Solving a nonlinear output regulation problem: zero miss distance of pure PNG

Presents a solution to the output regulation problem of a nonlinear system with time-varying disturbance: the system represents the well-known missile-target pursuit situation where the missile is guided by the pure proportional navigation guidance (PPNG) law while the target maneuvers with time-varying normal acceleration, and the problem is to prove the zero miss distance property of PPNG, which has been studied for decades without satisfactory success. To solve this problem, we construct a function by which a time sequence of the missile-to-target range is upper-bounded, and prove that the function is strictly decreasing, which is also proven to guarantee that there is always a sub-sequence that asymptotically converges to zero. The solution is given in the form of a necessary and sufficient condition guaranteeing the zero miss distance of PPNG