Minimum Time Control by Time Interval Optimization†

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Abstract
This paper presents a time interval optimization method for the determination of the minimum time for transfer of a system from an initial state to a desired state. The method is applicable to systems whose characteristic matrix has real or complex eigenvalues. The characteristic matrix and the control matrix may havo constant or time varying parameters. The time interval optimization (TIO method) provides a means of determining a sequence of trajectories. The successively determined trajectories are the result of corrections so that the respective sequence of end points of the trajectories will approach the desired point in state space. Each of the trajectories is time optimal from the initial point to whatever point is reached. When the correction routine brings the end point of a trajectory sufficiently near the desired point in state space the optimal control has been determined.

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