A stochastic strategy integrating wind compensation for trajectory tracking in aircraft motion control

This paper deals with the problem of steering an aircraft along a reference trajectory while counteracting the wind disturbance. We develop a control strategy where the aircraft nonlinear dynamics, physical limitations on the aircraft maneuverability, and passengers comfort are accounted for by feedback linearization and a suitable convex relaxation of constraints. A probabilistic constraint is introduced to account for the tracking error introduced by the stochastic wind disturbance. Since wind is represented by a Gaussian random field and its characteristics depend on both time and space, we identify on-the-fly a local autoregressive model via recursive least squares with forgetting factor. The probabilistic constraint formulation, the wind model update, and the re-computation of the control action jointly allow to account for the spatial variability of the random field and to obtain recursive feasibility in the receding horizon solution. A randomized method is adopted to obtain a convex relaxation of the resulting chance-constrained optimization problem, which can then be solved on-line, at low computational effort.