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51
Optimal coordinated motions of multiple agents moving on a plane
 SIAM J. Control and Optimization
, 2003
"... Abstract. We address the problem of optimal coordinated motions of multiple agents moving in the same planar region. The agents ’ motions must satisfy a separation constraint throughout the encounter to be conflictfree. The objective is to determine the conflictfree maneuvers (motions) with the le ..."
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Abstract. We address the problem of optimal coordinated motions of multiple agents moving in the same planar region. The agents ’ motions must satisfy a separation constraint throughout the encounter to be conflictfree. The objective is to determine the conflictfree maneuvers (motions) with the least combined energy, while taking into account the fact that agents may have different priorities. A formal classification of conflictfree maneuvers into homotopy types is introduced by using their braid representation. Various local and global optimality conditions are derived through variational analysis in the presence of the separation constraint. In the case of two agents, these optimality conditions allow us to construct the optimal maneuvers geometrically. For the general multiagent case, a convex optimization algorithm is proposed to compute within each homotopy type a solution to the optimization problem restricted to the class of multilegged maneuvers. Since the number of types grows explosively with the number of agents, a stochastic algorithm is suggested as the “type chooser”, thus leading to a randomized optimization algorithm.
A multiaircraft model for conflict detection and resolution algorithm validation
 HYBRIDGE Project IST200132460, Work Package WP1, Deliverable D1.4
, 2003
"... Title of document: A multiaircraft model for conflict detection and resolution algorithm evaluation Authors of document: W. Glover and J. Lygeros Deliverable number: D1.3 ..."
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Cited by 15 (4 self)
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Title of document: A multiaircraft model for conflict detection and resolution algorithm evaluation Authors of document: W. Glover and J. Lygeros Deliverable number: D1.3
Conflict probability and incrossing probability in air traffic management
 In IEEE Conference on Decision and Control, Las Vegas
, 2002
"... This paper studies performance metrics that are of use in the evaluation of conflict detection and resolution in air traffic management. The metrics studied are conflict probability and incrossing probability, both of which are closely related to the safety criteria used by the civil aviation commun ..."
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Cited by 14 (1 self)
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This paper studies performance metrics that are of use in the evaluation of conflict detection and resolution in air traffic management. The metrics studied are conflict probability and incrossing probability, both of which are closely related to the safety criteria used by the civil aviation community. The main contribution of this paper is to develop mathematical characterisations for these metrics, and to show typical differences in their behaviour through numerical evaluations of these metrics for some simple examples. 1
Flightmodebased aircraft conflict detection using a residualmean interacting multiple model algorithm
 in: Proceedings of the AIAA Guidance, Navigation, and Control Conference
, 2003
"... Based on the trajectory prediction error model proposed by Paielli and Erzberger, we propose nominal and probabilistic conflict detection algorithms using flight mode estimates as well as the aircraft current state estimates. This is different from previous conflict detection algorithms which use cu ..."
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Cited by 13 (2 self)
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Based on the trajectory prediction error model proposed by Paielli and Erzberger, we propose nominal and probabilistic conflict detection algorithms using flight mode estimates as well as the aircraft current state estimates. This is different from previous conflict detection algorithms which use current state estimates only. Our algorithms are therefore based on hybrid models of aircraft, which allow for both continuous dynamics and discrete mode switching. To obtain accurate state and mode estimates, we propose a modified version of the Interacting Multiple Model (IMM) algorithm designed by BarShalom et al. called the ResidualMean Interacting Multiple Model (RMIMM) method. RMIMM is a multiplemodelbased estimation algorithm based on a new likelihood function which uses the mean of the residual produced by each mode matched filter (usually Kalman filter), producing better mode estimates, and therefore better state estimates, than in the IMM case. We demonstrate our algorithm on multiple aircraft scenarios, and in the latter part of the paper, the probabilistic conflict detection algorithm is combined with the protocolbased conflict resolution algorithm, designed by the authors in earlier work.
Monte Carlo Optimization for Conflict Resolution in Air Traffic Control
 IEEE Trans. Intell. Transp. Syst
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Approximations of Stochastic Hybrid Systems
"... Abstract—This paper develops a notion of approximation for a class of stochastic hybrid systems that includes, as special cases, both jump linear stochastic systems and linear stochastic hybrid automata. Our approximation framework is based on the recently developed notion of the socalled stochasti ..."
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Cited by 12 (0 self)
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Abstract—This paper develops a notion of approximation for a class of stochastic hybrid systems that includes, as special cases, both jump linear stochastic systems and linear stochastic hybrid automata. Our approximation framework is based on the recently developed notion of the socalled stochastic simulation functions. These Lyapunovlike functions can be used to rigorously quantify the distance or error between a system and its approximate abstraction. For the class of jump linear stochastic systems and linear stochastic hybrid automata, we show that the computation of stochastic simulation functions can be cast as a tractable linear matrix inequality problem. This enables us to compute the modeling error incurred by abstracting some of the continuous dynamics, or by neglecting the influence of stochastic noise, or even the influence of stochastic discrete jumps. Index Terms—Approximation, bisimulation, stochastic hybrid systems, verification.
Cairano,“Optimal Control of Discrete Hybrid Stochastic Automata
 Hybrid Systems: Computation and Control, number 3414
, 2005
"... Abstract. This paper focuses on hybrid systems whose discrete state transitions depend on both deterministic and stochastic events. For such systems, after introducing a suitable hybrid model called Discrete Hybrid Stochastic Automaton (DHSA), different finitetime optimal control approaches are exa ..."
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Cited by 10 (1 self)
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Abstract. This paper focuses on hybrid systems whose discrete state transitions depend on both deterministic and stochastic events. For such systems, after introducing a suitable hybrid model called Discrete Hybrid Stochastic Automaton (DHSA), different finitetime optimal control approaches are examined: (1) Stochastic Hybrid Optimal Control (SHOC), which “optimistically ” determines the trajectory providing the best trade off between the tracking performance and the probability that stochastic events realize as expected, under specified chance constraints; (2) Robust Hybrid Optimal Control (RHOC) which, in addition, less optimistically, ensures that the system remains within a specified safety region for all possible realizations of stochastic events. Sufficient conditions for the asymptotic convergence of the state vector are given for recedinghorizon implementations of the above schemes. The proposed approaches are exemplified on a simple benchmark problem in production system management. 1
S.: Aircraft conflict prediction in the presence of a spatially correlated wind field
 IEEE Trans. on Intelligent Transportation Systems
, 2005
"... Abstract—In this paper, the problem of automated aircraft conflict prediction is studied for twoaircraft midair encounters. A model is introduced to predict the aircraft positions along some lookahead time horizon, during which each aircraft is trying to follow a prescribed flight plan despite the ..."
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Abstract—In this paper, the problem of automated aircraft conflict prediction is studied for twoaircraft midair encounters. A model is introduced to predict the aircraft positions along some lookahead time horizon, during which each aircraft is trying to follow a prescribed flight plan despite the presence of additive wind perturbations to its velocity. A spatial correlation structure is assumed for the wind perturbations such that the closer the two aircraft, the stronger the correlation between the perturbations to their velocities. Using this model, a method is introduced to evaluate the criticality of the encounter situation by estimating the probability of conflict, namely, the probability that the two aircraft come closer than a minimum allowed distance at some time instant during the lookahead time horizon. The proposed method is based on the introduction of a Markov chain approximation of the stochastic processes modeling the aircraft motions. Several generalizations of the proposed approach are also discussed. Index Terms—Air traffic control, conflict prediction, stochastic approximation, stochastic fields, stochastic modeling, wind correlation. I.
A Satisficing Approach to Aircraft Conflict Resolution
"... Abstract — Future generations of air traffic management systems will give appropriately equipped aircraft the freedom to change flight paths in realtime. This will require a conflict avoidance and resolution scheme that is both decentralized and cooperative. Satisficing game theory provides a theor ..."
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Cited by 7 (0 self)
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Abstract — Future generations of air traffic management systems will give appropriately equipped aircraft the freedom to change flight paths in realtime. This will require a conflict avoidance and resolution scheme that is both decentralized and cooperative. Satisficing game theory provides a theoretical framework in which autonomous decision makers may coordinate their decisions. A key feature of the theory is that satisficing decision makers form their preferences by taking into consideration the preferences of others, unlike conventional game theory which models agents that maximize selfinterest metrics. This makes possible situational altruism, a sophisticated form of unselfish behavior in which the preferences of another agent are accommodated provided that the other agent will actually take advantage of the sacrifice. This approach also makes possible the creation of groups in which every decision maker receives due consideration. We describe a solution to aircraft conflict resolution based on satisficing game theory. We present simulation results of a variety of scenarios in which the aircraft are limited to constantspeed headingchange maneuvers to avoid conflicts. We show that the satisficing approach results in behavior that is attractive both in terms of safety and performance. The results underscore the applicability of satisficing game theory to multiagent problems in which selfinterested participants are inclined to cooperation. I.
efficient associative processor solution to an air traffic control problem
 in Large Scale Parallel Processing IEEE Workshop at the International Parallel and Distributed Processing Symposium (IPDPS2010
, 2010
"... Abstract—This paper proposes a SIMD solution to air traffic control (ATC) using an enhanced SIMD machine model called an Associative Processor (AP). This differs from previous ATC systems that are designed for MIMD computers and have a great deal of difficulty meeting the predictability requirements ..."
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Cited by 6 (1 self)
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Abstract—This paper proposes a SIMD solution to air traffic control (ATC) using an enhanced SIMD machine model called an Associative Processor (AP). This differs from previous ATC systems that are designed for MIMD computers and have a great deal of difficulty meeting the predictability requirements for ATC, which are critical for meeting the strict certification standards required for safety critical software components. The proposed SIMD solution will support accurate and meaningful predictions of worst case execution times and will guarantee all deadlines are met. Also, the software will be much simpler and smaller in size than the current corresponding ATC software. An important consequence of these features is that the V&V (Validation and Verification) process will be considerably simpler than for current ATC software. Additionally, the associative processor is enhanced SIMD hardware and is considerably cheaper and simpler than the MIMD hardware currently used to support ATC. The ClearSpeed CSX600 accelerator is used to emulate the AP model. A preliminary implementation of the proposed method has been developed and experimental results comparing MIMD and CSX600 approaches are presented. The performance of CSX600 has better scalability, efficiency, and predictability than that of MIMD.