Invariants for feedback equivalence and Cauchy characteristic multifoliations of nonlinear control systems
The author develops in an abstract and formal way a theoretical framework for feedback equivalence of general nonlinear control systems \[ (1)\quad \dot x=f(x,u). \] In particular, the global aspects of equivalence are focused, and the role of Cauchy characteristics is emphasized. Let W be the submodule of vector fields associated with (1). The Cauchy characteristic system is defined by \[ (2)\quad C(W)=\{v\in W: [v,W]\subset W\}. \] Introducing the derived system W \(1=W+[W,W]\), allows us to iterate (2). Thus, a nested sequence of Cauchy characteristic systems is obtained. In this way, the author identifies geometric and numerical invariants under global feedback equivalence. The cases of affine and linear systems are considered. Finally, necessary conditions for global linearization under feedback are presented.
scientific article; zbMATH DE number 4055476
scientific article