Feedback linearization and backstepping: an equivalence in control design of strict-feedback form

Abstract

Abstract This paper investigates an equivalence between feedback linearization and backstepping control. Implications from equivalence are that stability and performance properties of one method are the same for another method. Thus, a property known to exist only for one method could be used to prove property also holds for another. Also, a suspected advantage of one method over the other could be proven to be a false conjecture. Control laws in both approaches are achieved by coordinate transformations and non-linear feedbacks. Further, resulting non-linear feedback control law achieved by feedback linearization method matches exactly with non-linear controller achieved by the backstepping control design. This equivalence is a general analytical match within the specific class of non-linear dynamic systems under investigation. Demonstrations are considered and validated via flight control of longitudinal dynamics of a high performance aircraft simulation model. Algorithms are tested and evaluated with analytical models and non-linear closed-loop simulation.