The exponential formula for the reachable set of a Lipschitz differential inclusion. (English) Zbl 0736.34015
A method of discrete approximation of the reachable set of a differential inclusion \(x'\in F(x)\), \(x(0)=\xi\), with \(F\) Lipschitzian, is proposed. (Similar results have been given by A. I. Panasyuk and V. I. Panasyuk [Math. Notes 27, 213-218 (1980); translation from Mat. Zametki 27, 429-437 (1980; Zbl 0443.49031)].) The result is applied to the problem of characterization of the value function of the optimal control problem of Mayer.
Reviewer: T.Rzezuchowski (Warszawa)
MSC:
34A60 | Ordinary differential inclusions |
49K24 | Optimal control problems with differential inclusions (nec./ suff.) (MSC2000) |
49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |