Section: New Results

New advances on backstepping

Participants : Frédéric Mazenc, Michael Malisoff [LSU] , Laurent Burlion [Rutgers Univ.] .

We worked on the problem of improving a major control design technique for nonlinear continuous-time systems called backstepping by using a fundamentally new approach which uses as key ingredient the introduction in the control of artificial delays or the use of dynamic extensions.

In the paper [24], we adopted a technique which is based on the introduction of pointwise delays (and not of distributed terms) to solve a challenging input-to-state stabilization problem for a chain of saturated integrators when the variables are not accurately measured. Let us observe that classical backstepping does not apply in the considered case.

In the paper [23], we constructed bounded globally asymptotically stabilizing output feedbacks for a family of nonlinear systems, using a dynamic extension and a converging-input-converging-state assumption. We provided sufficient conditions for this assumption to hold, in terms of Lyapunov functions. The novelty is that our construction provides formulas for the control bounds while allowing uncertainties that prevent the use of classical backstepping in cases where only part of the state variable is available. We illustrated our work with an engineering application: the single-link direct-drive manipulator.