Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

Magnetopause properties at the dusk magnetospheric flank from global magnetohydrodynamic simulations,the kinetic Vlasov equilibrium,and in situ observations--Potential implications for SMILE

We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscale 2(MMS2)spacecraft.We used global magnetohydrodynamic(MHD)simulations of the Earth’s magnetosphere(publicly available from the NASA-CCMC[National Aeronautics and Space Administration–Community Coordinated Modeling Center])and local Vlasov equilibrium models(based on kinetic models for tangential discontinuities)to extract spatial profiles of the plasma and field variables at the Earth’s MP.The global MHD simulations used initial solar wind conditions extracted from the OMNI database at the time epoch when the MMS2 observes the MP.The kinetic Vlasov model used asymptotic boundary conditions derived from the same in situ MMS measurements upstream or downstream of the MP.The global MHD simulations provide a three-dimensional image of the magnetosphere at the time when the MMS2 crosses the MP.The Vlasov model provides a one-dimensional local view of the MP derived from first principles of kinetic theory.The MMS2 experimental data also serve as a reference for comparing and validating the numerical simulations and modeling.We found that the MP transition layer formed in global MHD simulations was generally localized closer to the Earth(roughly by one Earth radius)from the position of the real MP observed by the MMS.We also found that the global MHD simulations overestimated the thickness of the MP transition by one order of magnitude for three analyzed variables:magnetic field,density,and tangential speed.The MP thickness derived from the local Vlasov equilibrium was consistent with observations for all three of these variables.The overestimation of density in the Vlasov equilibrium was reduced compared with the global MHD solutions.We discuss our results in the context of future SMILE(Solar wind Magnetosphere Ionosphere Link Explorer)campaigns for observing the Earth’s MP.

Numerical analysis for the free-boundary current reversal equilibrium in the AC plasma current operation in a tokamak

In recent decades, tokamak discharges with zero total toroidal current have been reported in tokamak experiments, and this is one of the key problems in alternating current(AC) operations.An efficient free-boundary equilibrium code is developed to investigate such advanced tokamak discharges with current reversal equilibrium configuration. The calculation results show that the reversal current equilibrium can maintain finite pressure and also has considerable effects on the position of the X-point and the magnetic separatrix shape, and hence also on the position of the strike point on the divertor plates, which is extremely useful for magnetic design, MHD stability analysis, and experimental data analysis etc. for the AC plasma current operation on tokamaks.

Kinetic equilibrium reconstruction with internal safety factor profile constraints on EAST tokamak

Reconstruction of plasma equilibrium plays an important role in the analysis and simulation of plasma experiments. The kinetic equilibrium reconstruction with pressure and edge current constraints has been employed on EAST tokamak. However, the internal safety factor(q) profile is not accurate. This paper proposes a new way of incorporating q profile constraints into kinetic equilibrium reconstruction. The q profile is yielded from the Polarimeter Interferometer(POINT)reconstruction. Virtual probes containing information on q profile constraints are added to inputs of the kinetic equilibrium reconstruction program to obtain the final equilibrium. The new equilibrium produces a more accurate internal q profile. This improved method would help analyze EAST experiments.

Effects of ionic liquids on the vapor-liquid equilibrium of 1,3,5-trioxane-water system at 101.3 kPa

Increasing the 1,3,5-trioxane(TOX) concentration in the equilibrated vapor phase of TOX-H_(2)O system has been recognized as a challenge for the azeotrope. Ionic liquids(ILs) were used to improve the relative volatility of TOX to H_(2)O and destroy the azeotrope in the TOX-H2O system. The vapor-liquid equilibrium of TOX-H2O system at 101.3 kPa was studied with the addition of 1-butyl-3-methylimidazolium hydrogen sulfate, 1-hexyl-3-methylimidazolium hydrogen sulfate and 1-butyl-3-methylimidazolium nitrate, respectively. The results showed that the volatility of TOX increased with the increase in IL dosage. And the volatility of water decreased with the increase in IL dosage. The relative volatility of TOX to H_(2)O was improved with the increase in ILs dosage. The azeotrope could be destroyed with an IL mole fraction of about 0.10. A non-random two-liquid(NRTL) model was successfully used to correlate the experimental data. The interaction parameters were obtained by fitting the experimental data with the model. The results indicated that a strong interaction existed between ILs and water. The strong interaction improved the volatility of TOX and inhibited the volatility of water, and then intensified the relative volatility of TOX to H_(2)O. The results showed that an ILs with strong polarity and hydrophilicity may be a potential additive to improve the TOX concentration in the equilibrated vapor phase.

Phase equilibrium data prediction and process optimizationin butadiene extraction process

In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene production by acetonitrile.The accuracy of five prediction methods,UNIFAC(UNIQUAC Functional-group Activity Coefficients),UNIFAC-LL,UNIFAC-LBY,UNIFAC-DMD and COSMO-RS,applied to the butadiene extraction process was verified using partial phase equilibrium data.The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system.COSMO-RS-predicted multiple systems showed good accuracy,and a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method.The predicted phase equilibrium data were checked for consistency.The NRTL-RK(non-Random Two Liquid-Redlich-Kwong Equation of State)and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data.Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process.The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2%compared to that using the commercial simulation software,Aspen Plus and its database.The average deviation was much smaller than that of the simulations using the Aspen Plus database(>10%),indicating that the obtained phase equilibrium data are highly accurate and reliable.The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided.This improves the accuracy and reliability of the design,optimization and control of the process,and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.

Multi-Objective Equilibrium Optimizer for Feature Selection in High-Dimensional English Speech Emotion Recognition

Speech emotion recognition(SER)uses acoustic analysis to find features for emotion recognition and examines variations in voice that are caused by emotions.The number of features acquired with acoustic analysis is extremely high,so we introduce a hybrid filter-wrapper feature selection algorithm based on an improved equilibrium optimizer for constructing an emotion recognition system.The proposed algorithm implements multi-objective emotion recognition with the minimum number of selected features and maximum accuracy.First,we use the information gain and Fisher Score to sort the features extracted from signals.Then,we employ a multi-objective ranking method to evaluate these features and assign different importance to them.Features with high rankings have a large probability of being selected.Finally,we propose a repair strategy to address the problem of duplicate solutions in multi-objective feature selection,which can improve the diversity of solutions and avoid falling into local traps.Using random forest and K-nearest neighbor classifiers,four English speech emotion datasets are employed to test the proposed algorithm(MBEO)as well as other multi-objective emotion identification techniques.The results illustrate that it performs well in inverted generational distance,hypervolume,Pareto solutions,and execution time,and MBEO is appropriate for high-dimensional English SER.

Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.

Magnetic diagnostics layout design for CFETR plasma equilibrium reconstruction

Plasma equilibrium reconstruction provides essential information for tokamak operation and physical analysis.An extensive and reliable set of magnetic diagnostics is required to obtain accurate plasma equilibrium.This study designs and optimizes the magnetic diagnostics layout for the reconstruction of the equilibrium of the plasma according to the scientific objectives,engineering design parameters,and limitations of the Chinese Fusion Engineering Test Reactor(CFETR).Based on the CFETR discharge simulation,magnetic measurement data are employed to reconstruct consistent plasma equilibrium parameters,and magnetic diagnostics'number and position are optimized by truncated Singular value decomposition,verifying the redundancy reliability of the magnetic diagnostics layout design.This provides a design solution for the layout of the magnetic diagnostics system required to control the plasma equilibrium of CFETR,and the developed design and optimization method can provide effective support to design magnetic diagnostics systems for future magnetic confinement fusion devices.

Intrinsic correlation between the generalized phase equilibrium condition and mechanical behaviors in hydrate-bearing sediments

The phase equilibrium and mechanical behaviors of natural gas hydrate-bearing sediment are essential for gas recovery from hydrate reservoirs.In heating closed systems,the temperature-pressure path of hydrate-bearing sediment deviates from that of pure bulk hydrate,reflecting the porous media effect in phase equilibrium.A generalized phase equilibrium equation was established for hydrate-bearing sediments,which indicates that both capillary and osmotic pressures cause the phase equilibrium curve to shift leftward on the temperature-pressure plane.In contrast to bulk hydrate,hydrate-bearing sediment always contains a certain amount of unhydrated water,which keeps phase equilibrium with the hydrate within the hydrate stability field.With changes in temperature and pressure,a portion of pore hydrate and unhydrated water may transform into each other,affecting the shear strength of hydrate-bearing sediment.A shear strength model is proposed to consider not only hydrate saturation but also the change in temperature and pressure of hydrate-bearing sediment.The model is validated by experimental data with various hydrate saturation,temperature and pressure conditions.The deformation induced by partial dissociation was studied through depressurization tests under constant effective stress.The reduction in gas pressure within the hydrate stability field indeed caused sediment deformation.The dissociation-induced deformation can be reasonably estimated as the difference in volume between hydrate-bearing and hydrate-free sediments from the compression curves.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Equilibrium reconstruction method for self-organized plasmas on reversed field pinches with polarimeter-interferometer

In the reversed field pinch(RFP),plasmas exhibit various self-organized states.Among these,the three-dimensional(3D)helical state known as the“quasi-single-helical”(QSH)state enhances RFP confinement.However,accurately describing the equilibrium is challenging due to the presence of 3D structures,magnetic islands,and chaotic regions.It is difficult to obtain a balance between the available diagnostic and the real equilibrium structure.To address this issue,we introduce KTX3DFit,a new 3D equilibrium reconstruction code specifically designed for the Keda Torus eXperiment(KTX)RFP.KTX3DFit utilizes the stepped-pressure equilibrium code(SPEC)to compute 3D equilibria and uses polarimetric interferometer signals from experiments.KTX3DFit is able to reconstruct equilibria in various states,including axisymmetric,doubleaxis helical(DAx),and single-helical-axis(SHAx)states.Notably,this study marks the first integration of the SPEC code with internal magnetic field data for equilibrium reconstruction and could be used for other 3D configurations.

Enhanced Hybrid Equilibrium Strategy in Fog-Cloud Computing Networks with Optimal Task Scheduling

More devices in the Intelligent Internet of Things(AIoT)result in an increased number of tasks that require low latency and real-time responsiveness,leading to an increased demand for computational resources.Cloud computing’s low-latency performance issues in AIoT scenarios have led researchers to explore fog computing as a complementary extension.However,the effective allocation of resources for task execution within fog environments,characterized by limitations and heterogeneity in computational resources,remains a formidable challenge.To tackle this challenge,in this study,we integrate fog computing and cloud computing.We begin by establishing a fog-cloud environment framework,followed by the formulation of a mathematical model for task scheduling.Lastly,we introduce an enhanced hybrid Equilibrium Optimizer(EHEO)tailored for AIoT task scheduling.The overarching objective is to decrease both the makespan and energy consumption of the fog-cloud system while accounting for task deadlines.The proposed EHEO method undergoes a thorough evaluation against multiple benchmark algorithms,encompassing metrics likemakespan,total energy consumption,success rate,and average waiting time.Comprehensive experimental results unequivocally demonstrate the superior performance of EHEO across all assessed metrics.Notably,in the most favorable conditions,EHEO significantly diminishes both the makespan and energy consumption by approximately 50%and 35.5%,respectively,compared to the secondbest performing approach,which affirms its efficacy in advancing the efficiency of AIoT task scheduling within fog-cloud networks.

Lithium-Ion Battery Pack Based on Fuzzy Logic Control Research on Multi-Layer Equilibrium Circuits

In order to solve the problem of inconsistent energy in the charging and discharging cycles of lithium-ion battery packs,a new multilayer equilibrium topology is designed in this paper.The structure adopts a hierarchical structure design,which includes intra-group equilibrium,primary inter-group equilibrium and secondary inter-group equilibrium.This structure greatly increases the number of equilibrium paths for lithium-ion batteries,thus shortening the time required for equilibrium,and improving the overall efficiency.In terms of control strategy,fuzzy logic control(FLC)is chosen to control the size of the equilibrium current during the equilibrium process.We performed rigorous modeling and simulation of the proposed system by MATLAB and Simulink software.Experiments show that the multilayer equilibrium circuit structure greatly exceeds the traditional single-layer equilibrium circuit in terms of efficacy,specifically,the Li-ion battery equilibrium speed is improved by 12.71%in static equilibrium,14.48%in charge equilibrium,and 11.19%in discharge equilibrium.In addition,compared with the maximum value algorithm,the use of the FLC algorithm reduces the equalization time by about 3.27%and improves the energy transfer efficiency by about 66.49%under the stationary condition,which verifies the feasibility of the equalization scheme.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

Analysis of Drug Medical Insurance Access Pricing Based on the Perspective of Binary Equilibrium

Objective To study the influencing factors in the process of national medical insurance negotiation and drug pricing from the dualistic equilibrium perspective,and to provide reference for the harmonious management of drug pricing in China.Methods Through the literature analysis and policy review,the pricing subject,pricing basis and price control system in the pricing process of medical-accessed medicines were analyzed from the perspective of binary equilibrium and harmonious management.Results and Conclusion It is found that four balances in the drug pricing process,two balances in pricing basis and three balances in price control system need to be considered,respectively.Drug pricing is the key content of national medical insurance access,which is also the hotspot of the policy in the pharmaceutical fields in recent years.Drug pricing not only reflects the value of drugs,but also reflects a lot of top-level designs of binary equilibriums in medical insurance policy.While the rational design of drug pricing requires the joint efforts of the government,pharmaceutical companies and relevant experts to comprehensively consider many equilibriums,so as to improve the relevant systems.

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.

Fully Distributed Nash Equilibrium Seeking for High-Order Players With Actuator Limitations

This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players' dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with adaptive and time-varying gains, the unknown actions for players are distributively estimated. Then, a fully distributed Nash equilibrium seeking strategy is exploited, showcasing its remarkable properties: (1) ensuring the boundedness of control inputs;(2) avoiding any global information/parameters;and (3) allowing the graph to be directed. Based on Lyapunov stability analysis, it is theoretically proved that the proposed distributed control strategy can lead all the players' actions to the Nash equilibrium. Finally, an illustrative example is given to validate effectiveness of the proposed method.

Quantum-Inspired Equilibrium Optimizer for Linear Antenna Array

With the rapid development of communication technology,the problem of antenna array optimization plays a crucial role.Among many types of antennas,line antenna arrays(LAA)are the most commonly applied,but the side lobe level(SLL)reduction is still a challenging problem.In the radiation process of the linear antenna array,the high side lobe level will interfere with the intensity of the antenna target radiation direction.Many conventional methods are ineffective in obtaining the maximumside lobe level in synthesis,and this paper proposed a quantum equilibrium optimizer(QEO)algorithm for line antenna arrays.Firstly,the linear antenna array model consists of an array element arrangement.Array factor(AF)can be expressed as the combination of array excitation amplitude and position in array space.Then,inspired by the powerful computing power of quantum computing,an improved quantum equilibrium optimizer combining quantum coding and quantum rotation gate strategy is proposed.Finally,the proposed quantum equilibrium optimizer is used to optimize the excitation amplitude of the array elements in the linear antenna array model by numerical simulation to minimize the interference of the side lobe level to the main lobe radiation.Six differentmetaheuristic algorithms are used to optimize the excitation amplitude in three different arrays of line antenna arrays,the experimental results indicated that the quantum equilibrium optimizer is more advantageous in obtaining the maximum side lobe level reduction.Compared with other metaheuristic optimization algorithms,the quantum equilibrium optimizer has advantages in terms of convergence speed and accuracy.