SUMMARY Optimality Conditions and Synthesis for the Minimum Time Problem.pdfVIP

c Journal of Mathematical Systems Estimation and Control BirkhauserBoston Vol No pp SUMMARY Optimality Conditions and Synthesis for the Minimum Time Problem y y y P Cannarsa H Frankowska ; C Sinestrari Intro duction In this pap er we are concerned with the minimum time optimal control problem for the system  y 0 t f y t ut t y x where x IR n and f IR n U IR n are given U b eing a complete separable metric space We assume that f is continuous and 8 i R c such that R u U f u is c R Lipschitz on B R ii k such that : x IR n supu 2U jf x u j k jx j A measurable function u U is called a control and the corresp onding solution of the state equation is denoted by y x u Given a nonempty closed set K IRn called the target and a p oint x K c we are interested in minimizing over all controls u the time taken for the solution y x u to reach K The value function denoted by T x inf ft y t x u K g u as x ranges over R n is called the Minimum Time function of the problem Received March received in nal form Novemb er Full electronic manuscript published January pp bytes Retrieval Co de y This research was supp orted by the Human Capital and Mobility Programme