Mohammad Sahadet Hossain - Academia.edu (original) (raw)

Papers by Mohammad Sahadet Hossain

Periodic control systems are of interest in many engineering and mechanical research. Many import... more Periodic control systems are of interest in many engineering and mechanical research. Many important analysis of periodic control systems directly links to the periodic matrix equations, i.e., periodic Lyapunov equations or periodic Riccati equations. This paper represents the iterative methods for solving a class of periodic Lyapunov equation, known as periodic projected discrete-time Lyapunov equation. A remarkable contribution of these types of equations are seen in control problems with periodic setting, and also in dimension reduction of periodic systems in descriptor forms. We explore the Smith iterations for the iterative solution of the projected discrete-time algebraic Lyapunov equation and analyze the cyclic and repeated structure of the periodic matrices to ensure the recursive computation of the periodic solutions. We also introduce an algorithm for computing the low-rank approximations of those iterative solutions. Computational results are illustrated at the end to rep...

In this paper, we establish a model reduction technique for periodic discrete-time descriptor sys... more In this paper, we establish a model reduction technique for periodic discrete-time descriptor systems exploiting the generalized inverses of the periodic singular matrix pairs associated with the systems. We compute the generalized inverses of periodic singular matrix pairs to implement a structure preserving iterative method for the solution of the periodic projected Lyapunov equations that arise in analysis and modelling of periodic discrete-time descriptor systems. We extend the Smith method to solve the large scale projected periodic discrete-time algebraic Lyapunov equations in lifted form. A low-rank version of this method is also presented, which avoids the explicit lifted formulation and works directly with the period matrix coefficients. Moreover, we consider an application of the Lyapunov solvers in balanced truncation model reduction of periodic discrete-time descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.

− In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. S... more − In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives lowrank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems. Keywords− LTI descriptor system, suboptimal shift parameter, Lyapunov equation, low rank Cholesky factor alternating direction implicit (LRCF-ADI), square root balanced truncation.

2021 6th International Conference on Inventive Computation Technologies (ICICT)

In this paper, a reduced order model technique based on Krylov subspace for linear discrete-time ... more In this paper, a reduced order model technique based on Krylov subspace for linear discrete-time periodic (LDTP) control system has been proposed. The proposed iterative algorithm conserves the exact structure of the original solution of LDTP Lyapunov functions while approximating them using Krylov iterations. This paper also exhibits how this proposed structure preserving algorithm generates a reduced order LDTP model. For confirming the efficiency and accuracy of this proposed algorithm numerical results are presented herewith this paper.

2022 International Conference on Innovations in Science, Engineering and Technology (ICISET)

2022 IEEE Global Engineering Education Conference (EDUCON)

2019 22nd International Conference on Computer and Information Technology (ICCIT), 2019

We have presented an efficient approach for reduce order modeling of discrete-time linear time-in... more We have presented an efficient approach for reduce order modeling of discrete-time linear time-invariant (DT-LTI) index-2 descriptor systems which arise in the study of control system. This paper is a follow up and advancement of our previous work [1]. The contribution of this paper lies in finding the projection free model order reduction (MOR) strategy for the index-2 linear descriptor systems. Instead of reformulating the descriptor system into a generalized system as of [1], we propose a simpler and more efficient MOR strategy where balanced truncation can be applied only in the finite parts of the matrices. We derive an unique method analogous to the Smith iteration method in order to solve the generalized discrete-time algebraic Lyapunov equations (DALEs) without explicitly computing the projection matrices. Finally, we confirm the accuracy and better efficiency of our proposed algorithm with the help of results acquired from numerical simulations.

2019 International Conference on Electrical, Computer and Communication Engineering (ECCE), 2019

In this paper, we present an efficient algorithm for model reduction of discrete-time index-2 des... more In this paper, we present an efficient algorithm for model reduction of discrete-time index-2 descriptor systems arising in context of linear time invariant (LTI) control and stability of descriptor systems. We propose a Smith-based iterative method for the model order reduction (MOR) strategy which consists of two stages. In the first stage, we reformulate the descriptor system into a generalized system by manipulating its system structure. Once the reformulated generalized system is obtained, it is amenable to a balanced truncation-based model order reduction strategy. The second stage of our work focuses on solving the generalized discrete-time algebraic Lyapunov equations (DALES) associated with the generalized system. Smith iterations are implemented to compute the solutions to these Lyapunov equations. Results from various numerical simulations are included to corroborate the high performance and accuracy of the proposed algorithms.

2017 4th International Conference on Advances in Electrical Engineering (ICAEE), 2017

In this paper, we discuss an iterative method for the model order reduction of continuous linear ... more In this paper, we discuss an iterative method for the model order reduction of continuous linear time-varying (LTV) periodic descriptor systems where the system's matrices are singular. The model order reduction strategy proposed here is focused on the linear time-invariant (LTI) reformulation of the LTV model through suitable discretization scheme. The resulting LTI system is reduced using a balanced truncation method. We use the Low-Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration to approximate the solutions of the corresponding time-invariant Lyapunov equations. Due to the singularity of the system's matrices, we have used the Pseudo-inverses to find the optimal shift parameters that are used in LRCF-ADI approximation. The step responses, bode plots and eigenstructures of both the original and reduced system are compared to indicate the accuracy of the proposed model reduction approach.

www.mpi-magdeburg.mpg.de/preprints We discuss a Krylov subspace projection method for model order... more www.mpi-magdeburg.mpg.de/preprints We discuss a Krylov subspace projection method for model order reduction of a special class of quadratic-bilinear descriptor systems. The goal is to extend the two-sided moment-matching method for quadratic-bilinear ODEs to descriptor systems in an efficient and reliable way. Recent results have shown that the direct application of interpolation based model reduction techniques to linear descrip-tor systems, without any modications, may lead to poor reduced-order systems. Therefore, for the analysis, we transform the quadratic-bilinear descriptor sys-tem into an equivalent quadratic-bilinear ODE system for which the moment-matching is performed. In view of implementation, we provide algorithms that identify the required Krylov subspaces without explicitly computing the projec-tors used in the analysis. The benets of our approach are illustrated for the quadratic-bilinear descriptor system of semi-discretized Navier-Stokes equations.

In the second-half of the past century the expeditious development of systems and control theory ... more In the second-half of the past century the expeditious development of systems and control theory together with the achievements of digital control and signal processing have set the stage for a renewed interest in the study of periodic dynamical systems, specially in aerospace realm, control of industrial processes, mechanical systems, modeling of periodic time-varying filters and networks, circuit simulation, and multirate sampleddata systems, etc. These complicated systems are composed of large numbers of separate devices and they are described by very large mathematical models consisting of more and more mathematical systems with very large dimensions. Simulations of such systems can be unacceptably expensive and time-consuming due to limited computer memory and CPU consumption. The idea of model reduction is that the large models should be replaced by smaller models which are amenable to fast and efficient simulation and which still capture the devices’ inputoutput behavior to a...

This paper surveys recent literature on the topic of student evaluations of teaching (SETs) to hi... more This paper surveys recent literature on the topic of student evaluations of teaching (SETs) to highlight the importance of SETs and the different factors that affect the SET scores. The paper conducts a cursory survey among the students of a private university of Bangladesh to find out what students think about the existing teaching evaluation process of the university and the instrument used for the evaluation. The survey results illustrate the view of the students on different issues related to SETs. In the end we added some recommendations on the basis of the survey finding that might help institutes develop effective SET tools and processes.

Results in Control and Optimization, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Numerical Algorithms, 2017

In this paper, we develop structure preserving iterative schemes to solve the periodic discrete-t... more In this paper, we develop structure preserving iterative schemes to solve the periodic discrete-time projected Lyapunov equations associated to analysis and design of discrete-time descriptor systems exploiting the reflexive generalized inverses of the periodic matrices associated with these systems. In particular, we extend the Smith method to solve the large scale projected periodic discrete-time algebraic Lyapunov equations in lifted form. A low-rank version of this method is also presented, avoiding the explicit lifted formulation and working directly with the periodic matrix coefficients. Moreover, we consider an application of the Lyapunov solvers in balanced truncation model reduction of periodic discrete-time descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.

Mathematical Problems in Engineering, 2017

We have presented the efficient techniques for the solutions of large-scale sparse projected peri... more We have presented the efficient techniques for the solutions of large-scale sparse projected periodic discrete-time Lyapunov equations in lifted form. These types of problems arise in model reduction and state feedback problems of periodic descriptor systems. Two most popular techniques to solve such Lyapunov equations iteratively are the low-rank alternating direction implicit (LR-ADI) method and the low-rank Smith method. The main contribution of this paper is to update the LR-ADI method by exploiting the ideas of the adaptive shift parameters computation and the efficient handling of complex shift parameters. These approaches efficiently reduce the computational cost with respect to time and memory. We also apply these iterative Lyapunov solvers in balanced truncation model reduction of periodic discrete-time descriptor systems. We illustrate numerical results to show the performance and accuracy of the proposed methods.

2014 International Conference on Electrical Engineering and Information & Communication Technology, 2014

In this paper, we discuss the structure preserving iterative solutions of large scale sparse proj... more In this paper, we discuss the structure preserving iterative solutions of large scale sparse projected periodic discrete-time algebraic Lyapunov equations which arise in periodic state feedback control problems and in model reduction of periodic descriptor systems. We extend the idea of computing the generalized inverses of periodic discrete-time descriptor systems using the left and right deflating projectors associated with the eigenstructures of the periodic singular matrix pairs. The computed periodic inverses are then used in the Smith iterative method to compute the iterative solutions of the projected periodic discrete-time algebraic Lyapunov equations. A low-rank version of this method is also presented, which can be used to compute low-rank approximations to the solutions of projected periodic discrete-time algebraic Lyapunov equations. Moreover, we consider an application of the Lyapunov solvers in balanced truncation model reduction of periodic discrete-time descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.

2015 International Conference on Electrical Engineering and Information Communication Technology (ICEEICT), 2015

In this paper, we propose a projection based iterative technique for model order reduction (MOR) ... more In this paper, we propose a projection based iterative technique for model order reduction (MOR) of time-varying periodic descriptor systems in continuous setting. This is a two sided projection technique which combines the SVD and the Krylov subspace method. We first apply a simple descretization scheme on our original periodic model, and reformulate an equivalent time-invariant form. We then reduce it with a two sided projection technique, where one side of this reduction technique is singular value decomposition (SVD) based Gramian approximation, and the other side is based on Krylov based projection. For the Krylov based projection method we mainly focus on the multipoint moment matching technique. The result is that the reduce model is asymptotically stable. Numerical results on a real life model have successfully substantiated the efficiency of our reduction process ensuring the stability of the reduce system.

Lecture Notes in Electrical Engineering, 2011

Linear periodic descriptor systems represent a broad class of time evolutionary processes in micr... more Linear periodic descriptor systems represent a broad class of time evolutionary processes in microelectronics and circuit simulation in particular. In this paper we consider discrete-time linear periodic descriptor systems and study the concepts of periodic reachability and observability of the systems based on earlier ideas of Chu et al. [1]. We define reachability and observability Gramians with respect to the whole period and show that they satisfy some projected generalized discrete-time periodic Lyapunov equations. We also study the concept of "lifted" representations of the original periodic system. For standard state-space systems, this is used to define Gramians via discrete-time Lyapunov equations, e.g., by Varga [2] (for algorithms, see also [3]) and for the analysis of periodic descriptor systems in [4]. Combining both concepts, we can also derive a definition of Gramians for periodic discrete-time descriptor systems. We discuss both approaches and propose model reduction methods based on balanced truncation, the Gramian definitions discussed before, and the resulting concepts of Hankel singular values. We illustrate the behaviour of the suggested model reduction techniques using numerical examples.

International Journal of Modeling and Optimization, 2015

Large, complex dynamical systems, such as, power systems, are very challenging task to model and ... more Large, complex dynamical systems, such as, power systems, are very challenging task to model and analysis. Numerous techniques have been developed to handle the difficulties arising from the size and complexity of typical realistic power system models. These complexities demand to formulate reduced order dynamic equivalent models of power systems in many applications and studies. Linearizing around the equilibrium point, a stable time invariant power system model leads to index 1 differential-algebraic (DAE) system. A balancing based model reduction technique for such a system is discussed in a paper of F. Freitas et al. in 2008. The main drawback of this method is to compute two Gramian factors of the system by solving two continuous-time algebraic Lyapunov equations. On the other hand interpolatory model reduction via iterative rational Krylov algorithm (IRKA) is computationally efficient since it requires only matrix-vector products or linear solvers. This paper contributes an interpolatory technique using IRKA for a class of index 1 DAE systems to obtain reduced standard ordinary differential (ODE) systems. We also show that a simple algebraic manipulation retrieve reduced index-1 DAE systems. The proposed technique is applied to a data of linearized power system models. Numerical results illustrate the efficiency of the techniques.

ABSTRACT We will present a projection approach for model reduction of linear time-varying descrip... more ABSTRACT We will present a projection approach for model reduction of linear time-varying descriptor systems based on earlier ideas in the work of Philips and others. The idea behind the proposed procedure is based on a multipoint rational approximation of the monodromy matrix of the corresponding dierential-algeb raic equation. This is realized by orthogonal projection onto a rational Krylov subspace. The algorithmic realization of the method employes recycling techniques for shifted Krylov subspaces and their invariance properties. The proposed method works eciently for macromodels, such as time varying circuit systems and models arising in network interconnection, on limited frequency ranges. Bode plots and step response are used to illustrate both the stability and accuracy of the reduced order models.