Abstract
In this paper fuel optimal control has been found for a second-order system. The system equation has an antagonist v. Controls u and v are both bounded. The performance criterion is minimized by u and by maximized by v. It is assumed that the system is brought from an ardbitrary initial state to the origin in bounded time 0 ≤ t ≤ T, where T is the upper bound on t. The state piano has been separated into different regions. For each initial state a specific sequence of strategy has been derived which is to be followed to bring the system to origin.
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