Control systems subordinated to a group action: Accessibility
Let M be an n-dimensional real \(C^{\infty}\) manifold; a polysystem on M is a family of \(C^{\infty}\) vector fields on M. Let G be a real connected Lie group which acts smoothly on M and let \(\Gamma\) be a subset of the Lie algebra of G. \(\Gamma\) defines a polysystem on M, the polysystem of the vector fields canonically induced by the elements of \(\Gamma\). Such a polysystem is called subordinated to a group action. A polysystem is transitive (controllable) on M if for each x, y belonging to M, there exists a trajectory of the polysystem which steers x to y. The authors give sufficient conditions for transitivity of a polysystem on GL(V) (V a finite dimensional vector space) associated to \(\Gamma =\{A+uB:\) \(u\in R\), A,\(B\in End(V)\}\).
scientific article; zbMATH DE number 3843578