A fast sampling method for estimating the domain of attraction

Most stabilizing controllers designed for nonlinear systems are valid only within a specific region of the state space, called the domain of attraction (DOA). Computation of the DoA is usually costly and time-consuming. This paper proposes a computationally effective sampling approach to estimate the DoAs of nonlinear systems in real time. This method is validated to approximate the DoAs of stable equilibria in several nonlinear systems. In addition, it is implemented for the passivity-based learning controller designed for a second-order dynamical system. Simulation and experimental results show that, in all cases studied, the proposed sampling technique quickly estimates the DoAs, corroborating its suitability for realtime applications