Robust dynamic routing of aircraft under uncertainty

Abstract

Much of the delay in the US National Airspace System (NAS) arises from convective weather. One major objective of our research is to take a less conservative route, where we take a risk of higher delay to atkin a better expected delay, instead of avoiding the bad weather zone completely. We address the single aircraft problem using a Markov decision process model and a stochastic dynamic programming algorithm, where the evolution of the weather is modeled as a stationary Markov chain. Our solution provides a -dynamic routing strategy for an aircraft that minimizes the expected delay. A significant improvement in delay is obtained by using our methods over the traditional methods. In addition, we propose an algorithm for dynamic routing where the solution is robust with respect to the estimation errors of the storm probabilities. To the Bellman equations, which are derived in solving the dynamic routing strategy of an aircraft, we add a further requirements: we assume that the transition probabilities are unknown, but bounded within a convex set. The uncertainty described in our approach is based on likelihood hctions. This makes the robust Dynamic Programming (DP) "tractable" (that is, not much more complicated than the original DP) and yet not conservative. Our algorithm optimizes the performance of the system, given there are errors in the estimation of the probabilities of the storms. OverviewAir traffic delay due to convective weather has grown rapidly over the last few years. Accorrlmg to the FAA, flight delays have increased by more than 58 percent since 1995, cancellations by 68 percent. The delay distribution can be described in the figure below:

Development of UAV Trajectory Management System Based on Fuzzy Logic Concepts

“…There are numerous ways of modeling obstacles in the literature, each of which is basically motivated by the nature of the specific threat events. 28,29 In particular, in this research, all present obstacles will be mathematically modeled in the form of a circle, inside of which the UAV will be vulnerable to the obstacle with a certain probability proportional to the distance away from the obstacle center, while outside this region the UAV is not at risk. The trajectory management task is to generate a feasible path between o and f considering all these obstacle areas.…”

On maximizing safety in stochastic aircraft trajectory planning with uncertain thunderstorm development

“…However, in the studied aircraft-weather conflict, the weather hazard was considered deterministic. In Nilim et al (2002), the authors addressed the problem of generating aircraft trajectories using a Markov decision problem where the evolution of the thunderstorms was modeled as a Markov chain. The transition probabilities were extracted from historical data using maximum-likelihood estimators.…”

Multiple model robust dynamic programming

“…The distribution can take many forms, ranging from additive output noise to sets of models. Some examples include additive or multiplicative state or control process noise on top of the nominal dynamics [2] [3], random variables in the process model [4], arbitrary state-dependent stochastic transition functions [5], and Markov decision processes (MDP) with known or even unknown transition probabilities [6].…”