A delay model for satellite constellation networks with inter-satellite links

Abstract

Within this paper we examine a non-geostationary satellite constellation network with inter-satellite links (ISLs) for global air traffic control (ATC) and air passenger communication (APC). More specifically, an analysis is done to investigate the impacts of different routing policies on the end-to-end delay, and a general model describing the delays is developed. All considerations are based on a Galileo-like satellite constellation network and real global flight data of all commercial flights during one day

LQ-Optimal Sampled-Data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability

“…by the Schur complement formula. In this case, C(φ) and D(φ), derived from the Cholesky decompositions (16), are unique in the following sense: For all φ ∈ M, there exist unique upper triangular matrices C(φ) and D(φ) with strictly positive diagonal entries such that (16) (19). In this section, we recall results from [5] on such an LQ problem for Markov jump systems.…”

“…Let us go back to the reduced LQ problem 3.3 for the Markov jump system (18) and the LQ cost (19), where the matricesĀ, C, and D are defined by (15) and (16). The Cholesky decompositions for all φ ∈ M in (16) requires heavy computational cost, but the weighting functions C and D appear only in R and V in the forms C C and D D. Hence, to compute an optimal control input u opt , we do not need the Cholesky decompositions in (16). Although we still need C to check the stochastic detectability of (C,Ā), we see from Proposition 4.7 below that it is enough to test the stochastic detectability of (C C,Ā) if C C is positive definite.…”

“…Next we study the stochastic detectability of the pair A ∈ H n sup and C ∈ H r×n sup . In our LQ problem, we need to check the stochastic detectability of (C,Ā) or (Q − W R −1 W ,Ā) in (15) and (16).…”

“…However, most of those syntheses of optimal controllers require online computation and are based on assumptions that the delays can take only finitely many values or be independent and identically-distributed random variables. In practice, communication delays take a continuum of values and need to be modeled by more general stochastic processes such as Markov processes in [3,15,16]. A notable exception can be found in [23], in which the authors have presented an offline computation method of delay-dependent LQ controllers for systems with continuous-valued Markovian delays.…”

Machine‐to‐machine communications via airliners

“…Let us define a point on the ground as covered by the proposed M2M architecture if a terminal can communicate with at least one airliner. To the aim of evaluating the achievable coverage, we focus on European and North American landmasses, and we perform simulations taking advantage of real traffic information contained in flight tracking databases . In particular, two different grids have been defined and studied, namely, for Europe, the latitude ranges from 35°N to 75°N, whereas the longitude is from 10°W to 40°E;for the North American landmasses, the latitude ranges from 15°N to 75°N, whereas the longitude is from 165°W to 50°W.…”