Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Noise Control Solutions for Diesel Generator Sets

A persistent challenge for Oman's energy infrastructure was the deafening rumble of diesel generators. The Silent Generator Project addressed this challenge, developing advanced generators that deliver power quietly and efficiently. Diesel generators have historically been notorious for being noisy and vibrational, making them unsuitable for sensitive environments. To dramatically reduce noise levels, the project utilized innovative materials and design modifications to ensure reliable and quiet electricity for various applications. In all directions, the project advanced the knowledge of noise reduction through rigorous testing and meticulous integration of insulators and mufflers. As a result, quieter, more sustainable energy production is on the way, marking a major advance in silent generator technology. Furthermore, the Silent Generator Project lays the foundation for more efficient and environmentally friendly diesel generator technologies in the future. As a result of this research, a new standard for quieter, greener energy generation is established, demonstrating the critical role noise reduction plays in energy generation. Additionally, this work also suggests future diesel generator technologies that are more efficient and environmentally friendly. As a result of this research, a new standard for quieter, greener energy generation is set, demonstrating the critical role noise reduction plays in energy generation.

Response of Over-summer Hydroponic Lettuce to Nutrient Solution Temperature Control

Temperature, as an important feature of hydroponic nutrient solution, is closely related to dissolved oxygen content of nutrient solution and growth status of plant roots. How to precisely adjust the temperature of nutrient solution is the key to obtain high quality and high yield of hydroponic vegetables over summer. With Lactuca sativa vat. crispa ＇Luosheng No.3＇ as the test material, the effect of chiller cooling technology on the temperature of nutrient solution, as well as on the yield and quality of Luosheng No.3, in over-summer hydroponic cultivation was studied. The results showed that the chiller cooling technology controlled the nutrient solution temperature in a reasonable range （（20 ± 1）℃） and promoted the growth and dry matter accumulation of Luosheng No.3, instead of affecting the quality. In short, the chiller cooling technology is applicable to the temperature regulation of nutrient solu- tion in hydroponics over summer.

Modeling, Optimization, and Control of Solution Purification Process in Zinc Hydrometallurgy

The solution purification process is an essential step in zinc hydrometallurgy. The performance of solution purification directly affects the normal functioning and economical benefits of zinc hydrometallurgy. This paper summarizes the authors' recent work on the modeling, optimization, and control of solution purification process. The online measurable property of the oxidation reduction potential(ORP) and the multiple reactors, multiple running statuses characteristic of the solution purification process are extensively utilized in this research. The absence of reliable online equipment for detecting the impurity ion concentration is circumvented by introducing the oxidationreduction potential into the kinetic model. A steady-state multiple reactors gradient optimization, unsteady-state operationalpattern adjustment strategy, and a process evaluation strategy based on the oxidation-reduction potential are proposed. The effectiveness of the proposed research is demonstrated by its industrial experiment.

ON THE ASYMPTOTICAL BEHAVIOUR OF SOLUTIONS OF A CLASS OF NONLINEAR CONTROL SYSTEMS

In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invariance principle of integral form, criteria of dichotomy and global asymptotical behaviour of solutions are obtained. This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

Two Positive Periodic Solutions of Delay Functional Difference System with Feedback Control

By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.

Analytic Solutions to Optimal Control Problems with Constraints

In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformulating a constrained optimal control problem into a global optimization problem. A differential flow is presented to deduce some optimality conditions for solving global optimizations, which can be considered as an extension and a supplement of the previous results in canonical duality theory. Some examples are given to illustrate the applicability of our results.

Periodic Solutions of a Cooperative System with State Feedback Control

In this paper, we propose a semi-continuous dynamical system to study the cooperative system with feedback control. Based on geometrical analysis and the analogue of Poincare criterion, the existence and stability of the positive order one periodic solutions are given. Numerical results are carried out to illustrate the feasibility of our main results.

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The Application of Synthetic Fuzzy Assessing Method in Measurement and Control System of Plating Solution Evaporator

The synthetic fuzzy assessing method is usually applied to sensory evaluation. The method has simple and reliable virtue, and it is consistent with objective evaluation results. Using this method, system status of plating solution evaporator is evaluated, and the result is applied to compensate a fuzzy controller. Experimental results have shown the correctness and the validity of the proposed approach.

Solutions for Large-Scale and Low-Cost Access to Space in the Future

The objective of this study is to identify the requirements of access to space for the future, the required methodology, key technologies and international cooperation mode. Firstly, the mission requirements and the challenges of current technologies to access to space are analyzed and summarized. The solutions and related key technologies to realize large-scale and low-cost access to space(L2 AS) are presented here, including the low-cost design of expendable launch vehicles and a reusable space transportation system, interface standardization, and new conceptual launchers. The mission modes based on launch vehicles to realize L2 AS and three future international collaboration modes are presented. Lastly, the relevant conclusions and suggestions are given.

Pollutant Sources and Foaming Control Measures of Decarbonization Solution in Natural Gas Purification Plant

Yanbei project of Schlumberger Copower Oilfield Engineering Co.,Ltd.-natural gas purification plant decarbonization unit is equipped with two sets of decarbonization systems(parallel operation).The two sets of systems adopt two tower process,full lean liquid circulation regeneration process,one tower absorption(absorption pressure 5.4mpag),one tower regeneration(regeneration temperature 95℃-110℃),purified natural gas carbon dioxide content≤2.5vol%,single set The treatment capacity is 2300 KM3/d.This paper introduces the problems existing in the decarbonization solution of the decarbonization unit in the natural gas purification plant in recent three years,analyzes the causes of pollutants affecting the quality of the decarbonization solution,and probes into the control measures for the pollution of the decarbonization solution,so as to provide reference.

The Time-Optimal Problems for Controlled Fuzzy R-Solutions

In the present paper, we show the some properties of the fuzzy R-solution of the control linear fuzzy differential inclusions and research the time-optimal problems for it.

Solution Domain Boundary Analysis Method and Its Application in Parameter Spaces of Nonlinear Gear System

Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.

Virtual straightening of scraper conveyor based on the position and attitude solution of industrial robot model

The movement of the floating connecting mechanism between a hydraulic support and scraper conveyor is space movement;thus,when the hydraulic support pushes the scraper conveyor,there is an error between the actual distance of the scraper conveyor and the theoretical moving distance.As a result,the scraper conveyor cannot obtain the straightness requirement.Therefore,the movement law of the floating connecting mechanism between the hydraulic support and scraper conveyor is analyzed and programmed into the Unity3D to realize accurate pushing of the scraper conveyor via hydraulic support.The Coal Seam?Equipment Joint Virtual Straightening System is established,and a straightening method based on the motion law of a floating connection is proposed as the default method of the system.In addition,a straightening simulation of the scraper conveyor was performed on a complex coal seam floor,the results demonstrate that the average straightening error of the scraper conveyor is within 2-8 mm,and is in direct proportion to the fluctuation of the coal seam floor in the strike of the seam with high accuracy,the straightness of scraper conveyor is more affected by the subsidence terrain during straightening than by the bulge terrain.And some conclusions are verified by experiment.Based on the verification of the relevant conclusions,a comparison and analysis of Longwall Automation Steering Committee(LASC)straightening technology and default straightening method in the simulation system shows that the straightness accuracy of LASC straightening technology under complex floor conditions is slightly less than that of the default straightening method in the proposed system.

Solution of Chemical Dynamic Optimization Using the Simultaneous Strategies

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control vari- ables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at dement knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refine- ment more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting dements to track optimal control profile breakpoints and ensure accurate state and centrol profiles. Four classic benchmarks of dynamic op- timization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferz,ble in improving the solution accuracy of chemical dy- namic optimization problem.

Multi-user Symmetric Cooperation Based on Nash Bargaining Solution in Cooperative Relay Networks

This paper presents a symmetric cooperation strategy for cooperative relay networks with multiple users. The multi-user symmetric cooperation model and the relay selection algorithm are proposed. Then, the time slot allocation problem is cast into a bargaining problem, and the optimal time slot allocation solution is obtained by Nash bargaining solution （NBS）. Moreover, we also consider the implementations of the cooperation strategy, i.e., the grouping and admission control algorithm. Simulation results show that users can obtain larger rates under the symmetric cooperation strategy than the non-cooperative case.

Solution and transcritical bifurcation of Burgers equation

Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region. The transcritical bifurcation exists in the （2 ＋ 1）-dimensional Burgers equation.

UNIQUENESS OF VISCOSITY SOLUTIONS OF STOCHASTIC HAMILTON-JACOBI EQUATIONS

This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the associated stochastic HJ equation.