To the Linearization Problem for Single-Input Control Affine Systems

Abstract

State feedback linearization is well-known as an effective tool to solve various problems for nonlinear control systems. An affine system is called to be state feedback linearizable if there exist smooth invertible changes of the state and the inputs which transform the system into a linear controllable system. If an affine system is not state feedback linearizable one can try to use orbital feedback linearization. An affine system is called to be orbital feedback linearizable if there exists time scaling which transforms the system into a state feedback linearizable system. As usual for affine systems, time scaling is considered to be depending only on the state. Recently, it has been shown that if time scaling depends both on the state and on the inputs, then it becomes possible to linearize affine systems which are not orbital feedback linearizable. In this paper, while considering such transformations, we suggest the new sufficient condition for linearizability of single-input control affine systems. We derive a system of partial differential equations which has to be solved in order to find an appropriate time scaling. We provide en example how the proposed approach can be applied to solve a terminal problem.