Optimal Proportional-Integral Guidance with Reduced Sensitivity to Target Maneuvers

This paper proposes a new optimal guidance law based on the proportional-integral (PI) concept to reduce the sensitivity to unknown target maneuvers. Compared to the existing PI guidance laws, the proposed guidance command is derived in the optimal control framework while guarantees finite-time convergence. The kinematics equation with respect to the zero-effort-miss (ZEM) is utilized and the integral ZEM is augmented as a new system state. The proposed guidance law is derived through the Schwarz's inequality method. The closed-form solution of the proposed guidance law is presented to provide better insight of its properties. Additionally, the working principle of the integral command is investigated to show why the proposed guidance law is robust against unknown target accelerations. The analytical results reveal that the proposed optimal guidance law is exactly the same as an instantaneous direct model reference adaptive guidance law with a prespecified reference model. The potential significance of the obtained results is that it can provide a point of connection between PI guidance laws and adaptive guidance laws. Therefore, it allows us to have better understanding of the physical meaning of both guidance laws and provides the possibility in designing a new guidance law that takes advantages of both approaches. Finally, the performance of the guidance law developed is demonstrated by nonlinear numerical simulations with extensive comparisons.