Loading...
Please wait, while we are loading the content...
On Nonlinear Controllability of Homogeneous Systems Linear in Control
| Content Provider | CiteSeerX |
|---|---|
| Author | Basar, Tamer Melody, James Bullo, Francesco |
| Abstract | This work considers small-time local controllability (STLC) of single- and multiple-input systems, _ x = f i u i where f (x) contains homogeneous polynomials and f 1 ; : : : ; fm are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree homogeneous systems STLC is equivalent to accessibility, provides a complete characterization of STLC for this class of systems. In the multiple-input case, transformations on the input space are applied to homogeneous systems of degree two, an example of this type of system being motion of a rigid-body in a plane. Such input transformations are related via consideration of a tensor on the tangent space to congruence transformation of a matrix to one with zeros on the diagonal. Conditions are given for successful neutralization of bad type (1,2) brackets via congruence transformations. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Constant Vector Field Input Space Multiple-input System State Dimension Nonlinear Controllability Homogeneous System Linear Small-time Local Controllability Bad Type Homogeneous Polynomial Successful Neutralization Odd-degree Homogeneous System Stlc Congruence Transformation Complete Characterization Homogeneous System Even-degree Homogeneity Precludes Stlc Input Transformation Multiple-input Case Obvious Result Single-input System Tangent Space |
| Content Type | Text |
