Configuration Controllability for Non-Zero Potential Mechanical Control Systems With Dissipation
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摘要: 在拉格朗日力学控制系统的仿射联络框架下，基于Sussmann对有限维流形上一般仿射非线性控制系统的能控性讨论，将简单力学控制系统短时间局部位形能控的一个可计算的充分条件推广到迷向耗散的系统上，并给出系统是平衡点能控的一个充分条件，其中，系统的拉格朗日函数为动能减势能A·D2在问题的讨论中，系统的能控李代数的向量场李括号运算，以及与系统位形流形的Levi-Civita联络相关的对称积起了重要作用．尽管势能项会使系统的位形能控性讨论复杂化，但Liouville向量场又简化了系统的能控李代数计算．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 conditon 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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Key words:
- mechanics /
- controllability /
- affine connection /
- symmetric product /
- isotropic dissipation
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[1] Nijmeijer H,van der Schaft A J.Nonlinear Dynamical Control Systems[M].New York-Heidelberg:Springer-Verlag,1990,349—392. [2] Murray R M.Nonlinear control of mechanical systems:a lagrangian perspective[J].Annual Reviews in Control,1997,21(2):31—42. doi: 10.1016/S1367-5788(97)00023-0 [3] Lewis A D,Murray R M.Configuration controllability of simple mechanical control systems[J].SIAM J Control Optimization,1997,35(3):766—790. doi: 10.1137/S0363012995287155 [4] Lewis A D.Aspects of geometric mechanics and control mechanical systems[D].Ph D thesis, Pasadena:California Institute of Technology,CA,1995，49—70. [5] Sussmann H J.A general theorem on local controllability[J].SIAM J Control Optimization,1987,25(1):158—194. doi: 10.1137/0325011 [6] Lewis A D,Murray R M. Decompositions of control systems on manifolds with an affine connection[J].Systems Control Letter,1997,31(1):199—205. doi: 10.1016/S0167-6911(97)00040-6 [7] Lewis A D.Simple mechanical control systems with constraints[J]. IEEE Transactions on Automatic Control,2000,45(8):1420—1436. doi: 10.1109/9.871752 [8] Monforte J C.Geometric Control and Numerical Aspects of Nonholonomic Systems[M].Lecture Notes in Mathematics 1793,Berlin-Heidelberg:Springer-Verlag,2002，194—198. [9] Vela P A,Morgansen K A,Burdick J W. Second order averaging methods and oscillatory control of underactuated mechanical systems[A].In:IEEE American Control Conference[C],2000，4672—4677. [10] Abraham R,Marsden J E,Ratiu T.Manifolds, Tensor Analysis, and Applications[M].2nd ed. Applied Mathematical Sciences 75, New York: Springer-Verlag, 1988，157—193. -
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