Optimal trajectories for RPAS with discrete controls and discrete constraints

Dynamic systems often have discrete controls or discrete decisions involved. Discrete Controls can only take values from a fixed set. At the same time, the choice of such controls introduces discrete changes in constraints. For instance, the discrete flap positions on an aircraft have discrete speed constraints. This paper describes a method for taking into account discrete controls in an optimal control problem. Discrete changes in the constraints are taken into account using vanishing constraints. The number of switches within the optimal solution is minimized by adding a penalty term to the cost function. The method is applied to an off-line optimization problem of a three degree of freedom (3DOF) aircraft model in which the switching structure of the flaps are optimized. Discrete constraints are implemented for the lift coefficient, the maximum calibrated airspeed and the vertical load factor.