A numerical algorithm for flexible linearization of substantially nonlinear ship mathematical models described by ordinary differential equations is proposed. The linearization can be performed over any pre-defined do...
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A numerical algorithm for flexible linearization of substantially nonlinear ship mathematical models described by ordinary differential equations is proposed. The linearization can be performed over any pre-defined domain in the state space or subspace in the least-square sense. A discrete set of points is created inside the domain of interest by means of a quasi-random sequence generator. Then, the exact model's responses are calculated on this set and a common least-square procedure is applied. Local or differential linearization can be performed with the same algorithm choosing an appropriately small domain around any point of interest in the state space. A numerical example for a typical directionally unstable vessel is given and studied is the influence of the number of the generated quasi-random points and of the linearization domain's dimensions.
Structure-preserving numerical techniques for computation of stable deflating subspaces, with applications in control systems design, are presented. The techniques use extended skew-Hamiltonian/Hamiltonian matrix penc...
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Structure-preserving numerical techniques for computation of stable deflating subspaces, with applications in control systems design, are presented. The techniques use extended skew-Hamiltonian/Hamiltonian matrix pencils, and specialized algorithms to exploit their structure: the symplectic URV decomposition, periodic QZ algorithm, solution of periodic Sylvester-like equations, etc. The structure-preserving approach has the potential to avoid the numerical difficulties which are encountered for a traditional, non-structured solution, returned by the currently available software tools.
Under the assumption that one of two given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that the...
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Under the assumption that one of two given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, the separability index is defined as the least energy of a proper auxiliary signal. A method for computation of this index is presented.
Abstract We discuss the solution of the fault detection problem in presence of parametric uncertainties. The basic approach is an extension of the nullspace method for constant systems to the case of linear parameter ...
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Abstract We discuss the solution of the fault detection problem in presence of parametric uncertainties. The basic approach is an extension of the nullspace method for constant systems to the case of linear parameter varying (LPV) models. In a general setting, we consider the case when part of the unknown parameters are non-measurable and part of them are measurable. The resulting LPV-gain scheduled fault detection filter provides robustness with respect to both types of parametric uncertainties. Symbolic and numerical computational procedures which underlie the proposed synthesis approach are discussed.
In this paper the implicitly restarted Arnoldi method is applied for the partial eigenanalysis of large power systems. The commonly used complex shift-invert and Cayley transformation are proved to be equivalent for i...
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In this paper the implicitly restarted Arnoldi method is applied for the partial eigenanalysis of large power systems. The commonly used complex shift-invert and Cayley transformation are proved to be equivalent for implicitly restarted Arnoldi method under certain conditions. New locking technique is exploited to compute eigenvalue clusters in real large power systems and extensions are made to apply for complex matrix. Comparisons are also made with two other variants of restarted Arnoldi method. The tests show that the implicitly restarted Arnoldi method is fast, robust, and reliable.
Abstract We consider a dynamic programming approach for solving optimal control problems of sampled continuous-time systems. Robustness to bounded noise and model uncertainties is provided by formulating the problem i...
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Abstract We consider a dynamic programming approach for solving optimal control problems of sampled continuous-time systems. Robustness to bounded noise and model uncertainties is provided by formulating the problem in the framework of differential games. We use a semi-Lagrangian scheme for the computation of the value function and the state feedback control law for constrained infinite horizon optimal control problems. The approach is illustrated with the optimal control of linear systems and nonlinear systems subject to bounded disturbances.
Linear Control Theory problems such as those of pole assignment by state, output feedback (centralised or decentralised), and zero assignment by input, or output squaring down may be reduced to a standard common probl...
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Linear Control Theory problems such as those of pole assignment by state, output feedback (centralised or decentralised), and zero assignment by input, or output squaring down may be reduced to a standard common problem known as the Determinantal assignment Problem (DAP) Giannakopoulos (1985). The aim of this paper is to develop and compare optimization algorithms for the computation of solutions of DAP. The developed numerical approaches may be used as a basis of a design technique centered around the frequency assignment problems.
Efficient, structure-exploiting techniques for input/output data processing in subspace-based multivariable system identification are investigated. The techniques are implemented in the system identification toolbox f...
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Efficient, structure-exploiting techniques for input/output data processing in subspace-based multivariable system identification are investigated. The techniques are implemented in the system identification toolbox for discrete-time systems, SLIDENT, incorporated in the freely available Fortran 77 S ubroutine L ibrary i n Co ntrol T heory (SLICOT). Besides drivers and computational routines, this toolbox provides M ATLAB interfaces, implementing several algorithmic approaches. Extensive numerical testing and comparisons with similar MATLAB tools show that SLIDENT is reliable, efficient, and powerful enough to solve industrial identification problems.
We propose a novel approach to solve systems of multivariate polynomial equations, using the column space of the Macaulay matrix that is constructed from the coefficients of these polynomials. A multidimensional reali...
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We propose a novel approach to solve systems of multivariate polynomial equations, using the column space of the Macaulay matrix that is constructed from the coefficients of these polynomials. A multidimensional realization problem in the null space of the Macaulay matrix results in an eigenvalue problem, the eigenvalues and eigenvectors of which yield the common roots of the system. Since this null space based algorithm uses well-established numerical linear algebra tools, like the singular value and eigenvalue decomposition, it finds the solutions within machine precision. In this paper, on the other hand, we determine a complementary approach to solve systems of multivariate polynomial equations, which considers the column space of the Macaulay matrix instead of its null space. This approach works directly on the data in the Macaulay matrix, which is sparse and structured. We provide a numerical example to illustrate our new approach and to compare it with the existing null space based root-finding algorithm.
In this paper we discuss the one dimensional heat equation and the wave equation subject to nonlocal conditions. We use the method of Laplace transforms. Finally, we obtain the solution by using a numerical technique ...
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In this paper we discuss the one dimensional heat equation and the wave equation subject to nonlocal conditions. We use the method of Laplace transforms. Finally, we obtain the solution by using a numerical technique for inverting the Laplace transforms.
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