Optimal abort landing trajectories in the presence of windshear

Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem

“…Higher order Runge Kutta schemes can also be written as (23) and with a function f h satisfying (22). For instance, the Heun scheme corresponds to the choice…”

“…y k ). Assumption (H1) and (22) imply that there exists R > 0 such that for any h > 0 and any k ≤ n, we have |y h k | ≤ R. This constant R can be chosen large enough such that every trajectory on a time interval I ⊂ [0, T ], starting from an initial position y h k would still remain in a ball of R d centred at 0 and with radius R. We set…”

“…This procedure consists in steering the aircraft to the maximum altitude that can reach in order to prevent a crash on the ground. In the references [22], [21], the authors propose a Chebyshev-type optimal control for which an approximate solution for the problem is derived along with the associated feedback control. This solution was improved in [11] and [12] by considering the switching structure of the problem that has bang-bang subarcs and singular arcs.…”

“…Here, we consider the same problem formulation as in [22,21,11,12]. The Hamilton Jacobi approach is used in order to characterize the value function and compute its numerical approximations.…”

Switching surfaces in linear differentialgames with a fixed instant of termination

“…The landing process was considered up to the instant when the end of the runway was reached. A control procedure using a switching surface, which is specified by a set of switching lines, was also tested [17,18] on model landing and take-off problems from [9][10][11][12][13][14][15][16][17][18][19][20][21]. A problem on the take-off run of an aircraft along the runway under conditions of windshear was considered in [22]; the control procedure investigated was also based on the construction of a switching surface.…”