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The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two. (English) Zbl 0951.49027
Summary: In previous papers we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems \(\dot v(t)= X(v(t)) +u(t)Y(v(t))\) with a terminal submanifold \(N\) of codimension one when the trajectories are not tangent to \(N\). We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimension \(n\geq 3\), out of a subvariety of \(N\) of codimension three, we have described all the local synthesis.

49K15 Optimality conditions for problems involving ordinary differential equations
34H05 Control problems involving ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
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