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.

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.

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.

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.

Optimal and robust control of population transfer in asymmetric quantum-dot molecules

We present an optimal and robust quantum control method for efficient population transfer in asymmetric double quantum-dot molecules.We derive a long-duration control scheme that allows for highly efficient population transfer by accurately controlling the amplitude of a narrow-bandwidth pulse.To overcome fluctuations in control field parameters,we employ a frequency-domain quantum optimal control theory method to optimize the spectral phase of a single pulse with broad bandwidth while preserving the spectral amplitude.It is shown that this spectral-phase-only optimization approach can successfully identify robust and optimal control fields,leading to efficient population transfer to the target state while concurrently suppressing population transfer to undesired states.The method demonstrates resilience to fluctuations in control field parameters,making it a promising approach for reliable and efficient population transfer in practical applications.

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.

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.

THEORY OF DYNAMIC OPTIMIZATION FOR MATERIALS HEATING PROCESS——CRITERION RESTRAINING METHOD

A criterion restraining mehod adopted to the dynamic optimization for materials heat- ing process has been developed,by regarding it as controlled object of a regulator in control theory and combining the optimal criterion of it.The method may be available to optimize fuel supply along furnace length and to provide a theoretical basis for the optimization of fuel supply in time-varying.For soaking pit,the calculation shows that in case of optimization by criterion restraining method,the thermal efficiency is 3.1 higher than the modelling prediction result.In comparison with heat flux-decomposing method,the thermal efficiency increased from 43.1 to 43.8%,and the energy consumption was reduced by 7.28% relative to the practical production data.

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.

Task analysis approach based on perceptual control theory

Based on perceptual control theory,a task analysis approach is proposed to describe more accurately user tasks in dynamic environments,which is of more powerful and flexible descriptive ability. Theoretically,a task meta model is established to describe the interactive process in an individual,dynamic,and flexible way.Methodologically,an implementation framework is illustrated to map the user-oriented description into implementation-oriented models,which will be as a technical tool to transform from a task model to a user interface prototype.

Call for Papers:Special Issue on "Recent Advances and New Directions in Switched Control Systems" ——Jounal of Control Theory and Application

Recently, switched control systems have been attracting much attention m the control community because the problems are not only academically challenging for the inherent complexity, but also of practical importance due to its wide ranges of applications in nature, engineering, and social sciences.

Call for papers Journal of Control Theory and Applications Special issue on Wireless sensor networks:from theory to practices and applications

Wireless Sensor Network （WSN） is characterized by the dense deployment of sensor nodes that continuously observe physical phenomenon. The main advantages of WSN include its low cost, rapid deployment, self-organization, and fault tolerance. WSN has received tremendous interests of various research communities,