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Biswa Nath Datta - One of the best experts on this subject based on the ideXlab platform.
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a new algorithm for generalized sylvester Observer Equation and its application to state and velocity estimations in vibrating systems
Numerical Linear Algebra With Applications, 2011Co-Authors: João Batista Da Paz Carvalho, Biswa Nath DattaAbstract:We propose a new algorithm for block-wise solution of the generalized Sylvester-Observer Equation XA−FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the Observer-Hessenberg-triangular form. It is a natural generalization of the widely known Observer-Hessenberg algorithm for the Sylvester-Observer Equation: XA−FX = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors. Copyright © 2010 John Wiley & Sons, Ltd.
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A new algorithm for generalized Sylvester‐Observer Equation and its application to state and velocity estimations in vibrating systems
Numerical Linear Algebra with Applications, 2010Co-Authors: João Batista Da Paz Carvalho, Biswa Nath DattaAbstract:We propose a new algorithm for block-wise solution of the generalized Sylvester-Observer Equation XA−FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the Observer-Hessenberg-triangular form. It is a natural generalization of the widely known Observer-Hessenberg algorithm for the Sylvester-Observer Equation: XA−FX = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors. Copyright © 2010 John Wiley & Sons, Ltd.
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Numerical Methods for Linear Control Systems - CHAPTER 12 – STATE ESTIMATION: Observer AND THE KALMAN FILTER
Numerical Methods for Linear Control Systems, 2004Co-Authors: Biswa Nath DattaAbstract:This chapter presents a well-known procedure “Kalman filtering” developed by Kalman for optimal estimation of the states of a stochastic system, followed by a brief discussion on the Linear Quadratic Gaussian problem that deals with optimization of a performance measure for a stochastic system. The chapter discusses how the states of a continuous-time system can be estimated. The discussions apply equally to the discrete-time systems, possibly with some minor changes. So the main focus is on the continuous-time case. The chapter describes two common procedures for state estimation: one, via eigenvalue assignment and the other, via solution of the Sylvester-Observer Equation. The chapter also describes two other numerical methods, especially designed for Sylvester-Observer Equation; both are based on the reduction of the observable pair to the Observer-Hessenberg pair and are recursive in nature. Both numerical methods seem to have good numerical properties.
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A Parallel Algorithm for the Sylvester Observer Equation
SIAM Journal on Scientific Computing, 1996Co-Authors: Christian Bischof, Biswa Nath Datta, Avijit PurkayasthaAbstract:We present a new algorithm for solving the Sylvester Observer Equation arising in the context of the Luenberger Observer. The algorithm embodies two main computational phases: the solution of several independent Equation systems and a series of matrix--matrix multiplications. The algorithm is, thus, well suited for parallel and high-performance computing. By reducing the coefficient matrix $A$ to lower-Hessenberg form, one can implement the algorithm efficiently, with few floating-point operations and little workspace. The algorithm has been successfully implemented on a CRAY C90. A comparison, both theoretical and experimental, has been made with the well-known Hessenberg--Schur algorithm which solves an arbitrary Sylvester Equation. Our theoretical analysis and experimental results confirm the superiority of the proposed algorithm, both in efficiency and speed, over the Hessenberg--Schur algorithm.
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A Parallel Algorithm for the Multi-input Sylvester-Observer Equation
1992 American Control Conference, 1992Co-Authors: Christian Bischof, Biswa Nath Datta, Avijit PurkayasthaAbstract:We present a new algorithm for solving the Multi-input Sylvester-Observer Equation. The algorithm embodies two main computational phases: the solution of a series of independent Equation systems, and a series of matrix-matrix multiplications. As such, the algorithm is well suited for a parallel machine. By reducing the coefficient matrix to lower Hessenberg form, one can implement the algorithm efficiently, with few floating-point operations and little workspace. We present experimental results on the CRAY Y-MP and the Siemens S600/10 that confirm the efficiency of our algorithm.
João Batista Da Paz Carvalho - One of the best experts on this subject based on the ideXlab platform.
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a new algorithm for generalized sylvester Observer Equation and its application to state and velocity estimations in vibrating systems
Numerical Linear Algebra With Applications, 2011Co-Authors: João Batista Da Paz Carvalho, Biswa Nath DattaAbstract:We propose a new algorithm for block-wise solution of the generalized Sylvester-Observer Equation XA−FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the Observer-Hessenberg-triangular form. It is a natural generalization of the widely known Observer-Hessenberg algorithm for the Sylvester-Observer Equation: XA−FX = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors. Copyright © 2010 John Wiley & Sons, Ltd.
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A new algorithm for generalized Sylvester‐Observer Equation and its application to state and velocity estimations in vibrating systems
Numerical Linear Algebra with Applications, 2010Co-Authors: João Batista Da Paz Carvalho, Biswa Nath DattaAbstract:We propose a new algorithm for block-wise solution of the generalized Sylvester-Observer Equation XA−FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the Observer-Hessenberg-triangular form. It is a natural generalization of the widely known Observer-Hessenberg algorithm for the Sylvester-Observer Equation: XA−FX = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors. Copyright © 2010 John Wiley & Sons, Ltd.
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A new block algorithm for full-rank solution of the Sylvester-Observer Equation
IEEE Transactions on Automatic Control, 2003Co-Authors: João Batista Da Paz Carvalho, Karabi Datta, Y. HongAbstract:A new block algorithm for computing a full rank solution of the Sylvester-Observer Equation arising in state estimation is proposed. The major computational kernels of this algorithm are: 1) solutions of standard Sylvester Equations, in each case of which one of the matrices is of much smaller order than that of the system matrix and (furthermore, this small matrix can be chosen arbitrarily), and 2) orthogonal reduction of small order matrices. There are numerically stable algorithms for performing these tasks including the Krylov-subspace methods for solving large and sparse Sylvester Equations. The proposed algorithm is also rich in Level 3 Basic Linear Algebra Subroutine (BLAS-3) computations and is thus suitable for high performance computing. Furthermore, the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.
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A new block algorithm for solving the Sylvester-Observer Equation
Proceedings of the 41st IEEE Conference on Decision and Control 2002., 1Co-Authors: João Batista Da Paz Carvalho, Karabi Datta, Y. HongAbstract:A new block algorithm for computing a full rank solution of the Sylvester-Observer Equation is proposed. The algorithm is structure preserving and rich in BLAS-3 computations and thus suitable for high performance computing. Furthermore, the results on numerical experiments on benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.
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A block algorithm for the Sylvester-Observer Equation arising in state-estimation
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 1Co-Authors: João Batista Da Paz Carvalho, Biswa Nath DattaAbstract:We propose an algorithm for solving the Sylvester-Observer Equation arising in the construction of the Luenberger Observer. The algorithm is a block-generalization of P. Van Dooren's (1981) scalar algorithm. It is more efficient than Van Dooren's algorithm and the recent block algorithm by B.N. Datta and D. Sarkissian (2000). Furthermore, the algorithm is well-suited for implementation on some of today's powerful high performance computers using the high-quality software package LAPACK.
Y. Hong - One of the best experts on this subject based on the ideXlab platform.
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A new block algorithm for full-rank solution of the Sylvester-Observer Equation
IEEE Transactions on Automatic Control, 2003Co-Authors: João Batista Da Paz Carvalho, Karabi Datta, Y. HongAbstract:A new block algorithm for computing a full rank solution of the Sylvester-Observer Equation arising in state estimation is proposed. The major computational kernels of this algorithm are: 1) solutions of standard Sylvester Equations, in each case of which one of the matrices is of much smaller order than that of the system matrix and (furthermore, this small matrix can be chosen arbitrarily), and 2) orthogonal reduction of small order matrices. There are numerically stable algorithms for performing these tasks including the Krylov-subspace methods for solving large and sparse Sylvester Equations. The proposed algorithm is also rich in Level 3 Basic Linear Algebra Subroutine (BLAS-3) computations and is thus suitable for high performance computing. Furthermore, the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.
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A new block algorithm for solving the Sylvester-Observer Equation
Proceedings of the 41st IEEE Conference on Decision and Control 2002., 1Co-Authors: João Batista Da Paz Carvalho, Karabi Datta, Y. HongAbstract:A new block algorithm for computing a full rank solution of the Sylvester-Observer Equation is proposed. The algorithm is structure preserving and rich in BLAS-3 computations and thus suitable for high performance computing. Furthermore, the results on numerical experiments on benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.
Youmin Zhang - One of the best experts on this subject based on the ideXlab platform.
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ACC - Fault detection and identification for bimodal piecewise affine systems
2009 American Control Conference, 2009Co-Authors: Nastaran Nayebpanah, Luis Rodrigues, Youmin ZhangAbstract:This paper presents for the first time a fault detection and identification technique for bimodal piecewise affine (PWA) systems. A Luenberger-based Observer structure is applied to the state estimation problem of the PWA system. The unknown value of the fault parameter is estimated by an Observer Equation obtained from a Lyapunov function. The design procedure is formulated as a set of linear matrix inequalities (LMIs) and guarantees global asymptotic stability of the estimation error, provided the norm of the input is upper and lower bounded by positive constants. The proposed method is applied to estimation of the amount of partial loss in control authority for a PWA model of a wheeled Mobile Robot (WMR).
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Fault Identification and Reconfigurable Control for Bimodal Piecewise
2009Co-Authors: Luis Rodrigues, Youmin ZhangAbstract:This paper addresses the design of a fault detec- tion and reconfigurable control structure for bimodal piecewise affine (PWA) systems. The PWA bimodal system will be designed to verify input-to-state stability (ISS) in closed loop. The proposed methodology is divided into two parts. First, a Luenberger-based Observer structure is proposed to solve the fault detection and identification (FDI) problem for bimodal PWA systems. The unknown value of the fault parameter is estimated by an Observer Equation, which is derived using a Lyapunov-based methodology. Then, the ISS property is proved for the Observer. Second, a fault-tolerant state feedback controller is synthesized for the PWA model. The controller is designed to deal with partial loss of control authority identified by the Observer. The ISS property is also proved for the controller. Finally, the ISS property for the interconnection of the controller and the Observer-based fault identification mechanism is studied. The design procedure is formulated as a set of linear matrix inequalities (LMIs), which can be solved efficiently using available software packages.
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ECC - Fault identification and reconfigurable control for bimodal piecewise affine systems
2009 European Control Conference (ECC), 2009Co-Authors: Nastaran Nayebpanah, Luis Rodrigues, Youmin ZhangAbstract:This paper addresses the design of a fault detection and reconfigurable control structure for bimodal piecewise affine (PWA) systems. The PWA bimodal system will be designed to verify input-to-state stability (ISS) in closed loop. The proposed methodology is divided into two parts. First, a Luenberger-based Observer structure is proposed to solve the fault detection and identification (FDI) problem for bimodal PWA systems. The unknown value of the fault parameter is estimated by an Observer Equation, which is derived using a Lyapunov-based methodology. Then, the ISS property is proved for the Observer. Second, a fault-tolerant state feedback controller is synthesized for the PWA model. The controller is designed to deal with partial loss of control authority identified by the Observer. The ISS property is also proved for the controller. Finally, the ISS property for the interconnection of the controller and the Observer-based fault identification mechanism is studied. The design procedure is formulated as a set of linear matrix inequalities (LMIs), which can be solved efficiently using available software packages.
Karabi Datta - One of the best experts on this subject based on the ideXlab platform.
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Unique Full-Rank Solution of the Sylvester-Observer Equation and Its Application to State Estimation in Control Design
Lecture Notes in Electrical Engineering, 2011Co-Authors: Karabi Datta, Mohan ThapaAbstract:Needs to be found, is a classical Equation. There has been much study, both from theoretical and computational view points, on this Equation. The results of existence and uniqueness are well-known and numerically effective algorithms have been developed in recent years (see, Datta [2]), to compute the solution.
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A new block algorithm for full-rank solution of the Sylvester-Observer Equation
IEEE Transactions on Automatic Control, 2003Co-Authors: João Batista Da Paz Carvalho, Karabi Datta, Y. HongAbstract:A new block algorithm for computing a full rank solution of the Sylvester-Observer Equation arising in state estimation is proposed. The major computational kernels of this algorithm are: 1) solutions of standard Sylvester Equations, in each case of which one of the matrices is of much smaller order than that of the system matrix and (furthermore, this small matrix can be chosen arbitrarily), and 2) orthogonal reduction of small order matrices. There are numerically stable algorithms for performing these tasks including the Krylov-subspace methods for solving large and sparse Sylvester Equations. The proposed algorithm is also rich in Level 3 Basic Linear Algebra Subroutine (BLAS-3) computations and is thus suitable for high performance computing. Furthermore, the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.
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A new block algorithm for solving the Sylvester-Observer Equation
Proceedings of the 41st IEEE Conference on Decision and Control 2002., 1Co-Authors: João Batista Da Paz Carvalho, Karabi Datta, Y. HongAbstract:A new block algorithm for computing a full rank solution of the Sylvester-Observer Equation is proposed. The algorithm is structure preserving and rich in BLAS-3 computations and thus suitable for high performance computing. Furthermore, the results on numerical experiments on benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.
