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| In this work we consider an optimal impulsive control problem in which the system dynamics is excited by a regular Borel measure. Using a recent notion of impulsive control solution introduced in the literature we show that the general optimal impulsive control can discretized by Euler method so that a subsequence of optimal solutions of the discretized problems do converge to an optimal solution of the original problem. For the convergence analysis we will introduce a metric taking into account the state and impulsive control spaces jointly. The convergence is then of the entire control processes, states and impulsive controls. This notion of convergence used here is neither weak star nor in the graph as previously studied in the literature. In the end we discuss an example illustrating the features of the Euler discretization for impulsive systems as well as the convergence of the optimal solutions of the discrete problems to the continuous one. |
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