The diagnostics of safety zones in motion planning

This article describes the sets of safety states from which a controlled motion is able to evade certain dangerous zones which in turn may be the reachability tubes of other controlled systems. In the general case, these safety sets are decribed as level sets to solutions of some Hamilton–Jacobi–Bellman (HJB) type equations. In the linear case such level sets may be calculated through duality techniques of nonlinear analysis.