Bank-to-turn guidance law using Lyapunov function and nonzero effort miss

A guidance law that directly computes the pitch acceleration and roll angle commands for Bank-To-Turn missiles is presented. The nonzero effort miss is introduced, and a Lyapunov function is defined in terms of nonzero effort miss. Lyapunov's stability theorem is used to obtain a guidance law that completely eliminates the trigonometric polar conversion, which conversion is necessary when the guidance commands and the input to the pitch and the roll autopilots are given in different coordinate systems. When the new guidance law is used, the missile tends to maintain its acceleration command above a certain level during its flight and thereby avoid a mathematical singularity that arises when a trigonometric inverse function is used to compute the roll command. A representative engagement scenario is used to demonstrate the effectiveness of the proposed guidance law. Numerical simulation results are compared with previous results and with results obtained using a proportional navigation guidance law that uses a polar conversion.