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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.

MSC:
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
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