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.

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.

Game theory approach to optimal capital cost allocation in pollution control

This paper tries to integrate game theory, a very useful tool to resolve conflict phenomena, with optimal capital cost allocation issue in total emission control. First the necessity of allocating optimal capital costs fairly and reasonably among polluters in total emission control was analyzed. Then the possibility of applying game theory to the issue of the optimal capital cost allocation was expounded. Next the cooperative N person game model of the optimal capital cost allocation and its solution ways including method based on Shapley value, least core method, weak least core methods, proportional least core method, CGA method, MCRS method and so on were delineated. Finally through application of these methods it was concluded that to apply game theory in the optimal capital cost allocation issue is helpful to implement the total emission control planning schemes successfully, to control pollution effectively, and to ensure sustainable development.

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.

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.

A Stochastic Optimal Control Theory to Model Spontaneous Breathing

Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.

Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is introduced into the feedback system.However,due to the introduction of control input into the feedback system,the optimal state feedback control methods can not be applied directly.To address this problem,an augmented system and an augmented performance index function are proposed firstly.Thus,the general nonlinear system is transformed into an affine nonlinear system.The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically.It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function.Moreover,an adaptive dynamic programming(ADP)technique is utilized to implement the optimal parallel tracking control using a critic neural network(NN)to approximate the value function online.The stability analysis of the closed-loop system is performed using the Lyapunov theory,and the tracking error and NN weights errors are uniformly ultimately bounded(UUB).Also,the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals.Finally,the effectiveness of the developed optimal parallel control method is verified in two cases.

Randomized Algorithms for Probabilistic Optimal Robust Performance Controller Design

Polynomial-time randomized algorithms were constructed to approximately solve optimal robust performance controller design problems in probabilistic sense and the rigorous mathematical justification of the approach was given. The randomized algorithms here were based on a property from statistical learning theory known as (uniform) convergence of empirical means (UCEM). It is argued that in order to assess the performance of a controller as the plant varies over a pre-specified family, it is better to use the average performance of the controller as the objective function to be optimized, rather than its worst-case performance. The approach is illustrated to be efficient through an example.

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.

Optimal Design for Anti-Skid Control of Electric Vehicles by Fuzzy Approach

In this paper,a new fuzzy approach is applied to optimal design of the anti-skid control for electric vehicles.The anti-skid control is used to maintain the wheel speed when there are uncertainties.The control is able to provide an appropriate torque for wheels when the vehicle is about to skid.The friction coefficient and the moments of inertia of wheels and motor are considered as uncertain parameters.These nonlinear,bounded and time-varying uncertainties are described by fuzzy set theory.The control is deterministic and is not based on IF-THEN fuzzy rules.Then,the optimal design for this fuzzy system and control cost is proposed by fuzzy information.In this way,the uniform boundedness and uniform ultimate boundedness are guaranteed and the average fuzzy performance is minimized.Numerical simulations show that the control can prevent vehicle skidding with the minimum control cost under uncertainties.

Optimal traffic light control method for a single intersecti on basedon hybrid systems

A single intersection of two phases is selected as a model to put forward a new optimal time-planning scheme for traffic light based on the model of hybrid automata for single intersection. A method of optimization is proposed for hybrid systems, and the average queue length over all queues is used as an objective function to find an optimal switching scheme for traffic light. It is illustrated that traffic light control for single intersection is a typical hybrid system, and the optimal planning-time scheme can be obtained using the optimal hybrid systems control based on the two stages method.

On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

Fast Solvers of Fredholm Optimal Control Problems

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

基于改进粒子群优化权函数的直流微电网H_(∞)控制策略

直流微电网中常常含有恒功率负载(constant power loads,CPLs),其负阻抗特性会降低系统的稳定性,造成直流母线电压波动甚至崩溃。因此,首先建立了直流微电网的小信号模型,使用根轨迹法分析了恒功率负载对系统稳定性的影响;其次提出一种基于混合灵敏度优化的电压控制策略,提升了直流微电网系统的稳定性,并采用改进粒子群优化(particle swarm optimization,PSO)算法对权函数进行了优化,进一步提升了鲁棒控制器的性能;最后采用Matlab/Simulink仿真算例进行验证,仿真结果表明提出的鲁棒控制器减小了母线电压的波动,有效提升了直流微电网系统的稳定性。

A Predator-prey Particle Swarm Optimization Approach to Multiple UCAV Air Combat Modeled by Dynamic Game Theory

Dynamic game theory has received considerable attention as a promising technique for formulating control actions for agents in an extended complex enterprise that involves an adversary. At each decision making step, each side seeks the best scheme with the purpose of maximizing its own objective function. In this paper, a game theoretic approach based on predatorprey particle swarm optimization (PP-PSO) is presented, and the dynamic task assignment problem for multiple unmanned combat aerial vehicles (UCAVs) in military operation is decomposed and modeled as a two-player game at each decision stage. The optimal assignment scheme of each stage is regarded as a mixed Nash equilibrium, which can be solved by using the PP-PSO. The effectiveness of our proposed methodology is verified by a typical example of an air military operation that involves two opposing forces: the attacking force Red and the defense force Blue. © 2014 Chinese Association of Automation.

Designing and Optimization of Fuzzy Sliding Mode Controller for Nonlinear Systems

For enhancing the control effectiveness,we firstly design a fuzzy logic based sliding mode controller(FSMC)for nonlinear crane systems.On basis of overhead crane dynamic characteristic,the sliding mode function with regard to trolley position and payload angle.Additionally,in order to eliminate the chattering problem of sliding mode control,the fuzzy logic theory is adopted to soften the control performance.Moreover,aiming at the FSMC parameter setting problem,a DE algorithm based optimization scheme is proposed for enhancing the control performance.Finally,by implementing the computer simulation,the DE based FSMC can effectively tackle the overhead crane sway problem and avoid unexpected accident greatly.

Multi-objective optimization for voltage and frequency control of smart grids based on controllable loads

The output uncertainty of high-proportion distributed power generation severely affects the system voltage and frequency.Simultaneously,controllable loads have also annually increased,which markedly improve the capability for nodal-power control.To maintain the system frequency and voltage magnitude around rated values,a new multi-objective optimization model for both voltage and frequency control is proposed.Moreover,a great similarity between the multiobjective optimization and game problems appears.To reduce the strong subjectivity of the traditional methods,the idea and method of the game theory are introduced into the solution.According to the present situational data and analysis of the voltage and frequency sensitivities to nodal-power variations,the design variables involved in the voltage and frequency control are classified into two strategy spaces for players using hierarchical clustering.Finally,the effectiveness and rationality of the proposed control are verified in MATLAB.

A population-feedback control based algorithm for well trajectory optimization using proxy model

Wellbore instability is one of the concerns in the field of drilling engineering.This phenomenon is affected by several factors such as azimuth,inclination angle,in-situ stress,mud weight,and rock strength parameters.Among these factors,azimuth,inclination angle,and mud weight are controllable.The objective of this paper is to introduce a new procedure based on elastoplastic theory in wellbore stability solution to determine the optimum well trajectory and global minimum mud pressure required(GMMPR).Genetic algorithm(GA) was applied as a main optimization engine that employs proportional feedback controller to obtain the minimum mud pressure required(MMPR).The feedback function repeatedly calculated and updated the error between the simulated and set point of normalized yielded zone area(NYZA).To reduce computation expenses,an artificial neural network(ANN) was used as a proxy(surrogate model) to approximate the behavior of the actual wellbore model.The methodology was applied to a directional well in southwestern Iranian oilfield.The results demonstrated that the error between the predicted GMMPR and practical safe mud pressure was 4%for elastoplastic method,and 22%for conventional elastic solution.

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.

Robust Topology Optimization of Vehicle Suspension Control Arm

A robust topology optimization design framework is developed to solve lightweight structural design problems under uncertain conditions. To enhance the calculation accuracy and flexibility of the statistical moments of robust analysis, number theory integral method is applied to sample point selection and weight assignment. Both the structure topology optimization and number theory integral methods are combined to form a new robust topology optimization method. A suspension control arm problem is provided as a demonstration of robust topology optimization methods under loading uncertainties. Based on the results of deterministic and robust topology optimization, it is demonstrated that the proposed robust topology optimization method can produce a more robust design than that obtained by deterministic topology optimization. It is also found that this new approach is easy to apply in the existing commercial topology optimization software and thus feasible in practical engineering problems.