State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.

Analysis on Stochastic Passage Characteristics for Gun Barrel in Shooting Domain

Aiming at some weapon systems with shooting domain,the stochastic passage characteristics of the barrel were studied.On the basis of the exact definition of the stochastic passage characteristics,its opportunity-awaiting time,residence time and stochastic passage period were given by using the transition probability matrix,and they all obeyed the geometry distributions.Their means and variances were also derived,and the relations between the time indexes and the structure and parameters of weapon control system were established.Finally,the creditability of the conclusions was verified by the test data of weapon system in proving ground.

Using Markov chains to predict the natural progression of diabetic retinopathy

AIM: To study the natural progression of diabetic retinopathy in patients with type 2 diabetes.METHODS: This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy(NPDR) were treated.Markov Chains and Chi-square test were used for statistical analysis.RESULTS: We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference(P =0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07 y in moderate NPDR, be in the severe NPDR state for 1.33 y before moving into PDR for roughly8 y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29 y.CONCLUSION: Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR.However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy(PDR) and stay in that state for long periods before transitioning into blindness.

Characterization of geological uncertainties from limited boreholes using copula-based coupled Markov chains for underground construction

This paper proposes an efficient method for quantifying the stratigraphic uncertainties and modeling the geological formations based on boreholes.Two Markov chains are used to describe the soil transitions along different directions,and the transition probability matrices(TPMs)of the Markov chains are analytically expressed by copulas.This copula expression is efficient since it can represent a large TPM by a few unknown parameters.Due to the analytical expression of the TPMs,the likelihood function of the Markov chain model is given in an explicit form.The estimation of the TPMs is then re-casted as a multi-objective constrained optimization problem that aims to maximize the likelihoods of two independent Markov chains subject to a set of parameter constraints.Unlike the method which determines the TPMs by counting the number of transitions between soil types,the proposed method is more statistically sound.Moreover,a random path sampling method is presented to avoid the directional effect problem in simulations.The soil type at a location is inferred from its nearest known neighbors along the cardinal directions.A general form of the conditional probability,based on Pickard’s theorem and Bayes rule,is presented for the soil type generation.The proposed stratigraphic characterization and simulation method is applied to real borehole data collected from a construction site in Wuhan,China.It is illustrated that the proposed method is accurate in prediction and does not show an inclination during simulation.

Estimating Digital Inter-Symbol Interference Channel Blindly Based on the One-Step Branch Transition Rules in Trellises

A novel discrete-time digital inter-symbol interference (ISI) channel blind estimation sub-optimal algorithm is proposed. This algorithm reduces the complexity of the optimal maximum likelihood sequence estimation (MLSE) considerably based on the one-step branch transition rules in trellises, and is suitable for the estimation of the channels with small lengths of ISI.

Prediction of End-Use Energy Consumption in a Region of Northwest China

End-use energy consumption can reflect the industrial development of a country and the living standards of its residents. The study of end-use energy consumption can provide a solid basis for industrial restructuring, energy saving, and emission reduction. In this paper, we analyzed the end-use energy consumption of a region in Northwestern China, and applied the Markov prediction method to forecast the future demand of different types of end-use energy. This provides a reference for the energy structure optimization in the Northwestern China.

Research on pedestrian escape route without visibility based on Markov chain model

It is a pioneering work to use a Markov chain model to study the pedestrian escape route without visibility.In this paper,based on the Markov chain probability transition matrix,the algorithms with random numbers and the spatial-grid,an escape route in a limited invisible space is obtained.Six pace states(standing,crawling,walking,leaping,jogging,and running)are applied to describe the characteristics of pedestrian behaviors.Besides,eight main direction changes are used to describe the transition characteristic of a pedestrian.At the same time,this paper analyzes the escape route from two views,i.e.,pedestrian pace states and directions.The research results show that the Markov chain model is more realistic as a means of studying pedestrian escape routes.

A Markov chain model of mixing kinetics for ternary mixture of dissimilar particulate solids

This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained