Almost feedback linearizable systems of the class C1 and solving the constructive controllability problem

Abstract

Abstract We propose a method of solving the controllability problem using almost linearizable control systems. Developing an idea of triangular systems, proposed by the first author of this paper in 1973, we introduce a wider class of almost triangular systems for which it is possible to find explicitly a control steering the system from one given point to another given point. We give conditions of almost linearizability for nonlinear single-input systems of the class $C^{1}$ and discuss a method of solving the controllability problem for such systems.