OPTIMAL CONTROL IN ABORT LANDING OF A PASSENGER AIRCRAFT

Abstract

The landing of a passenger airplane in the presence of a windshear is a threat to the safety in aviation. In the present paper some first results are given which are concerned with the abort landing of an aircraft in such a serious situation. Mathematically, this flight maneuver can be described by a minimax or Čebyšev optimal control problem where the ground clearance, or in other words, the minimal altitude is to be maximized. By transforming this minimax problem into an optimal control problem of standard form, a state constraint has to be taken into account which is of order three here. Besides this third order state constraint the model contains another state constraint which is of first order. Since the control variable appears linearly the set of admissible controls must be compact. Moreover, the problem contains nonsmooth data arising from the approximations of the aerodynamic forces and the prescribed distribution of the wind velocity components. Due to the complexity of the constraints and because of the fact that the Hamiltonian is not regular, the obtained switching structure is very complicated showing nearly all features which can appear when solving such problems. There are subarcs of very different types among which we found bang-bang and singular subarcs as well as boundary subarcs of both state constraints and also a touch point of the third order state constraint. Boundary arcs are known to be impossible for regular Hamiltonians and odd-ordered state constraints if the order exceeds 2. Numerically this real-life optimal control problem is solved by solving the multipoint boundary value problem based on necessary conditions using the well-known multiple shooting method in connection with an appropriate homotopy strategy.