Sussmann, H. J. Regular synthesis for time-optimal control of single-input real analytic systems in the plane. (English) Zbl 0701.93035 SIAM J. Control Optimization 25, No. 5, 1145-1162 (1987). 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. Cited in 1 ReviewCited in 15 Documents MSC: 93B50 Synthesis problems 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 34C40 Ordinary differential equations and systems on manifolds Keywords:time-optimal control; real analytic affine nonlinear systems; real analytic two-dimensional manifold; feedback control laws PDFBibTeX XMLCite \textit{H. J. Sussmann}, SIAM J. Control Optim. 25, 1145--1162 (1987; Zbl 0701.93035) Full Text: DOI