Configuration controllability for non-zero potential mechanical control systems with dissipation |
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Authors: | Kang Jian-ling Wang Hong Ye Hua-wen |
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Institution: | Department of Applied Mathematics, Donghua University, Shanghai 200051, P.R.China;College of Mathematics and the PMC Key Laboratory ME of China,;
Nankai University, Tianjin 300071, P.R.China;Department of Automatic Control, Northwest Polytechnical University,;
Xi'an 710072, P.R.China |
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Abstract: | Within the affine connection framework of Lagrangian control systems, based on the results of Sussmann on controllability of general affine control systems defined on a finite-dimensional manifold, a computable sufficient condition of configuration controllability for the simple mechanical control systems was extended to the case of systems with strictly dissipative energy terms of linear isotropic nature, and a sufficient condition of equilibrium controllability for the systems was also given, where Lagrangian is kinetic energy minus potential energy. Lie bracketting of vector fields in controllable Lie algebra, and the symmetric product associated with Levi-Civita connection show virtues in the discussion. Liouville vector field simplified the computation of controllable Lie algebra for the systems, although the terms of potential energy complicated the study of configuration controllability. |
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Keywords: | mechanics controllability affine connection symmetric product isotropic dissipation |
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