Markov Parameters Research Articles

Structured parametric epidemic models

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton–Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number ℛ0 and the stability of the model in the equilibrium is studied using ℛ0 in terms of the model parameters.

Asymptotic stochastic stability of solutions to dynamic systems with Markov parameters

This article analyzes the stability of solutions of stochastic dynamic systems with the entire prehistory and Markov disturbance. A theorem on sufficient conditions of the asymptotic stochastic stability of solutions of such dynamic systems is formulated and proved.

Filtered-dynamic-inversion control for unknown minimum-phase systems with unknown-and-unmeasured disturbances

This article presents a filtered-dynamic-inversion controller for multi-input multi-output linear minimum-phase systems. The controller requires limited model information, specifically, knowledge of the relative degree and the first nonzero Markov parameter. Furthermore, the controller is effective for stabilisation, command following and rejection of unknown-and-unmeasured disturbances. This article analyses the stability and closed-loop performance (i.e. command following error) of filtered dynamic inversion, which is a single-parameter high-parameter-stabilising controller. We show that for sufficiently large parameter the closed-loop is asymptotically stable, and the average power of the performance signal is arbitrarily small.

State Estimation for Nonlinear Discrete-Time Systems with Markov Jumps and Nonhomogeneous Transition Probabilities

State estimation problem is addressed for a class of nonlinear discrete-time systems with Markov parameters and nonhomogeneous transition probabilities (TPs). In this paper, the optimal estimation mechanism of transition probability matrix is proposed in the minimum mean square error sense to show some critical points. Based on this mechanism, the extended Kalman filters are employed as the subfilters to obtain the subestimates with corresponding models. A novel operator which fuses the prior knowledge and the posterior information embedded in observations is developed to modify the posterior mode probabilities. A meaningful example is presented to illustrate the effectiveness of our method.

Cramér-Rao Bounds for Polynomial Signal Estimation Using Sensors With AR(1) Drift

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively studied in the literature, the loss of estimation performance due to systematic errors like drift have rarely been looked into. In this paper, we derive closed-form Fisher Information matrix and subsequently Cram\'er-Rao bounds (upto reasonable approximation) for the estimation accuracy of drift-corrupted signals. We assume a polynomial time-series as the representative signal and an autoregressive process model for the drift. When the Markov parameter for drift \rho<1, we show that the first-order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. For \rho=1, i.e., when the drift is non-stationary, we show that the constant part of a signal can only be estimated inconsistently (non-zero asymptotic variance). Practical usage of the results are demonstrated through the analysis of 1) networks with multiple sensors and 2) bandwidth limited networks communicating only quantized observations.

Decreasing the damage in smart structures using integrated online DDA/ISMP and semi-active control

Integrated structural health monitoring (SHM) and vibration control has been considered recently by researchers. Up to now, all of the research in the field of integrated SHM and vibration control has been conducted using control devices and control algorithms to enhance system identification and damage detection. In this study, online SHM is used to improve the performance of structural vibration control, unlike previous research. Also, a proposed algorithm including integrated online SHM and a semi-active control strategy is used to reduce both damage and seismic response of the main structure due to strong seismic disturbance. In the proposed algorithm the nonlinear behavior of the building structure is simulated during the excitation. Then, using the measured data and the damage detection algorithm based on identified system Markov parameters (DDA/ISMP), a method proposed by the authors, damage corresponding to axial and bending stiffness of all structural elements is identified. In this study, a 20 t MR damper is employed as a control device to mitigate both damage and dynamic response of the building structure. Also, the interaction between SHM and a semi-active control strategy is assessed. To illustrate the efficiency of the proposed algorithm, a two bay two story steel braced frame structure is used. By defining the damage index and damage rate index, the input current of the MR damper is generated using a fuzzy logic controller. The obtained results show that the possibility of smart building creation is provided using the proposed algorithm. In comparison to the widely used strategy of only vibration control, it is shown that the proposed algorithm is more effective. Furthermore, in the proposed algorithm, the total consumed current intensity and generated control forces are considerably less than for the strategy of only vibration control.

A particle-filter information potential method for tracking and monitoring maneuvering targets using a mobile sensor agent

The problem of tracking and monitoring moving targets using mobile sensor agents (MSAs) is relevant to a variety of applications, including monitoring of endangered species, civilian security, and military surveillance. This paper presents a new information potential field approach for computing the motion plans and control inputs of a MSA, based on the feedback obtained from a modified particle filter used for tracking multiple moving targets in a region of interest. A modified particle filter is presented that implements a new sampling method based on supporting intervals of normal probability density functions. The method accounts for the latest sensor measurements by adapting a mixture representation of the target probability density functions (PDFs). The target motion is modeled as a semi-Markov jump process, such that the target PDFs, or the PDFs of the Markov parameters, can be updated based on real-time sensor measurements by a centralized processing unit or MSAs supervisor. A new information potential method is presented that computes an artificial potential function based on the output of the modified particle filter. Using this artificial potential, the sensors compute feedback control inputs that allow them to track and monitor a maneuvering target over time, using a bounded field of view (FOV).

Damage detection algorithm based on identified system Markov parameters (DDA/ISMP) in building structures with limited sensors

In this study, a new approach for global/local damage detection in a finite element model of structures, with limited sensors, is proposed using identified system Markov parameters. The proposed damage detection is directly related to the Markov parameters, locations of actuators and sensors. Also there is no explicit relation between DDA/ISMP and mode shapes. So, it is unnecessary to install a sensor at each DOF for measuring output to identify mode shapes unlike the other damage detection techniques in which mode shapes play an important role in damage identification. The stiffness of all elements of a structure is identified using the proposed DDA/ISMP. The effects of noise, numbers and locations of sensors on the identification precision are investigated. The results demonstrate that, with the limited sensors and the noise contamination in the measured responses, the DDA/ISMP can effectively identify the locations, types and quantities of damages, both locally and globally. To illustrate the efficiency of DDA/ISMP, a four-storey steel moment frame structure and a five-storey shear building are used. Our numerical results show that the DDA/ISMP technique in damage detection is more effective than the scheme proposed by Xu et al. Also, the time consumed in DDA/ISMP is considerably less than the method introduced by Xu.

From polynomial matrices to markov parameters and back: Theory and numerical algorithms

We consider polynomial matrix representations of MIMO linear systems and their connection to Markov parameters. Specifically, we consider polynomial matrix models in an arbitrary operator ρ, and develop theory and numerical algorithms for transforming polynomial matrix models into Markov parameter models, and vice versa. We also provide numerical examples to illustrate the proposed algorithms.

Formula omitted] robust and networked control of discrete-time MJLS through LMIs

This paper addresses the H∞ state-feedback control of Markov Jump Linear Systems (MJLS) through Linear Matrix Inequalities (LMIs). First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This result allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than the one already available. For the case where each transition probability is considered unknown and belonging to a given interval, we also prove that our conditions are less conservative than a previous result from the literature. Under cluster availability of the Markov modes, we incorporate several models for measurement transmission network channels, such as the generalized Gilbert–Elliot, Fritchman or McCullough ones, into the MJLS framework. An example is solved for illustration and comparisons.

Modeling Electromechanical Overcurrent Relays Using Singular Value Decomposition

This paper presents a practical and effective novel approach to curve fit electromechanical (EM) overcurrent (OC) relay characteristics. Based on singular value decomposition (SVD), the curves are fitted with equation in state space under modal coordinates. The relationships between transfer function and Markov parameters are adopted in this research to represent the characteristic curves of EM OC relays. This study applies the proposed method to two EM OC relays: the GE IAC51 relay with moderately inverse‐time characteristic and the ABB CO‐8 relay with inverse‐time characteristic. The maximum absolute values of errors of hundreds of sample points taken from four time dial settings (TDS) for each relay between the actual characteristic curves and the corresponding values from the curve‐fitting equations are within the range of 10 milliseconds. Finally, this study compares the SVD with the adaptive network and fuzzy inference system (ANFIS) to demonstrate its accuracy and identification robustness.

Sylvester Equations and the Factorization of the Error System in Krylov Subspace Methods

AbstractThis paper presents a factorization of the error system that arises in model reduction of linear time invariant systems by Krylov subspace methods. The factorization is introduced for reduced models that match moments and/or Markov parameters of the original system with multiple inputs and outputs. Furthermore, dual results are given for the reduction with input and output Krylov subspaces. To this end, this work constitutes a generalization of [Wolf et al. (2011)] where the factorization was first presented for a special case. The results emerge from an investigation of the Sylvester equations that arise in the context of Krylov subspaces. To that effect, previous results on Sylvester equations are revised and extended in this paper. The theoretic results on Krylov subspaces that are presented here can be useful in error analysis and in the selection of expansion points in Krylov-based model order reduction.

Autonomous Decentralized System Identification by Markov Parameter Estimation Using Distributed Smart Wireless Sensor Networks

Decentralized data processing has the benefit of improving wireless monitoring system scalability, reducing the amount of wireless communications, and reducing overall power consumption. In this study, a system identification strategy for single-input multi-output (SIMO) subspace system identification is proposed based on Markov parameters. The method is specifically customized for embedment within the decentralized computational framework of a wireless sensor network. By using the computational resources of wireless sensors, individual sensor nodes perform local data processing to identify the Markov parameters of a structural system. The data storage and wireless communication requirements of Markov parameters are significantly less than that required by the original raw data, resulting in the preservation of scarce system resources such as communication bandwidth and battery power. Then, the estimated Markov parameters are wirelessly communicated to a wireless sensor network base station where the global structural properties are assembled by execution of the eigensystem realization algorithm, an indirect subspace system identification method. The proposed strategy is evaluated using input-output and output-only data recorded during dynamic testing of a cantilevered balcony in a historic building (Hill Auditorium, Ann Arbor, MI).

Probing the NASA Generic Transport Aircraft in Real-Time for Health Monitoring

This brief paper describes the development of a pulse compression probing algorithm for real-time monitoring of nonlinear dynamic systems. The probing outputs of a system being monitored are estimates of the sequences of Markov parameters at the current operating point. By imposing signal to noise ratios at both the controlled outputs and the probing outputs, the probing inputs are designed to be non-intrusive and with the intention that the resulting probing outputs are unaffected by other applied signals to the system. The probing algorithm is implemented on a Virtex-5 field-programmable gate-array evaluation platform to expedite real-time processing, and is applied to monitoring the health of the NASA Generic Transport Aircraft Model (GTM). Samples of probing output residuals are evaluated using the Hotelling'sT2-test for change detection when significant noise is present in the system. This brief paper focuses its discussion on the method of rapid collection of independent samples to reduce detection delay.

Asymptotics of the state vector of delayed impulsive diffusion systems with Markov parameters

The sufficient conditions of the global asymptotic stochastic stability and global asymptotic p-stability are obtained for delayed diffusion dynamic systems of random structure with Markov-chain type external impulsive disturbances. The results are illustrated by three stochastic models that describe real objects.

A 2D systems approach to iterative learning control for discrete linear processes with zero Markov parameters

In this article a new approach to iterative learning control for the practically relevant case of deterministic discrete linear plants with uniform rank greater than unity is developed. The analysis is undertaken in a 2D systems setting that, by using a strong form of stability for linear repetitive processes, allows simultaneous consideration of both trial-to-trial error convergence and along the trial performance, resulting in design algorithms that can be computed using linear matrix inequalities (LMIs). Finally, the control laws are experimentally verified on a gantry robot that replicates a pick and place operation commonly found in a number of applications to which iterative learning control is applicable.

A discriminative model-constrained EM approach to 3D MRI brain tissue classification and intensity non-uniformity correction

We describe a fully automated method for tissue classification, which is the segmentation into cerebral gray matter (GM), cerebral white matter (WM), and cerebral spinal fluid (CSF), and intensity non-uniformity (INU) correction in brain magnetic resonance imaging (MRI) volumes. It combines supervised MRI modality-specific discriminative modeling and unsupervised statistical expectation maximization (EM) segmentation into an integrated Bayesian framework. While both the parametric observation models and the non-parametrically modeled INUs are estimated via EM during segmentation itself, a Markov random field (MRF) prior model regularizes segmentation and parameter estimation. Firstly, the regularization takes into account knowledge about spatial and appearance-related homogeneity of segments in terms of pairwise clique potentials of adjacent voxels. Secondly and more importantly, patient-specific knowledge about the global spatial distribution of brain tissue is incorporated into the segmentation process via unary clique potentials. They are based on a strong discriminative model provided by a probabilistic boosting tree (PBT) for classifying image voxels. It relies on the surrounding context and alignment-based features derived from a probabilistic anatomical atlas. The context considered is encoded by 3D Haar-like features of reduced INU sensitivity. Alignment is carried out fully automatically by means of an affine registration algorithm minimizing cross-correlation. Both types of features do not immediately use the observed intensities provided by the MRI modality but instead rely on specifically transformed features, which are less sensitive to MRI artifacts. Detailed quantitative evaluations on standard phantom scans and standard real-world data show the accuracy and robustness of the proposed method. They also demonstrate relative superiority in comparison to other state-of-the-art approaches to this kind of computational task: our method achieves average Dice coefficients of 0.93 ± 0.03 (WM) and 0.90 ± 0.05 (GM) on simulated mono-spectral and 0.94 ± 0.02 (WM) and 0.92 ± 0.04 (GM) on simulated multi-spectral data from the BrainWeb repository. The scores are 0.81 ± 0.09 (WM) and 0.82 ± 0.06 (GM) and 0.87 ± 0.05 (WM) and 0.83 ± 0.12 (GM) for the two collections of real-world data sets—consisting of 20 and 18 volumes, respectively—provided by the Internet Brain Segmentation Repository.

H∞ State Feedback Control of Discrete-time Markov Jump Linear Systems through Linear Matrix Inequalities

AbstractThis paper addresses the H∞ state-feedback control design problem of discrete-time Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This results allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than one available in the current literature. An example is solved for illustration and comparisons.

Finite zeros of positive linear continuous-time systems

The notion of finite zeros of continuous-time positive linear systems is introduced. It is shown that such zeros are real numbers. It is also shown that a square positive strictly proper or proper system of uniform rank with observability matrix of full column rank has no finite zeros. The problem of zeroing the system output for positive systems is defined. It is shown that a square positive strictly proper or proper system of uniform rank with observability matrix of full column rank has no nontrivial output-zeroing inputs. The obtained results remain valid for non-square positive systems with the first nonzero Markov parameter of full column rank.

Decision Making Platform Supported on ICTs: Application to the Management of Ground Handling Operations at an Airport

AbstractThe required harmonization of information and communication technologies (ICTs) with operational decision-making demands new alignment software techniques, especially at shop floor level. This alignment exists when people, systems, processes and technology are properly positioned to support company strategies; which in turn support the overall mission and goals. But the required integration is not easy as physical elements, implementation platforms and shop floor management operate as black boxes with a conspicuous lack of information sharing. In order to face this situation, this paper proposes the use in environmental alignment of concepts and technologies coming from manufacturing control. The application of an agent-based alignment supported by new “Visibility Frameworks” (as EPC Information Services) in scheduling levels is presented. A layered agent space is used in adapted platforms, where the interaction protocol between them and the decision making process, are based on sharing Markov reward parameters. This paper proposes the use of Markov parameters so as to maintain the system aligned, reflecting the company's global policy guidelines in every single decision taken in the plant, terminal or logistic centre. A software tool has been developed/deployed by which it has been possible to test these new ideas in the ground handling management of the Ciudad Real Central Airport.