We investigate the parametrization issue for discrete-time stable all-pass multivariable systems by means of a Schur algorithm involving a Nudel-man interpolation condition. A recursive construction of balanced realiz...
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We investigate the parametrization issue for discrete-time stable all-pass multivariable systems by means of a Schur algorithm involving a Nudel-man interpolation condition. A recursive construction of balanced realizations is associated with it, that possesses a very good numerical behavior. Several atlases of charts or families of local parametrizations are presented and for each atlas a chart selection strategy is proposed. These parametrizations allow for solving optimization problems within the fields of system identification and optimal control.
This work proposes a predictive controller with interpolation in order to improve the behaviour of a typical MPC when the system presents constraints. Particularly, it is interesting to see how the interpolation, betw...
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This work proposes a predictive controller with interpolation in order to improve the behaviour of a typical MPC when the system presents constraints. Particularly, it is interesting to see how the interpolation, between the solution of the optimal unconstrained problem and other feasible solutions, assures the stability of the system in presence of disturbances. The system in which the controller is applied is a two-link robot manipulator arm. The predictive controller is inserted in an adaptive perturbation scheme to change adequately the nominal inputs, given by an inverse dynamics controller, in order to reject the disturbances produced. The efficiency of the proposed strategy is shown by simulation.
An efficient DFT-based frequency offset estimation technique is presented for orthogonal frequency division multiplexing (OFDM) digital communication systems. The performance of the proposed scheme is confirmed by com...
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An efficient DFT-based frequency offset estimation technique is presented for orthogonal frequency division multiplexing (OFDM) digital communication systems. The performance of the proposed scheme is confirmed by computer simulation for 16-QAM signals with class I Rife and Vincent windows.
Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic spate. A survey of interpolation procedures us...
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Cauchy-Vandermonde systems consist of rational functions with prescribed poles. They are complex ECT-systems allowing Hermite interpolation for any dimension of the basic spate. A survey of interpolation procedures using CV-systems is given, some equipped with short new proofs, which generalize the well-known formulas of Lagrange, Neville-Aitken and Newton for interpolation by algebraic polynomials. The arithmetical complexitiy is O(N-2) for N Hermits data. Also, inversion formulas for the Cauchy-Vandermonde matrix are surveyed. Moreover, a new algorithm solving the system of N linear Cauchy-Vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions. As an application construction of rational B-splines with prescribed poles is discussed. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 41A05;65D05.
State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi-dimensional interpolation formula. It is shown that under certain assumptions the estimators perform better t...
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State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi-dimensional interpolation formula. It is shown that under certain assumptions the estimators perform better than estimators based on Taylor approximations. Nevertheless, the implementation is significantly simpler as no derivatives are required. Thus, it is believed that the new state estimators can replace well-known estimators, such as the extended Kalman filter (EKF) and its higher-order relatives, in most practical applications. (C) 2000 Elsevier Science Ltd. All rights reserved.
In this paper a solution is given for the problem of approximation of any given multivariate probability distribution function by a mixture of normal distributions or, in general case, a mixture of some other distribu...
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In this paper a solution is given for the problem of approximation of any given multivariate probability distribution function by a mixture of normal distributions or, in general case, a mixture of some other distributions suitable for the given particular case. The analogous problem is solved for distribution functions of stochastic processes, i.e. an interpolation time-dependent polynomial is constructed which approximates the distribution function in the uniform metric.
Two new state estimation filters for nonlinear systems are derived in this paper. The filters are based on a multi-dimensional extension of Stirling's interpolation formula for approximation of the nonlinear trans...
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Two new state estimation filters for nonlinear systems are derived in this paper. The filters are based on a multi-dimensional extension of Stirling's interpolation formula for approximation of the nonlinear transformations. The filters can be shown to perform better than filters based on Taylor approximations. Yet, they can be implemented more easily as no derivatives are required. Thus, it is believed that the new filters can replace well-known estimators, such as the extended Kalman filter (EKF) and its higher order relatives.
New numerical procedures are proposed to solve the symmetric matrix polynomial equation A(T)(-s) X(s) + X-T(-s) A(s)= 2B(s) that is frequently encountered in control and signal processing. An interpolation approach is...
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New numerical procedures are proposed to solve the symmetric matrix polynomial equation A(T)(-s) X(s) + X-T(-s) A(s)= 2B(s) that is frequently encountered in control and signal processing. An interpolation approach is presented that takes full advantage of symmetry properties and leads to an equivalent reduced-size linear system of equations. It results in a simple and general characterization of all solutions of expected column degrees. Several new theoretical results concerning stability theory and reduced Sylvester resultant matrices are also developed and used to conclude a priori on the existence of a solution. By means of numerical experiments, it is shown that our algorithms are more efficient than older methods and, namely, appear to be numerically reliable. (C) 1998 Elsevier Science Ltd. All rights reserved.
An asymptotically fast algorithm for solving the generalized rational interpolation problem is presented, This problem has been studied as part of system theory and is related to the solution of the classical and Welc...
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An asymptotically fast algorithm for solving the generalized rational interpolation problem is presented, This problem has been studied as part of system theory and is related to the solution of the classical and Welch-Berlekamp key equations which arise in Reed-Solomon decoding, The algorithm can also be used to compute the linear complexity profile of a binary sequence of length m using only O(m(log m)(2) log log m) bit operations.
A procedure is shown to construct a rational transfer function that is real-valued and positive on the imaginary axis. The degree of the solution is lowered with respect to solutions based on existing algorithms. The ...
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A procedure is shown to construct a rational transfer function that is real-valued and positive on the imaginary axis. The degree of the solution is lowered with respect to solutions based on existing algorithms. The results can be applied to problems such as the robust strictly positive real problem. (C) 1997 Elsevier Science Ltd.
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