Coordinate‐Invariant Linear Quadratic Control

Abstract

This paper shows how the linear quadratic regulator (LQR) designs in different coordinate choices are related. Given the LQR design in one coordinate choice, it is shown that the LQR design for an alternate coordinate choice can be recovered through use of the nonlinear and linearized coordinate transformations. This provides the analyst a method of comparing coordinate choices that is more straightforward than previously suggested methods involving nonlinearity indices.