Markov Mode Research Articles

Improved dynamic event-triggered [formula omitted] control for networked fuzzy singularly perturbed systems with hidden Markov fading channels

In this paper, the dynamic event-triggered H∞ control problem is explored for networked fuzzy slow sampling singularly perturbed systems (S3PSs) subject to hidden Markov fading channels. To alleviate the communication burden more effectively, an improved dynamic event-triggered scheme (DETS) is constructed for networked fuzzy S3PSs, under which two auxiliary internal dynamic variables are considered into event-triggered condition. The fading channel phenomena with randomly time-varying amplitudes are characterized by the finite state Markov process. Meanwhile, considering the actual network mode may be unmeasurable, a hidden Markov mode detector is exploited to estimate the actual network mode, by which the control signal can be adjusted appropriately. By constructing the singular perturbation parameter (SPP)-dependent Lyapunov functional, sufficient conditions are obtained to guarantee the mean square stability of networked fuzzy S3PSs. Besides, the numerical ill-conditioned problem of networked fuzzy S3PSs can be avoided. Finally, a tunnel diode circuit example is proposed to illustrate the effectiveness of the main results.

Penerapan Metode Grey-Markov(1,1) Untuk Peramalan Penerimaan di Kantor Pengawasan dan Pelayanan Bea Cukai Tipe Madya Pabean Cikarang

The Customs Supervision and Service Office is given a revenue target that must be achieved annually. However, revenue at the Customs Supervision and Service Office tends to fluctuate because it is strongly influenced by various external factors that are difficult to predict. Projections need to be done to see if the given revenue target can be achieved. This study aims to conduct forecasting so that it can be estimated how much revenue will be at the end of the year (December 2023). Research is conducted using the Grey(1,1) and Grey-Markov(1,1) models. The analysis results show that the Grey-Markov(1,1) model provides better forecasting accuracy compared to the Grey(1,1) model with a MAPE value of 5.390541% and a Posterior Error Ratio of 0.190644. These results show that the Grey Markov(1,1) model is more accurate than the Markov(1,1) mode, and that this method (Grey Markov(1,1)) is very good for forecasting with little data.

Antidisturbance Control for Hidden Markovian Jump Systems: Asynchronous Disturbance Observer Approach

This paper investigates the anti-disturbance control issue for a class of Markovian jump systems (MJSs) with matched/mismatched disturbances by using disturbance observer approach. A key feature here is that the external disturbance is considered to be generated by a Markovian jump exogenous dynamics, in which the disturbance mode may not be synchronized with the system mode. Meanwhile, it is supposed that both system and disturbance modes can just be estimated via a hidden Markov mode detector. To overcome the possible obstacle in handling dual hidden Markov modes, a mapping technique for continuous-time Markov chain is provided firstly. Then, a novel asynchronous disturbance observer is developed to estimate the external disturbance by utilizing the detected mode. Based upon the estimated disturbance, asynchronous anti-disturbance controllers are investigated for matched and mismatched disturbance cases, respectively. By employing a decoupling technique with the idea of completing the square, sufficient conditions are established for guaranteeing the stability in probability of the resultant closed-loop systems. Finally, two numerical examples are provided to verify the effectiveness of the proposed asynchronous anti-disturbance control approaches under inaccessible system and disturbance modes.

Output feedback H∞ control for discrete time singularly perturbed systems with Markov lossy network: The round-robin-like protocol case

In this paper, the output feedback H∞ control is investigated for the networked singularly perturbed systems (SPSs) with Markov lossy network, in which the packet loss probability varies in different modes. A new network mode-dependent round-robin-like protocol (RRLP) is introduced to the networked SPSs, which can dynamically adjust the number of the selected sensor nodes according to the network environment condition. Based on this RRLP and Markov lossy network, a Markov mode and scheduling order co-dependent output feedback controller is constructed to ensure the system control performance. By constructing a novel Lyapunov-Krasovskii functional dependent on the singular perturbation parameter, Markov mode, and scheduling order simultaneously, sufficient conditions of mean square stability for SPSs are obtained, and numerical stiffness is avoided. Finally, a direct current motor-controlled inverted pendulum example is proposed to verify the effectiveness of our main results.

Cost-utility analysis of add-on dapagliflozin in heart failure with preserved or mildly reduced ejection fraction.

The DELIVER study demonstrates a significant improvement in cardiovascular death or hospitalization for heart failure among heart failure with mildly reduced ejection fraction (HFmrEF) or heart failure with preserved ejection fraction (HFpEF).Cost-utility of the adjunct use of dapagliflozin to standard therapy among patients with HFpEF or HFmrEF remains unclear. A five-state Markov mode was constructed to project health and clinical outcomes of the adjunct use of dapagliflozin to standard therapy among 65-year-old patients with HFpEF or HFmrEF. A cost-utility analysis was performed based on the DELIVER study and national statistical database. The cost and utility was inflated to 2022 by the usual discount rate of 5%. The primary outcomes were total cost and quality-adjusted life-years (QALYs) per patients as well as the incremental cost-effectiveness ratio. Sensitivity analyses were also applied. Over a 15year lifetime horizon, the average cost per patient was $7245.77 and $5407.55 in the dapagliflozin group and the standard group, along with an incremental cost of $1838.22. The average QALYs per patient was 6.00 QALYs and 5.84 QALYs in the dapagliflozin group and the standard group, along with an incremental QALYs of 0.15 QALYs, resulting in the incremental cost-effectiveness ratio of $11865.33/QALY, which was below the willingness-to-pay (WTP) of $12652.5/QALY. The univariate sensitivity analysis indicated the cardiovascular death in both group was the most sensitive variable. Probability sensitivity analysis revealed that when the WTP thresholds were $12652.5/QALY and $37957.5/QALY, the probabilities of being cost-effective with dapagliflozin as an add-on were 54.6% and 71.6%, respectively. From a public healthcare system perspective, the adjunct use of dapagliflozin to standard therapy among patients with HFpEF or HFmrEF generated advantages in cost-effectiveness in China at a WTP of $12652.5/QALY, which promoted the rational use of dapagliflozin for heart failure.

Finite‐time exponentially extended dissipative filtering for singular time‐delay Markov jump systems with quantized outputs based on hidden Markov mode

AbstractThis article investigates finite‐time exponentially extended dissipative filtering for singular Markov jump systems with time‐varying delays and quantized outputs. The filter and quantizer are both mode‐dependent and their modes are asynchronous with the system modes, which are described by hidden Markov model. A more general performance index named as finite‐time exponentially extended dissipativity is employed to make the concept of extended dissipativity in infinite‐time domain suitable for the finite‐time case. With the aid of a series of novel and effective schemes, sufficient conditions are established to guarantee that the filtering error dynamics are finite‐time stochastically bounded with the exponentially extended dissipative performance. An asynchronous filter is successfully designed by solving a set of linear matrices inequalities. Finally, numerical examples are given to demonstrate the effectiveness of proposed methods.

Improved Dynamic Event-Triggered Control for Nonlinear Systems with Fading Channels

This paper is devoted to the protocol-based control design for nonlinear systems with fading channels. Distinguished from the existing event-triggering criteria associated with only two consecutive packets, an improved dynamic event-triggered protocol is formulated, which accounts for some historical available transmitted packets. As a consequence, the number of triggering times can be reduced efficiently while maintaining desired control performance. Meanwhile, the time-varying fading channel is described by a Markov process within finite space, whose mode can be detected via a hidden Markov mode detector. Based on Lyapunov stability theory, sufficient conditions are derived to achieve the stochastic stability of the closed-loop system. In the end, the validity of the derived results is verified through an application study.

Regulation of Markov Jump Linear Systems Subject to Polytopic Uncertainties

When discrete-time Markov jump linear systems are prone to the damaging effects of polytopic uncertainties, it is necessary to address all the vertices of each Markov mode in order to properly design robust controllers. To this end, we propose a robust recursive linear–quadratic regulator for this class of systems. We define a quadratic min–max optimization problem by combining least-squares and penalty functions in a unified framework. We design a one-step cost function to encompass the entire set of vertices of each mode altogether, while maintaining its quadratic structure and the convexity of the problem. The solution is then obtained recursively and does not require numerical optimization packages. We establish conditions for convergence and stability by extending the matrix structure of the recursive solution. In addition, we provide numerical and real-world application examples to validate our method and to emphasize recursiveness and diminished computational effort.

State-dependent hedge strategy for crude oil spot and futures markets

Relying on the hidden Markov model improved by the particle swarm optimization algorithm (PSO-HMM), we develop a dual-decision method to address the issue of state-dependent futures hedging. Our approach is attractive in two ways. First, it uses the PSO algorithm to overcome the shortcomings of the traditional algorithm, which can easily fall into the local optima to estimate parameters in a hidden Markov mode. Second, this paper proposes a new hedge position adjustment method based on the identified market states, instead of sticking to the hedge position calculated by the commonly used GARCH-type models to achieve a better trade-off between risk hedging and return acquisition. Specifically, we first improve the accuracy of parameter measurement and employ the PSO-HMM to identify two market states, bear and bull, and fully illustrate the rationality and effectiveness of the proposed model. Based on the market states identified, we then adjust the hedge ratio estimated by GARCH-type models and compare the hedging effects of no hedge, model-driven, and state-dependent strategies. Our empirical results show that the PSO-HMM method can improve the accuracy of state identification over the classical HMM. The market state-dependent hedging strategy has better performance than other strategies when it comes to the trade-off between the return and the risk of a hedged portfolio. Furthermore, robustness checks under different conditions confirm that the state-dependent hedging strategy outperforms the model-driven hedging and no hedge strategies. Thus, our research sheds new light on conventional hedging models.

Formula omitted] and [formula omitted] Control with sector bound optimization for Continuous Time Markov Jump Lur’e Systems

This paper addresses the H2 and H∞ control of Markov Jump Systems subject to a class of nonlinearities that include them on the Lur’e system framework, with sector slope optimization. The proposed controllers are robust to nonlinearities belonging to a sector. We propose mode-dependent controllers; in other words, the Markov mode θ(t) is available to controllers. The design of such controllers considers the optimization of the H2 and H∞ costs as well as the sector slope, which determines the class of accepted nonlinearities. The results are illustrated through two practical examples: coupled electrical machines and the semi-active suspension of a quarter car.

Hybrid asynchronous sliding mode control for hidden Markovian jump systems under optimized design

This article is concerned with the hybrid design of transition rates and asynchronous sliding mode control (SMC) law for continuous-time Markovian jump systems with matched disturbances. First, a sufficient condition is established to ensure the stochastic ultimate boundedness (SUB) of the unforced systems, which are driven only by using the designed stabilizing transition rates. Furthermore, by considering the system modes are unavailable for the controller, a hidden Markov mode detector is introduced to emit the detection modes. Based on the mode detection probabilities, a hybrid design approach is proposed by co-designing of transition rates and asynchronous SMC law, which ensures the SUB and disturbance attenuation performance of the resulted closed-loop systems. The obtained sufficient conditions are solved via two iterative optimization algorithms, which combine cone complementarity linearization and genetic algorithm. Finally, a numerical example with three comparison cases is provided to illustrate the proposed results.

Cost-effectiveness analysis of the prevention of mother-to-child transmission of HIV

BackgroundThe number of HIV-positive pregnant women accounted for about 10% of China’s total over the past few years in Liangshan Prefecture, Sichuan province in China. Although cost-effectiveness of the PMTCT of HIV have been evaluated in other previous studies, no specific study has been conducted in Liangshan prefecture, nor has the expenses paid individually by HIV-positive pregnant women been included. The purpose of this study was to evaluate both the short-term and long-term cost-effectiveness of PMTCT of HIV in Liangshan Prefecture from the social perspective.MethodsFrom December 2018 to January 2019, individual expenses and the other costs were collected: individual expenses of 133 recruited HIV-positive pregnant women registered in the National Information System of Prevention of Mother-to-Child Transmission of HIV, Syphilis, and HBV, and the other costs from local maternal and child healthcare hospitals, Centers for Disease Control and Prevention, and general hospitals. The costs, the number of pediatric infections averted from being HIV infected were analyzed. And, Life years gained by pediatric infections averted were calculated by using a life table. Besides, Direct benefit was calculated through a Markov mode. Furthermore, One-way sensitivity analysis was conducted for key variables affecting the benefit–cost ratio.ResultsThe estimated number of pediatric infections averted was 164.The total cost was USD 114.1 million, including direct medical costs, direct non-medical costs, and indirect costs, which were USD 54.2 million, USD 53.4 million, and USD 6.5 million, respectively. 630.6 person-years discounted to 2017 were gained at a 3% annual rate, and cost per life year gained was USD 1809.50. Direct benefits were USD 198.4 million, indirect benefits USD 82.5 million, and the benefit–cost ratio was 1.5. The sensitivity analysis showed that if PMTCT costs hypothetically ranged from USD 85.6 million to USD 142.6 million, benefit–cost ratio would vary from 1.0 to 2.3.ConclusionsPMTCT of HIV in Liangshan Prefecture was very cost-effective. It was a great economic burden of PMTCT on HIV-positive pregnant women and their families to take individual expenses. Therefore, it could be suggested that individual expenses should be covered as much as possible by different types of financing.

Noninvasive prenatal prediction of fetal haplotype with Spearman rank correlation analysis model.

BackgroundNoninvasive prenatal testing (NIPT) has been widely used clinically to detect fetal chromosomal aneuploidy with high accuracy rates, gradually replacing traditional serological screening. However, the application of NIPT for monogenic diseases is still in an immature stage of exploration. The detection of mutations in peripheral blood of pregnant women requires precise qualitative and quantitative techniques, which limits its application. The bioinformatic strategies based on the SNP (single nucleotide polymorphism) linkage analysis are more practical, which can be divided into two types depending on whether proband information is needed. Hidden Markov Mode (HMM) and Sequential probability ratio test (SPRT) are suitable for families with probands. In contrast, methods based on databases and population demographic information are suitable for families without probands.MethodsIn this study, we proposed a Spearman rank correlation analysis method to infer the fetal haplotypes based on core family information. Allele frequencies of SNPs that were used to construct parental haplotypes were calculated as sets of nonparametric variables, in contrast to their theoretical values represented by a fetal fraction (FF). The effects on the calculation of the fetal concentration of two DNA enrichment methods, multiple‐PCR amplification, and targeted hybrid capture, were compared, and the heterozygosity distribution of SNPs within pedigrees was analyzed to reveal the best conditions for the model application.ResultsPredictions of the paternal haplotype inheritance were in line with expectations for both DNA library construction methods, while for maternal haplotype inheritance prediction, the rates were 96.55% for method multiple‐PCR amplification and 95.8% for method targeted hybrid capture.ConclusionPositive prediction rates showed that the maternal haplotype prediction was not as accurate as paternal one, due to the large amount of maternal noise in the mother's peripheral blood. Although this model is relatively immature, it provides a new perspective for noninvasive prenatal clinical tests of monogenic diseases.

Optimized hybrid design with stabilizing transition probability for stochastic Markovian jump systems under hidden Markov mode detector

AbstractThe transition probability synthesis problem is addressed for discrete‐time Markovian jump linear system (MJLS) with state‐dependent multiplicative noises. The proposed mode‐dependent parametric approach is employed to derive the necessary and sufficient condition for ensuring the existence of the stabilizing transition probability matrix (TPM). A key feature here is that the system mode is considered to be unavailable to the controller but can just be observed via a hidden Markov mode detector. To this end, a hybrid design is developed by co‐designing the stabilizing TPM and the asynchronous mode‐dependent state‐feedback controller. A rank‐constrained nonconvex problem is formulated to solve the hybrid design strategy. Specifically, a binary genetic algorithm (GA) is introduced for overcoming the computation difficulties arising from searching optimized mode‐dependent parameters. Finally, two numerical examples are provided to verify the effectiveness and advantages of the proposed hybrid design strategy via GA.

Observer‐based adaptive neural networks control for Markovian jump nonlinear systems with partial mode information and input saturation

AbstractThe observer‐based adaptive neural networks control problem is studied in this article for nonlinear Markovian jump systems (MJSs) with partial mode information and input saturation. The existing adaptive control scheme for MJSs works only when the Markov mode of system is completely known. For this reason, the concept of partial mode information of Markov chain is embedded into the framework of adaptive backstepping method and then a mode detector is set to emit the mode. To achieve the control objective, only the emitted mode is used to design the state observer and adaptive control scheme. Besides, an auxiliary signal is introduced in MJSs to compensate the effect of input saturation and this signal appears in controller as the input of neural networks instead of a separate term, which makes the form of proposed controller simpler than that in the literature. Finally, a numerical example and a practical example are provided to demonstrate the feasibility of our control scheme.

Модель реального обменного курса рубля с марковскими переключениями режимов (Model of the Real Exchange Rate of the Ruble With Markov Mode Switches)

Russian Abstract: В работе анализируется взаимосвязь реального обменного курса рубля и реальных цен на нефть на основе модели коррекции ошибок с марковскими переключениями режимов, позволяющей учесть изменения политики курсообразования. Показано, что в период 1999-2018 гг. хорошо разделяются два режима динамики реального курса: с быстрым и медленным приспособлением к долгосрочному равновесию в ответ на шоки цены нефти. При этом не отвергается гипотеза о том, что долгосрочная взаимосвязь между реальным обменным курсом и ценой на нефть инвариантна к изменению режима. Также показано, что, несмотря на переход к плавающему обменному курсу, в последние годы периодически идентифицируется режим негибкого курсообразования, что может быть связано с новым бюджетным правилом, согласно которому с февраля 2017 г. Минфин России ежемесячно покупал иностранную валюту в объеме превышения фактических поступлений нефтегазовых доходов над уровнем нефтегазовых доходов федерального бюджета, сформированного при цене на нефть марки “Юралс” 40 долларов США за баррель. English Abstract: The paper analyzes the relationship between the real Russian ruble exchange rate and real oil prices using the error correction model with Markov regime switching, which allows for changes in exchange rate policy. It is found that during the period 1999-2018 real exchange rate dynamics was characterized by two clearly distinguishable regimes, one with fast and the other with slow adjustment to long-term equilibrium in response to oil price shocks. Further model testing shows that long-term relationship between real exchange rate and oil price is invariant to regime change. It is also found that, despite adoption of a floating exchange rate policy in 2014, inflexible real exchange rate regime has been periodically identified in recent years. This could be due to the new budget rule, according to which Russian Ministry of Finance in February 2017 started purchasing foreign currencies in amount of excess oil and gas earnings of the federal budget.

Genetic-Algorithm-Assisted Sliding-Mode Control for Networked State-Saturated Systems Over Hidden Markov Fading Channels.

The sliding-mode control (SMC) problem is studied in this article for state-saturated systems over a class of time-varying fading channels. The underlying fading channels, whose channel fading amplitudes (characterized by the expectation and variance) are allowed to be different, are modeled as a finite-state Markov process. A key feature of the problem addressed is to use a hidden Markov mode detector to estimate the actual network mode. The novel model of hidden Markov fading channels (HMFCs) is shown to be more general yet practical than the existing fading channel models. Based on a linear sliding surface, a switching-type SMC law is dedicatedly constructed by just using the estimated network mode. By exploiting the concept of stochastic Lyapunov stability and the approach of hidden Markov models, sufficient conditions are obtained for the resultant SMC systems that ensure both the mean-square stability and the reachability with a sliding region. With the aid of the Hadamard product, a binary genetic algorithm (GA) is developed to solve the proposed SMC design problem subject to some nonconvex constraints induced by the state saturations and the fading channels, where the proposed GA is based on the objective function for optimal reachability. Finally, a numerical example is employed to verify the proposed GA-assisted SMC scheme over the HMFCs.

Asynchronous H∞ control for uncertain singular stochastic Markov jump systems with multiplicative noise based on hidden Markov mode

This paper is dedicated to the asynchronous H∞ output feedback control for a class of discrete-time uncertain singular stochastic Markov jump systems (SSMJSs) with multiplicative noise. The parametric uncertainties here are allowed to be norm-bounded. The asynchronous phenomenon between original modes and controller modes leads to the resultant closed-loop system constructing a hidden Markov model (HMM). A convinced and detailed proof for the first time is proposed to ensure nominal SSMJSs with multiplicative noise and completely known information to be stochastically admissible with a prescribed H∞ performance. To conquer the nonlinear difficulties incurred by the coupling of Lyapunov variables and controller gains, several effective strategies such as the matrix augmentation, special decomposition and introduction of auxiliary matrices are used. Furthermore, even in the simultaneous presence of singularity, multiplicative noise, parametric uncertainties as well as partial observation information, an asynchronous output feedback controller is successfully designed such that the uncertain SSMJS with multiplicative noise is stochastically admissible while achieving the required H∞ performance. Finally, numerical examples are presented to demonstrate the effectiveness of proposed results.

Prediction of Road Traffic Accidents based on Rolling-optimized Grey Markov Mode

In order to solve the problem that the accuracy of the accident prediction is affected by the time-effectiveness of the forecast data, the paper introduces the rolling optimization strategy based on the original data of the road traffic accident in the road section, and further establishes the rolling optimization-grey Markov dynamic prediction model. Using the Markov chain theory to explore the transition law between different states, the development trend of road traffic accidents volume is predicted, and the prediction accuracy of the random time series is further improved. Case analysis proves that the method has better prediction accuracy and practicability over a certain period of time, which can provide reference for road traffic accident prediction analysis and traffic safety early warning

Hidden Markov Model Based Fault Detection for Networked Singularly Perturbed Systems

Based on a hidden Markov model (HMM), the issue of fault detection (FD) is investigated for singularly perturbed systems with their measurements transmitted over a bandwidth-limited communication network. A homogeneous Markov chain is adopted to model packet dropouts and time delays simultaneously, whose mode transition probabilities are assumed to be partially unknown. The discrepancies between the Markov modes and their observed ones have been noted, which are reflected by a hidden Markov process. An HMM-based FD filter (FDF) is aimed to be designed such that the stochastic stability and prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance are ensured for the resulting filtering error dynamics of FD. A new Lyapunov-Krasovskii functional is constructed, which is with the Markov mode and the singular perturbation parameter (SPP). With the aid of up-to-date techniques in handing time delays, a sufficient condition based on linear matrix inequalities (LMIs) is derived which provides a design scheme of such an FDF. The FDF parameters are given and the SPP's admissible bounds are evaluated when the LMIs have feasible solutions. The performance of the designed FDF is demonstrated by two examples.