Robust distributed adaptive consensus for linear multiagent systems with uncertain topologies

This paper focuses on the robust mean-square consensus control problem for linear multiagent systems over randomly switching signed interaction topologies. The stochastic process is governed by a time-homogeneous Markov chain with partly unknown transition rates. Sufficient conditions for a consensus in the form of linear matrix inequalities are given via distributed adaptive control based on parameter-dependent Lyapunov functions. The adaptive control protocols require only the neighbor information of the agents, and the algorithm that designs the protocols reduces the influence of the communication topology on the consensus, which can prevent undesirable interaction impacts. Moreover, the disturbance rejection problem is addressed as an extension. Finally, two simulations are utilized to illustrate the effectiveness of the algorithms.

Load Frequency Control for Power Systems with Actuator Faults within a Finite-Time Interval

This paper is concerned with the issue of finite-time H ∞ load frequency control for power systems with actuator faults. Concerning various disturbances, the actuator fault is modeled by a homogeneous Markov chain. The aperiodic sampling data controller is designed to alleviate the conservatism of attained results. Based on a new piecewise Lyapunov functional, some novel sufficient criteria are established, and the resulting power system is stochastic finite-time bounded. Finally, a single-area power system is adjusted to verify the effectiveness of the attained results.

Research on Stereo Library Based on Homogeneous Markov Chain

The intelligent inventory has not yet been implemented in the automated three-dimensional library. The warehouse basically relies on the accounts of the warehouse. It is really necessary to check the pallets manually with the help of a stacker, or venture into the aisle to check on the spot, or install radio frequency identification (RFID) on the pallet. The radio frequency recognition device on the stacker’s loading platform obtains the information of a specific pallet to achieve a physical inventory. After investigation, the results that can pass the three-dimensional library system automatic library are still blank. For the three-dimensional library, the intelligent inventory is of great significance to the actual production. It can automatically identify whether the goods in the designated cargo space are consistent with the storage according to the needs of the warehouse manager, so the demand for the intelligent inventory is very urgent.

Sovereign Default Forecasting in the Era of the COVID-19 Crisis

The COVID-19 crisis has revealed the economic vulnerability of various countries and, thus, has instigated the systematic exploration and forecasting of sovereign default risks. Multivariate statistical and stochastic process-based sovereign default risk forecasting has a 50-year developmental history. This article describes a continuous, non-homogeneous Markov chain method as the basis for a COVID-19-related sovereign default risk forecast model. It demonstrates the estimation of sovereign probabilities of default (PDs) over a five-year horizon period with the developed model reflecting the impact of the COVID-19 crisis. The COVID-19-adopted Markov model estimates PDs for most countries, including those that are advanced with AAA and AA ratings, to suggest that no sovereign nation’s economy is secure from the financial impact of the COVID-19 pandemic. The dynamics of the estimated PDs are indicative of contemporary evidence as experienced in the recent financial crisis. The empirical results of this article have policy implications for foreign investors, sovereign lenders, export finance institutions, foreign trade experts, risk management professionals, and policymakers in the field of finance. The developed model can be used to timely recognize potential problems with sovereign entities in the current COVID-19 crisis and to take appropriate mitigating actions.

Sequential statistical decision making in problems of data flows analysis

In the problems of data flows analysis, the problems of statistical decision making on parameters of observed data flows are important. For their solution it is proposed to use sequential statistical decision rules. The rules are constructed for three models of observation flows: sequence of independent homogeneous observations; sequence of observations forming a time series with a trend; sequence of dependent observations forming a homogeneous Markov chain. For each case the situation is considered, where the model describes the observed stochastic data with a distortion. "Outliers" ("contamination") are used as the admissible distortions that adequately describe the majority of situations appear in practice. For such situations the families of sequential decision rules are proposed, and robust decision rules are constructed that allow to reduce influence of distortion to the efficiency characteristics. The results of computer experiments are given to illustrate the constructed decision rules.

A probabilistic model for risk assessment and predicting the health risk of occupational exposure to pesticides in agriculture

Introduction. The main point is the influence of a complex of chemical and physical stressors on agricultural machine operators. The processes of occurrence and interaction of harmful factors are probable. Markov processes are a convenient model that can describe the behaviour of physical processes with random dynamics. Purpose of the work: was to develop a probabilistic model of risk assessment for agriculture workers during the application of pesticides based on Markov processes’ theory and evaluate with the help of the developed model the probability of occurrence, the degree of severity and the prediction of the different influence of adverse factors on the operator. Materials and methods. The mechanized treatment of pesticide is presented in the form of a system, the states of which are ranked according to the degree of danger to the operator: from non-dangerous to dangerous. The transition occurs under the influence of negative factors and is characterized by the probability of pij transition. Based on the marked graph of the system states, a stochastic matrix P[ij] of transition probabilities was constructed in one step. There are formulas by which it is possible to calculate the state of systems in k steps for a homogeneous and non-homogeneous Markov chain. Results. Based on Markov chains’ theory, the system’s behaviour is modelled when using single-component preparations based on imidacloprid for rod spraying of field crops. Received vector of probabilities of possible hazardous conditions for the employee after each hour of spraying within 10 hours. After 6 hours of working, the probabilistic risk for the operator to stay in a non-dangerous state is about 50 %, and the probability risk of going into a dangerous - at 24 %. The stationary probability distribution results show the inevitability of the transition to a hazardous state of the system if enough steps have been taken. Conclusion. With this model, you can supplement the operator’s health risk assessment system, analyze, compare and summarize the results of years of research. The calculated statistical probabilities can be used in the development of new hygiene regulations with using pesticides.

An Analysis of a Storage System for a Wind Farm with Ramp-Rate Limitation

This paper provides evidence on how the variability of the power produced by a wind farm and its revenue are affected by implementing a ramp-rate limitation strategy and by adding a storage device to the system. The wind farm receives penalties whenever the ramp-rate limitations are not respected and may be supported by batteries to avoid this scenario. In this paper, we model the battery usage as a discrete time homogeneous Markov chain with rewards thanks to which it is possible to simulate the state of the charge of the battery and to calculate the amount of penalties suffered by the wind farm during any period. An application is performed considering the power produced by a hypothetical wind turbine located in Sardinia (Italy) using real wind speed data and electricity prices from a period of 10 years. We applied the concept of ramp-rate limitation on our hourly dataset, studying several limitation scenarios and battery capacities.

Design of a recommendation system based on the transition graph

A recommendation system has been built for a web resource’s users that applies statistics about user activities to provide recommendations. The purpose of the system operation is to provide recommendations in the form of an orderly sequence of HTML pages of the resource suggested for the user. The ranking procedure uses statistical information about user transitions between web resource pages. The web resource model is represented in the form of a web graph; the user behavior model is shown as a graph of transitions between resource pages. The web graph is represented by an adjacency matrix; for the transition graph, a weighted matrix of probabilities of transitions between the vertices of the graph has been constructed. It was taken into consideration that user transitions between pages of a web resource may involve entering a URL in the address bar of a browser or by clicking on a link in the current page. The user’s transition between vertices in a finite graph according to probabilities determined by the weight of the graph’s edges is represented by a homogeneous Markov chain and is considered a process of random walk on the graph with the possibility of moving to a random vertex. Random Walk with Restarts was used to rank web resource pages for a particular user. Numerical analysis has been performed for an actual online store website. The initial data on user sessions are divided into training and test samples. According to the training sample, a weighted matrix of the probability of user transitions between web resource pages was constructed. To assess the quality of the built recommendation system, the accuracy, completeness, and Half-life Utility metrics were used. On the elements of the test sample, the accuracy value of 65‒68 % was obtained, the optimal number of elements in the recommendation list was determined. The influence of model parameters on the quality of recommendation systems was investigated.