Data-Driven Stabilization of Nonlinear Systems with Rational Dynamics

Robin Strässer, Julian Berberich, Frank Allgöwer

In this paper, we present a data-driven controller design method for continuous-time nonlinear systems with rational system dynamics, using no model knowledge but only measured data affected by noise. We first extend recent results on data-driven control for linear time-invariant systems by presenting a purely data-driven representation of unknown nonlinear systems with rational dynamics. By applying robust control techniques to this parametrization, we obtain sum-of-squares based criteria for designing controllers with closed-loop robust stability guarantees for all continuous-time systems with rational system dynamics which are consistent with the measured data and the assumed noise bound. Finally, we apply the developed approach to a numerical example.

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