Convexity of the reachable set of nonlinear systems under L_2 bounded controls

摘要

Recently [7, 8] the new convexity principle has been validated. It states that a nonlinear image of a small ball in a Hilbert space is convex, provided that the map in C~(1,1) and the center of the ball is a regular point of the map. We demonstrate how the result can be exploited to guarantee the convexity of the reachable set for some nonlinear control systems with L_2-bounded control. This provides existence and uniqueness of the solution in some optimal control problems as well as necessary and sufficient optimally conditions and effective iterative methods for finding the solution.