Optimal trajectories of high-thrust aircraft

Future fighter aircraft may have sufficient thrust to sustain maximum-turn-rate flight at the corner velocity where the limits on the maximum lift coefficient and maximum normal-acceleration load factor are met simultaneously. Unfortunately, the usual necessary optimal control conditions break down on these corner velocity arcs. This paper presents a set of necessary optimality conditions which must hold when corner velocity arcs are part of an optimal aircraft trajectory. First, these necessary conditions are obtained for a general class of problems with two state-dependent control variable inequality constraints. The resulting conditions are identical to those for optimal control problems with state variable inequality constraints. These necessary conditions then are applied to optimal trajectory problems with high-thrust aircraft. Two sample solutions to the problem of minimum time-to-turn through a specified heading angle are presented to illustrate some of the features of optimal trajectories with sustained maximum-turn-rate corner velocity arcs.