Showing papers on "Markov chain published in 2023"

Non-Fragile <i>H</i>∞ Synchronization for Markov Jump Singularly Perturbed Coupled Neural Networks Subject to Double-Layer Switching Regulation

Abstract: This work explores the H∞ synchronization issue for singularly perturbed coupled neural networks (SPCNNs) affected by both nonlinear constraints and gain uncertainties, in which a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used. The first layer of switching regulation is the Markov chain to characterize the switching stochastic properties of the systems suffering from random component failures and sudden environmental disturbances. Meanwhile, PDTSR, as the second-layer switching regulation, is used to depict the variations in the transition probability of the aforementioned Markov chain. For systems under double-layer switching regulation, the purpose of the addressed issue is to design a mode-dependent synchronization controller for the network with the desired controller gains calculated by solving convex optimization problems. As such, new sufficient conditions are established to ensure that the synchronization error systems are mean-square exponentially stable with a specified level of the H∞ performance. Eventually, the solvability and validity of the proposed control scheme are illustrated through a numerical simulation.

SMC for Discrete-Time Nonlinear Semi-Markovian Switching Systems With Partly Unknown Semi-Markov Kernel

Abstract: This article is devoted to the discrete-time sliding mode control (DSMC) for nonlinear semi-Markovian switching systems (S-MSSs). Motivated by the fact that the complete information of the semi-Markov Kernel is difficult to be obtained in practical applications, it is recognized to be partly unknown as the most common mean. By utilizing the prior information of the sojourn-time upper bound for each switching mode, sufficient conditions under the equivalent DSMC law are proposed for the mean square stability. Moreover, the designed DSMC law realizes the finite-time reachability of the sliding region, and makes the sliding dynamics converge to the predesignated sliding region in a finite time. In the end, a numerical example and an electronic throttle model are given to validate the proposed control strategy.

Distributed Filtering for Semi-Markov-Type Sensor Networks With Hybrid Sojourn-Time Distributions—A Nonmonotonic Approach

Abstract: This article examines the distributed filtering problem for a general class of filtering systems consisting of distributed time-delayed plant and filtering networks with semi-Markov-type topology switching (SMTTS). The SMTTS implies the topology sojourn time can be a hybrid function of different types of probabilistic distributions, typically, binomial distribution used to model unreliable communication links between the filtering nodes and Weibull distribution employed to depict the cumulative abrasion failure. First, by properly constructing a sojourn-time-dependent Lyapunov–Krasovski function (STDLKF), both time-varying topology-dependent filter and topology-dependent filter are designed. Second, a novel nonmonotonic approach with less design conservatism is developed by relaxing the monotonic requirement of STDLKF within each topology sojourn time. Moreover, an algorithm with less computational effort is proposed to generate a semi-Markov chain from a given Markov renewal chain. Simulation examples, including a microgrid islanded system, are presented to testify the generality and elucidate the practical potential of the nonmonotonic approach.

Event-Triggered Control for Markov Jump Systems Subject to Mismatched Modes and Strict Dissipativity

Abstract: In order to save network resources of discrete-time Markov jump systems, an event-triggered control framework is employed in this article. The threshold parameter in the event-triggered mechanism is designed as a diagonal matrix in which all elements can be adjusted according to system performance requirements. The hidden Markov model is introduced to characterize the asynchronization between the controller and controlled system. The effect of randomly occurring gain fluctuations is taken into account during the controller design. For the purpose of guaranteeing that the closed-loop system is stochastically stable and satisfies the strictly $(\mathcal {D}_{1},\mathcal {D}_{2},\mathcal {D}_{3})-\gamma -$ dissipative performance, sufficient conditions are constructed by employing the Lyapunov function and stochastic analysis. After linearization, the proposed controller gains are obtained by solving the linear matrix inequalities. Ultimately, a practical example of the dc motor device is used to illustrate the effectiveness of the proposed new design technique.

Output-Feedback Control for Fuzzy Singularly Perturbed Systems: A Nonhomogeneous Stochastic Communication Protocol Approach

Abstract: In this study, the output-feedback control (OFC) strategy design problem is explored for a type of Takagi–Sugeno fuzzy singular perturbed system. To alleviate the communication load and improve the reliability of signal transmission, a novel stochastic communication protocol (SCP) is proposed. In particular, the SCP is scheduled based on a nonhomogeneous Markov chain, where the time-varying transition probability matrix is characterized by a polytope-structure-based set. Different from the existing homogeneous Markov SCP, a nonhomogeneous Markov SCP depicts the data transmission in a more reasonable manner. To detect the actual network mode, a hidden Markov process observer is addressed. By virtue of the hidden Markov model with partly unidentified detection probabilities, an asynchronous OFC law is formulated. By establishing a novel Lyapunov–Krasovskii functional with a singular perturbation parameter and a nonhomogeneous Markov process, a sufficient condition is exploited to guarantee the stochastic stability of the resulting system, and the solution for the asynchronous controller is portrayed. Eventually, the validity of the attained methodology is expressed through a practical example.

Analytically pricing exchange options with stochastic liquidity and regime switching

Abstract: We investigate the valuation of exchange options when the market is affected by changing economic conditions as well as liquidity risks. The volatility and expected returns of both stocks are assumed to be controlled by a continuous-time Markov chain to reflect the effects of varying economic conditions, and a liquidity discounting factor is employed to capture the impact of market liquidity on stock prices. Once the model has been established, we construct a risk-neutral measure with the use of regime-switching Esscher transform, and the characteristic function is then derived in an analytical form, so that a closed-form formula for exchange options can be presented. We further analyze the effects of the two considered factors on exchange option prices numerically.

Fast Markov Clustering Algorithm Based on Belief Dynamics

Abstract: Graph clustering is one of the most significant, challenging, and valuable topic in the analysis of real complex networks. To detect the cluster configuration accurately and efficiently, we propose a new Markov clustering algorithm based on the limit state of the belief dynamics model. First, we present a new belief dynamics model, which focuses beliefs of multicontent and randomly broadcasting information. A strict proof is provided for the convergence of nodes’ normalized beliefs in complex networks. Second, we introduce a new Markov clustering algorithm (denoted as BMCL) by employing a belief dynamics model, which guarantees the ideal cluster configuration. Following the trajectory of the belief convergence, each node is mapped into the corresponding cluster repeatedly. The proposed BMCL algorithm is highly efficient: the convergence speed of the proposed algorithm researches $O(TN)$ in sparse networks. Last, we implement several experiments to evaluate the performance of the proposed methods.

Investigating zero-state and steady-state performance of MEWMA-CoDa control chart using variable sampling interval

Abstract: Traditional process monitoring control charts (CCs) focused on sampling methods using fixed sampling intervals (FSIs). The variable sampling intervals (VSIs) scheme is receiving increasing attention, in which the sampling interval (SI) length varies according to the process monitoring statistics. A shorter SI is considered when the process quality indicates the possibility of an out-of-control (OOC) situation; otherwise, a longer SI is preferred. The VSI multivariate exponentially moving average for compositional data (VSI-MEWMACoDa) CC based on a coordinate representation using isometric log-ratio (ilr) transformation is proposed in this study. A methodology is proposed to obtain the optimal parameters by considering the zero-state (ZS) average time to signal (ZATS) and the steady-state (SS) average time to signal (SATS). The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain (CTMC) method for both cases, the ZS and the SS using a fixed value of in-control (IC) ATS0. Simulation results demonstrate that the VSI-MEWMACoDa CC has significantly decreased the OOC average time to signal (ATS) than the FSIMEWMACoDa CC. Moreover, it is found that the number of variables (d) has a negative impact on the ATS of the VSI-MEWMACoDa CC, and the subgroup size (n) has a mildly positive impact on the ATS of the VSI-MEWMACoDa CC. At the same time, the SATS of the VSI-MEWMACoDa CC is less than the ZATS of the VSI-MEWMACoDa CC for all the values of n and d. The proposed VSI-MEWMACoDa CC under steady-State performs effectively compared to its competitors, such as the FSI-MEWMACoDa CC, the VSI-T2CoDa CC and the FSI-T2CoDa CC. An example of an industrial problem from a plant in Europe is also given to study the statistical significance of the VSI-MEWMACoDa CC.

UAV-Assisted Task Offloading in Vehicular Edge Computing Networks

Abstract: Vehicular edge computing (VEC) provides an effective task offloading paradigm by pushing cloud resources to the vehicular network edges, e.g., road side units (RSUs). However, overloaded RSUs are likely to occur especially in urban aggregation areas, possibly leading to greatly compromised offloading performance. Inspired by this, this paper explores this situation by introducing an unmanned aerial vehicle (UAV) to address the VEC overload problem. Specifically, we formulate a novel online UAV-assisted vehicular task offloading problem to minimize vehicular task delay under the long-term UAV energy constraint. To solve the formulated problem, we first decouple the long-term energy constraint based on the Lyapunov optimization technique. In this way, the problem can be solved in a real-time manner without requiring future information. Then, we construct a Markov chain based on Markov approximation optimization to find out the close-to-optimal UAV-assisted offloading strategies. Furthermore, we derive a mathematical analysis to rigorously demonstrate the offloading performance of the proposed algorithm. Additionally, the simulation results show that the proposed method outperforms the baselines by significantly reducing the vehicular task delay constrained by the long-term UAV energy budget under various system parameters, such as the energy budget and computation workloads.

SimuExplorer: Visual Exploration of Game Simulation in Table Tennis

Abstract: We propose SimuExplorer, a visualization system to help analysts explore how player behaviors impact scoring rates in table tennis. Such analysis is indispensable for analysts and coaches, who aim to formulate training plans that can help players improve. However, it is challenging to identify the impacts of individual behaviors, as well as to understand how these impacts are generated and accumulated gradually over the course of a game. To address these challenges, we worked closely with experts who work for a top national table tennis team to design SimuExplorer. The SimuExplorer system integrates a Markov chain model to simulate individual and cumulative impacts of particular behaviors. It then provides flow and matrix views to help users visualize and interpret these impacts. We demonstrate the usefulness of the system with case studies and expert interviews. The experts think highly of the system and have obtained insights into players’ behaviors using it.

Performance Modelling and Quantitative Analysis of Vehicular Edge Computing With Bursty Task Arrivals

Abstract: The quantitative performance analysis plays a critical role in assessing the capability of vehicular edge computing (VEC) systems to meet the requirements of vehicular applications. However, developing accurate analytical models for VEC systems is extremely challenging due to the unique features of intelligent vehicular applications. Specifically, recent work revealed that the tasks generated by intelligent vehicular applications exhibit a high degree of burstiness, rendering the existing models that were designed based on the assumption of the non-bursty Poisson process unsuitable for VEC systems. To fill this gap, we developed an original analytical model to investigate the performance of VEC systems with bursty task arrivals. To facilitate vehicle cooperation, a new priority-based resource allocation scheme is exploited to schedule the tasks of vehicular applications, which are modelled by a Markov Modulated Poisson Process (MMPP). Next, a multi-state Markov chain is established to investigate the impact of load sharing strategy on the performance of VEC systems. Then, the end-to-end transmission latency is derived based on the proposed model. Comprehensive experiments are conducted to validate the accuracy of this analytical model under various system configurations. Furthermore, the developed model is used as a cost-effective tool to investigate the performance bottleneck of VEC systems.

Coordination for Multienergy Microgrids Using Multiagent Reinforcement Learning

Abstract: Multienergy microgrids (MEMGs) have significant potential to offer high energy utilization efficiency and system flexibility. The coordination of these MEMGs poses challenges due to the various system dynamics and uncertainties and the need to preserve privacy. This article proposes a double auction (DA)-market-based coordination framework. As such, MEMGs can not only schedule their own energy components but also trade energy with others in the DA market. After that, we formulate this problem as Markov games and propose a multiagent reinforcement learning method by making use of the DA market public information to enhance the stability with privacy perseverance. Case studies involving a real-world scenario validate the superior performance of the proposed method in reducing both the energy costs and the carbon emissions.

Chasing collective variables using temporal data-driven strategies

Abstract: Abstract Abstract The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N′-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

H∞Bipartite Synchronization of Double-Layer Markov Switched Cooperation-Competition Neural Networks: A Distributed Dynamic Event-Triggered Mechanism.

Abstract: In this article, the H∞ bipartite synchronization issue is studied for a class of discrete-time coupled switched neural networks with antagonistic interactions via a distributed dynamic event-triggered control scheme. Essentially different from most current literature, the topology switching of the investigated signed graph is governed by a double-layer switching signal, which integrates a flexible deterministic switching regularity, the persistent dwell-time switching, into a Markov chain to represent the variation of transition probability. Considering the coexistence of cooperative and antagonistic interactions among nodes, the bipartite synchronization of which the dynamics of nodes converge to values with the same modulus but the opposite signs is explored. A distributed control strategy based on the dynamic event-triggered mechanism is utilized to achieve this goal. Under this circumstance, the information update of the controller presents an aperiodic manner, and the frequency of data transmission can be reduced extensively. Thereafter, by constructing a novel Lyapunov function depending on both the switching signal and the internal dynamic nonnegative variable of the triggering mechanism, the exponential stability of bipartite synchronization error systems in the mean-square sense is analyzed. Finally, two simulation examples are provided to illustrate the effectiveness of the derived results.

A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems

Abstract: In this article, we present a data-driven learning model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated, which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach. Finally, we show that the data-driven value function of the learning MPC converges from above to its nominal counterpart as the sample size grows to infinity. We illustrate our approach on a numerical example.

Traffic-Driven Epidemic Spreading in Networks: Considering the Transition of Infection From Being Mild to Severe

Abstract: Realistic epidemic spreading is usually driven by traffic flow in networks, which is not captured in classic diffusion models. Moreover, the progress of a node's infection from mild to severe phase has not been particularly addressed in previous epidemic modeling. To address these issues, we propose a novel traffic-driven epidemic spreading model by introducing a new epidemic state, that is, the severe state, which characterizes the serious infection of a node different from the initial mild infection. We derive the dynamic equations of our model with the tools of individual-based mean-field approximation and continuous-time Markov chain. We find that, besides infection and recovery rates, the epidemic threshold of our model is determined by the largest real eigenvalue of a communication frequency matrix we construct. Finally, we study how the epidemic spreading is influenced by representative distributions of infection control resources. In particular, we observe that the uniform and Weibull distributions of control resources, which have very close performance, are much better than the Pareto distribution in suppressing the epidemic spreading.

Coevolution of epidemic and infodemic on higher-order networks

Abstract: Gathering events, e.g., going to gyms and meetings, are ubiquitous and crucial in the spreading phenomena, which induce higher-order interactions, and thus can be described as higher-order networks. Previous studies on the coevolution of epidemic-infodemic dynamics ignored the higher-order interactions in the social system, which affects our understanding of the reality spreading. We propose a mathematical framework for the coevolution of epidemic and infodemic on higher-order networks described by simplicial complex, and introduce the Microscopic Markov Chain Approach (MMCA) and mean-field approach to establish the dynamic process. We study the coevolution mathematical model on both artificial simplicial complex and real-world higher-order networks and find that the higher-order interactions show a ’double-edged sword’ role in shaping epidemic size, which is dependent on the breakout of infodemic. Furthermore, the higher-order networks enrich the phase diagram, inducing the emergence of discontinuous phase transition, hysteresis loop region, double transition and inter-epidemic region.

Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier–Stokes equations: Existence and nonuniqueness

Abstract: We are concerned with the three-dimensional incompressible Navier–Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in L2 we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result, in particular, implies nonuniqueness in law. Second, we prove nonuniqueness of the associated Markov processes in a suitably chosen class of analytically weak solutions satisfying a relaxed form of an energy inequality. Translated to the deterministic setting, we obtain nonuniqueness of the associated semiflows.

An open queueing model for flexible manufacturing systems with multiple part types and general purpose pallets

Abstract: We evaluate the performance of a Flexible Manufacturing System (FMS), that manufactures multiple part types loaded on general purpose pallets. We model the FMS as an open queueing network with restricted capacity. The performance of the queueing network is approximated by applying a generalization of the so-called aggregation method (or flow-equivalent server method) for queueing networks. The resulting R-dimensional Markov process (where R denotes the number of part types) can be analyzed by the matrix-geometric approach. Unfortunately, the proposed method becomes numerically intractable for large values of R. We therefore also present a type aggregation method that reduces solving the R-dimensional problem to solving R two-dimensional problems. Furthermore, we present an alternative way to generalize the aggregation method. In this generalization the multiple part type network is modeled as a network with a single chain in which parts may change class. Numerical results are given to test and compare the accuracy of the three approximation methods.

Multi-Target Markov Boundary Discovery: Theory, Algorithm, and Application

Abstract: Markov boundary (MB) has been widely studied in single-target scenarios. Relatively few works focus on the MB discovery for variable set due to the complex variable relationships, where an MB variable might contain predictive information about several targets. This paper investigates the multi-target MB discovery, aiming to distinguish the common MB variables (shared by multiple targets) and the target-specific MB variables (associated with single targets). Considering the multiplicity of MB, the relation between common MB variables and equivalent information is studied. We find that common MB variables are determined by equivalent information through different mechanisms, which is relevant to the existence of the target correlation. Based on the analysis of these mechanisms, we propose a multi-target MB discovery algorithm to identify these two types of variables, whose variant also achieves superiority and interpretability in feature selection tasks. Extensive experiments demonstrate the efficacy of these contributions.

On the Bimodal Gumbel Model with Application to Environmental Data

Abstract: The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of the Gumbel distribution thatcan be an alternative to model bimodal data. We derive the analytical shapes of the corresponding probability density function and thehazard rate function and provide graphical illustrations. Furthermore, We have discussed the properties of this density such as mode, bimodality, moment generating function and moments. Our results were verified using the Markov chain Monte Carlo simulation method. The maximum likelihood method is used for parameters estimation. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed distribution.