Response to control input is of significance to the application of real-time active flow control (AFC). In this paper, a novel data-driven framework is used to discover the underlying physics of the dynamic response p...
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Response to control input is of significance to the application of real-time active flow control (AFC). In this paper, a novel data-driven framework is used to discover the underlying physics of the dynamic response process of fluidic thrust vectoring (FTV), a typical application of AFC. In the proposed framework, sparse identification of a nonlinear dynamics (SINDy) algorithm is used to identify the governing equations of the flow control responses of sets of noisy measurement data. The clustering algorithm is then used to seek the generalized coefficients of basis functions for different sets of data, which improve the robustness of the model to noisy measurement data. First, a simulated mechanical system is used to validate the effect of the framework. To simplify the modeling, control performance and characteristics are investigated in a detailed manner. Then a dimensionless parameter Delta Cp based on the pressure coefficient is found to exhibit a linear relationship with the vector angle under different working conditions. This parameter is introduced in the proposed framework to model the dynamic process of response to control input. The obtained governing equations can describe the dynamic process accurately based on the validation of testing data. The form of the governing equation is rewritten and analyzed based on the control theory, revealing the physics of this process, which is significant to practical AFC implementation.
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.
The surge of deep-space probes makes it unsustainable to navigate them with standard radiometric tracking. Autonomous interplanetary satellites represent a solution to this problem. In this work, a vision-based naviga...
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The surge of deep-space probes makes it unsustainable to navigate them with standard radiometric tracking. Autonomous interplanetary satellites represent a solution to this problem. In this work, a vision-based navigation algorithm is built by combining an orbit determination method with an image processing pipeline suitable for interplanetary transfers of autonomous platforms. To increase the computational efficiency of the algorithm, an extended Kalman filter is selected as state estimator, fed by the positions of the planets extracted from deep-space images. An enhancement of the estimation accuracy is performed by applying an optimal strategy to select the best pair of planets to track. Moreover, a novel analytical measurement model for deep-space navigation is developed providing a first-order approximation of the light-aberration and light-time effects. Algorithm performance is tested on a high-fidelity, Earth-Mars interplanetary transfer, showing the algorithm applicability for deep-space navigation.
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