Three-Dimension Guidance Law and Capture Region Analysis

A new three-dimension nonlinear H_∞ guidance law is proposed to intercept an unknown maneuvering target. By using the modified polar coordinate (MPC), nonlinear relative motion equations only contain three state variables. Then we apply the nonlinear H_∞ control theory into system equations to get an analytic H_∞ guidance law, which has the same expression as true proportional navigation (TPN). The proposed H_∞ guidance law can ensure system L₂ gain less than or equal to a positive constant. Some results of performance analysis including capture region, capture region with acceleration constraint, an integral expression of time-to-go, and miss distance are derived analytically. Particularly, the capture region with acceleration constraint is an important improvement upon the capture region of TPN and is significant for applications. Finally, some numerical examples illustrate the theories clearly, and some simulations are conducted to validate the academic results.