Extended optimal guidance law with impact angle and acceleration constriants

The extended optimal guidance law with terminal constraints of miss distance and impact angle is derived by the Schwartz inequality. To reduce terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go's reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.