Numerical solution of constrained nonlinear optimal control problem is an important field in a wide range of applications in science and engineering. The real time solution for an optimal control problem is a challenge issue especially the state constrained handling. Missile trajectory shaping with terminal bunt manoeuvre with state constaints is addressed. The problem can be stated as an optimal control problem in which an objective function is minimised satisfying a series of constraints on the trajectory which includes state and control constraints. Numerical solution based on a direct multiple shooting is proposed. As an example the method has been implemented to a design of optimal trajectory for a missile where the missile must struck the target by vertical dive. The qualitative analysis and physical interpretation of the numerical solutions are given.
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