Data-driven asymptotic stabilization for discrete-time nonlinear systems |
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Affiliation: | 1. Department of Aerospace & Ocean Engineering, Virginia Tech, Blacksburg, VA 24061, USA;2. Department of Industrial & Enterprise Systems Engineering, University of Illinois, Urbana, IL 61801, USA |
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Abstract: | In this paper, we propose a data-driven feedback controller design method based on Lyapunov approach, which can guarantee the asymptotic stability of the closed-loop and enlarge the estimate of domain of attraction (DOA) for the closed-loop. First, sufficient conditions for a feedback controller asymptotically stabilizing the discrete-time nonlinear plant are proposed. That is, if a feedback controller belongs to an open set consisting of pairs of control input and state, whose elements can make the difference of a control Lyapunov function (CLF) to be negative-definite, then the controller asymptotically stabilizes the plant. Then, for a given CLF candidate, an algorithm, to estimate the open set only using data, is proposed. With the estimate, it is checked whether the candidate is or is not a CLF. If it is, a feedback controller is designed just using data, which satisfies sufficient conditions mentioned above. Finally, the estimate of DOA for closed-loop is enlarged by finding an appropriate CLF from a CLF candidate set based on data. Because the controller is designed directly from data, complexity in building the model and modeling error are avoided. |
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Keywords: | Control Lyapunov function Domain of attraction Data-driven control Stabilization Nonlinear Discrete-time |
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