Nonlinear optimal guidance for intercepting a stationary target

The problem of optimally guiding an interceptor to a stationary target is studied in a nonlinear setting. First of all, it is shown that a global solution does not exist for the typical free-time minimum-effort nonlinear optimal intercept problem. This leads to consideration of the linear combination of the control effort and engagement duration as the objective function. The necessary conditions for the optimal intercept problem with the new objective function are found to be parameterized by a scalar, reducing the problem of deriving the optimal guidance law to the problem of finding the zeros of a real-valued function. Moreover, a semianalytical form for the real-valued function is devised, and the interval for its zeros is restricted, allowing the use of a brute-force search to efficiently find all the zeros. As a result, the nonlinear optimal guidance law can be efficiently established. Finally, the characteristics of the guidance law are exemplified and studied through simulations, showing that the nonlinear optimal guidance law performs better than the conventional proportional navigation, especially for cases with large initial heading errors.