Lie Transform Construction of Exponential Normal Form Observers

Abstract Motivated by a class of nonlinear regulator problems associated with systems that experience actuator failure, this work discusses the construction of nonlinear observers in normal form using a systematic and elegant method of transformation, namely Lie Transforms. It is shown how the transformation, which is the solution of a Homological Equation, and the observer gain matrix, which is a series of matrix homogenous polynomials, can be sequentially computed. An illustrative example is given and experience with using these observers is discussed.