On the Accessibility Problem in Control Theory

Abstract

Publisher Summary This chapter highlights accessibility problem in control theory. The Caratheodory's work on the Lagrange variational problem is applicable to the accessibility problem. This is considered that suppose H ⊂ V (M) defines a nonsingular Pfaffian system on M, with D (H) = V (M). Then, for x 0 ∈ M, φ(P (H, x 0 )) = M, that is, every point is accessible from x 0 . This leaves open the stability problem. The chapter states the Chow's theorem and then restates the result of the theorem in forms suggesting generalizations to more general path systems.