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This paper investigates the controllability and optimal control of higher order incomplete Boolean control networks (BCNs) with impulsive effects by using the semi-tensor product of matrices. First, the incomplete logical system is expressed as an algebraic form, based on which several necessary and sufficient conditions for the controllability are presented. Then, the Mayer-type optimal control issue is studied and the optimal control design algorithms are established. At last, the study of illustrative examples shows the effectiveness of the obtained new results.