Derivation of Optimal Guidance Laws for Non-Quadratic Criterion

In this paper, optimal guidance laws are derived using non-quadratic criterion, i.e., the magnitude of the commanded acceleration to the power of q> 1 for integer and non-integer values. A time-to-go weighting function is also included. The final time is fixed. Since thereduced-order differential equations of zero-effort miss distance (ZEM) and zero-effort velocity error (ZEV) are used in the derivation, the results are applicable for a class of guidance problems with different formulations of ZEM and ZEV equations for midcourse and terminalphases, both in aerial and space missions. An explicit solution is derived when the final velocity is free. If the final velocity is fixed, solution leads to a set of algebraic equations for costates for special values of q. For these values of q, the solution can be implemented onboard. In this type of formulation, the equations will be singular for minimum fuel problem (q=1). The time-to-go weighted optimal energy guidance laws (q=2) for highorder control systems are special cases of the present solution.

Keywords:

optimal guidance strategies , non-quadratic performance index , trajectory optimization , minimum fuel guidance.