Infinite-dimensional linearization and extended adjoint method for nonlinear homing loop analysis

Abstract

The adjoint method for boundary value problem in linear homing loop analysis is extended to nonlinear analysis. By truncating an infinite-dimensional linearization of the nonlinear differential equation, and then writing its adjoint as usual, one obtains a series-expansion approximation of the nonlinear solution. Under appropriate conditions, quantities such as the miss distance can be estimated with an accuracy that improves as the truncation dimension increases. The approach is illustrated with two planar homing problems with nonlinear equations of motion. © 2003 by the author.