A controllability minimum principle

A controllability minimum principle and two associated transversality conditions are presented, dealing with the controllability of nonlinear systems. The theorems represent necessary conditions for a control function to generate a system path which lies in the boundary of the set of points that are controllable to a target. The theorems presented here are controllability counterparts to Pontryagin's maximum principle, and undoubtedly these results will seem familiar or may have occurred to other researchers in the area of optimal control. The purpose of this paper is to make the distinction explicit and to establish the validity of these controllability theorems on their own merits. The theorems are demonstrated using a simple example and the principal result (a controllability minimum principle) is shown to be equivalent to the Kalman controllability criterion for linear systems.