Strict feedforward control systems, linearisability, and convergent normal forms

Abstract

This article discusses the feedback equivalence of multi-inputs feedforward control systems via smooth (resp. analytic) feedback transformations. We first address the state (resp. feedback) linearisation problem, and provide easily computable algorithms that yield explicit state (resp. feedback) linearising coordinates for systems in strict feedforward form. The application of the algorithms does not require checking the commutativity (resp. involutivity) of the distributions associated with the system, and the algorithms fail after few steps if the system is not linearisable. In the latter case, the algorithms are extended to provide coordinate systems bringing the system into a normal form which is a smooth (resp. analytic) counterpart of Kang's formal normal form. Illustrative examples for both the linearisation and convergent normal form include the vertical take off and landing aircraft, the multi-vehicle wireless testbed among others.