Control theory can provide useful insights into the properties of controlled,dynamic systems. One important property of nonlinear systems is the region ofattraction (ROA), a safe subset of the state space in which a given controllerrenders an equilibrium point asymptotically stable. The ROA is typicallyestimated based on a model of the system. However, since models are only anapproximation of the real world, the resulting estimated safe region cancontain states outside the ROA of the real system. This is not acceptable insafety-critical applications. In this paper, we consider an approach thatlearns the ROA from experiments on a real system, without ever leaving the trueROA and, thus, without risking safety-critical failures. Based on regularityassumptions on the model errors in terms of a Gaussian process prior, we use anunderlying Lyapunov function in order to determine a region in which anequilibrium point is asymptotically stable with high probability. Moreover, weprovide an algorithm to actively and safely explore the state space in order toexpand the ROA estimate. We demonstrate the effectiveness of this method insimulation.
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