A robust aircraft control approach in the presence of wind using viability theory

This paper presents a control concept for the application of viability kernels for aircraft control in the presence of wind disturbances. The viability (leadership) kernel of an appropriate conflict control problem with state constraints is computed using a grid approximation. In this differential game formulation, the first player is represented by the aircraft controls and the second player by the wind disturbances. The viability kernel represents a subset in the state space, in which the aircraft can be held arbitrarily long even if the opposing player uses any admissible control. Due to the curse of dimensionality in the grid solution, the computation of the viability kernel is restricted to low dimensional state spaces, which poses a challenge for the application in aircraft control. In our approach, the viability kernel is computed in the state space of the translational dynamics and the attitude kinematics. This reduces the dimensionality of the viability kernel to a six dimensional state space that can be handled by grid computers. The trajectory from the viability kernel solution is then tracked by the inner-loop controller based on a nonlinear dynamic inversion (NDI) control structure. The approach is illustrated using a simplified A300 aircraft model for cruise flight in the presence of wind.