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.


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.)
Full Text: DOI