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| A discrete linear-quadratic optimal control problem for two sequentially acting controlled systems is considered. Matching conditions for trajectories at the switch point are absent, however the minimized functional depends on values of a state trajectory in the left and right sides from the switch point. State trajectories have fixed left and right points. Control optimality conditions in the maximum principle form are derived. The solvability of the considered problem is established. The algorithm for solving the problem is given, which is based on sequential solving some initial value problems. The formula for the minimal value of the performance index is also obtained.
The similar result for continuous problems has been presented in [1].
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References
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[1] G.A. Kurina and Y. Zhou, Decomposition of Linear-Quadratic Optimal
Control Problems for Two-Steps Systems, Doklady Mathematics,
vol. 83, no. 2, 2011, pp. 275--277. |
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