Transition Function Research Articles

On the use of fuzzy preorders and asymmetric distances for multi-robot communication

<abstract><p>One of the main problems to be addressed in a multi-robot system is the selection of the best robot, or group of them, to carry out a specific task. Among the large number of solutions provided to allocate tasks to a group of robots, this work focuses on swarm-like approaches, and more specifically on response-threshold algorithms, where each robot selects the next task to perform by following a Markov process. To the best of our knowledge, the current response-threshold algorithms do not provide any formal method to generate new transition functions between tasks. Thus, this paper provides, for the first time, a mathematical model, as based on the so-called fuzzy preorders, for the allocation of tasks to a collective of robots with communication capabilities. In our previous work, we proved that transitions in the aforementioned process can be modeled as fuzzy preorders, constructed through the aggregation of asymmetric distances, in such a way that each robot makes its decision without taking into account the decisions of its teammates. Now, we extend this model in such a way that each robot will take into account the number of robots previously allocated for each task. To implement this method, a very simple communication mechanism has been considered. Several simulations have been carried out in order to validate our approach. The results confirm that fuzzy preorders are able to model the evolution of the system when this type of communication is considered and show when and how the communication process improves the system's performance. Experimental results show the existence of a set of good values for the maximum communication distance between robots and that these values depend on the distribution of the tasks in the environment. Thus, in some cases, a better communication mechanism does not imply better results.</p></abstract>

Experimental determination of the parameters of the adaptive support of the power unit of the machine-tractor unit

The research aim is to experimentally determine the parameters of the adaptive support of the power unit of the machine-tractor unit. The need to use adaptive supports for power plants of machine-tractor units is due to a change in their speed and load modes of operation in a wide range. The currently used supports have constant parameters, which are determined, as a rule, by statistical characteristics and characteristics of the nominal operating mode. Reducing the negative impact of vibration on the efficient performance of the power plant is proposed by creating supports with adjustable characteristics. Changes in the damping parameters of the used supports, depending on the modes of its operation, will reduce the vibration amplitudes of the power plant in the entire range of its operation, which will improve its performance indicators. The stiffness and damping coefficient were chosen as the determined parameters of the support. For this, experimental transition functions are fixed on a non-motorized stand, and they are approximated by solutions of differential equations of the first, second and third orders. The previously obtained curves are smoothed. The order of the differential equations depends on the type of transition functions and are selected according to numerical criteria. The adequacy of the obtained values is checked by comparing the experimental and theoretical curves. The scientific novelty lies in the methodological and technical diagnostics based on differential equations that was considered for agricultural units for the first time. The proposed methodology is of interest to engineers and technicians involved in the design of efficient supports for power plants of machine-tractor units.

Синтез обнаруживающих тестов для нечетких автоматов с конечной памятью

The problem of test synthesis for fuzzy automata with finite memory is considered. The paper is based on the results obtained by the author earlier. They study linear automata (LA), a subclass of which are automata with finite memory (AFM). Both types of automata are used as models in diagnostics of discrete devices and in other applications. The advantages of LA are simplicity of realization and availability of developed mathematical apparatus for their study. AFMs allow describing the dependencies between inputs and outputs in the past and present moments of time without using states of the automata. This property is used in the development of finite-automation cryptosystems, in the generation of exhaustive tests for discrete devices, in the formulation of fuzzy rules of logical inference and others. The paper proposes a method for synthesis of detecting tests for fuzzy AFMs, based on reducing it to the case of its analog for crisp AFMs. Fuzzy AFM (as a subclass of LA) can be described using transition and output functions represented as equations with characteristic matrices. Fuzzy AFM is realized using matrices containing some fuzzy elements. These elements obtain values randomly from alternative sets given for them. The other (crisp) elements of the matrices are fixed values from the field GF(p), over which the AFM is defined. After all possible substitutions in the matrices of fuzzy AFM of all fuzzy elements (from alternative sets) we obtain a set of crisp automata describing the "behavior" of the considered fuzzy automaton under all possible "scenarios" of substitutions. Each faulty AFM is obtained by changing the values of the elements of its characteristic matrices. As a set of admissible faults, all possible changes in these matrices obtained by substitutions and insertion of fault introduction are considered. Now we can use the method of test synthesis proposed earlier by the author of the submitted paper, organizing the procedure of sequential analysis and comparison of "behavior" of crisp pairs (faultless AFM, faulty AFM). The AFMs obtained after substitutions should be used sequentially as faultless AFMs and as faulty AFMs after faults have been introduced. Conclusions about the faultless AFM or the presence of a fault in it are made on the basis of analyzing the totality of the results obtained. A generalization of the synthesis method proposed earlier by the author of the submitted paper the is described for µ-defined (and synchronizable) AFMs. The method is based on obtaining tests as solutions of systems of linear equations, for which there is a well-developed mathematical apparatus in algebra.

Neural Network Model-Based Reinforcement Learning Control for AUV 3-D Path Following

Autonomous underwater vehicles (AUVs) have become important tools in the ocean exploration and have drawn considerable attention. Precise control for AUVs is the prerequisite to effectively execute underwater tasks. However, the classical control methods such as model predictive control (MPC) rely heavily on the dynamics model of the controlled system which is difficult to obtain for AUVs. To address this issue, a new reinforcement learning (RL) framework for AUV path-following control is proposed in this paper. Specifically, we propose a novel actor-model-critic (AMC) architecture integrating a neural network model with the traditional actor-critic architecture. The neural network model is designed to learn the state transition function to explore the spatio-temporal change patterns of the AUV as well as the surrounding environment. Based on the AMC architecture, a RL-based controller agent named ModelPPO is constructed to control the AUV. With the required sailing speed achieved by a traditional proportional-integral (PI) controller, ModelPPO can control the rudder and elevator fins so that the AUV follows the desired path. Finally, a simulation platform is built to evaluate the performance of the proposed method that is compared with MPC and other RL-based methods. The obtained results demonstrate that the proposed method can achieve better performance than other methods, which demonstrate the great potential of the advanced artificial intelligence methods in solving the traditional motion control problems for intelligent vehicles.

Combining Counterfactual Regret Minimization With Information Gain to Solve Extensive Games With Unknown Environments

Counterfactual regret minimization (CFR) is an effective algorithm for solving extensive‐form games with imperfect information (IIEGs). However, CFR is only allowed to be applied in known environments, where the transition function of the chance player and the reward function of the terminal node in IIEGs are known. In uncertain situations, such as reinforcement learning (RL) problems, CFR is not applicable. Thus, applying CFR in unknown environments is a significant challenge that can also address some difficulties in the real world. Currently, advanced solutions require more interactions with the environment and are limited by large single‐sampling variances to narrow the gap with the real environment. In this paper, we propose a method that combines CFR with information gain to compute the Nash equilibrium (NE) of IIEGs with unknown environments. We use a curiosity‐driven approach to explore unknown environments and minimize the discrepancy between uncertain and real environments. In addition, by incorporating information into the reward, the average strategy calculated by CFR can be directly implemented as the interaction policy with the environment, thereby improving the exploration efficiency of our method in uncertain environments. Through experiments on standard testbeds such as Kuhn poker and Leduc poker, our method significantly reduces the number of interactions with the environment compared to the different baselines and computes a more accurate approximate NE within the same number of interaction rounds.

A Novel Three-coil WPT System with Automatic CC-CV Transition Function

A Novel Three-coil WPT System with Automatic CC-CV Transition Function

COMPARATIVE ANALYSIS OF THE SUSTAINABILITY OF FINANCIAL PROCESSES IN JSC «UKRSIBBANK» AND JSC «PRIVATBANK» USING METHODS OF MODELING ECONOMIC DYNAMICS

Objective. The objective of the present article is to conduct a comparative analysis of the stability of financial processes in JSC «Ukrsibbank» and JSC «PrivatBank» using methods of modeling economic dynamics. Methods. The following methods were used to analyze the areas of application of economic dynamics modeling methods to compare the stability of financial processes in JSC «Ukrsibbank» and JSC «PrivatBank»: the basics of the mathematical apparatus for the analysis of transient processes, correlation and autocorrelation analysis, the methodology for determining the coefficients of impulse-transitional and transient functions, methods of constructing differential models, Laplace transformation and obtaining transition functions, the basics of mathematics of imaginary quantities, methods of obtaining amplitude-phase and frequency characteristics of the object under study, methods of stability analysis of controlled dynamic processes. Results. According to the results of a comparative analysis of the stability of financial processes in JSC «Ukrsibbank» and JSC «PrivatBank», it was established that the impulse-transitional and transitional functions for JSC «PrivatBank» have a more pronounced oscillatory character, which indicates a greater level of seasonality and cyclicality of financial processes in this particular bank, in addition, it reaches higher absolute values, which indicates a greater effect of the multiplier of investments for obtaining income of this bank. It is substantiated that since the line of the amplitude-phase-frequency characteristic for both banks does not cover the point (-1;0), this indicates the stability of the studied profit-making processes and their ability to self-leveling in the event of random disturbances and force majeure circumstances. On the basis of the schedule of amplitude-phase-frequency characteristic for PrivatBank JSC, it was determined that for this bank there is a certain limit of minimum values, below which the change of the investigated influential variables (the size of the loan portfolio, the total volume of contributions and deposits of individuals) does not affect the change in net profit. For JSC «Ukrsibbank» there is no such limit at any minimum values of the selected influential variables. The expediency of applying the mathematical apparatus of analysis of transient processes (in particular, construction of a differential model, transfer, impulse transient and transient function) for researching the process of obtaining a bank's net profit depending on the dynamic changes of its other financial indicators is substantiated. By constructing the amplitude-phase-frequency characteristic of the simulated transient process of changes in bank profit, the stability of the studied process was assessed and it was determined to what extent the existing dependence between the dynamic states of the net profit indicator is resistant to external disturbances and force majeure circumstances.

Synthesis and Characterization of SrTiO3 Doped with Bi(CH3COO)3

Synthesis of Strontium Titanate (SrTiO3) doped with Bismuth Acetatem (Bi(CH3COO)3) has been successfully carried out with varying concentrations of 0%; 0.5%; 1%; and 1.5% impurity in weight percent. The concentrated solution was dripped onto a P- type silicon substrate (1 0 0) using the Chemical Solution Deposition (CSD) method and spin coating technique. Annealing process was carried out with a temperature increase of 1.67oC/minute and held at 850oC for 8 hours and then cooled to room temperature for 12 hours. The film thickness was determined by the volumetric method, resulting in values of 3.9 μm, 4.3 μm, 4.7 μm and 5.1 μm. The analysis of optical properties with the Kubelka-Munk function for the direct transition results a band gap of 3.46 - 3.56 eV. Analysis of the XRD results was carried out using the Cramer-Cohen method and obtained lattice parameters (a=b=c) of Strontium Titanate (SrTiO3) doped with Bismuth Acetate (Bi(CH3COO)3) with various concentrations of 0%; 0.5%; 1%; and 1.5% are 3.835 Å, 3.837 Å, 3.909 Å, 3.913 Å respectively with a cubic crystal structure. This is because the ionic radius of bismuth (1.32 Å) is larger than that of strontium (1.17 Å), so bismuth will replace strontium in thin films. This replacement causes the lattice parameter values to increase, and effects the XRD spectral curve at the preferred peak (1 1 0) shift to the left. This shows that the doping bismuth has entered the strontium host.

Computational study of associations between the synaptic conductance of STN and GPe and the development of Parkinson's disease.

There is evidence that the subthalamic nucleus (STN) and globus pallidus pars externa (GPe) involve in the development of Parkinson's disease, a neurodegenerative disorder characterized by motor and non-motor symptoms and loss of dopaminergic neurons in which the error index (EI) in firing patterns is widely used to address the related issues. Whether and how this interaction mechanism of STN and GPe affects EI in Parkinson's disease is uncertain. To account for this, we propose a kind of basal ganglia-thalamic network model associated with Parkinson's disease coupled with neurons, and investigate the effect of synaptic conductance of STN and GPe on EI in this network, as well as their internal relationship under EI as an index. The results show a relationship like a piecewise function between the error index and the slope of the state transition function of synaptic conductance from STN to GPe ( ) and from GPe to STN ( ). And there is an approximate negative correlation between EI and . Increasing and decreasing can improve the fidelity of thalamus information transmission and alleviate Parkinson's disease effectively. These obtained results can give some theoretical evidence that the abnormal synaptic releases of STN and GPe may be the symptoms of the development of Parkinson's disease, and further enrich the understanding of the pathogenesis and treatment mechanism of Parkinson's disease.

Analysis of the yearly transition function in measles disease modeling.

Globally, there were an estimated 9.8 million measles cases and 207 500 measles deaths in 2019. As the effort to eliminate measles around the world continues, modeling remains a valuable tool for public health decision-makers and program implementers. This study presents a novel approach to the use of a yearly transition function that formulates mathematically the vaccine schedules for different age groups while accounting for the effects of the age of vaccination, the timing of vaccination, and disease seasonality on the yearly number of measles cases in a country. The methodology presented adds to an existing modeling framework and expands its analysis, making its utilization more adjustable for the user and contributing to its conceptual clarity. This article also adjusts for the temporal interaction between vaccination and exposure to disease, applying adjustments to estimated yearly counts of cases and the number of vaccines administered that increase population immunity. These new model features provide the ability to forecast and compare the effects of different vaccination timing scenarios and seasonality of transmission on the expected disease incidence. Although the work presented is applied to the example of measles, it has potential relevance to modeling other vaccine-preventable diseases.

Modelling the progression of illicit substance use patterns from real-world evidence.

To investigate an innovative pharmacometrics approach that addresses the challenges of using real-world evidence to model the progression of illicit substance use. The modelling strategy analysed real-world data from the National Longitudinal Study of Adolescent to Adult Health (AddHealth) survey using survival analyses and differential equations. Respondents were categorized into drug-naïve, active users and nonusers. The transitions between categories were modelled using interval-censored parametric survival analysis. The resulting hazard rate functions were used as time-dependent rate constants in a differential equation system. Covariate models for sex and depression status were assessed. AddHealth enrolled 6504 American teenagers (median age 16 years, range 11-21 years); this cohort was followed with five interviews over a 22-year period; the median age at the last interview was 38 years (range 34-45 years). The percentages of illicit drug users at Interviews 1-5 were 7.7%, 5.9%, 15.8%, 21.4% and 0.98%, respectively. The generalized gamma distribution emerged as the preferred model for the survival functions for transitions between categories. Age-dependent prevalence was obtained from the differential equation system. Active drug use was more prevalent in males, increased in adolescence and college years, peaked at 24 years, and decreased to low levels by 35 years. Depression, which was more frequent in females, increased the drug-naïve-active user transition rates but not the active user-nonuser and nonuser-active user transition rates. The evidence did not support an interaction between sex and depression. The model provided a satisfactory approximation for the age-dependent progression of illicit substance use from preadolescence to early middle age.

INFORMATION CAPABILITIES OF THE TRANSITION FUNCTION OF THE HYDROGEN STORAGE AND SUPPLY SYSTEM GAS GENERATOR TO ASSESS ITS FIRE HAZARD LEVEL

To estimate the level of fire hazard of hydrogen storage and supply systems, it is advisable to use reliability indicators, in particular, of their core element, which is a gas generator. Such indicators include indicators of amplitude and phase reliability of the gas generator, which are determined through the Laplace function. The arguments of this function are the relative errors of the parameters of the gas generator, which are determined by its transition function. Three options for determining the parameters of the gas generator have been developed, the feature of which is obtaining information about its parameters at two a priori given moments. The magnitudes of these moments do not exceed the time of the transient process. In the a priori specified moments, the values of the transient fraction are measured (option 1), and the values of its derivative (option 2) or the value of the integral of the transient function (option 3) are additionally measured. Algorithms for processing the received information have been developed for all options, the implementation of which ensures the determination of gas generator parameters. In terms of its structure, the second option for determining gas generator parameters is the simplest, which has 1.5 times fewer arithmetic operations compared to the first option. In addition, the second option for determining the parameters of the gas generator is invariant to the value of the time parameters that determine the measurement moments. The results of determining the parameters of the gas generator and their nominal values are used to determine the arguments of the Laplace functions. We have specified that when determining the parameters of the gas generator, the complexing method can be used, which involves the implementation of all three information processing algorithms. As an example of the second option of determining gas generator parameters, the structural diagram of the algorithm is presented. We have emphasised that the implementation of the developed algorithms for determining the parameters of the gas generator has no subjective factor associated with the use of expert judgments. Keywords: gas generator, fire hazard level, transition function.

Modelling of mould growth on pine sapwood: the preliminary analysis of input parameters in a logistic mould growth model

This paper deals with a logistic growth equation which was used for calculations of mould development on wood in time. The values of input parameters were determined by mutual comparisons of the logistic growth equation and synthetic mould growth data. Synthetic mould growth curves were calculated by the Finnish mould growth model for pine sapwood. A transition function between dimensionless mould index (the state variable of the Finnish mould growth model) and microscopic mould coverage fraction (the state variable of the logistic mould growth model) was proposed to facilitate numerical comparisons between both models. The insight to input parameters of the logistic mould growth model was then gained by plotting optimal values of parameters as a function of temperature and relative humidity, or moisture content. The setting of input parameters in mould growth models was then briefly discussed. It is concluded that further development of mould growth models should be based on systematic comparison with mould growth experiments. Not only growth under favourable conditions, but also the regrowth process after desiccation period must be correctly addressed in the model.

Renormalized chemical kinetics and benchmark quantum mechanical rates: activation energies and tunnelling transitivities for the reactions of fluorine atoms with H2 and HD

Experimental, theoretical and computational chemical kinetics contribute to progress both in molecular and materials sciences and in biochemistry, exploring the gap between elementary processes and complex systems. Stationary state quantum mechanics and statistical thermodynamics provide interpretive tools and instruments for classical molecular dynamics simulations for stable or metastable structures and near-equilibrium situations. Chemical reaction kinetics plays a key role at the mesoscales: time-dependent and evolution problems are typically tackled phenomenologically, and reactions through intermediates and transition states need be investigated and modelled. In this paper, scaling and renormalization procedures are developed beyond the Arrhenius equation and the Transition State Theory, regarding two key observables in reaction kinetics, the rate “constant” as a function of temperature (and its reciprocal, the generalised lifetime), and the apparent activation energy (and its reciprocal, the transitivity function). Coupled first-order equations—dependent on time and on temperature—are formulated in alternative coupling scheme they link experimental results to effective modelling, or vice versa molecular dynamics simulations to predictions. The passage from thermal to tunnelling regimes is uniformly treated and applied to converged quantum mechanical calculations of rate constants available for the prototypical three-atom reactions of fluorine atoms with both H2 and HD: these are exothermic processes dominated by moderate tunnel, needing formal extension to cover the low-temperature regime where aspects of universal behaviour are shown to emerge. The results that have been validated towards experimental information in the 10–350 K temperature range, document the complexity of commonly considered “elementary” chemical reactions: they are relevant for modelling atmospheric and astrophysical environments. Perspectives are indicated of advances towards other types of transitions and to a global generality of processes of interest in applied chemical kinetics in biophysics and in astrochemistry.

Threshold Impact of Remittances on Real Exchange Rates for WAEMU: A Panel Smooth Transition Regression Approach

This paper explores the nonlinear relationship between workers’ remittances and real effective exchange rates for West African Economic and Monetary Union (WAEMU) member countries using the panel smooth transition regression (PSTR). The PSTR was estimated with one transition function and one location parameter as dictated by the diagnostic tests. The diagnostic tests reveal that the relationship between workers’ remittances and real effective rates is nonlinear. The estimated threshold value is 3.07%. The results reveal that increases in workers’ remittances have a depreciating effect on real effective exchange rates in regime one, associated with threshold value of less than 3.07%. However, in the second regime when the threshold value is greater than or equal to 3.07%, increases in workers remittances have an appreciating impact on real effective exchange rates. These results substantiate that the relationship between workers’ remittances and real effective exchange rates is asymmetric and as such should be modeled accordingly. Above all, the results confirm the presence of Dutch disease effect in the second regime where the estimated coefficient on workers’ remittances is negative and statistically significant. However, there is no evidence of Dutch disease effect in the first regime where the regression coefficient on workers remittances is positive and also statistically significant. Policy implications are discussed.

Structural, electronic and magnetic properties of the CuFeO[formula omitted] multiferroic compound

The structural, electronic and magnetic properties of the delafossite material CuFeO2 were studied using Density Functional Theory (DFT) combined with Monte Carlo simulation (MCS). The structural stability was verified in this work and showed that this material is antiferromagnetic (AFM). The density of states (DOS) carried out using the generalized Perdew–Burke–Ernzerhof gradient (PBE-GGA), Tran-Balaha modified Becke–Johnson exchange potentials (TB-mBJ; nmBJ) and the GGA＋ U show that the compound has a metallic behavior in PBE-GGA and semiconductor behavior in TB-mBJ, nmBJ and GGA＋ U approximations. The obtained partial magnetic moment was used to study the magnetic behavior by Monte Carlo simulation, particularly, the evolution of magnetization as a function of temperature and phase transition. The results of MCS showed the presence of two-phase transitions: ferromagnetic–antiferromagnetic (FM-AFM) first-order phase transition and antiferromagnetic–paramagnetic (AFM-PM) second-order phase transition. The Neel temperatures found are TN2=11.2 K for the first transition and TN1=16.6 K for the second transition.

Copula-based modeling and simulation of 3D systems of curved fibers by isolating intrinsic fiber properties and external effects

In this paper we lay the foundation for data-driven 3D analysis of virtual fiber systems with respect to their microstructure and functionality. In particular, we develop a stochastic 3D model for systems of curved fibers similar to nonwovens, which is fitted to tomographic image data. By systematic variations of model parameters, efficient computer-based scenario analyses can be performed to get a deeper insight how effective properties of this type of functional materials depend on their 3D microstructure. In a first step, we consider single fibers as polygonal tracks which can be modeled by a third-order Markov chain. For constructing the transition function of the Markov chain, we formalize the intuitive notions of intrinsic fiber properties and external effects and build a copula-based transition function such that both aspects can be varied independently. Using this single-fiber model, in a second step we derive a model for the entire fiber system observed in a bounded sampling window and fit it to two different 3D datasets of nonwovens measured by CT imaging. Considering various geometric descriptors of the 3D microstructure related to effective properties of the pore space, we evaluate the goodness of model fit by comparing geometric descriptors of the 3D morphology of model realizations with those of tomographic image data.

An illness-death multistate model to implement delta adjustment and reference-based imputation with time-to-event endpoints.

With a treatment policy strategy, therapies are evaluated regardless of the disturbance caused by intercurrent events (ICEs). Implementing this estimand is challenging if subjects are not followed up after the ICE. This circumstance can be dealt with using delta adjustment (DA) or reference-based (RB) imputation. In the survival field, DA and RB imputation have been researched so far using multiple imputation (MI). Here, we present a fully analytical solution. We use the illness-death multistate model with the following transitions: (a) from the initial state to the event of interest, (b) from the initial state to the ICE, and (c) from the ICE to the event. We estimate the intensity function of transitions (a) and (b) using flexible parametric survival models. Transition (c) is assumed unobserved but identifiable using DA or RB imputation assumptions. Various rules have been considered: no ICE effect, DA under proportional hazards (PH) or additive hazards (AH), jump to reference (J2R), and (either PH or AH) copy increment from reference. We obtain the marginal survival curve of interest by calculating, via numerical integration, the probability of transitioning from the initial state to the event of interest regardless of having passed or not by the ICE state. We use the delta method to obtain standard errors (SEs). Finally, we quantify the performance of the proposed estimator through simulations and compare it against MI. Our analytical solution is more efficient than MI and avoids SE misestimation-a known phenomenon associated with Rubin's variance equation.

Hierarchical critic learning optimal control for lower limb exoskeleton robots with prescribed constraints

AbstractThis paper presents a hierarchical critic learning optimal control (H‐CLOC) strategy for a lower limb exoskeleton system with prescribed state constraints. The prescribed state constraints of the exoskeleton are mathematically modeled by means of a state error transition function, which transforms the constrained state into an equivalent new unconstrained state. A hierarchical framework including a high‐level motion trajectory planner and a low‐level critic learning (CL) controller is proposed for optimal control of the exoskeleton. The estimation of human motion intentions is achieved using dynamic movement primitives (DMPs), which are capable of accurately replicating the original training trajectories during motion. The CL algorithm is implemented on the transformed unconstrained system while enhancing the learning capability of the proposed algorithm for the exoskeleton. The optimal control with prescribed constraints is analyzed for stability using the Lyapunov theorem. Finally, simulation results validate the effectiveness of the proposed H‐CLOC strategy for lower limb exoskeletons.

A Distributed Dynamic Inertia-Droop Control Strategy Based on Multi-Agent Deep Reinforcement Learning for Multiple Paralleled VSGs

The virtual synchronous generator (VSG) control method for energy storage is a promising way to improve the frequency stability of the power system with large-scale renewable energy. However, due to the mismatch parameters, power oscillations may occur when multiple VSGs are connected in parallel to the grid. In this paper, the relationship between oscillation and the inertia-droop parameters distribution of multiple paralleled VSGs is derived by the simplified frequency response model. Furthermore, to coordinate the inertia-droop parameters of paralleled VSGs for oscillation damping, this paper formulates the parameter tuning problem as a Markov game with an unknown transition function and proposes a distributed dynamic inertia-droop control strategy based on multi-agent deep reinforcement learning (MADRL). Based on the local and adjacent VSG information, each agent learns the optimal inertia-droop control parameters independently by interacting with the environment. The soft-actor-critic (SAC) framework is introduced to train each agent. The well-trained agent can modify the parameters of VSG dynamically to suppress the power oscillation under different operating conditions. Finally, several time-domain results demonstrate the effectiveness and robustness of the proposed approach.