Generalized optimal impact-angle-control guidance with terminal acceleration response constraint

To study the optimal impact-angle-control guidance problem with multiple terminal constraints, a generalized optimal impact-angle-control guidance law with terminal acceleration response constraint (GOIACGL-TARC) is proposed. In the deriving, a time-to-go −nth power weighted object function is adopted to derived the GOIACGL-TARC and a general expression of GOIACGL-TARC is presented. Based on the general expression of GOIACGL-TARC, three guidance laws, GOIACGL-TARC1/TACC0/TACC1 are proposed and the inheritance relationship between GOIACGL-TACC0/TACC1/TARC1 and the conventional optimal guidance law with impact angle constraint is demonstrated. Performance analysis of the proposed guidance laws shows that in the case of GOIACGL-TACC0, the terminal acceleration is not zero at n = 0 and only as n > 0, the terminal acceleration converges to zero; in the case of GOIACGL-TACC1 and GOIACGL-TARC1, GOIACGL-TARC1 can guarantee the acceleration response to reach the exactly zero value but GOIACGL-TACC1 cannot, which can only guarantee the acceleration command to reach the exactly zero value. It is pointed out that compared with the biased proportional navigation guidance law, GOIACGL-TARC1 has an outstanding guidance performance in acceleration response, miss distance, and terminal impact angle error.