Contract Mechanism of Water Environment Regulation for Small and Medium Sized Enterprises Based on Optimal Control Theory

The small and scattered enterprise pattern in the county economy has formed numerous sporadic pollution sources, hindering the centralized treatment of the water environment, increasing the cost and difficulty of treatment. How enterprises can make reasonable decisions on their water environment behavior based on the external environment and their own factors is of great significance for scientifically and effectively designing water environment regulation mechanisms. Based on optimal control theory, this study investigates the design of contractual mechanisms for water environmental regulation for small and medium-sized enterprises. The enterprise is regarded as an independent economic entity that can adopt optimal control strategies to maximize its own interests. Based on the participation of multiple subjects including the government, enterprises, and the public, an optimal control strategy model for enterprises under contractual water environmental regulation is constructed using optimal control theory, and a method for calculating the amount of unit pollutant penalties is derived. The water pollutant treatment cost data of a paper company is selected to conduct empirical numerical analysis on the model. The results show that the increase in the probability of government regulation and public participation, as well as the decrease in local government protection for enterprises, can achieve the same regulatory effect while reducing the number of administrative penalties per unit. Finally, the implementation process of contractual water environmental regulation for small and medium-sized enterprises is designed.

Unified Control Theory from PID to ACPID

To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all intricate factors, including internal dynamics and external bounded disturbance, into a single total disturbance. This enables the mapping of various nonlinear systems onto a linear disturbance system. Based on the theory of PID control and the characteristic equation of a critically damping system, Zeng’s stabilization rules (ZSR) and an ACPID control force based on a single speed factor have been designed. ACPID control theory is both simple and practical, with significant scientific significance and application value in the field of control engineering.

From Control Theory to Gravitational Waves

When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D1:η→ξ such that Dξ = η implies D1η = 0. When D is involutive, the procedure provides successive first-order involutive operators D1,...,Dn when the ground manifold has dimension n. Conversely, when D1 is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D1η = 0. If this is possible, that is when the differential module defined by D1 is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D1 is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D1 is formally surjective, controllability just amounts to the formal injectivity of ad(D1), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4). We prove that all these works are already explicitly using the self-adjoint Einstein operator, which cannot be parametrized and the comparison needs no comment. As a byproduct, they are all based on a confusion between the so-called div operator D2 induced from the Bianchi operator and the Cauchy operator, adjoint of the Killing operator D which is parametrizing the Riemann operator D1 for an arbitrary n. This purely mathematical result deeply questions the origin and existence of gravitational waves, both with the mathematical foundations of general relativity. As a matter of fact, this new framework provides a totally open domain of applications for computer algebra as the quoted test can be studied by means of Pommaret bases and related recent packages.

Risk assessment of high-speed railway CTC system based on improved game theory and cloud model

Purpose-In order to solve the problem of inaccurate calculation of index weights,subjectivity and uncertainty of index assessment in the risk assessment process,this study aims to propose a scientific and reasonable centralized traffic control(CTC)system risk assessment method.Design/methodologylapproach-First,system-theoretic process analysis(STPA)is used to conduct risk analysis on the CTC system and constructs risk assessment indexes based on this analysis.Then,to enhance the accuracy of weight calculation,the fuzzy analytical hierarchy process(FAHP),fuzzy decision-making trial and evaluation laboratory(FDEMATEL)and entropy weight method are employed to calculate the subjective weight,relative weight and objective weight of each index.These three types of weights are combined using game theory to obtain the combined weight for each index.To reduce subjectivity and uncertainty in the assessment process,the backward cloud generator method is utilized to obtain the numerical character(NC)of the cloud model for each index.The NCs of the indexes are then weighted to derive the comprehensive cloud for risk assessment of the CTC system.This cloud model is used to obtain the CTC system's comprehensive risk assessment.The model's similarity measurement method gauges the likeness between the comprehensive risk assessment cloud and the risk standard cloud.Finally,this process yields the risk assessment results for the CTC system.Findings-The cloud model can handle the subjectivity and fuzziness in the risk assessment process well.The cloud model-based risk assessment method was applied to the CTC system risk assessment of a railway group and achieved good results.Originality/value-This study provides a cloud model-based method for risk assessment of CTC systems,which accurately calculates the weight of risk indexes and uses cloud models to reduce uncertainty and subjectivity in the assessment,achieving effective risk assessment of CTC systems.It can provide a reference and theoretical basis for risk management of the CTC system.

Ecological Remediation Measures for Non-point Source Pollution Based on Source-Sink Landscape Theory: A Case Study of Huanghou Basin

The growth of society and population has led to a range of water pollution issues.Among these,non-point source pollution assessment and treatment pose a particular challenge due to its formation mechanism.This has become a focal point and challenge in water pollution treatment research.The study area for this research was the Huanghou basin in Guizhou Province,southwest China.The land use type of the basin was analyzed using remote sensing technology,and water quality data was collected by distributing points throughout the basin,based on source-sink landscape theory.The distribution map of the basin’s source-sink landscape and the results of water quality data accurately and efficiently identified the areas with high risk of non-point source pollution in the western and southwestern residential and agricultural areas of the upper basin.Hence,a strategy of“increasing sinks and decreasing sources”was proposed.The strategy was implemented at both macro and micro levels to address non-point source pollution in the basin using ecological remediation techniques.The work to control karst rocky desertification should continue at a macro level.The rocky desertification area in the basin should gradually transform into grassland and forested land,while increasing the overall area of the sink landscape.Ecological restoration techniques,such as slope planting,riparian zone vegetation restoration,increasing plant abundance,and restoring aquatic plants,can effectively control non-point source pollution at the micro level.Compared to traditional control methods,this remediation strategy focuses on source and process control.It is more effective and does not require large-scale water pollution control projects,which can save a lot of environmental control funds and management costs.Therefore,it has greater research significance and application value.

Power Control Algorithm of Cognitive Radio Based on Non-Cooperative Game Theory

This paper addresses the power con- trol problems of Cognitive Radio （CR） trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the Quality of Service （QoS） standards for primary users is considered and a non-cooperative game power control model. Based on the proposed model, we developed a logical utility function based on the Signal-to-Interference-Noise Ratio （S/NR） and a novel algorithm network power control. that is suitable for CR Then, the existence and uniqueness of the Nash Equilibrium （NE） in our utility function are proved by the principle of game theory and the corresponding optimi- zations. Compared to traditional algorithms, the proposed one could converge to an NE in 3-5 iterative operations by setting an appropriate pricing factor. Finally, simulation results ver- ified the stability and superiority of the novel algorithm in flat-fading channel environments.

Stability condition of FAST TCP in high speed network on the basis of control theory

Considering the instability of data transferred existing in high speed network, a new method is proposed for improving the stability using control theory. Under this method, the mathematical model of such a network is established. Stability condition is derived from the mathematical model. Several simulation experiments are performed. The results show that the method can increase the stability of data transferred in terms of the congestion window, queue size, and sending rate of the source.

Structural Model Updating of Jacket Platform by Control Theory Using Vibration Measurement Approach

The identification of variations in the dynamic behavior of structures is an important subject in structural integrity assessment.Improvement and servicing of offshore platforms in the marine environment with constant changing,requires understanding the real behavior of these structures to prevent possible failure.In this work,empirical and numerical models of jacket structure are investigated.A test on experimental modal analysis is accomplished to acquire the response of structure and a mathematical model of the jacket structure is also performed.Then,based on the control theory using developed reduction system,the matrices of the platform model is calibrated and updated.The current methodology can be applied to prepare the finite element model to be more adaptable to the empirical model.Calibrated results with the proposed approach in this paper are very close to those of the actual model and also this technique leads to a reduction in the amount of calculations and expenses.The research clearly confirms that the dynamic behavior of fixed marine structures should be designed and assessed considering the calibrated analytical models for the safety of these structures.

Optimization of anchorage support parameters for soft rock tunnel based on displacement control theory

In the construction of a soft rock tunnel,it is critical to accurately estimate the pre-stressed anchor support parameters for surrounding rock reinforcement;otherwise,engineering disasters may occur.This paper presents a support parameter selection method that aims to allow deformation as a control objective,which was applied to the tunnel located in Muzailing Highway,Min County,Dingxi City,Gansu Province,China.Through theoretical analysis,we have identified five factors that influence pre-stressing anchorages.The selection of mechanical parameters for the rock mass was carried out using an inverse analysis method.Compared with the measured data,the maximum displacement error of the numerical simulation results was only 0.07 m.The length of anchor cable,circumferential spacing of anchor cable,longitudinal spacing,and pre-stress index are adopted as the input parameters for the support vector machine neural network model based on particle swarm optimization(PSO-LSSVM).Besides,the vault subsidence and the maximum deformation of surrounding rock are considered as output values(performance indices).The goodness of fit between the predicted values and the simulated values exceeds 0.9.Finally,all support parameters within the acceptable deformation range are calculated.The optimal support variables are derived by considering the construction cost and duration.The field application results show that it is feasible to construct the sample database utilizing the numerical simulation approach by taking the displacement as the control target and using the neural network to specify the appropriate support parameters.

Applications of Graph Theory to Gross Error Detection for GPS Geodetic Control Networks

This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components Δ X, Δ Y and Δ Z sum up to zero.If the sum of the respective vector components ∑X,∑Y and ∑Z in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re_observed.After successful screening of errors by graph theory,network adjustment can be carried out.In this paper,the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.

Theory and Practice of Water Pollution Prevention and Control for Inflowing Rivers in Taihu Valley

The pollutants from the 15 rivers inflowing into Lake Taihu accounted for about 80% of the total amount of the pollutants inflowing into Lake Taihu. Therefore, overall treatment of the inflowing rivers of Taihu Lake is of great importance to the improvement of water environment in the valley and the eutrophication status in th lake. Firstly, the basic ideas, key taches and main methods for water pollution control of inflow rivers of Taihu Lake was put forward in this article, Basic on these theories, the pollutant source status in the comprehensive treatment zone of the 15 major inflow rivers was analysized, the countermeasures of pollution control and main regulation projects were introduced, and the total abatement of pollutants was predicted. With the implement of regulation projects, the number of rivers with water quality worse than Grade V among the 15 major inflow rivers had come from 9 to 3, and the eutrophication status of Taihu Lake had changed from medium level to light level. The overall treatment of the major inflow rivers of the Taihu Lake had achieved initial success.

Frequency detection of self-adaption control based on chaotic theory

Low-order Duffing and high-order Rossler chaotic oscillator are connected together and new self-adaption frequency detection method is presented. The frequency difference control between unknown signal and the periodic driving force is realized in this paper and the self-adaption is obtained. Thus, the detection precision and speed are promoted. The limitation that there are too many chaotic oscillators in Duffing system is broken. Meanwhile the disadvantage that the detection speed is lower in R ssler chaotic control is overcome. The self-adaption choice of frequency difference control is realized using the Duffing and Rssler different chaotic oscillators to obtain unknown signal frequency. The simulation results show that the presented method is feasible and effective.

Optimal Adaptive Control of a Class of Stochastic Systems Using Game Theory

This paper attempts to study a optimal adaptive con tr ol problem using game theory, and proposes an important practical result that an adaptive processes is a set of sufficient conditions under which pure strategy is essentially complete, and thus the fact that yield a very useful desirable pu re optimal control rule.

Equivalent sample theory of networked control systems and its application

The equivalent sample theory and its application in analysis of networked control system （NCS） are presented. After analyzing NCS＇s scheduling in master-slave mode, the characteristics of time delay and sample are summarized. Looking on master station visiting the slave station as a special sample process, the theory of equivalent sample is presented. And based on it, the stability of a kind of NCS is analyzed. The criterion to determine the upper bound of transmission delay is introduced, which guarantees the stability. Finally, an example with simulation shows the availability and usability of this analysis method.

OPTIMIZATION OF CUT-OFF GRADE IN OPEN-PIT BASED ON CONTROL THEORY

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Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory

The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.