The differential correction algorithm for generalized rational functions is described, and two theorems on convergence and order of convergence are given. An example shows that the order of convergence may deteriorate...
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The differential correction algorithm for generalized rational functions is described, and two theorems on convergence and order of convergence are given. An example shows that the order of convergence may deteriorate from superlinear to linear when a best generalized rational approximation does not exist.
After being initially launched into the parking orbit, a spacecraft usually implements several maneuvers to insert its nominal orbit as the geostationary orbit for global communication, a Halo orbit to survey the sola...
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After being initially launched into the parking orbit, a spacecraft usually implements several maneuvers to insert its nominal orbit as the geostationary orbit for global communication, a Halo orbit to survey the solar wind, and an adjacent orbit to rendezvous with other spacecraft. The transfer problem between two different trajectories is very important in academic research and practical engineering. Trajectory correction maneuvers are necessary to keep actual flight trajectories near the nominal ones because of the errors produced by control maneuvers, measurements, launching, and modeling. However, an inappropriate strategy costs more time and fuel and may even result in mission failure. This study investigates optimal maneuver strategies from the stochastic control viewpoint to track interesting and typical trajectories, including the Halo-transfer and Lambert rendezvous orbits. This study proposes an improved correctionalgorithm to eliminate modeling errors for reference transfer trajectories. Moreover, this study develops an innovative approach to obtain the optimal correction maneuver strategy that uses the stochastic control theory in determining corrections and adopts the genetic-algorithm and Monte Carlo joint simulation to yield the schedules of maneuvers. Finally, numerical simulations indicate that the proposed approach has potential applications in the tracking of reference trajectories in closed-loop correction maneuvers.
In this paper, we focus on the problem of computing multiband filtering characteristics with a guarantee on their global optimality with respect to a Zolotarev-like criterion. An iterative algorithm based on linear pr...
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In this paper, we focus on the problem of computing multiband filtering characteristics with a guarantee on their global optimality with respect to a Zolotarev-like criterion. An iterative algorithm based on linear programming is presented. This algorithm ensures quadratic convergence to the optimal solution. We also provide an equiripple-like criterion that allows one to check in a very simple manner whether a computed filtering function is optimal or not. The latter is used to analyze two practical design examples based on asymmetric dual-band specifications. In particular, it is shown that the selectivity of the dual-band response does not necessarily increase with the filter's crder. This study yields some striking results when compared to the usual single-band situation, and introduces the idea that for certain asymmetric specifications some of the filter order values are more suitable than others. Finally, the practical implementations of the filtering devices in inline dual-mode cavities and stacked single-mode cavities are detailed.
In [R. Hettich and P. Zencke, Teubner Studienbücher Mathematik, Leipzig, Stuttgart, 1982] and [G. Speich, Ph.D. thesis, University of Bonn, Bonn, 1981] a Newton-type differential correction algorithm for general ...
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In [R. Hettich and P. Zencke, Teubner Studienbücher Mathematik, Leipzig, Stuttgart, 1982] and [G. Speich, Ph.D. thesis, University of Bonn, Bonn, 1981] a Newton-type differential correction algorithm for general rational Chebyshev approximation has been introduced that has been shown to be globally convergent and superlinearly convergent under assumptions weaker than the common condition of unique solutions. Using recent results on parametric semi-infinite programming [Math. Programming, 38 (1987), pp. 323–340], it can be shown that all essential assumptions can be dropped without destroying superlinear convergence. Moreover, additional constraints on the problem, such as restrictions on the range, can be treated without destroying the favorable properties of the algorithm.
The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differentialcorrection al...
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The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differentialcorrection method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.
The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping s...
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The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to . A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.
In this paper a new method for the synthesis of asymmetric multi-band filters is presented. The major improvement of the latter is that it not only computes optimal reflection zeros but also optimal transmission zeros...
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ISBN:
(纸本)9781424406876
In this paper a new method for the synthesis of asymmetric multi-band filters is presented. The major improvement of the latter is that it not only computes optimal reflection zeros but also optimal transmission zeros of the filtering function of the usual low-pass prototype. The computational part consists of a differentialcorrection-like algorithm proven to be convergent, and which guarantees the optimality of the response. Practical information is given for the implementation of such an algorithm.. The process is validated by the design of a dual-band filter from asymmetric specifications, which yields a 9th degree filter.
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation-precisely the case where rational functions outperform polynomials by a landslide...
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Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation-precisely the case where rational functions outperform polynomials by a landslide. We show that far more robust algorithms than previously available can be developed by making use of rational barycentric representations whose support points are chosen in an adaptive fashion as the approximant is computed. Three variants of this barycentric strategy are all shown to be powerful: (1) a classical Remez algorithm, (2) an "AAA-Lawson" method of iteratively reweighted least-squares, and (3) a differential correction algorithm. Our preferred combination, implemented in the Chebfun MINIMAX code, is to use (2) in an initial phase and then switch to (1) for generically quadratic convergence. By such methods we can calculate approximations up to type (80, 80) of vertical bar x vertical bar on [-1,1] in standard 16-digit floating point arithmetic, a problem for which Varga, Ruttan, and Carpenter [Math. USSR Sb., 74 (1993), pp. 271-290] required 200-digit extended precision.
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