Velocity maximizing suboptimal control law for agile turn of air-to-air missile

In this paper, optimal control problems considering agile turn of missile as maximizing terminal velocity at boost phase are dealt. The missile in the phase experiences dramatic variation in velocity, mass and angle of attack within finite duration. This research at first, classifies the missile models into two different cases; longitudinal motion and lateral motion, but all of the models neglect aerodynamic forces. Each model has an optimal solution known as Bang-Singular Control, and the corresponding optimal control as well as switching condition for Bang to Singular is analytically derived. After the derivation of optimal solutions, two different suboptimal control laws which are based on the optimal solutions and capable of aerodynamic forces are proposed. The first law uses the optimal solution directly while the other incorporates theoretical aerodynamic equations. A comparison between results from the proposed control laws, results from PD type control law and optimal results from a commercial optimization tool are presented and usefulness of proposed method is validated through the comparison.