Time-scale separation redesigns for stabilization and performance recovery of uncertain nonlinear systems

In this paper we propose two different time-scale separation based robust redesign techniques which recover the trajectories of a nominal control design in the presence of uncertain nonlinearities. We first consider additive input uncertainties and design a high-gain filter to estimate the uncertainty. We then employ the fast variables arising from this filter in the feedback control law to cancel the effect of the uncertainties in the plant. We next extend this design to systems with uncertain input nonlinearities in which case we design two sets of high gain filters-the first to estimate the input uncertainty over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. Using singular perturbation theory we prove that the trajectories of the respective two-time-scale and three-time scale redesigned systems approach those of the nominal system when the filter gains are increased. We illustrate the redesigns by applying them to various physically motivated examples.

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