A new algorithm for designing free-return lunar flyby trajectories between the Earth and the moon is developed. The pseudostate theory is adopted to get the initial solution of the free-return trajectory. Using this i...
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A new algorithm for designing free-return lunar flyby trajectories between the Earth and the moon is developed. The pseudostate theory is adopted to get the initial solution of the free-return trajectory. Using this initial solution, an improved differential-correction method is employed to find the final solution with a more complicated dynamic model. Compared with the original differential-correction method, the improved one can extend the convergence domain and have a fast convergence speed. A large number of numerical examples are carried out to test the reliability and efficiency of the algorithm, and also study the global features of free-return lunar flyby trajectories. The features are mainly affected by the geometric relationship between the Earth and the moon, the altitude of perilune, and the transfer time from perigee to perilune.
In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration s...
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In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2].
In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of systems of variationa...
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In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of systems of variational inequalities for two inverse strongly accretive mappings in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as improvement, supplementation, development and extension of the corresponding results in some references to a great extent.
In this paper, the problem of l(1)-induced controller design for discrete-time positive systems is investigated with the use of linear Lyapunov function. An analytical method to compute the exact value of l(1)-induced...
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In this paper, the problem of l(1)-induced controller design for discrete-time positive systems is investigated with the use of linear Lyapunov function. An analytical method to compute the exact value of l(1)-induced norm is first presented. Then, a novel characterization for stability and l(1)-induced performance is proposed. Based on the characterization, a necessary and sufficient condition for the existence of desired controllers is derived, and an iterative convex optimization approach is developed to solve the condition. In addition, the synthesis of the state-feedback controller for single-input multiple-output (SIMO) positive systems is investigated. For this special case, an analytic solution is established to show how the optimal l(1)-induced controller can be designed, and some links to the spectral radius of the closed-loop systems are provided. Finally, the theoretical results are illustrated through a numerical example. (c) 2013 Elsevier Ltd. All rights reserved.
This paper studies the two-impulse cotangent rendezvous problem between two coplanar elliptical orbits. This problem requires the same flight time for two spacecraft and a cotangent transfer between the initial and fi...
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This paper studies the two-impulse cotangent rendezvous problem between two coplanar elliptical orbits. This problem requires the same flight time for two spacecraft and a cotangent transfer between the initial and final orbits. For two coplanar circular orbits, the closed-form solution is obtained and its total cost is equal to that of the Hohmann transfer. However, for two coplanar elliptical orbits, the solutions are obtained only by a numerical iterative algorithm. There are many solutions for the multiple-revolution case. Moreover, the minimum-fuel two-impulse cotangent transfer can be expressed as the true anomaly of final orbit. With the minimum-fuel transfer, a simple method for the optimal revolution numbers is proposed based on the first-order Taylor series expansion of the flight-time equation. Then, the minimum-fuel two-impulse cotangent rendezvous is obtained by calculating and comparing two or four candidates. Two numerical examples are provided to apply the proposed technique for all solutions and the minimum-fuel solution to the two-impulse cotangent rendezvous problem.
Non-negative tensor factorization (NTF) has been successfully used to extract significant characteristics from polyadic data, such as data in social networks. Because these polyadic data have multiple dimensions (e.g....
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Non-negative tensor factorization (NTF) has been successfully used to extract significant characteristics from polyadic data, such as data in social networks. Because these polyadic data have multiple dimensions (e.g., the author, content, and timestamp of a blog post), NTF fits in naturally and extracts data characteristics jointly from different data dimensions. In the traditional NTF, all information comes from the observed data, and therefore, the end users have no control over the outcomes. However, in many applications very often, the end users have certain prior knowledge, such as the demographic information about individuals in a social network or a pre-constructed ontology on the contents and therefore prefer the data characteristics extracting by NTF being consistent with such prior knowledge. To allow users' prior knowledge to be naturally incorporated into NTF, in this paper, we present a general framework-FacetCube-that extends the standard NTF. The new framework allows the end users to control the factorization outputs at three different levels for each of the data dimensions. The proposed framework is intuitively appealing in that it has a close connection to the probabilistic generative models. In addition to introducing the framework, we provide an iterative algorithm for computing the optimal solution to the framework. We also develop an efficient implementation of the algorithm that consists of several techniques to make our framework scalable to large data sets. Extensive experimental studies on a paper citation data set and a blog data set demonstrate that our new framework is able to effectively incorporate users' prior knowledge, improves performance over the traditional NTF on the task of personalized recommendation, and is scalable to large data sets from real-life applications.
Discrete tomography deals with tomographic reconstruction of greyscale images for which the set of possible grey levels is discrete and small. Here, we develop a discrete approximate reconstruction algorithm. Our algo...
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Discrete tomography deals with tomographic reconstruction of greyscale images for which the set of possible grey levels is discrete and small. Here, we develop a discrete approximate reconstruction algorithm. Our algorithm computes an image that has only grey values belonging to a given finite set. It also guarantees that the difference between the given projections and the projections of the reconstructed discrete image is bounded. The bound, which is computable, is independent of the image size. We present reconstruction experiments for a range of phantom images and a varying number of grey values.
A case study of an aerial solution designed to provide useful and quick information in a postfire scenario was reported. Controlled bonfires were successfully detected and geolocated, and both quantitative and visual ...
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A case study of an aerial solution designed to provide useful and quick information in a postfire scenario was reported. Controlled bonfires were successfully detected and geolocated, and both quantitative and visual information was sent to the ground station in near-real time. The processing time of the presented algorithms proved to be adequate for the conditions of the proposed flight. Despite the use of inexpensive sensors, the accuracy of the geolocation algorithm was on the order of a few meters, which is sufficient to accommodate the needs of firefighters. When considering the mean value of the geolocations obtained for the same hot spot in different images, the accuracy improved to centimeters. The attitude and synchronization errors appeared to have the greatest influence on the results. A thorough calibration of the sensors and a specific type of filtering, such as the Kalman filter, could be used to improve the reliability and accuracy of the sensor measurements.
The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on the viscosity approximation method, we combine the GPA and averaged mapping approach to pro...
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The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on the viscosity approximation method, we combine the GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of an equilibrium and a constrained convex minimization problem for the first time in this paper. Under suitable conditions, strong convergence theorems are obtained. MSC: 46N10, 47J20, 74G60.
In this paper, we introduce new iterative algorithms for finding a common element of the set of solutions of a general system of nonlinear variational inequalities with perturbed mappings and the set of common fixed p...
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In this paper, we introduce new iterative algorithms for finding a common element of the set of solutions of a general system of nonlinear variational inequalities with perturbed mappings and the set of common fixed points of a one-parameter nonexpansive semigroup in Banach spaces. Furthermore, we prove the strong convergence theorems of the sequence generated by these iterative algorithms under some suitable conditions. The results obtained in this paper extend the recent ones announced by many others. Mathematics Subject Classification (2010): 47H09, 47J05, 47J25, 49J40, 65J15.
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