Biased Optimal Guidance for a Bank-to-Turn Missile

The problem here is to derive and test a practical terminal-phase guidance law for controlling the pitch acceleration and roll rate of a bank-to-turn missile with zero autopilot lags, so as to minimize spuared miss distance without requiring overly large commands. At the suggestion of P. Travers, an acceleration bias is introduced to prevent excessive roll commands due to noise. The Separation Theorem is invoked and the guidance (control) law is derived by applying optimal control theory, linearizing the nonlinear plant equation around the present missile orientation and obtaining a closed-form solution. The optimal pitch-acceleration and roll-rate commands are respectively proportional to two components of the projected, constant-bias, miss distance, with a resemblance to earlier derivations and proportional navigation. Simulation results herein and other related work confirm the suitability of the guidance law.