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An optimum PN guidance law for maneuvering target is developed using optimal control theory. By estimating the target position and setting the cost function, the guidance law can be deduced even without knowing the missile lateral acceleration. Since the quadratic cost function can make a compromise between the miss distance andthe control constraint, the optimum guidance law obtained is more general. Also, introduced line of sight rate as the input, a practical form of this guidance law is derived. The simulation results show the effectiveness of the guidance laws.