Multi-mode sensing intelligent regulation and control method for argon stirring in RH (Ruhrstahl Heraeus) refining process

Abstract

The invention relates to the technical field of ferrous metallurgy refining process control, and particularly discloses a multi-modal perception RH refining process argon stirring intelligent regulation and control method, which comprises the following steps: 1) visual perception: generating an enhanced feature map by adopting a dual-channel image of a multispectral imaging module through a self-adaptive weighted fusion algorithm; 2) dynamic fusion: integrating multi-dimensional process parameters by a multi-modal data fusion module, and constructing a dynamic feature weight distribution model based on an attention mechanism; 3) predictive control: designing a feedforward-feedback composite control architecture, adopting a variable gain PID algorithm for a basic loop, and performing hardware-level fusion on PID output and predictive compensation amount on an embedded platform by a control instruction synthesis module; according to the invention, the problems of light reflection and oxidation film interference are solved through wavelength complementation, and high-precision bright region detection under complex working conditions is realized; the predictive composite control strategy fuses the steady-state performance of the PID and the dynamic compensation advantage of the LSTM, and the response speed and the anti-interference capability of the system are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of steel metallurgical refining process control, and in particular to a multi-modal sensing argon stirring intelligent control method for RH refining process. Background Art

[0002] In the RH refining process, the bright area on the slag surface formed by argon bottom blowing directly reflects the stirring intensity of the molten steel. Existing technologies generally use fixed threshold control or open-loop regulation based on empirical formulas, which suffer from three technical drawbacks: First, manual visual judgment of the bright surface area is affected by factors such as ambient lighting and operator experience. Measured data shows that operators on different shifts vary in their judgments of the same operating conditions; second, conventional PID control algorithms fail to consider the coupling effect between dynamic temperature field changes and argon bubble diameter distribution, which can easily cause flow rate fluctuations when switching steel grades or when air bricks become clogged; third, existing visual inspection systems often use single-spectrum imaging technology, which has a high false detection rate under complex conditions such as molten steel splashing and smoke interference. Traditional control methods often result in argon overshoot exceeding 40% of the set value in the late stages of refining.

[0003] In response to the complex operating conditions of bottom-blowing argon control during RH vacuum refining, traditional manual adjustment methods suffer from large subjective errors, delayed dynamic response, and lack of parameter coupling, resulting in low argon utilization and unstable molten steel purity. In existing technologies, single spectral imaging systems suffer from significant detection errors under the interference of molten steel splashing and smoke, and conventional control strategies struggle to cope with the coupled effects of pipeline pressure fluctuations and temperature fields. Therefore, a multimodal sensing method for intelligent argon stirring control during the RH refining process was designed to address the issues of delayed response and insufficient control accuracy associated with manual adjustment of argon flow rate during traditional RH vacuum refining. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a multimodal sensing method for intelligently controlling argon agitation during the RH refining process. By constructing a multidimensional feature extraction system for the ladle slag surface and combining it with a deep neural network and predictive control algorithm, this method enables real-time and precise regulation of argon mass flow. This system overcomes the limitations of traditional single-parameter control. Through the collaborative use of visible light and near-infrared dual-channel imaging, an improved target detection network, and a predictive composite control algorithm, it achieves real-time and precise regulation of argon flow, breaking through the technical bottlenecks of traditional methods. This method significantly reduces argon consumption while ensuring molten steel purity, providing technical support for green and efficient steelmaking.

[0005] The technical solution adopted by the present invention to solve the technical problem is: a multi-modal sensing argon stirring intelligent control method for RH refining process, comprising the following steps:

[0006] 1) Visual perception: The dual-channel images of the multispectral imaging module are used to generate enhanced feature maps through an adaptive weighted fusion algorithm;

[0007] 2) Dynamic fusion: The multimodal data fusion module integrates multi-dimensional process parameters and constructs a dynamic feature weight allocation model based on the attention mechanism;

[0008] 3) Predictive control: A feedforward-feedback composite control architecture is designed. The basic loop adopts a variable-gain PID algorithm. The control instruction synthesis module integrates the PID output and the predicted compensation at the hardware level on the embedded platform.

[0009] Specifically, the multispectral imaging module in step 1) adopts a dual-channel industrial-grade camera, the visible light channel 400-700nm captures the morphological features of the bright area of the slag surface, and the near-infrared channel 850-1700nm penetrates the surface oxide film to obtain the deep temperature distribution. The dual-channel image generates an enhanced feature map through an adaptive weighted fusion algorithm, and the edge detection mask of the visible light image and the radiation intensity distribution of the near-infrared channel dynamically adjust the weight coefficient to improve the intersection-over-union ratio of bright area detection in low-contrast scenes; the feature parsing module adopts an improved YOLOv8 network architecture, adds a morphological constraint branch on the basis of the traditional target detection branch, supervises the bright area contour features through the Fourier descriptor, and the network loss function integrates the bounding box regression loss, category focus loss and morphological constraint loss.

[0010] Specifically, the generation mechanism of the weight coefficient for dynamically adjusting the radiation intensity distribution of the infrared channel includes the following steps:

[0011] (1) Data preprocessing: The visible light channel (400-700 nm) uses an edge detection algorithm to extract the morphological features of the bright area on the slag surface and generate an edge mask; the near-infrared channel (850-1700 nm) obtains the deep temperature information of the molten steel based on the thermal radiation intensity distribution map;

[0012] (2) Weight allocation: For each pixel, the edge intensity of the visible light image and the radiation intensity contrast of the near-infrared image are calculated; in low-contrast areas, the weight coefficient of the near-infrared channel increases because it has strong penetrating power and can effectively supplement the details missing from the visible light.

[0013] (3) Weight formula: W IR =σ Vis +σ IR , W Vis =1-W IR ; Wherein, σIR is the standard deviation of local contrast in the near-infrared channel; σVis is the standard deviation of local contrast in the visible light channel;

[0014] (4) Dynamic adjustment: A sliding window mechanism is used to update the weights of local areas in real time to ensure that the fused image can maintain high detection accuracy under complex working conditions.

[0015] Specifically, the Fourier descriptor is used to supervise the bright area contour feature supervision method. The Fourier descriptor is used to supervise the neural network to learn the geometric shape of the bright area of the slag surface. The specific steps are as follows:

[0016] (1) Contour extraction: Extract the boundary point coordinate sequence (x i ,y i ), converted to the plural form z i =x i +jy i ;

[0017] (2) Fourier transform: Perform discrete Fourier transform DFT on the complex sequence to obtain the frequency domain coefficients {F k}, retain the low-frequency components, such as the first 10 coefficients, as the Fourier descriptor describing the overall shape of the contour;

[0018] (3) Loss function design: In the improved YOLOv8 network, a new morphological constraint branch is added to predict the Fourier descriptor of the contour. The loss function includes: bounding box regression loss, category focus loss, and morphological constraint loss. The morphological constraint loss is to calculate the mean square error (MSE) between the predicted and true Fourier coefficients:

[0019] L shape =N1 k-1 ∑ N ∥F kpred -F ktrue ∥2;

[0020] Through multi-task learning, the network simultaneously optimizes object localization and shape accuracy.

[0021] Specifically, the dynamic feature weight distribution model in step 2) determines the temperature gradient sensitivity coefficient and the historical flow attenuation factor through the particle swarm optimization algorithm, and can capture flow feature anomalies in the early stage of air brick blockage.

[0022] Specifically, the process of establishing the fusion model of the multi-dimensional process parameters is as follows:

[0023] (1) Feature normalization: Each parameter is standardized to eliminate dimensional differences;

[0024] (2) Attention mechanism design: Input feature vector F∈R 12 Generate query, key, and value matrices through the fully connected layer;

[0025] Calculate attention weight: α i=softmax(d k QK iT );

[0026] The weighted fusion feature is F fused =∑α i V i ;

[0027] (3) Particle swarm optimization (PSO): used to determine the temperature gradient sensitivity coefficient β and the flow attenuation factor γ. The optimization goal is to minimize the prediction error in the historical data and iteratively update the particle position until convergence.

[0028] Specifically, the proportional coefficient of the variable gain PID algorithm in step 3) is dynamically adjusted according to the rate of change of the bright area area, the integral and differential terms are designed with adaptive laws through Lyapunov stability analysis, the feedforward compensation amount is predicted by the LSTM network to predict the working condition disturbance in the next 3 seconds, the network input includes the historical flow sequence, the temperature field gradient and the bright area morphological factor, and the output layer adopts a residual connection structure to reduce the prediction error.

[0029] Specifically, the steps of the variable gain PID algorithm to ensure system stability through the Lyapunov method are as follows:

[0030] (1) Define the error state: Let the control error e(t) = r(t) - y(t), where r(t) is the set value and y(t) is the system output;

[0031] (2) Constructing the Lyapunov function: Select the positive definite function V(t) = 21e2(t) + 21λθ ～ 2(t), where θ ～ is the parameter estimation error, λ>0 is the adjustment coefficient;

[0032] (3) Stability analysis: Derivative V˙(t) = ee˙ + λθ ～ θ ～ ˙;

[0033] Substitute into the PID control law u=K p e+K i ∫edt+K ddtde and adaptive law K˙p=-γ p e2, ensure V˙(t)≤0;

[0034] (4) Adaptive law design: Derivation of the integral term K through stability conditions i (t) and the differential term K d (t), for example: K˙i=α∫edt,K˙d=βdtde, where α and β are determined by Lyapunov conditions, ensuring the global stability of the system under time-varying conditions.

[0035] The present invention has the following beneficial effects:

[0036] The multimodal sensing intelligent control method for argon stirring in the RH refining process designed in the present invention constructs a full-chain control system of "visual perception-dynamic fusion-predictive control". Multispectral imaging technology breaks through the limitations of single-channel detection and solves the interference problem of reflection and oxide film through wavelength complementarity; the improved YOLOv8 network introduces morphological constraint branches to achieve high-precision bright area detection under complex working conditions; the predictive composite control strategy combines the steady-state performance of PID and the dynamic compensation advantages of LSTM, significantly improving the system response speed and anti-interference ability. DETAILED DESCRIPTION

[0037] The technical solutions in the embodiments of the present invention will be described in detail below. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] A multimodal sensing method for intelligent control of argon stirring in the RH refining process is proposed. The system hardware consists of a multispectral imaging module, an edge computing unit, and a process control unit.

[0039] 1. Visual Perception: The multispectral imaging module uses a dual-channel image processing algorithm to generate an enhanced feature map using dual-channel industrial-grade cameras. The visible light channel (400-700nm) captures the morphological characteristics of bright areas on the slag surface, while the near-infrared channel (850-1700nm) penetrates the surface oxide film to obtain the deep-layer temperature distribution. The dual-channel images are then fused using an adaptive weighted algorithm to generate an enhanced feature map. The weight coefficients of the visible light image's edge detection mask and the radiation intensity distribution of the near-infrared channel are dynamically adjusted to improve the intersection-over-union ratio (IOR) of bright area detection in low-contrast scenes. The feature parsing module utilizes an improved YOLOv8 network architecture, adding a morphological constraint branch to the traditional object detection branch. The bright area contour features are supervised by Fourier descriptors. The network loss function integrates bounding box regression loss, class focus loss, and morphological constraint loss. After transfer learning training, the recognition accuracy of irregular bright areas is improved by 16.5% compared to the baseline model. The network inference speed is optimized to 12 milliseconds per frame, meeting real-time control requirements.

[0040] The generation mechanism of the dynamic adjustment weight coefficient of the infrared channel radiation intensity distribution includes the following steps:

[0041] (1) Data preprocessing: The visible light channel (400-700 nm) uses an edge detection algorithm to extract the morphological features of the bright area on the slag surface and generate an edge mask; the near-infrared channel (850-1700 nm) obtains the deep temperature information of the molten steel based on the thermal radiation intensity distribution map.

[0042] (2) Weight allocation: For each pixel, the edge intensity of the visible light image and the radiation intensity contrast of the near-infrared image are calculated; in low-contrast areas, the weight coefficient of the near-infrared channel increases because it has strong penetrability and can effectively supplement the details missing from the visible light.

[0043] (3) Weight formula: W IR =σ Vis +σ IR , W Vis =1-W IR ; Among them, σIR is the local contrast standard deviation of the near-infrared channel; σVis is the local contrast standard deviation of the visible light channel.

[0044] (4) Dynamic adjustment: A sliding window mechanism is used to update the weights of local areas in real time to ensure that the fused image can maintain high detection accuracy under complex working conditions.

[0045] Fourier descriptor is used to supervise the contour features of bright areas. Fourier descriptor is used to supervise the neural network to learn the geometric shape of the bright areas on the slag surface. The specific steps are as follows:

[0046] (1) Contour extraction: Extract the boundary point coordinate sequence (x i ,y i ), converted to the plural form z i =x i +jy i ;

[0047] (2) Fourier transform: Perform discrete Fourier transform DFT on the complex sequence to obtain the frequency domain coefficients {F k}, retain the low-frequency components, such as the first 10 coefficients, as the Fourier descriptor describing the overall shape of the contour;

[0048] (3) Loss function design: In the improved YOLOv8 network, a new morphological constraint branch is added to predict the Fourier descriptor of the contour. The loss function includes: bounding box regression loss, category focus loss, and morphological constraint loss. The morphological constraint loss is to calculate the mean square error (MSE) between the predicted and true Fourier coefficients:

[0049] L shape =N1 k-1 ∑ N ∥F kpred -F ktrue ∥2;

[0050] Through multi-task learning, the network simultaneously optimizes object localization and shape accuracy.

[0051] 2. Dynamic fusion: The multimodal data fusion module integrates multidimensional process parameters, including but not limited to 12-dimensional process parameters such as temperature gradient field, argon pressure pulsation, and molten steel composition, to construct a dynamic feature weight allocation model based on the attention mechanism. The dynamic feature weight allocation model uses a particle swarm optimization algorithm to determine the temperature gradient sensitivity coefficient and the historical flow attenuation factor. It can capture flow characteristic anomalies in the early stage of air brick blockage and trigger an early warning 4.8 seconds earlier than traditional threshold detection methods.

[0052] The process of establishing the fusion model of multi-dimensional process parameters is as follows:

[0053] (1) Feature normalization: Each parameter is standardized to eliminate dimensional differences.

[0054] (2) Attention mechanism design: Input feature vector F∈R 12 Generate query, key, and value matrices through the fully connected layer;

[0055] Calculate attention weight: α i =softmax(d k QK iT ).

[0056] The weighted fusion feature is F fused =∑α i V i .

[0057] (3) Particle swarm optimization (PSO): used to determine the temperature gradient sensitivity coefficient β and the flow attenuation factor γ. The optimization goal is to minimize the prediction error in the historical data and iteratively update the particle position until convergence.

[0058] 3. Predictive Control: In terms of control strategy, a feedforward-feedback composite control architecture was designed. The basic loop utilizes a variable-gain PID algorithm, whose proportional coefficient is dynamically adjusted based on the rate of change of the bright area. Adaptive laws are designed for the integral and differential terms using Lyapunov stability analysis to ensure system robustness under time-varying conditions. The feedforward compensation is calculated using an LSTM network that predicts operating disturbances three seconds into the future. The network inputs include historical flow rates, temperature gradients, and bright area morphology factors. The output layer utilizes a residual connection structure to minimize prediction error. Field testing has shown that the root mean square error (RMS) of disturbance prediction is within 0.8%. A control command synthesis module integrates the PID output with the predicted compensation at the hardware level on the embedded platform. With a control period of 10 milliseconds, the overall system response time is reduced to 0.6 seconds.

[0059] The steps of the variable gain PID algorithm to ensure system stability through the Lyapunov method are as follows:

[0060] (1) Define the error state: Let the control error e(t) = r(t) - y(t), where r(t) is the set value and y(t) is the system output.

[0061] (2) Constructing the Lyapunov function: Select the positive definite function V(t) = 21e2(t) + 21λθ ～ 2(t), where θ ～ is the parameter estimation error, and λ>0 is the adjustment coefficient.

[0062] (3) Stability analysis: Derivative V˙(t) = ee˙ + λθ ～ θ ～ ˙.

[0063] Substitute into the PID control law u=K p e+K i ∫edt+K ddtde and adaptive law K˙p=-γ p e2, ensure that V˙(t)≤0.

[0064] (4) Adaptive law design: Derivation of the integral term K through stability conditions i (t) and the differential term K d (t), for example: K˙i=α∫edt,K˙d=βdtde, where α and β are determined by Lyapunov conditions, ensuring the global stability of the system under time-varying conditions.

[0065] During implementation, the imaging module is installed 3.5 meters directly above the ladle, at a 50° angle to the vertical to fully cover the slag surface. The protective housing utilizes a circulating water cooling design to ensure stable operation even in high-temperature environments of 85°C. The edge computing unit deploys a lightweight inference engine. The image preprocessing stage utilizes a combination of adaptive histogram equalization and morphological filtering to eliminate molten steel splash noise, keeping processing time to under 8 milliseconds. The process control unit communicates with the actuator via Industrial Ethernet. The mass flow meter achieves a sampling accuracy of 0.5% FS, and the electric control valve utilizes microstepping technology to achieve 0.1% adjustment of the opening. A three-level response strategy is designed for the exception handling mechanism: When a blockage in a permeable brick is detected, the control automatically switches to flow-pressure decoupling control mode; when the argon pipeline pressure suddenly changes by more than 15%, the feedforward compensation enhancement module is activated; and when the system exceeds the error limit for three consecutive control cycles, the expert knowledge base intervenes and resets the parameters.

[0066] In the industrial verification of a 210-ton RH refining unit in a steel plant, the data of 152 consecutive heat runs showed that the argon consumption per unit increased from 1.85m3 to 1.85m3. 3 / t dropped to 1.08m 3 / t; Bright area control accuracy reaches ±2.5cm 2In the abnormal working condition of the 19th batch of breathable bricks, the system identified the characteristics in advance and switched the control mode to avoid unplanned downtime losses. The third-party test report shows that the system can 3 Even in harsh environments with electromagnetic interference strengths of 10V / m, the control command transmission success rate reaches 99.98%, meeting the requirements of continuous production on metallurgical sites. Furthermore, the system's modular design supports rapid configuration of process parameters. When switching to refining modes for different steel grades, adaptive adjustment time is less than 30 seconds, significantly improving production line flexibility.

[0067] The present invention is not limited to the above-mentioned embodiments. Anyone should be aware that any structural changes made under the guidance of the present invention, and any technical solutions that are the same or similar to those of the present invention, fall within the scope of protection of the present invention.

[0068] The technology, shape, and structure not described in detail in the present invention are all well-known technologies.

Claims

1. A multi-modal sensing argon stirring intelligent control method for RH refining process, characterized by: The following steps are involved: 1) Visual perception: The dual-channel images of the multispectral imaging module are used to generate enhanced feature maps through an adaptive weighted fusion algorithm; 2) Dynamic fusion: The multimodal data fusion module integrates multi-dimensional process parameters and constructs a dynamic feature weight allocation model based on the attention mechanism; 3) Predictive control: A feedforward-feedback composite control architecture is designed. The basic loop adopts a variable-gain PID algorithm. The control instruction synthesis module integrates the PID output and the predicted compensation at the hardware level on the embedded platform.

2. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 1 is characterized in that: The multispectral imaging module in step 1) uses a dual-channel industrial-grade camera, the visible light channel 400-700nm captures the morphological features of the bright area of the slag surface, and the near-infrared channel 850-1700nm penetrates the surface oxide film to obtain the deep temperature distribution. The dual-channel image generates an enhanced feature map through an adaptive weighted fusion algorithm, and the edge detection mask of the visible light image and the radiation intensity distribution of the near-infrared channel dynamically adjust the weight coefficient; the feature analysis module adopts an improved YOLOv8 network architecture, adds a morphological constraint branch on the basis of the traditional target detection branch, supervises the contour features of the bright area through the Fourier descriptor, and the network loss function integrates the bounding box regression loss, the category focus loss and the morphological constraint loss.

3. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 2 is characterized in that: The generation mechanism of the dynamic adjustment weight coefficient of the infrared channel radiation intensity distribution includes the following steps: (1) Data preprocessing: The visible light channel (400-700 nm) uses an edge detection algorithm to extract the morphological features of the bright area on the slag surface and generate an edge mask; the near-infrared channel (850-1700 nm) obtains the deep temperature information of the molten steel based on the thermal radiation intensity distribution map; (2) Weight allocation: For each pixel, the edge intensity of the visible light image and the radiation intensity contrast of the near-infrared image are calculated; in low-contrast areas, the weight coefficient of the near-infrared channel increases because it has strong penetrating power and can effectively supplement the details missing from the visible light. (3) Weight formula: W IR =σ Vis +σ IR , W Vis =1-W IR ; Wherein, σIR is the standard deviation of local contrast in the near-infrared channel; σVis is the standard deviation of local contrast in the visible light channel; (4) Dynamic adjustment: A sliding window mechanism is used to update the weights of local areas in real time to ensure that the fused image can maintain high detection accuracy under complex working conditions.

4. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 2 is characterized in that: The Fourier descriptor is used to supervise the bright area contour features of the supervised method. The Fourier descriptor is used to supervise the neural network to learn the geometric shape of the bright area of the slag surface. The specific steps are as follows: (1) Contour extraction: Extract the boundary point coordinate sequence (x i ,y i ), converted to the plural form z i =x i +jy i ; (2) Fourier transform: Perform discrete Fourier transform DFT on the complex sequence to obtain the frequency domain coefficients {F k }, retain the low-frequency components, such as the first 10 coefficients, as the Fourier descriptor describing the overall shape of the contour; (3) Loss function design: In the improved YOLOv8 network, a new morphological constraint branch is added to predict the Fourier descriptor of the contour. The loss function includes: bounding box regression loss, category focus loss, and morphological constraint loss. The morphological constraint loss is to calculate the mean square error (MSE) between the predicted and true Fourier coefficients: L shape =N1 k-1 ∑ N ∥F kpred -F ktrue ∥2; Through multi-task learning, the network simultaneously optimizes object localization and shape accuracy.

5. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 1 is characterized in that: The dynamic feature weight distribution model in step 2) determines the temperature gradient sensitivity coefficient and the historical flow attenuation factor through the particle swarm optimization algorithm, and can capture flow feature anomalies in the early stage of air brick blockage.

6. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 1 is characterized in that: The process of establishing the fusion model of the multi-dimensional process parameters is as follows: (1) Feature normalization: Each parameter is standardized to eliminate dimensional differences; (2) Attention mechanism design: Input feature vector F∈R 12 Generate query, key, and value matrices through the fully connected layer; Calculate attention weight: α i =softmax(d k QK iT ); The weighted fusion feature is F fused =∑α i V i ; (3) Particle swarm optimization (PSO): used to determine the temperature gradient sensitivity coefficient β and the flow attenuation factor γ. The optimization goal is to minimize the prediction error in the historical data and iteratively update the particle position until convergence.

7. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 1 is characterized in that: The proportional coefficient of the variable gain PID algorithm in step 3) is dynamically adjusted according to the rate of change of the bright area. The integral and differential terms are designed with adaptive laws through Lyapunov stability analysis. The feedforward compensation is predicted by the LSTM network for the next 3 seconds of operating disturbances. The network input includes historical flow sequences, temperature field gradients, and bright area morphological factors. The output layer uses a residual connection structure to reduce prediction errors.

8. The multimodal sensing RH refining process argon stirring intelligent control method according to claim 7 is characterized in that: The steps of the variable gain PID algorithm to ensure system stability through the Lyapunov method are as follows: (1) Define the error state: Let the control error e(t) = r(t) - y(t), where r(t) is the set value and y(t) is the system output; (2) Constructing the Lyapunov function: Select the positive definite function V(t) = 21e2(t) + 21λθ ～ 2(t), where θ ～ is the parameter estimation error, λ>0 is the adjustment coefficient; (3) Stability analysis: Derivative V˙(t) = ee˙ + λθ ～ θ ～ ˙; Substitute into the PID control law u=K p e+K i ∫edt+K ddtde and adaptive law K˙p=-γ p e2, ensure V˙(t)≤0; (4) Adaptive law design: Derivation of the integral term K through stability conditions i (t) and the differential term K d (t), for example: K˙i=α∫edt,K˙d=βdtde, where α and β are determined by Lyapunov conditions, ensuring the global stability of the system under time-varying conditions.