The design of optimal guidance law with multi-constraints using block pulse functions

When there are time-varying parameters in motion equations, the optimal guidance law with multi-constraints generally cannot be solved analytically. Based on block pulse functions, a design method of optimal guidance law is presented combining optimal control theory and numerical value computation for time-varying systems. The presented guidance law can optimize the combination of landing angle, miss distance, and control energy consumption. Using both the proposed guidance law and the proportional navigation law, ballistic simulations are made. Compared to the proportional navigation law, the optimal guidance law is able to more than double the landing angle. Because of the steep terminal trajectory, the strike accuracy and damage effects are increased. Averaging the time-varying coefficients of the optimal guidance law, a suboptimal guidance law is obtained. This guidance law is simpler and can make the terminal trajectory steep too. Therefore, it could be applied to projects more easily and requires less onboard computational resources. However, it consumes slightly more control energy than the optimal guidance law.