Trajectory optimization for Missile-borne SAR imaging phase via Gauss Pseudospectral Method

Azimuth resolution of Missile-borne synthetic aperture radar(SAR) is affected by the trajectory and look angle. In order to acquire the fixed azimuth resolution within a minimum time for SAR imaging seeker, a new approach of solving optimal control problem, that is, Gauss Pseudospectral Method(GPM), is proposed to optimize imaging phase trajectory of Missile-borne SAR. First of all, optimization model of imaging phase is built, the missile command acceleration is used as control variables, the minimum dwell time is used as objective function and expression of objective function, imaging constraint as well as over loading constraint is proposed. And then, the state and control variables is discretized by GPM. Through this transformation, the continuous-time optimal control problem is transcribed to a nonlinear programming (NLP). At last, GPOPS software package based on matlab is used to solve this problem. Simulation results show that a smooth trajectory can be got by GPM, and GPM isn´t sensitive to initial value of state and control variables. Compared with genetic algorithm, GPM have a faster solution speed and a better robustness.