In deriving the conditions for a minimum, the value of the performance index for the minimum is compared with that of an admissible comparison path. An admissible comparison path satisfies the differential constraints, the prescribed initial conditions, and the prescribed final conditions, and it lies in the neighborhood of the minimum. The admissible comparison path is composed of a first-order part, a second-order part, and so on. The notion of controllability is that a control perturbation can be found which drives the first-order or the linearized state equation from a point close to the minimal path to the first-order or linearized final conditions.
KeywordsTransition Matrix Final Time Minimal Path Controllability Matrix Navigation Problem
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