Stochastic optimal control for aircraft conflict resolution under wind uncertainty

Near-Optimal Control for Aircraft Conflict Resolution in the Presence of Uncertainty

“…In this section, we introduce the stochastic aircraft dynamics including spatially correlated wind uncertainty and briefly review our previously developed conflict-detection and -resolution algorithms based on the PCE and pseudospectral methods [10].…”

“…The stochastic optimal control problem for conflict resolution is also solved by a Markov chain approximation and the Jacobi iteration [9], but the problem becomes intractable for the high-dimensional continuous state space and a large number of the discrete states. In previous work [10], a stochastic optimal control method for conflict resolution under spatially correlated wind uncertainty [11,12] was developed based on the polynomial chaos expansion (PCE) algorithm [13,14] and the pseudospectral method [15][16][17]. The PCE algorithm can quantify uncertainties in the complex nonlinear dynamical systems with high computational efficiency, and the pseudospectral method can solve the nonlinear optimal control problems effectively.…”

“…The aircraft dynamics containing the spatially correlated wind error become complex because of the complicated stochastic models, and nonlinear optimal control problems for such complex dynamical systems are challenging to solve and require sophisticated optimization approaches. Our developed stochastic optimal control method incorporating the PCE algorithm into the pseudospectral method could deal with stochastic elements and solve the challenging stochastic optimal control problems [10]. However, it requires us to solve the computationally expensive stochastic optimal control problems to obtain the optimal conflict-resolution trajectories under wind uncertainty.…”

“…The proposed nearoptimal conflict-resolution algorithm enables pilots to determine near-optimal conflict-resolution trajectories and maneuvers in real time based on the information of current conditions of their own aircraft and the nearby aircraft received via a datalink called the Automatic Dependent Surveillance-Broadcast. This study is focused on the two-dimensional aircraft-aircraft and aircraft-weather conflict-resolution problem, whereas the aircraft-aircraft conflictresolution problem in the three-dimensional terminal airspace is considered in previous research [10]. To consider more the general conflict-resolution problem, as to the uncertainties, the airspeed measurement error and the uncertainty contained in the moving convective weather region are considered as well, as the spatially correlated wind error.…”

“…Section II presents the stochastic aircraft dynamics and reviews the probabilistic conflict-detection andresolution algorithms developed in previous work [10]. In Sec.…”