Discussion on: “Backstepping Controller Design Using Neural Networks for a Fighter Aircraft”

Abstract

The paper by Sadati et al. presents a neural network(NN) based adaptive backstepping design for flightcontrol systems of fighter aircraft in high angle-of-attack (AoA) and/or high angular rate regimes. Theflight control system is designed for command fol-lowingoftheAoA,sideslipangle,androllangleaboutthe velocity vector. The design is an adaptive statefeedback design in which the NN is trained online tocompensate for uncertainties due to parametric var-iations in the aerodynamic coefficients and due to asudden change in aircraft dynamics in the event offailure or battle damage. The NN update laws arederived using Lyapunov-like stability analysis toprove uniform ultimate boundedness of the closed-loop system errors. The design of flight control sys-tems that are capable of delivering high performancein such regimes is very challenging due to the highlynonlinear and unsteady phenomena associated withhigh AoA flight and the modeling uncertainty. Thenonlinear adaptive control design provided in thepaper by Sadati et al. is thus an important contribu-tion to this problem. We first provide some commentsthat could have been included in the paper to clarifythe contributions and proceed to describe furtherdirections for research.The authors have commented in the introductionon the differences between feedback linearization andbackstepping approaches in nonlinear control design,and their motivation for choosing the backsteppingapproach. In our opinion, the authors should havementioned that the most significant reason why abackstepping design could be preferred over a feed-backlinearizationdesign isthat abacksteppingdesigncan account for unmatched uncertainties. However inproblems where both approaches are applicable, webelieve that backstepping designs can be more com-plex than feedback linearization designs. This can beseen in problems where there are multiple loops to bestabilized. Backstepping designs require choosinggains for stabilizing each individual loop and in gen-eral for the inner-loops the design could be high-gain.In addition, time derivatives of the intermediate con-trol commands appear in each step of the back-stepping procedure[e.g.,Eqs. (26),(29)and(30)ofthepaper]. These time derivatives cannot be directlycomputed when the plant model is unknown andapproximate techniques have to be developed.The authors have mentioned that one motivationfor pursuing the backstepping approach in flightcontrol systems design is that explicit time-scaleseparation assumptions are not required. While this istrue, we would like to bring to the authors’ attentionan adaptive NN-augmented feedback linearizationapproach in an almost identical problem [1]. Theapproachin[1]alsodoesnotrelyonexplicittime-scaleseparation assumption. The authors’ can carry out acomparison study of their approach with that in [1]that will illustrate the relative merits of the respectiveapproaches.