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Regular synthesis for time-optimal control of single-input real analytic systems in the plane. (English) Zbl 0696.93026
The author examines time-optimal control for real analytic affine nonlinear systems of the form $$\dot x=F(x)+uG(x)$$. Here $$x\in M$$, a real analytic two-dimensional manifold, F and G are real analytic vector fields on M, and $$| u| \leq 1$$. The main result is Theorem 3.1 which states that for u in a class of $$C^ k$$ feedback control laws the maximum principle produces necessary and sufficient conditions for optimality.

MSC:
 93B50 Synthesis problems 34C40 Ordinary differential equations and systems on manifolds 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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