一类非完整系统的全局镇定

当非完整系统只能局部转换为链式形式时, 由于存在变换奇异点集合, 针对链式系统所设计的全局反馈控制律只能局部镇定原非完整系统, 而且当期望状态接近奇异点时, 闭环系统的吸引区很小. 本文针对一类可局部转换为链式系统的非完整系统, 首先利用吸引区是状态空间中的一个不变集且与变换奇异点集不相交的条件导出了一个吸引区的不变子集, 然后给出了将系统状态从任意点驱动到吸引区不变子集内的开环控制算法, 最后结合开环控制和闭环控制得到一种混合控制算法. 该混合控制算法可以保证任意不在变换奇异点集合内的期望状态是全局渐近稳定的. 对平面两转动关节空间机器人的仿真结果证实了算法的有效性.

Global Stabilization of a Class of Nonholonomic Systems

Due to the existence of singular sets of state and input transformations, the global feedback control laws developed for nonholonomic chained systems can only locally stabilize the original nonholonomic systems, which are locally convertible to nonholonomic chained form, and the size of attractive manifold of the closed-loop system becomes very small when the desired state is near to the singular sets. The global stabilization problem of a class of nonholonomic systems locally convertible to nonholonomic chained form is investigated in this paper. Firstly, a subset of attractive manifold is derived based on the condition that the attractive manifold is an invariant set with no intersetion with the transformation singular sets. Then, an open-loop control scheme is developed to drive an arbitrary initial state to the subset of attractive manifold. By combining the open-loop and feedback control schemes, a hybrid control strategy is finally proposed, guaranteeing that any nonsingular desired state is globally asymptotically stable. Simulation results for a two- link planar space robot show the effectiveness of the proposed hybrid control scheme.