Cannarsa, Piermarco; Sinestrari, Carlo On a class of nonlinear time optimal control problems. (English) Zbl 0867.49016 Discrete Contin. Dyn. Syst. 1, No. 2, 285-300 (1995). Summary: We consider the minimum time optimal control problem for systems of the form \[ y'(t)=f(y(t),u(t)),\quad y(t)\in\mathbb{R}^n,\quad u(t)\in U\subset\mathbb{R}^d. \] We assume \(f(x,U)\) to be a convex set with \(C^1\) boundary for all \(x\in\mathbb{R}^n\) and the target \(\mathcal K\) to satisfy an interior sphere condition. For such problems we prove necessary and sufficient optimality conditions using the properties of the minimum time function \(T(x)\). Moreover, we give a local description of the singular set of \(T\). Cited in 7 Documents MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 49L20 Dynamic programming in optimal control and differential games 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games Keywords:minimum time optimal control problem; necessary and sufficient optimality conditions; minimum time function PDFBibTeX XMLCite \textit{P. Cannarsa} and \textit{C. Sinestrari}, Discrete Contin. Dyn. Syst. 1, No. 2, 285--300 (1995; Zbl 0867.49016) Full Text: DOI