Flight Path Angle Reversal of an Air-to-Air Missile in Minimum Time Using Pseudo-spectral Method

The pseudo-spectral (PS) method has been applied in this paper to design an optimal guidance strategy for an air-to-air missile to completely reverse its flight path angle in minimum time, while simultaneously assuring a designated state constraint (Mach number) at the end of the turning. The missile has to reverse its direction as quickly as possible so as to intercept the target in the rear hemisphere. The PS method is found to give good results while steering the vehicle in the reverse direction and almost exactly satisfying the final Mach number constraint. The key idea of PS method is to discretize the optimal control problem and solve for the resulting low-dimensional nonlinear programming problem in real time. PS discretization demands a relatively lower number of grid points which thereby reduces the computational time. Both Chebyshev and Legendre polynomial approximation have been successfully used to solve the problem and the results from both are consistent.