Reachability of targets subject to disturbances bounded by convex sets

A moving target set Xt is specified for the state x(t) of a linear differential system (L) corrupted by additive noise w(·). Xt is said to be strongly reachable from (L) if an admissible control u(·) can be found guaranteeing the transfer of the state to the target for all noise fluctuations w(·)∊W and all initial states x 0∊X 0. (W and X 0 are prescribed closed and bounded convex sets.) Using the theory of conjugacy correspondence, we develop necessary and sufficient conditions for strong reachability. Furthermore, a technique is also provided for constructing a control u(·) which achieves the transfer. Finally, an algorithm is proposed for computation of numerical solutions for the ease when X 0 and Xt are endowed with polyhedral structures. The application of the theory is illustrated via a numerical example.