This paper presents the design of a singular-perturbation-based optimal guidance with constraints on terminal flight-path angle and angle of attack. By modeling the flight-control system dynamics as a first-order system, the angle of attack is introduced into the performance index as a state variable. To solve the resulting high-order optimal guidance problem analytically, the posed optimal guidance problem is divided into two sub-problems by utilizing the singular perturbation method according to two time scales: range, altitude, and flight-path angle are the slow time-scale variables while the angle of attack is the fast time-scale variable. The outer solutions are the optimal control of the slow-scale subsystem. Thereafter, by applying the stretching transformation, the fast-scale subsystem establishes the relationships between the outer solutions and acceleration command. Then, the optimal command can be obtained by solving the fast-scale subsystem also using the optimal control theory. The proposed guidance can achieve a near-zero terminal acceleration as well as a small miss distance. The superior performance of the guidance is demonstrated by adequate trajectory simulations.
Applications of Singular Perturbation Techniques to Control Problems