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.

Adaptive Optimal Output Regulation of Interconnected Singularly Perturbed Systems With Application to Power Systems

This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the slow and fast characteristics among system states,the interconnected SPS is decomposed into the slow time-scale dynamics and the fast timescale dynamics through singular perturbation theory.For the fast time-scale dynamics with interconnections,we devise a decentralized optimal control strategy by selecting appropriate weight matrices in the cost function.For the slow time-scale dynamics with unknown system parameters,an off-policy RL algorithm with convergence guarantee is given to learn the optimal control strategy in terms of measurement data.By combining the slow and fast controllers,we establish the composite decentralized adaptive optimal output regulator,and rigorously analyze the stability and optimality of the closed-loop system.The proposed decomposition design not only bypasses the numerical stiffness but also alleviates the high-dimensionality.The efficacy of the proposed methodology is validated by a load-frequency control application of a two-area power system.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

Advanced Policy Learning Near-Optimal Regulation

Designing advanced design techniques for feedback stabilization and optimization of complex systems is important to the modern control field. In this paper, a near-optimal regulation method for general nonaffine dynamics is developed with the help of policy learning. For addressing the nonaffine nonlinearity, a pre-compensator is constructed, so that the augmented system can be formulated as affine-like form. Different cost functions are defined for original and transformed controlled plants and then their relationship is analyzed in detail. Additionally, an adaptive critic algorithm involving stability guarantee is employed to solve the augmented optimal control problem. At last, several case studies are conducted for verifying the stability, robustness, and optimality of a torsional pendulum plant with suitable cost.

Method for secondary spring load equalization of railway vehicles with two-stage spring suspension: Modeling and optimal regulation

To ensure running safety,the secondary spring loads of railway vehicles must be well equalized.Due to the coupling interactive effects of these hyper static suspended structures,the equalization adjustment through shimming procedure is quite complex.Therefore,an effective and reliable method in application is developed in this paper.Firstly,the best regulation of spring load is solved based on a mechanical model of the secondary suspension system,providing a target for actual adjustment.To reveal the relationship between secondary spring load distribution and shim quantity sequence,a forecasting model is constructed and then modified experimentally with consideration of car body’s elastic deformation.Further,a gradient-based algorithm with a momentum operation is proposed for the load optimization.Effectiveness of the whole method has been verified on a test rig.It is experimentally confirmed that this research provides an important basis for achieving an optimal regulation of spring load distribution for multiple types of railway vehicles.

Incentive Mechanism Design for Public Goods Provision:Price Cap Regulation and Optimal Regulation

This paper studies the mechanism design that induces firms to provide public goods under two regulatory means： price cap regulation and optimal regulation, respectively. We first outline two models of monopoly regulation with unobservable marginal costs and effort, which can be regard as an optimal problem with dual restrictions. By solving this problem, we get the two optimal regulatory mechanisms to induce the provision of public goods. Further, by comparative statics, the conclusion is drawn that the welfare loss as sociated with price cap regulation, with respective to optimal regulation, increases more with increase of the expense of public goods.

Optimal Design of Deforming Regulation for Compact Continuous Rolling Mill with Balanced Load

If the draught of each mill stand is limited by forced bite condition for compact continuous mill,the rolling load difference between one mill stand and another is very big.If deforming regulation of relative load for each mill stand is approximate to the same,the productive capacity of compact continuous mill can be brought into full play,and also the safety running and the smooth rolling of mill can be ensured.

Distributionally Robust Newsvendor Model for Fresh Products under Cap-and-Offset Regulation

The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information.We construct a distributionally robust optimization model and use the Karush-Kuhn-Tucker(KKT)conditions to solve the analytic formula of optimal solutions.By comparing the models with and without investing in sustainable technologies,we examine the effect of sustainable technologies on the operational management decisions of the retailer.Finally,some computational examples are applied to analyze the impact of critical factors on operational strategies,and some managerial insights are given based on the analysis results.

Examining the Relationship of Optimism and Emotion Regulation Strategies with General Health among Students of University of Sistan and Baluchestan

Background and Objective: Individuals apply various emotion regulation strategies, some of which are adaptive and others are maladaptive affecting people’s general health. Moreover, individual life-orientation including favorable expectancies about future (optimism) is associated with health-related behaviors. The purpose of the present study was to investigate the relationship of optimism and emotion regulation strategies with general health of university students. Materials and Methods: This was a correlational study. In this regard, 182 students of University of Sistan and Baluchestan (70 males and 112 females) were chosen. The statistical population of the present study consisted of all undergraduate students of the university of Sistan and Baluchestan in the second semester of the 2009-2010 academic year. Considering the nature of the current study, the correlational method was applied. Based on Krejcie and Morgan’s table, a sample of 200 subjects was selected from students majored at different fields including human sciences, basic sciences and technical-engineering through applying multi-stage random sampling method. Eighteen incomplete questionnaire forms were excluded. Finally, data obtained from 182 subjects (112 females, 70 males) were analyzed. The mean age was 21.1 year-old and standard deviation of the sample was 2.06. Samplings were assessed using the Revised Life-Orientation Test (LOT-R), Emotion Regulation Questionnaire (ERQ) and General Health-28 Questionnaire (GHQ-28). Data were analyzed using the Pearson correlation coefficient and regression analysis. Results: Findings showed that there was a significant positive relationship between optimism and general health (r = 0.22, p < 0.01). Among all research variables, i.e. optimism and emotion regulation strategies (cognitive reappraisal and expressive suppression), only optimism was able to predict 0.06 percent of variance of general health (p < 0.001). Conclusion: Optimists have higher general health and consistent with other findings, optimism is associated with higher levels of applying coping strategies and lower levels of avoidance.

Predictive Functional Controller with a Similar Proportional Integral Optimal Regulator Structure:Comparison with Traditional Predic-tive Functional Controller and Application to Heavy Oil Coking Equipment

By extending the system's state variables,a novel predictive functional controller has been developed.The structure of this controller is similar to that of classical proportional integral(PI)optimal controller and in-cludes a control block that can perform a feed-forward control of future P-step set points.It considers both the state variables and the output errors in its cost function,which results in enhanced control performance compared with traditional state space predictive functional control(TSSPFC)methods that consider only the predictive output er-rors.The predictive functional controller(PFC)has been compared with TSSPFC in terms of tracking ability,dis-turbance rejection,and also based on its application to heavy oil coking equipment.The results obtained show the effectiveness of the controller.

Optimization and Regulation Policy for Land Use Changes Based on Low-carbon Emission in Developed Regions of China

Land use and cover change(LUCC) is one of the important causes of the Earth’s carbon cycle imbalances resulting from failure in optimizing land use. The solution to this problem has been the hotspot of research in land and environmental science. We took 'low carbon', 'energy saving' and 'high-efficiency' as the goals of land use optimization,and integrated Markov-CA(Cellular Automaton),the Grid-Fractal model and GIS,in order to study carbon emission objective function,to establish a simulation method for land use spatial allocation optimization,to evaluate the effect of the method on carbon emissions. Regulation policy on three types of land use spatial allocation was proposed,including 'low-carbon type', 'low-carbon-economic type' and 'economic type'. We applied the method to analyze the land use spatial allocation in Taixing City of the 'Yangtze River Delta' regions in China,and obtained the following results:(i) The three optimization types would improve carbon emissions by 3. 21%,1. 80% and 0. 36% respectively in 2020,compared with 2010;(ii) The actual planning for 2020 was close to the 'low-carbon-economic type';(iii) The optimization method and regulation policy,combining local optimization and global control,could meet the sustainable multi-objective requirements for low-carbon constraints of land use spatial allocation. The result of this research could also serve as a reference for exploration into patterns of regional low-carbon land use and measures for energy saving and emission reduction.

Optimization of Regulation Valve Location for Heating System

This paper mainly studied how to determine the best location of the self-operated flow control valve at the heating system entrance.Since the location of regulating valve directly affects the pipe network performance,the simulation and analysis of pressure change in heating system was carried out with Computational Fluid Dynamics(CFD)software.The study shows the best location of regulating valve varies with the change of the supply and return pipe length when the heating area of each user is small,and when the heating area of each user is large(2 000 000～3 000 000 m2),the best location is on the supply pipe.

Regulation Flexibility Assessment and Optimal Aggregation Strategy of Greenhouse Loads in Modern Agricultural Parks

With advances in modern agricultural parks,the rural energy structure has undergone profound change,leading to the emergence of an agricultural energy internet.This integrated system combines agricultural energy utilization,the information internet,and agricultural production.Accordingly,this study proposes a regulation flexibility assessment approach and optimal aggregation strategy of greenhouse loads(GHLs)for modern agricultural parks.First,taking into account the operational characteristics of typical GHLs,refined load demand models for lighting,humidification,and temperature-controlled loads are established.Secondly,the recursive least squares method-based parameter identification method is designed to accurately determine key GHL model parameters.Finally,based on the regulation flexibility of quantitatively evaluated GHLs,GHLs are optimally aggregated into multiple flexible aggregators considering minimal operational cost and greenhouse environmental constraints.The results indicate that the proposed regulation flexibility assessment approach and optimal aggregation strategy of GHLs can alleviate the peak regulation pressure on power grids by flexibly shifting the load demands of GHLs.

THE INVERSE PROBLEM OF OPTIMAL REGULATORS AND ITS AP-PLICATION

This paper presents a new solution to the inverse problem of linear optimal regulators to minimize a cost function and meet the requirements of relative stability in the presence of a constant but unknown disturbance. A state feedback matrix is developed using Lyapunov’s second method. Moreover, the relationships between the state feedback matrix and the cost function are obtained, and a formula to solve the weighting matrices is suggest- ed. The developed method is applied successfully to design the horizontal loops in the inertial navigation system.

Optimal Unit Commitment with Renewable Energy in Regulated and Deregulated Systems

In this paper, the impact of the wind power generation system on the total cost and profit of the system is studied by using the proposed procedure of binary Sine Cosine (BSC) optimization algorithm with optimal priority list (OPL) algorithm. As well, investigate the advantages of system transformation from a regulated system to a deregulated system and the difference in the objective functions of the two systems. The suggested procedure is carried out in two parallel algorithms;The goal of the first algorithm is to reduce the space of searching by using OPL, while the second algorithm adjusts BSC to get the optimal economic dispatch with minimum operation cost of the unit commitment (UCP) problem in the regulated system. But, in the deregulated system, the second algorithm adopts the BSC technique to find the optimal solution to the profit-based unit commitment problem (PBUCP), through the fast of researching the BSC technique. The proposed procedure is applied to IEEE 10-unit test system integrated with the wind generator system. While the second is an actual system in the Egyptian site at Hurghada. The results of this algorithm are compared with previous literature to illustrate the efficiency and capability of this algorithm. Based on the results obtained in the regulated system, the suggested procedure gives better results than the algorithm in previous literature, saves computational efforts, and increases the efficiency of the output power of each unit in the system and lowers the price of kWh. Besides, in the deregulated system the profit is high and the system is more reliable.

Distributed Periodic Event-Triggered Optimal Control of DC Microgrids Based on Virtual Incremental Cost

This article presents a distributed periodic eventtriggered(PET)optimal control scheme to achieve generation cost minimization and average bus voltage regulation in DC microgrids.In order to accommodate the generation constraints of the distributed generators(DGs),a virtual incremental cost is firstly designed,based on which an optimality condition is derived to facilitate the control design.To meet the discrete-time(DT)nature of modern control systems,the optimal controller is directly developed in the DT domain.Afterward,to reduce the communication requirement among the controllers,a distributed event-triggered mechanism is introduced for the DT optimal controller.The event-triggered condition is detected periodically and therefore naturally avoids the Zeno phenomenon.The closed-loop system stability is proved by the Lyapunov synthesis for switched systems.The generation cost minimization and average bus voltage regulation are obtained at the equilibrium point.Finally,switch-level microgrid simulations validate the performance of the proposed optimal controller.

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.

Model and Algorithm for the Optimal Controlled Partitioning of Power Systems

解列是电力系统在故障时结构完整性得不到保证的情况下分裂为2个或多个孤立稳定运行子系统的过程或操作。及时恰当的主动解列操作将能有效地避免因保护连锁动作使得电力系统被动解列而崩溃所造成的巨额经济损失。结合图论中的相关概念和输电网最优解列的物理过程，建立电力系统最优主动解列断面选择问题的完整数学模型，并基于含连通图约束的背包问题（connected graph constrained knapsack problem，CGKP）及其求解算法提出“搜索＋调整”的2阶段求解方法。为降低问题的复杂性，将完整数学模型分解成图的最优平衡分割问题和基于优化潮流的调节问题，并分2个阶段分别求解。其中，图的最优平衡分割问题又被分解成多个CGKP，利用基于含CGKP的图分割方法进行求解。所提出的主动解列策略具有较强理论基础，计算复杂度低，算例的计算结果证明了该模型及算法的正确性和有效性。

Design for Two-degree-of-freedom PID Regulator Based on Improved Generalized Extremal Optimization Algorithm

A kind of new design method for two-degree-of-freedom(2DOF)PID regulator was presented,in which,a new global search heuristic--improved generalized extremal optimization(GEO)algorithm is applied to the parameter optimization design of 2DOF PID regulator.The simulated results show that very good dynamic response performance of both command tracking and disturbance rejection characteristics can be achieved simultaneously.At the same time,the comparisons of simulation results with the improved GA,the basic GEO and the improved GEO were given.From the comparisons,it is shown that the improved GEO algorithm is competitive in performance with the GA and basic GEO and is an attractive tool to be used in the design of two-degree-of-freedom PID regulator.

Optimal Feedback Control of Nonlinear Variable-Speed Marine Current Turbine Using a Two-Mass Model

This paper presents a contribution related to the control of nonlinear variable-speed marine current turbine(MCT)without pitch operating below the rated marine current speed.Given that the operation of the MCT can be divided into several operating zones on the basis of the marine current speed,the system control objectives are different for each zone.To deal with this issue,we develop a new control approach based on a linear quadratic regulator with variable generator torque.Our proposed approach enables the optimization of the rotational speed of the turbine,which maximizes the power extracted by the MCT and minimizes the transient loads on the drivetrain.The novelty of our study is the use of a real profile of marine current speed from the northern coasts of Morocco.The simulation results obtained using MATLAB Simulink indicate the effectiveness and robustness of the proposed control approach on the electrical and mechanical parameters with the variations of marine current speed.