In this study, we develop an adaptive-critic-based controller to steer an agile missile that has a constraint on the minimum flight Mach number from various initial Mach numbers to a given final Mach number in minimum time while completely reversing its flightpath angle. This class of bounded state space, free final time problems is very difficult to solve due to discontinuities in costates at the constraint boundaries. We use a two-neural-network structure called adaptive critic in this study to carry out the optimization process. This structure obtains an optimal controller through solving optimal control-related equations resulting from a Hamiltonian formulation. Detailed derivations of equations and conditions on the constraint boundary are provided. For numerical experiments, we consider vertical plane scenarios. Flight Mach number and the flightpath angle are the states and the aerodynamic angle of attack is treated as the control. Numerical results bring out some attractive features of the adaptive critic approach and show that this formulation works very well in guiding the missile to its final conditions for this state constrained optimization problem from an envelope of initial conditions
