Virtual Target Approach for Emulation of Optimal Guidance Using Proportional Navigation

This study proposes a virtual target approach for the emulation of optimal guidance on a legacy platform. A constant-speed unicycle agent using the proportional navigation guidance law is required to approach a given final configuration from the initial one while minimizing a quadratic cost functional that includes terminal miss, heading error, and control effort. The approach is based on the pursuit of an externally transmitted sequence of stationary or moving virtual targets, in which the initialization parameters are periodically updated at fixed times. The problem of finding the parameters of the virtual targets is reduced to an equivalent discrete-time optimal control problem of a particular structure. In one particular case, this problem was reduced to a linear–quadratic optimal control problem, which can be solved using a Riccati procedure. The obtained solutions were shown to outperform the intuitive waypoint guidance, in which the waypoints were sampled from the linear–quadratic optimal solution, whereas the solution using moving virtual targets was close to the full optimal solution for a wide range of boundary conditions.