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.

Robustness-tracking control based on sliding mode and H_∞ theory for linear servo system

A robustness-tracking control scheme based on combining H_∞ robust control and sliding mode control is proposed for a direct drive AC permanent-magnet linear motor servo system to solve the conflict between tracking and robustness of the linear servo system. The sliding mode tracking controller is designed to ensure the system has a fast tracking characteristic to the command, and the H_∞ robustness controller suppresses the disturbances well within the close loop(including the load and the end effect force of linear motor etc.) and effectively minimizes the chattering of sliding mode control which influences the steady state performance of the system. Simulation results show that this control scheme enhances the track-command-ability and the robustness of the linear servo system, and in addition, it has a strong robustness to parameter variations and resistance disturbances.

重放攻击下多智能体系统H_(∞)一致性PID控制

本文针对一类带有加性噪声和乘性噪声的离散多智能体系统,研究重放攻击下多智能体系统的H_(∞)一致性比例-积分-微分(PID)控制问题.首先,根据智能体的测量输出设计状态观测器,对智能体的状态进行有效估计,观测器设计过程中考虑了系统测量输出从传感器传输到观测器过程中受到重放网络攻击的影响.然后,利用智能体与其邻居智能体的估计状态差设计PID控制器.利用李雅普诺夫稳定性理论和代数图论,证明在该控制策略下,多智能体系统在重放攻击存在的情况下达到预期的H_(∞)性能指标.最后,利用线性矩阵不等式(LMI)方法求解观测器和控制器增益,利用数值仿真验证了所设计的观测器和PID控制器的有效性.

非线性系统无需初始条件预设性能有界H_(∞)容错控制

针对一类具有外部扰动和传感器故障的非线性系统,本文研究了其自适应预设性能有界H_(∞) 容错控制问题.本文提出一种新的预设性能控制设计方法,使得预设性能函数的选择与系统被约束变量的初始状态完全无关,用一种全新的方式解决了传统预设性能方法的控制效果依赖被约束变量初始条件的问题.基于该设计方法和有界H_(∞) 控制方法,在未知系统初始条件的情况下获得了系统的自适应预设性能有界H_(∞) 控制器.本文所设计的控制器能够保证系统中的所有信号都是有界稳定的,系统的输出变量能够被预设性能函数约束,并且对于外部干扰具有很好的抑制作用.最后,仿真结果验证了该控制器的可行性及有效性.

三阶三次幂非线性混沌电路的自适应反馈控制和H_(∞)控制

针对三阶三次幂非线性混沌电路,研究其控制问题.首先,给出系统的Lyapunov指数和混沌吸引子,验证系统存在复杂的混沌现象;其次,用自适应反馈控制方法和H_(∞)状态反馈控制方法,设计参数已知和参数未知的自适应反馈控制器以及H_(∞)状态反馈控制器,将混沌系统状态稳定到平衡点上;最后,通过MATLAB软件进行数值仿真验证控制器的有效性,并对两种控制器的控制效果进行比较.

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。

H_∞ SYNCHRONIZATION CONTROL OF LINEAR SYSTEMS AND ITS APPLICATION TO WAFER-RETICAL STAGE

For the outputs of two nth-order linear control systems to work insynchronization and meanwhile to track their commands, a H_(infinity) synchronization control schemeis presented. In terms of two uncoupled single variable linear systems, a multivariable coupledsystem is established by choosing one output and the difference of the two outputs as a new outputvector, so that both command tracking and synchronization properties can be demonstrated by aH_(infinity) performance index. To improve the synchronization and trailing performance and toguarantee the system robust stability, the mixed sensitivity H_(infinity), design methodology isadopted. The presented synchronization scheme is then extended to the case where one of the twosystems include two input variables, and then applied to the position synchronization control of awafer-retical stage. The wafer-reticle stage consists of a wafer stage, a reticle coarse stage, anda reticle fine stage. The reticle coarse stage picks up the reticle fine stage. The three stagesought to tack their commands, but synchronization between the wafer stage and the reticle fine stagemust be stressed in the tracking process. In the application, by appropriately determining theweighting matrices for the sensitivity function and the complementary sensitivity function, asatisfactory KL synchronization controller is obtained to realize highly accurate positionsynchronization, and to guarantee tracking performance. The above results are verified by simulationexperiments.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

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.

Distributed power control algorithm based on game theory for wireless sensor networks

Energy saving is the most important issue in research and development for wireless sensor networks. A power control mechanism can reduce the power consumption of the whole network. Because the character of wireless sensor networks is restrictive energy, this paper proposes a distributed power control algorithm based on game theory for wireless sensor networks which objects of which are reducing power consumption and decreasing overhead and increasing network lifetime. The game theory and OPNET simulation shows that the power control algorithm converges to a Nash Equilibrium when decisions are updated according to a better response dynamic.

Robust H_∞ guaranteed cost satisfactory fault-tolerant control for discrete-time systems with quadratic D stabilizability

The problem of robust H∞ guaranteed cost satisfactory fault-tolerant control with quadratic D stabilizability against actuator failures is investigated for a class of discrete-time systems with value-bounded uncertainties existing in both the state and control input matrices.Based on a more practical and general model of actuator continuous gain failures,taking the transient property,robust behaviour on H∞ performance and quadratic cost performance requirements into consideration,sufficient conditions for the existence of satisfactory fault-tolerant controller are given and the effective design steps with constraints of multiple performance indices are provided.Meanwhile,the consistency of the regional pole index,H∞ norm-bound constraint and cost performance indices is set up for fault-tolerant control.A simulation example shows the effectiveness of the proposed method.

Robust H_∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.

具有H_(∞)性能的输入受限三级倒立摆控制器设计

【目的】针对直线三级倒立摆控制输入受限下的稳摆控制问题,设计了具有H_(∞)性能的输入受限三级倒立摆控制器。【方法】利用线性矩阵不等式(LMI)方法,将控制输入约束问题转化为利用线性矩阵不等式求解优化值的优化问题,经Lyapunov稳定性推导出符合条件的LMI,利用MATLAB中的LMI工具箱求解得到有效的K。进一步在控制输入受限下引入H_(∞)性能指标,使所设计的控制输入受限下的算法具有H_(∞)性能。【结果】仿真结果表明,该控制器对于控制输入受限下的复杂高阶次不稳定系统具有很好的控制效果。【结论】控制输入信号在给定的受限范围内实现了三级倒立摆的稳摆要求,且引入H_(∞)性能指标后控制输入和摆杆波动更小。

H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.

Multivariable Decoupling Predictive Control Based on QFT Theory and Application in CSTR Chemical Process

A novel method of incorporating generalized predictive control (GPC) algorithms based on quantitative feedback theory (QFT) principles is proposed for solving the feedback control problem of the highly uncertain and cross-coupling plants. The quantitative feedback theory decouples the multi-input and multi-output (MIMO) plant and is also used to reduce the uncertainties of the system, stabilize the system, and achieve tracking performance of the system to a certain extent. Single-input and single-output (SISO) generalized predictive control is used to achieve performance with higher performance. In GPC, the model is identified on-line, which is based on the QFT input and the plant output signals. The simulation results show that the performance of the system is superior to the performance when only QFT is used for highly uncertain MIMO plants.

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.

Unified Smith Predictor Based H_∞ Wide-Area Damping Controller to Improve the Control Resiliency to Communication Failure

Inter-area low frequency oscillation in power system is one of the major problems for bulk power transmission through weak tie lines.Use of wide-area signal is more effective than the local area signal in damping out the inter-area oscillations.Wide area measurement system(WAMS)is convenient to transmit the wide area signal through the communication channel to the remote location.Communication failure is one of the disastrous phenomena in a communication channel.In this paper,a dual input single output(DISO)Hm controller is designed to build the control resiliency by employing two highest observability ranking wide area signals with respect to the critical damping inter-area mode.The proposed controller can provide sufficient damping to the system and also the system remains stabilized if one of the wide-area signals is lost.The time delay is an unwanted phenomenon that degrades the performance of the controllers.The unified Smith predictor approach is used to design a Hm controller to handle the time delay.Kundur's two-area and IEEE-39 bus test systems are considered to verify the effectiveness of the proposed controller.From the simulation results,it is verified that,the proposed controller provides excellent damping performance at normal communication and improves the controller resiliency to counteract the communication failure.

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.