• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Control and stabilization of a class of nonlinear systems with symmetry.
【24h】

Control and stabilization of a class of nonlinear systems with symmetry.

机译：一类具有对称性的非线性系统的控制和镇定。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The focus of this dissertation is to study issues related to controllability and stabilization of a class of underactuated mechanical systems with symmetry. In particular we look at systems whose configuration can be identified with a Lie group and the reduced equations are of the Lie-Poisson type. Examples of such systems include hovercraft, spacecraft and autonomous underwater vehicles. We present sufficient conditions for the controllability of affine nonlinear control systems where the drift vector field is a Lie-Poisson reduced Hamiltonian vector field. In this setting we show that depending on the existence of a radially unbounded Lyapunov type function, the drift vector field of the reduced system is weakly positively Poisson stable. The weak positive Poisson stability along with the Lie algebra rank condition is used to show controllability. These controllability results are then extended to the unreduced dynamics. Sufficient conditions for controllability are presented in both cases where the symmetry group is compact and noncompact.; We also present a constructive approach to design feedback laws to stabilize relative equilibria of these systems. The approach is based on the observation that, under certain hypotheses the fixed points of the Lie-Poisson dynamics belong to a locally immersed equilibrium submanifold. The existence of such equilibrium manifolds, along with the center manifold theory is used to design stabilizing feedback laws.
机译：本文的重点是研究与一类对称的欠驱动机械系统的可控性和稳定性有关的问题。特别地，我们看一看其配置可以用李群识别的系统，并且简化后的方程是李-泊松型的。这种系统的例子包括气垫船，航天器和自主水下航行器。我们为仿射非线性控制系统的可控性提供了充分的条件，其中漂移矢量场是李-泊松约简哈密顿矢量场。在这种情况下，我们表明，根据径向无界Lyapunov型函数的存在，简化系统的漂移矢量场呈弱正泊松稳定态。弱的正泊松稳定性以及李代数秩条件用于显示可控性。然后将这些可控制性结果扩展到未简化的动力学。在对称群紧凑且不紧凑的两种情况下，都给出了可控性的充分条件。我们还提出了一种建设性的方法来设计反馈定律，以稳定这些系统的相对平衡。该方法基于以下观察结果：在某些假设下，Lie-Poisson动力学的固定点属于局部沉浸的平衡子流形。这种平衡流形的存在以及中心流形理论被用于设计稳定的反馈定律。

著录项

  • 作者

    Manikonda, Vikram.;

  • 作者单位

    University of Maryland College Park.;

  • 授予单位 University of Maryland College Park.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 1997
  • 页码 142 p.
  • 总页数 142
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 无线电电子学、电信技术;
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号