The finite-horizon optimal compensation problem is considered in the case of linear time-varying discrete-time systems with deterministic and white stochastic parameters and quadratic criteria. The dimensions of the c...
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The finite-horizon optimal compensation problem is considered in the case of linear time-varying discrete-time systems with deterministic and white stochastic parameters and quadratic criteria. The dimensions of the compensator are a priori fixed and may be time varying. Also the dimensions of the system may be time varying. Strengthened discrete-time optimal projection equations (SDOPE) are developed which, within the class of minimal compensators, are equivalent to the first-order necessary optimality conditions. Based on the SDOPE and their associated boundary conditions, two numerical algorithms are presented to solve the two point boundary value problem. One is a homotopy algorithm while the second iterates the SDOPE repeatedly forward and backward in time. The latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation Riccati equations, associated with the full-order problem for systems with deterministic parameters. The algorithms are illustrated with a numerical example. The case of systems with deterministic parameters will be treated as a special case of systems with white parameters. (C) 1999 Elsevier Science Ltd. All rights reserved.
The numerical solution of the Ffowcs Williams-Hawkings equation (Ffowcs Williams, J. E., and Hawkings, D. L., "Sound Generation by Turbulence and Surfaces in Arbitrary Motion," Philosophical Transactions of ...
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The numerical solution of the Ffowcs Williams-Hawkings equation (Ffowcs Williams, J. E., and Hawkings, D. L., "Sound Generation by Turbulence and Surfaces in Arbitrary Motion," Philosophical Transactions of the Royal Society, Vol. A264, No. 1151, 1969, pp. 321-342) on a rotating supersonic domain is discussed. Based on the emission-surface algorithm, the adopted solver performs the integration on the so-called acoustic domain to avoid the Doppler singularity in the integral kernels. The presence of multiple emission times for the supersonic source points and the particular time evolution of the integration domain force the use of a particular data-fitting procedure on both the geometrical and integral quantities. The algorithm may he used in the numerical prediction of the quadrupole source term for helicopter rotors operating at a high transonic regime and in the aeroacoustic analysis of the modern propeller blades, rotating at supersonic tip speed.
Apparatus for instantaneous regression rate measurements based on a simple plane-capacitor geometry and circuit theory is described, and results from a prototype setup are presented for both metallized and nonmetalliz...
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Apparatus for instantaneous regression rate measurements based on a simple plane-capacitor geometry and circuit theory is described, and results from a prototype setup are presented for both metallized and nonmetallized AP composite propellants at p approximate to 1 bar. The experiments show the apparatus is potentially effective as an instantaneous burning rate diagnostic only for the nonmetallized composite propellant. For metallized propellants the technique offers potential as 1) a go/no-go technique and 2) a monitor for the onset of bulk activity inside the gaseous part of the flame. Some tentative general conclusions about the:applicability of electric field diagnostics for solid propellants are suggested.
Given a rational matrix G with complex coefficients and a domain Gamma in the closed complex plane, both arbitrary, we develop a complete theory of coprime factorizations of G over Gamma, with denominators of McMillan...
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Given a rational matrix G with complex coefficients and a domain Gamma in the closed complex plane, both arbitrary, we develop a complete theory of coprime factorizations of G over Gamma, with denominators of McMillan degree as small as possible. The main tool is a general pole displacement theorem which gives conditions for an invertible rational matrix to dislocate by multiplication a part of the poles of G. We apply this result to obtain the parametrized class of all coprime factorizations over Gamma with denominators of minimal McMillan degree n(b)-the number of poles of G outside Gamma. Specific choices of the parameters and of Gamma allow us to determine coprime factorizations, as for instance, with polynomial, proper, or stable factors. Further, we consider the case in which the denominator has a certain symmetry, namely it is J all-pass with respect either to the imaginary axis or to the unit circle. We give necessary and sufficient solvability conditions for the problem of coprime factorization with J all-pass denominator of McMillan degree n(b) and, when a solution exists, we give a construction of the class of coprime factors. When no such solution exists, we discuss the existence of, and give solutions to, coprime factorizations with J all-pass denominators of minimal McMillan degree (> n(b)). All the developments are carried out in terms of descriptor realizations associated with rational matrices, leading to explicit and computationally efficient formulas.
A guideline for determining the stabilization parameters of the Baumgarte technique is developed. The guideline, based on the stability limits of the numerical algorithms used and the chosen integration step size, is ...
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A guideline for determining the stabilization parameters of the Baumgarte technique is developed. The guideline, based on the stability limits of the numerical algorithms used and the chosen integration step size, is used to systematically determine the stabilization parameter. A crank-mechanism problem is considered as a numerical example. numerical results indicate that the proposed guideline yields a more accurate and robust solution than arbitrarily determined parameters in simulating multibody dynamic systems. (AIAA)
Repetitive Markov processes form a class of processes where the generator matrix has a particular repeating form. Many queueing models fall in this category such as M/M/1 queues, quasi-birth-and-death processes, and p...
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Repetitive Markov processes form a class of processes where the generator matrix has a particular repeating form. Many queueing models fall in this category such as M/M/1 queues, quasi-birth-and-death processes, and processes with M/G/1 or GI/M/1 generator matrices. in this paper, a new iterative scheme is proposed for computing the stationary probabilities of such processes. An infinite state process is approximated by a finite state process by lumping an infinite number of states into a super-state. What we call the feedback rate, the conditional expected rate of flow from the super-state to the remaining states, given the process is in the super-state, is approximated simultaneously with the steady state probabilities. The method is theoretically developed and numerically tested for quasi-birth-and-death processes. It turns out that the new concept of the feedback rate can be effectively used in computing the stationary probabilities.
This paper analyzes the performance of two different methods for solving discrete-time periodic Riccati equations. The first approach is based on the computation of the periodic Schur form of the monodromy matrices, t...
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This paper analyzes the performance of two different methods for solving discrete-time periodic Riccati equations. The first approach is based on the computation of the periodic Schur form of the monodromy matrices, the reordering of the eigenvalues in this form, and the solution of certain linear systems. The second approach performs a sequence of orthogonal swaps in the monodromy matrices, and then employs the so-called matrix disk function, to solve the equations. numerical experiments arts reported for both methods on serial and shared memory platforms.
The paper considers mathematical modelling of once-through power station boiler and numerical algorithm for simulation of the model. Fast and numerically stable algorithm based on the linearisation of model equations ...
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The paper considers mathematical modelling of once-through power station boiler and numerical algorithm for simulation of the model. Fast and numerically stable algorithm based on the linearisation of model equations and on the simultaneous solving of differential and algebraic equations is proposed. The paper also presents the design of steam temperature regulator by using the method of projective controls. Dynamic behaviour of the system closed with optimal linear quadratic regulator is taken as the reference system. The desired proprieties of the reference system are retained and solutions for superheated steam temperature regulator are determined.
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.
In this paper we introduce a common problem in electronic measurements and electrical engineering: finding the first root from the left of an equation in the presence of some initial conditions. We present examples of...
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In this paper we introduce a common problem in electronic measurements and electrical engineering: finding the first root from the left of an equation in the presence of some initial conditions. We present examples of electrotechnical devices (analog signal filtering), where it is necessary to solve it. Two new methods for solving this problem, based on global optimization ideas, are introduced. The first uses the exact a priori given global Lipschitz constant for the first derivative. The second method adaptively estimates local Lipschitz constants during the search. Both algorithms either find the first root from the left or determine the global minimizers (in the case when the objective function has no roots). Sufficient conditions for convergence of the new methods to the desired solution are established in both cases. The results of numerical experiments for real problems and a set of test functions are also presented.
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