Extremal Synthesis for Generic Planar Systems |
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Authors: | Ugo Boscain Benedetto Piccoli |
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Affiliation: | (1) SISSA–ISAS, Via Beirut 2-4, 34014 Trieste, Italy;(2) DIIMA, Universitá di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy |
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Abstract: | For a generic single-input planar control system we analyze the structure of the set of extremals for the time-optimal problem. Generically all extremals are finite concatenations of regular arcs that are bang or correspond to a smooth feedback. Moreover, the support of extremals is a Whitney stratified set. We collect these information in the definition of extremal synthesis. In the cotangent bundle, we give a topological classification of the singularities of the extremal synthesis and study the projections of the support of extremals (regarded as a two-dimensional object, after normalization) from 2 × S
1 to the plane. With respect to the Whitney classical singularities here we deal with a stratified set with edges and corners, and along with cusps and folds, we find other stable singularities. |
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Keywords: | optimal control synthesis theory projection singularities |
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