Feedback Equivalence of Nonlinear Control Systems: A Survey on Formal Approach

This paper is a survey devoted to the formal approach to the feedback equivalence problem for nonlinear control systems. We show how classical Poincare’s approach, developed for dynamical systems, generalizes to control systems for continuous and discrete-time. We present normal forms and canonical forms for nonlinear control systems (single-input and multi-input, control-affine and general). We use the formal approach to study symmetries of nonlinear control systems as well as discuss special forms: linear and feedforward. We illustrate presented forms by various examples in dimensions 3 and 4.