The simplest nontrivial case admitting visualization is a three-dimensional space with a curve as a singular manifold. We consider two such examples. The first one (Problem 6.1) is a modification of Fuller’s problem. This is required to minimize the weighted mean-square deviation of a massive object from the origin. The role of the control belongs to a bounded force and the weight is the discounted factor e−αt. The second example (Problem 6.2) is a time-optimal problem for some control system of third order.
KeywordsManifold Torque Dition
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