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Decomposition of discrete linear-quadratic optimal control problems for switching systems

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  • A discrete linear-quadratic optimal control problem for two controlled systems acting sequentially is considered. Matching conditions for trajectories at the switching point are absent, however the minimized functional depends on values of a state trajectory at the left and right sides from the switching point. State trajectories have fixed left and right points. We derive control optimality conditions in the maximum principle form. The unique solvability of the considered problem is established. The algorithm for solving the problem is given, which is based on solving sequentially some initial value problems. The formula for the minimal value of the performance index is also obtained. The transformation reducing the discrete problem with switching point to a problem without one is presented only in a special case.
    Mathematics Subject Classification: Primary: 49N10, 93C30, 93C55; Secondary: 49K21.

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