This paper presents an efficient indirect optimization method for the time- and fuel-optimal low-thrust many-revolution transfers with averaged dynamics. Compared with the previous indirect method, the proposed method...
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This paper presents an efficient indirect optimization method for the time- and fuel-optimal low-thrust many-revolution transfers with averaged dynamics. Compared with the previous indirect method, the proposed method involves a new set of variables and several near-optimal control laws to formulate the two-point boundary value problem based on three practical assumptions. Then, the costate transformations between two reference frames are first derived with respect to the the corresponding Eulerian angles, such that the switching function can be expressed with a six-degree polynomial function and the number of parameters used to determine the energy-optimal solutions is reduced to 6. Finally, a neural network is trained to generated the initial guesses, and the solution algorithms for solving the time- and fuel-optimal problem are formulated. Numerical simulations demonstrate that the convergence ratio of initial guesses is higher than 98%, the proposed assumptions are reasonable for guaranteeing the near optimality, and the presented method can obtain convergent solutions within tenths of a second for the Earth- and moon-centered external/interior transfers considering the shadow J2 and third-body perturbations.
We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut parameterized above the Edwards-ErdAs bound is fixed-parameter tractable: we give an algorithm that for any c...
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We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut parameterized above the Edwards-ErdAs bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices and m edges finds a cut of size in time 2 (O(k))a <...n (4), or decides that no such cut exists. This answers a long-standing open question from parameterized complexity that has been posed a number of times over the past 15 years. Our algorithm has asymptotically optimal running time, under the Exponential Time Hypothesis, and is strengthened by a polynomial-time computable kernel of polynomial size.
Tutte proved that every 3-vertex-connected graph G on more than 4 vertices has a contractible edge. Barnette and Grunbaum proved the existence of a removable edge in the same setting. We show that the sequence of cont...
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Tutte proved that every 3-vertex-connected graph G on more than 4 vertices has a contractible edge. Barnette and Grunbaum proved the existence of a removable edge in the same setting. We show that the sequence of contractions and the sequence of removals from G to K (4) can be computed in O(|V|(2)) time by extending Barnette's and Grunbaum's theorem. As an application, we derive a certificate for the 3-vertex-connectivity of graphs that can be easily computed and verified.
We consider Boolean formulas where logical implication (-->) is the only operator and all variables, except at most one (denoted z), occur at most twice. We show that the problem of determining falsifiability for f...
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We consider Boolean formulas where logical implication (-->) is the only operator and all variables, except at most one (denoted z), occur at most twice. We show that the problem of determining falsifiability for formulas of this class is NP-complete but if the number of occurrences of z is restricted to be at most k then there is an O(\F\(k)) algorithm for certifying falsisability. We show this hierarchy of formulas, indexed on k, is interesting because even lower levels (e.g., k = 2) are not subsumed by several well-known polynomial time solvable classes of formulas. (C) 1999 Elsevier Science B.V. All rights reserved.
Given a point s and a set of h pairwise disjoint polygonal obstacles with a total of n vertices in the plane, suppose a triangulation of the space outside the obstacles is given;we present an O(n+hlogh) time and O(n) ...
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Given a point s and a set of h pairwise disjoint polygonal obstacles with a total of n vertices in the plane, suppose a triangulation of the space outside the obstacles is given;we present an O(n+hlogh) time and O(n) space algorithm for building a data structure (called shortest path map) of size O(n) such that for any query point t, the length of an L1 shortest obstacle-avoiding path from s to t can be computed in O(logn) time and the actual path can be reported in additional time proportional to the number of edges of the path. The previously best algorithm computes such a shortest path map in O(nlogn) time and O(n) space. So our algorithm is faster when h is relatively small. Further, our techniques can be extended to obtain improved results for other related problems, e.g., computing the L1 geodesic Voronoi diagram for a set of point sites among the obstacles.
The concept of a basis matrix is introduced to investigate the trade-off between complexity and storage for multiplication in a finite field. The effect on the storage requirements of using polynomial and normal bases...
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The concept of a basis matrix is introduced to investigate the trade-off between complexity and storage for multiplication in a finite field. The effect on the storage requirements of using polynomial and normal bases for element representation is also considered.
In many large, distributed or mobile networks, broadcast algorithms are used to update information stored at the nodes. In this paper, we propose a new model of communication based on rendezvous and analyze a multi-ho...
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In many large, distributed or mobile networks, broadcast algorithms are used to update information stored at the nodes. In this paper, we propose a new model of communication based on rendezvous and analyze a multi-hop distributed algorithm to broadcast a message in a synchronous setting. In the rendezvous model, two neighbors a and v can communicate if and only if a calls v and v calls a simultaneously. Thus, nodes a and v obtain a rendezvous at a meeting point. If m is the number of meeting points, the network can be modeled by a graph of n vertices and m edges. At each round, every vertex chooses a random neighbor and there is a rendezvous if an edge has been chosen by its two extremities. Rendezvous enable an exchange of information between the two entities. We get sharp lower and upper bounds on the time complexity in terms of number of rounds to broadcast: we show that, for any graph, the expected number of rounds is between Inn and O(n(2)). For these two bounds, we prove that there exist some graphs for which the expected number of rounds is either O(ln(n)) or Omega(n(2)). For specific topologies, additional bounds are given. (C) 2006 Elsevier Inc. All rights reserved.
In space mission sets like on-orbit servicing and manufacturing, agents in close proximity may operate too close to yield resolved localization solutions to operators. This requires that the system maintain a catalog ...
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In space mission sets like on-orbit servicing and manufacturing, agents in close proximity may operate too close to yield resolved localization solutions to operators. This requires that the system maintain a catalog of its local neighborhood;however, this imposes a large burden on each agent to update its catalog. This paper considers the case of multiple satellites each maintaining their catalog. Specifically, this paper considers the case of numerous noncooperative objects and a collection of agents operating in the same local environment. The goal of each agent is to maintain their catalog of all bodies (objects and agents) within this neighborhood through onboard angles-only measurements and cooperative communication with the other agents. A central supervisor selects the target body for each agent, a local controller tracks the selected target body for each agent, and a local estimator coalesces both an agent's measurements and state estimates provided by neighboring agents within the communication graph. Numerical results are provided to demonstrate the supervisor's ability to select an appropriate target subject to an uncertainty threshold, the controller's ability to track the selected target, and the estimator's ability to maintain an accurate and precise estimate of each of the bodies in the local environment.
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