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| Received:December 18, 2003Revised:February 03, 2005 |
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| Controllability for single-input mechanical control systems with dissipation |
| Jianling KANG, Hong WANG, Huawen YE |
| (Department of Applied Mathematics ,Donghua University ,Shanghai 200051 , China ;College of Mathematics and the PMC Key Lab ME of China ,Nankai University , Tianjin 300071 , China ;Department of Automatic Control ,Northwestern Polytechnical University , Xi’an Shaanxi 710072 , China) |
| Abstract: |
| Within the affine connection framework of Lagrangian control systems , based on the results of Sussmann on small- time locally controllability of single- input affine nonlinear control systems , the controllability results for mechanical control systems with single- input are extended to the case of the systems with isotropic damping ,where the Lagrangian is the kinetic energy associated with a Riemannian metric. A sufficient condition of negative small- time locally controllability for the system is obtained. Then ,it is demonstrated that such systems are small- time locally configuration controllable if and only if the dimension of the configuration manifold is one. Finally , two examples are given to illustrate the results. Lie bracketting of vector fields and the symmetric product show the advantages in the discussion. |
| Key words: Mechanics Controllability Affine connection Symmetric product Isotropic dissipation |
