Linearizable feedforward systems: A special class

Abstract

Abstract-We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow an easy computation of the linearizing coordinates and thus provide a stabilizing feedback controller for the original system. They can also be implemented via software like mathematica/matlab/maple using simple integrations, derivations of functions.

Feedback Linearizable Feedforward Systems: A Special Class

“…We suppose that 6FFnice is linearly controllable and, in particular, (@f j =@x j+1 )(0) 6 = 0 for 1 j n 0 1. We recall briefly the main result of [17].…”

“…What made (SFF)-systems appealing is that a stabilizing feedback controller can always be constructed when their linear approximation around the equilibrium is controllable [22], [23]. Problem 1 were tackled in [17] for the feedforward case. If there is a component f j or g j that is nonlinear with respect to the variable xj, then finding an explicit linearizing coordinates becomes extremely difficult and might necessitate solving PDEs.…”

“…1 1 A special thank you to Linda G. for her invaluable assistance. and were introduced in [9], [10] (see also [17], [20] beyond that class), where it is showed that a linearizing coordinates is…”

Inverse optimal control for linearizable nonlinear systems with input delays

“…It is revealed that the family of feedforward systems contains a substantial class that is linearizable by a diffeomorphic coordinate change in [15,16]. An algorithm along with explicit transformations that linearizes a class of feedforward nonlinear systems is in [21]. Sufficient and necessary conditions are given for a control-affine mechanical system that can be transformed into a linear system by a diffeomorphism coordinate change in [20].…”

Global Stabilization of Feedforward Systems Under Perturbations in Sampling Schedule

“…However, nonlinear feedforward systems of the form (1.1) under hypothesis (1.2) rarely belong to one of the above classes (an exception is the class of linearizable feedforward systems; see [24,[49][50][51][52]). On the other hand, there are well-established standard control design methodologies that guarantee stabilization of system (1.1) under sampled-data control with zero-order hold [10,22,23,26,27,[41][42][43][44][45] but only in the practical and semiglobal sense.…”