×

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.)
PDF BibTeX XML Cite
Full Text: DOI