semi-Markov Chain Research Articles

Novel event-triggered protocol to sliding mode control for singular semi-Markov jump systems

This study presents a memory-based sliding mode control for singular semi-Markov jump systems using a novel dynamic-memory event-triggered protocol. Based on the average dwell-time strategy, a deterministic switching signal was developed to adjust the variation of the semi-Markov chains. Randomly occurring deception attacks are considered owing to the existence of an adversary. Furthermore, to enhance transmission efficiency and achieve better control performance, a novel dynamic-memory triggering condition is proposed, in which both historical transmitted data and two auxiliary dynamic variables are implemented. Based on the proposed protocol and Lyapunov theory, some parameter-dependent sufficient criteria are established to guarantee mean-square exponential stability and strictly dissipative performance, and the desired memory-based sliding mode controller is designed. Finally, two simulation examples were presented to verify the effectiveness of the proposed methodology.

Weighted-indexed semi-Markov model: calibration and application to financial modeling

We address the calibration issues of the weighted-indexed semi-Markov chain (WISMC) model applied to high-frequency financial data. Specifically, we propose to automate the discretization of the price returns and the volatility index by using four different approaches, two based on statistical quantities, namely, the quantile and sigma discretization, and two derived by the application of two popular machine learning algorithms, namely the k-means and Gaussian mixture model (GMM). Moreover, by comparing the Bayesian information criterion (BIC) scores, the GMM approach allows for the selection of the number of states of returns and index. An application to Bitcoin prices at 1-min and 1-s intervals shows the validity and usefulness of the proposed discretization approaches. In particular, GMM discretization is well suited for high-frequency returns, whereas the quantile approach works better for low-frequency intervals. Finally, by comparing the results of the Monte Carlo simulation, we show that the WISMC model, applied with the proposed discretization, can reproduce the long-range serial correlation of the squared returns, which is typical of the financial markets and, in particular, the cryptocurrency market.

Formation Control of Wheeled Mobile Robots With Multiple Virtual Leaders Under Communication Failures

To alleviate the threat of communication failures, a formation control system (FCS) with multiple virtual leaders and semi-Markov switching topologies is proposed in this article. A time-varying formation tracking protocol with an error compensation term is introduced to mitigate the effects among the real leader and the virtual leaders. Sufficient and necessary conditions are derived based on the Routh–Hurwitz criterion. Then, a semi-Markov chain with communication delay is presented to characterize the topology switching process in different communication failure scenarios. The FCS is constructed with a varying gain controller, and its tracking performance is analyzed with the Lyapunov–Krasovskii functional. Finally, substantial experiments with Quanser Qbot2 mobile formation demonstrate the effectiveness of position and velocity tracking for FCS.

Decoding and Re-estimation of fuzzy hidden semi Markov chain with observation dependent state

Decoding and Re-estimation of fuzzy hidden semi Markov chain with observation dependent state

Improvement of accident prevention measures in cases of spontaneous derailment of railway rolling stock

There has been researched on railway station tracks to determine the method of automatically stopping motion content in cases where Motion Content has gone away on its own. Even today, there are mainly cases of spontaneous movement of the composition of the movement to the side where the slope of the Railway Station roads decreases. This leads to many casualties and accidents caused by the spontaneous movement of trains at railway stations. By applying the proposed method of automatically stopping the rolling stock without human intervention, the law of conservation of mechanics, and determining the number of brake shoes set by the system device, the losses that may occur in stopping the rolling stock are achieved. In addition, the features of equipping the places of automatic stopping of the rolling stock with devices in the case of rolling stock leaving by themselves on the existing railway station tracks were considered. Also, the algorithm of operation of the system for automatic stopping of the moving parts that have gone away on their own is given of this system safety to determine semi-Markov chain for based on the system a mathematical model of safety was created. Microprocessor to the system based on by itself gone the rest movement contents to stop intended automated from devices use there is a niche in the station ways account received devices without work to algorithms and trains movement speed mutually dependence provided without by itself moving gone movement units safety provide through accidents took is taken. This prevents potential accidents, increases the reliability of system use, and leads to cost-effectiveness in system use.

Finite-time fault-tolerant consensus for leader-following multi-agent systems with semi-Markov switching topologies

This paper investigates the finite-time leader-following consensus problem for multi-agent systems with switching topologies. First of all, consider the characteristic of failures, a failure distribution model which is more in line with the actual situation is established, and a semi-Markov chain is used to describe the topology switching of the multi-agent system, in which the transfer rate is time-varying. Secondly, based on the past state information, a topology-dependent consensus protocol is established, then the fault-tolerant consensus problem of leader-following multi-agent is transformed into the issue of system stability, according to the mode-dependent Lyapunov function and the finite time stochastic theorem, the sufficient conditions for the stability of the closed-loop system and the constraints of average residence time are obtained. In addition, an initial-state based H ∞ performance index is proposed to reduce the influence of zero initial conditions on the system. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Hidden Semi-Markov Models to Segment Reading Phases from Eye Movements.

Our objective is to analyze scanpaths acquired through participants achieving a reading task aiming at answering a binary question: Is the text related or not to some given target topic? We propose a data-driven method based on hidden semi-Markov chains to segment scanpaths into phases deduced from the model states, which are shown to represent different cognitive strategies: normal reading, fast reading, information search, and slow confirmation. These phases were confirmed using different external covariates, among which semantic information extracted from texts. Analyses highlighted some strong preference of specific participants for specific strategies and more globally, large individual variability in eye-movement characteristics, as accounted for by random effects. As a perspective, the possibility of improving reading models by accounting for possible heterogeneity sources during reading is discussed.

Probabilistic Approach to Modelling, Identification and Prediction of Environmental Pollution

The probabilistic general model of environmental pollution process based on the semi-Markov one is developed and presented in the paper. The semi-Markov chain model approach is based on using prior information to predict the characteristic of some systems. Now, the semi-Markov process is used for the environmental pollution assessment. The methods and procedures to estimate the environmental pollution process’s basic parameters such as the vector of initial probabilities and the matrix of probabilities of transition between the process’s states as well as the methods and procedures to identify the process conditional sojourn times’ distributions at the particular environmental pollution states and their mean values are proposed and defined. Next, the formulae to predict the main characteristics of the environmental pollution process such as the limit values of transient probabilities and mean total sojourn times in the particular states in the fixed time interval are given. Finally, the application of the presented model and methods for modelling, identification and prediction of the air environmental pollution process generated by sulphur dioxide within the exemplary industrial agglomeration is proposed.

Probabilistic optimization of preventive maintenance inspection rates by considering correlations among maintenance costs, duration, and states transition probabilities

Power system degradation has highly motivated utilities to perform preventive maintenance. Inadequate inspection and maintenance could lead to early failures. However, too much of them could be very costly; thus, many studies have been conducted to achieve the optimal inspection and maintenance rates. Previous studies have only considered the transition from a deterioration, repair, or inspection state to another one probabilistically. However, in practice, repair and maintenance costs and duration also vary randomly and are correlated with each other. This study proposes a probabilistic approach by considering all the aforementioned correlations and uncertainties to find the optimal inspection rates. The approach can incorporate the dependent deterioration phenomenon among different system/equipment components in the maintenance process. Additionally, a simple judgment matrix is assumed to estimate the present deterioration state before performing inspections or maintenance activities. The matrix makes classical approaches more usable from a practical point of view. A semi-Markov chain based on Monte Carlo simulations employing 95 percentiles of the total cost is utilized to determine the optimal inspection rates. Finally, the proposed method is applied to the distribution circuit breakers (CBs) of the Roy Billinton test system (RBTS) for illustration. The numerical results show that considering the correlations and uncertainties can change the optimal inspection rates and reduce the calculated costs and/or unavailability in comparison to the conventional approaches. Furthermore, the results indicate that the method is simple and accurate and can be integrated into asset management tools for the maintenance decision-making process.

Evaluation of a joint replenishment policy with sales-based threshold and stochastic demand

In this study, we consider a stochastic joint replenishment problem with Poisson demand, where multiple items are replenished jointly through a common supplier. We study a novel type of joint replenishment policy controlled by a sales threshold, under which new orders are placed to restore every item’s inventory position to a base-stock level when the system’s accumulated sales generated since the last order reach a certain threshold. The sales threshold enables our model to capture multiple items’ value heterogeneity that has been ignored by the quantity-based threshold in traditional joint replenishment control policy. We first characterize the inventory dynamics of the joint replenishment model by the semi-Markov chain method and then provide an approach to evaluate the exact long-run average system inventory-related costs. We further provide an approach to optimize the joint replenishment policy. Numerical experiments are conducted to compare the sales-based threshold policy with the traditional quantity-based threshold policy. Our results show that the sales-based threshold policy can significantly outperform the quantity-based threshold policy, especially for a system with a high holding cost rate, short lead time, low fixed ordering cost, and large heterogeneity among products. This is because the sales-based threshold adds an extra dimension to differentiate the products in addition to the use of different stock levels for multiple items. Our results help practitioners understand the underlying factors that drive the effectiveness of the sales-based threshold policy.

Quantile hidden semi-Markov models for multivariate time series.

This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states’ sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11222-022-10130-1.

Finite-time control of discrete-time semi-Markov jump linear systems: A self-triggered MPC approach

In this paper, a self-triggered model predictive control (MPC) strategy is developed for discrete-time semi-Markov jump linear systems to achieve a desired finite-time performance. To obtain the multi-step predictive states when system mode jumping is subject to the semi-Markov chain, the concept of multi-step semi-Markov kernel is addressed. Meanwhile, a self-triggered scheme is formulated to predict sampling instants automatically and to reduce the computational burden of the on-line solving of MPC. Furthermore, the co-design of the self-triggered scheme and the MPC approach is adjusted to design the control input when keeping the state trajectories within a pre-specified bound over a given time interval. Finally, a numerical example and a population ecological system are introduced to evaluate the effectiveness of the proposed control.

Finite-frequency control for nonlinear semi-Markov jump systems with piecewise transition probabilities

Considering the frequency effect of external disturbances, this paper concerns the finite-frequency control problem for nonlinear semi-Markov jump systems (SMJSs) with piecewise transition probabilities (TPs) via the Takagi–Sugeno (T–S) fuzzy modeling approach. More precisely, the piecewise TPs are assumed to switch stochastically within limits, which implies that the corresponding distributions of sojourn time (ST) also vary randomly. Furthermore, another upper semi-Markov chain is utilized to characterize TPs variation in a finite set. With the aid of Finsler’s lemma and Parseval’s theorem, sufficient criteria for the controlled SMJS are constructed to meet the desired disturbance attenuation performance in the frequency domain. Then, the mode-dependent controllers are developed to use the TP information more efficiently. In particular, a novel matrix method is proposed to decouple the mode-dependent variables and controller gains by selecting slack matrices. Eventually, a numerical example is transmitted to demonstrate the validity and merits of established results.

A two-dimensional maintenance optimization framework balancing hazard risk and energy consumption rates

Numerous power assets, such as power cables and refrigerator, have inevitably confronted with severe energy consumption problems. An essential topic in maintenance engineering of such assets is to balance energy consumption mitigation and malfunction risk control, such that to reduce production/delivery losses. This paper established a novel proactive maintenance framework, which arranges two dimensions of control limits to control maintenance frequencies: (a) operational age and (b) consumption severity to guide repair and spare part replacement. The energy consumption process is structured by a Semi-Markov chain. The asset is preventively replaced upon a certain operational age, or when the unit time energy consumption reaches a pre-specified threshold, given that the time to scheduled age-based replacement is greater than a threshold. The maintenance optimization model is formulated, followed by an in-depth exploration of its analytical structures. The superior performance of the proposed framework over conventional maintenance policies is demonstrated by a numerical experiment on high-voltage power cables.

Asymptotic properties of words in semi-Markov sequences

It is well known that some enzymes, proteins, amino-acids between other biological molecules have more than one way to be coded in the DNA. That means, there are some biological molecules that can be identified by a set of sequences. For instance, the enzyme SmaI can be recognized by the words [Formula: see text] and [Formula: see text]. In this paper, we count the number of times that a biological sequence occurs through the DNA by any of its configurations, i.e. we provide the strong law of large numbers for a word sequence. To achieve our goal, we consider that DNA is modeled by an ergodic semi-Markov chain. We also present the Central Limit Theorem. Additionally, we compute the first hitting position of a set of words.

SMC for Uncertain Discrete-Time Semi-Markov Switching Systems

This brief is concerned with the mode-dependent sliding mode control (SMC) for uncertain discrete-time semi-Markov switching systems (S-MSSs). The switching is governed by a semi-Markov chain with a discrete-time semi-Markov kernel (SMK). First, a sliding mode surface (SMS) is constructed to be related to the current switching mode. Second, by means of the upper bound of the sojourn time (ST), some feasible conditions are derived to guarantee <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -error mean square stability for the corresponding S-MSSs. Third, an appropriate SMC law is established to drive the state onto the specified sliding domain. Finally, an F-404 aircraft model validates the proposed control algorithm.

Injection attack estimation of networked control systems subject to hidden DoS attack

This paper is concerned with the injection attack estimation for a class of networked control systems with Deny-of-Service (DoS) attack, where unknown signals are injected into the sensor reading and actuator. The main goal is to design an estimator to estimate the injected signals subject to stochastic hidden DoS attack. By introducing a semi-Markov chain, the complex aperiodic sampling behavior caused by DoS attack is first modeled as a stochastic switching system. By using the Lyapunov stability theory and stochastic system analysis method, the σ-error mean square stability (σ-EMSS) conditions of estimation error system are then derived and the state of the attack estimation error system is shown to be uniformly ultimately bounded. Some linear matrix inequalities are proposed to determine the estimation gain matrices. Finally, both simulation and experimental studies on the motor system are conducted, and the effectiveness of the main results are demonstrated.

Adaptive Event-Triggered Quantized Communication-Based Distributed Estimation Over Sensor Networks With Semi-Markovian Switching Topologies

This paper presents a distributed state estimation method for nonlinear systems over sensor networks with Semi-Markovian switching topologies (S-MSTs). An adaptive event-triggered quantization scheme (AETQS) is developed to reduce the communication and computation burden for bandwidth-constrained sensor networks, where the quantified measurement data is determined by the specific event triggering condition. The filtering network topology evolves over time, which is assumed to be governed by a Semi-Markov chain. Based on the Semi-Markov kernel theory and Lyapunov stability theory, sufficient conditions are obtained to guarantee that the error dynamics has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -error mean square stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance, which is given in the form of linear matrix inequalities. Then, the optimal disturbance attenuation level, initial triggering thresholds, and elapsed-time-dependent distributed filter gains can be determined by addressing a convex optimization problem. Finally, two numerical examples are presented to verify the effectiveness of the proposed approach.

Energy-Efficient Traffic Steering in Millimeter-Wave Dual Connectivity Discontinuous Reception Framework

The Dual connectivity (DC) technology is a robust solution for Internet service providers (ISP) to evolve their legacy infrastructures with less cost to speed up the progress of fifth-generation (5G) services coverage. DC enables the traditional network to connect to multiple New Radio (NR) Node B (gNBs). A well-known scheme is the non-standalone (NSA) NR. In this case, the user equipment (UEs) could access the network via both the evolved Node B (eNB) and the gNB. However, some research has indicated that the UEs in such a configuration suffer from power consumption problems. UEs are typically configured with discontinuous reception (DRX) mechanism to save power. However, most current systems do not investigate and optimize the DRX parameters. To the authors’ best knowledge, this work is the first to combine DRX with traffic steering for the UEs in the NSA NR system. A traffic steering algorithm is proposed to improve the coordination between the eNB and the gNB. We used a semi-Markov chain model to analyze power consumption and average delay. Compared with standard DRX operated in LTE, NR, and DC, we verified that the proposed model achieves power-saving gains without incurring an additional delay. The results indicated that the UE could save considerable power with an optimized system configuration.

Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields

Probability resembles the ancient Roman God Janus since, like Janus, probability also has a face with two different sides, which correspond to the metaphorical gateways and transitions between the past and the future [...]