triggering time interval under self-triggering control, provided by an embodiment of the present invention. Figure 7This is a surface diagram showing the change in the internal temperature distribution of the reactor under the action of the adaptive self-triggering optimal control method, provided in an embodiment of the present invention. Detailed Implementation

[0016] 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.

[0017] This invention provides an adaptive self-triggered optimal control method for catalytic rod reactors, comprising the following steps: S1. Control input for cooling material based on time-triggered operation A temperature field model of the catalyst rod reaction process is described by a high-dissipation partial differential equation system, and a low-order slow subsystem characterizing the high-dissipation partial differential equation system is obtained after order reduction, where the time variable... ; S2. Construct the corresponding Hamiltonian function based on the performance indicators of the low-order slow subsystem, and obtain the optimal control strategy under time-triggered control based on the Hamiltonian function. ,based on The optimal control strategy under self-triggered control is then obtained. The Hamiltonian function is transformed into the HJB equation, where Representing the time modes of a low-order slow subsystem ; S3. Construct a data-driven adaptive dynamic programming-based evaluation-execution dual-network self-triggering controller to output the adaptive self-triggering optimal strategy. : S31. Evaluation Network: Using a neural network structure to continuously approximate the optimal value function of the HJB equation. and output The estimated value ; S32. Execution Network: Based on and gradient Building a data-driven And according to the preset self-triggered update mechanism, at the trigger time, Update it, and then send the updated version. Apply to the controlled object.

[0018] To further implement the above technical solution, the temperature field model for the catalyst rod reaction process in S1 is as follows: ; In the formula, The temperature distribution inside the reactor, , Represents the spatial variables inside the reactor. and They are respectively The lower and upper boundaries, and Control inputs and temperature output The matrix, For spatial differential operators, and These are the boundary conditions for the lower and upper boundaries of the temperature state distribution inside the reactor, respectively. for The initial temperature distribution inside the reactor.

[0019] To further implement the above technical solution, in S1, the high-dissipation partial differential equation system is reduced in order based on the spatiotemporal separation method, and then, from the perspective of separating the fast and slow modes of the system, a low-order slow subsystem is obtained, wherein the low-order slow subsystem is specifically as follows: ; In the formula, Represents the modes of a low-order slow subsystem The derivative, express The initial mode of the low-order slow subsystem at time t, Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation and They are respectively and with space basis functions The input and output matrices of the low-order slow subsystem obtained after the inner product operation are, where Indicates the index of the spatial basis function. and Control inputs and temperature output The matrix, This is the output of the low-order slow subsystem.

[0020] To further implement the above technical solution, the specific content of S2 is as follows: (1) Constructing performance indicators of low-order slow subsystems : ; In the formula, yes The weighted matrix, yes The weighted matrix, Represents the modes of a low-order slow subsystem; (2) Based on the performance indicators of low-order slow subsystems Constructing Hamiltonian functions for high dissipation partial differential equation systems : ; in, Value function The transpose of the gradient, Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation, where Indicates the index of the spatial basis function; (3) Transform the Hamiltonian function into the HJB equation, i.e.: make This refers to the optimal control strategy under time-triggered conditions. Under the influence of the action, the minimum value of the Hamiltonian function is zero, where, For optimal value function The gradient; According to the principle of first-order optimality, for the Hamiltonian function... about By taking the partial derivatives, we obtain the optimal control strategy for a high-dissipation partial differential equation system under time-triggered conditions. ,Right now: ; ; in, for The inverse matrix, for with space basis functions The input matrix of the low-order slow subsystem obtained after the inner product operation, where Indicates the index of the spatial basis function. To control input Matrix; based on Then the optimal control strategy under self-triggered control can be obtained. for: ; in, This represents the gradient of the function representing the optimal value at the trigger moment. Indicates the first A trigger moment, Indicates the trigger time index. The available time modes for the controller are defined as follows: when at the trigger moment, i.e. The controller can use the system's time mode at the current moment, i.e. When it is a non-triggered moment, i.e. The controller can use the system's time mode at the previous trigger moment, i.e. ; Based on The HJB equation is obtained as follows: .

[0021] To further implement the above technical solution, the specific content of S3 includes: In the evaluation network, a neural network structure is introduced to approximate the optimal value function of the HJB equation. Evaluate the estimated value of the network output optimal value function. : ; in, For activation function, weight Estimated value; For execution networks: based on and gradient We obtained the adaptive self-triggering optimal control strategy for a high-dissipation partial differential equation system driven by data. : ; In the formula, yes The weighted matrix, for with space basis functions The input matrix of the low-order slow subsystem obtained after the inner product operation, where Indicates the index of the spatial basis function. To control input The matrix, for The transpose of the gradient, when The weight at the current trigger time As an estimate, i.e. ;when The weight of the previous trigger moment As an estimate, i.e. ; Time-triggered Hamiltonian function Depend on and Composition, self-triggered Hamiltonian function Depend on and Composition, according to and The difference is defined as the residual. And by minimizing the square of the residuals To approximate the true weights of the evaluation network, where ; Constructing an update law for evaluating network weights using gradient descent : ; In the formula, For learning rate, For adaptive parameters, For Lyapunov functions to be radially unbounded, , ; According to the law of renewal The evaluation network parameters were adjusted and iterated multiple times. When the network converges to the optimal value, executing the network will output the optimal value. .

[0022] To further implement the above technical solution, the specific details of obtaining the preset self-triggered update mechanism include: Modal derivatives of low-order slow subsystems norm Represented as: ; in, It is a number greater than zero; Denotes the Euclidean vector norm; Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation; and They are respectively and with space basis functions The input and output matrices of the low-order slow subsystem obtained after the inner product operation are, where Indicates the index of the spatial basis function. and Control inputs and temperature output Matrix; Based on the adaptive self-triggering optimal control strategy in S3 The Lipschitz conditions are as follows: ; in, for norm, It is a number greater than zero; according to Boundedness, for time Mathematical operations based on the Lipschitz conditions yield the following: ; ; ; ; ; in, Modal error is defined as follows: ; Using the comparison lemma, at the self-triggered moment get: ; ; in, A threshold that includes status and control information; threshold The design is then expressed as the following inequality relationship: ; in, Numbers greater than zero; Let be a positive real number; It is an identity matrix; Through inequality transformations and logarithmic operations, the self-triggered update mechanism is specifically represented as follows: ; in, Represented as based on the current trigger time The next triggering time; and the triggering interval in S32 satisfies .

[0023] The invention will be further illustrated below through specific experiments: The adaptive self-triggering optimal control method studied in this invention was applied to an industrial spatiotemporal reaction process, exemplified by a catalytic rod reactor, to verify the effectiveness and convergence of the method. This chemical transfer reaction process is a typical zero-order exothermic catalytic reaction, such as... Figure 2As shown. Reactant A is fed into the reactor at the inlet, and product B, after reaction transformation, is output from the other end. Because this reaction is exothermic, a cooling medium must be continuously introduced from the outside to balance the heat released by the reaction in order to maintain the uniformity and constancy of the temperature field inside the reactor. The following high-dissipation partial differential equation expresses the mathematical description model of this reaction process: ; in, For the input of cooling material under adaptive self-trigger control, Where is the diffusion coefficient. The heat in the reaction heat, To activate energy, This represents the heat transfer coefficient. The model also employs Dirichlet boundary conditions, i.e. The initial conditions of this model are: .

[0024] Appropriate selection of initial parameters for simulation verification: In this embodiment, the diffusion coefficient in the catalyst rod reactor of the above-mentioned industrial preparation process is... The heat in the reaction heat Activate energy Heat transfer coefficient , In evaluating the weight parameter update law of a network, the parameters... and Set them to 1 and 0.08 respectively.

[0025] First, the system state of the catalytic reaction, characterized by a high-dissipation partial differential equation system, was collected to obtain a dataset representing the spatiotemporal evolution characteristics of the system. Then, spatial basis functions were extracted from the data using a spatiotemporal separation method. These basis functions reflect the main spatial distribution characteristics of the catalytic reaction process. After calculation and screening, two spatial basis functions were finally selected as the spatial basis for subsequent self-triggered adaptive optimal control, such as... Figure 3 (a) and Figure 3 As shown in (b).

[0026] This invention is applied to tubular catalytic reactions: cooling substances, controlled by the weights of an evaluation network and an adaptive self-triggering optimal control strategy, continuously act on the catalytic reaction process to gradually stabilize the internal temperature distribution of the reactor. The adaptive self-triggering optimal control input is as follows: Figure 4 As shown, The control input representing the cooling substance during the catalytic reaction, under the influence of the self-triggering mechanism, shows a step-like distribution in its trajectory. The convergence process of the weight norm of the neural network over time is evaluated as follows: Figure 5 As shown, it can be seen that the weights for evaluating the neural network will eventually converge to a fixed value. Figure 6As shown, under self-triggering control, the triggering time interval exhibits a segmented distribution. This effectively demonstrates the dynamic prediction of the next triggering moment by the adaptive self-triggering optimal control method, significantly reducing data transmission and computation costs during the reaction process. Figure 7 The surface plot depicts the change in the internal temperature distribution of the reactor under the adaptive self-triggering optimal control method, showing the process of the system converging from the initial state to near zero.

[0027] In summary, the adaptive self-triggering optimal control method proposed in this invention can maintain stability and achieve rapid convergence under complex operating conditions described by high-dissipation partial differential equations. The proposed method is not only applicable to the optimal control of catalytic rod reactors but can also be extended to other industrial processes with high-dissipation spatiotemporal distribution characteristics. For example, in the field of new energy material preparation, it can be used for the high-temperature sintering process of lithium-ion battery cathode materials and the synthesis and heat treatment process of new battery materials; in the metallurgical industry, it can be used for blast furnace ironmaking and aluminum alloy forging; and in the semiconductor manufacturing field, it can be used for the Czochralski silicon single crystal growth process. Facing the complex operating conditions of nonlinearity, large hysteresis, and multivariate coupling in the above-mentioned actual industrial preparation processes, this method does not require a precise mechanistic model. Through data-driven learning and non-periodic control updates, it achieves efficient and robust optimal control.

[0028] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. An adaptive self-triggered optimal control method for catalytic rod reactors, characterized in that, Includes the following steps: S1. Control input for cooling material based on time-triggered operation A temperature field model of the catalyst rod reaction process is described by a high-dissipation partial differential equation system, and a low-order slow subsystem characterizing the high-dissipation partial differential equation system is obtained after order reduction, where the time variable... ; S2. Construct the corresponding Hamiltonian function based on the performance indicators of the low-order slow subsystem, and obtain the optimal control strategy under time-triggered control based on the Hamiltonian function. ,based on The optimal control strategy under self-triggered control is then obtained. The Hamiltonian function is transformed into the HJB equation, where Representing the time modes of a low-order slow subsystem ; S3. Construct a data-driven adaptive dynamic programming-based evaluation-execution dual-network self-triggering controller to output the adaptive self-triggering optimal strategy. : S31. Evaluation Network: Using a neural network structure to continuously approximate the optimal value function of the HJB equation. and output The estimated value ; S32. Execution Network: Based on and gradient Building a data-driven And according to the preset self-triggered update mechanism, at the trigger time, Update it, and then send the updated version. Apply to the controlled object.

2. The adaptive self-triggering optimal control method for a catalytic rod reactor according to claim 1, characterized in that, The temperature field model for the catalyst rod reaction process in S1 is: ； In the formula, The temperature distribution inside the reactor, , Represents the spatial variables inside the reactor. and They are respectively The lower and upper boundaries, and Control inputs and temperature output The matrix, For spatial differential operators, and These are the boundary conditions for the lower and upper boundaries of the temperature state distribution inside the reactor, respectively. for The initial temperature distribution inside the reactor.

3. The adaptive self-triggering optimal control method for a catalytic rod reactor according to claim 1, characterized in that, In S1, the high-dissipation partial differential equation system is reduced in order based on the spatiotemporal separation method. Then, from the perspective of separating the fast and slow modes of the system, a low-order slow subsystem is obtained, which is specifically as follows: ； In the formula, Represents the modes of a low-order slow subsystem The derivative, express The initial mode of the low-order slow subsystem at time t, Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation and They are respectively and with space basis functions The input and output matrices of the low-order slow subsystem obtained after the inner product operation are, where Indicates the index of the spatial basis function. and Control inputs and temperature output The matrix, This is the output of the low-order slow subsystem.

4. The adaptive self-triggering optimal control method for a catalytic rod reactor according to claim 1, characterized in that, The specific content of S2 is as follows: (1) Constructing performance indicators of low-order slow subsystems : ； In the formula, yes The weighted matrix, yes The weighted matrix; (2) Based on the performance indicators of low-order slow subsystems Constructing Hamiltonian functions for high dissipation partial differential equation systems : ； in, Value function The transpose of the gradient, Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation, where Indicates the index of the spatial basis function; (3) Transform the Hamiltonian function into the HJB equation, i.e.: make This refers to the optimal control strategy under time-triggered conditions. Under the influence of the action, the minimum value of the Hamiltonian function is zero, where, For optimal value function The gradient; According to the principle of first-order optimality, for the Hamiltonian function... about By taking the partial derivatives, we obtain the optimal control strategy for a high-dissipation partial differential equation system under time-triggered conditions. ,Right now: ； ； in, for The inverse matrix, for with space basis functions The input matrix of the low-order slow subsystem obtained after the inner product operation, where Indicates the index of the spatial basis function. To control input Matrix; based on Then the optimal control strategy under self-triggered control can be obtained. for: ； in, This represents the gradient of the function representing the optimal value at the trigger moment. Indicates the first A trigger moment, Indicates the trigger time index. The available time modes for the controller are defined as follows: when at the trigger moment, i.e. The controller can use the system's time mode at the current moment, i.e. When it is at a non-triggered moment, i.e. The controller can use the system's time mode at the previous trigger moment, i.e. ; Based on The HJB equation is obtained as follows: 。 5. The adaptive self-triggered optimal control method for a catalyst rod reactor according to claim 1, characterized in that, The specific content of S3 includes: In the evaluation network, a neural network structure is introduced to approximate the optimal value function of the HJB equation. Evaluate the estimated value of the network output optimal value function. : ； in, For activation function, weight Estimated value; For execution networks: based on and gradient We obtained the adaptive self-triggering optimal control strategy for a high-dissipation partial differential equation system driven by data. : ； In the formula, yes The weighted matrix, for with space basis functions The input matrix of the low-order slow subsystem obtained after the inner product operation, where Indicates the index of the spatial basis function. To control input The matrix, for The transpose of the gradient, when The weight at the current trigger time As an estimate, i.e. ;when The weight of the previous trigger moment As an estimate, i.e. ; Time-triggered Hamiltonian function Depend on and Composition, self-triggered Hamiltonian function Depend on and Composition, according to and The difference is defined as the residual. And by minimizing the square of the residuals To approximate the true weights of the evaluation network, where ; Constructing an update law for evaluating network weights using gradient descent : ； In the formula, For learning rate, For adaptive parameters, For Lyapunov functions to be radially unbounded, , ; According to the law of renewal The evaluation network parameters were adjusted and iterated multiple times. When the network converges to the optimal value, executing the network will output the optimal value. .

6. The adaptive self-triggering optimal control method for a catalytic rod reactor according to claim 1, characterized in that, The specific details of obtaining the preset self-triggered update mechanism include: Modal derivatives of low-order slow subsystems norm Represented as: ； in, It is a number greater than zero; Denotes the Euclidean vector norm; Spatial differential operators in high dissipation partial differential equation system models and space basis functions The function obtained after the inner product operation; and They are respectively and with space basis functions The input and output matrices of the low-order slow subsystem obtained after the inner product operation are, where Indicates the index of the spatial basis function. and Control inputs and temperature output Matrix; Based on the adaptive self-triggering optimal control strategy in S3 The Lipschitz conditions are as follows: ； in, for norm, It is a number greater than zero; according to Boundedness, for time Mathematical operations based on the Lipschitz conditions yield the following: ； ； ； ； ； in, Modal error is defined as follows: ; Using the comparison lemma, at the self-triggered moment get: ； ； in, A threshold that includes status and control information; threshold The design then adopts the following inequality relationship: ； in, Numbers greater than zero; Let be a positive real number; It is an identity matrix; Through inequality transformations and logarithmic operations, the self-triggered update mechanism is specifically represented as follows: ； in, Represented as based on the current trigger time The next triggering time; and the triggering interval in S32 satisfies .

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