Section: New Results

Backstepping with artificial delays

Participants : Frederic Mazenc, Michael Malisoff [LSU, USA] , Laurent Burlion [ONERA] , Victor Gibert [Airbus] , Jerome Weston [LSU, USA] .

We worked on the problem of improving a fundamental control design technique called backstepping.

We provided in [54] a new backstepping control design for time-varying systems with input delays. The result was obtained by the introduction of a constant 'artificial' pointwise delay in the input and a dynamic extension. Thus it is significantly different from backstepping results for systems with delay in the input as presented in previous contributions. The result in [54] ensures global asymptotic convergence for a broad class of partially linear systems with an arbitrarily large number of integrators. We used only one artificial delay, and we assumed that the nonlinear subsystems satisfy a converging-input-converging-state assumption. When the nonlinear subsystem is control affine with the state of the first integrator as the control, we provided sufficient conditions for our converging-input- converging-state assumption to hold.