Nonlinear Ship Control: An Opportunity for Applied Mathematicians

本研究探讨欠驱动机械系统非线性控制理论中的一些基本设计问题。 在我们最近的工作欠驱动船舶控制的基础上，我们将采取进一步的控制问题的表面船舶与不完整的状态信息和环境干扰的存在。 在这些约束条件下，由于船舶往往是欠驱动的，并且是高度非线性的，因此实现全局稳定性的鲁棒性是困难的。 分离原理的缺乏，一般的非线性观测器的设计，和一般的鲁棒工具，使这个问题具有挑战性。 为了在这个问题上取得进展，我们将使用从常微分方程和偏微分方程的分析技术，以及在非完整力学和非线性控制的最新成果。该研究项目将特别关注不完整状态信息的稳定性和对环境干扰具有鲁棒性的轨迹跟踪。欠驱动机械系统是指驱动器数目小于系统自由度的系统。它们出现在海洋船舶和许多其他航空航天和海洋系统中，如卫星和水下航行器。 该项目的一个主要目标是为涉及这些系统的实际应用开发一个高性能控制的数学框架。从这项研究中得到的面向性能的控制器将通过计算机仿真和实验进行验证。

This research addresses some fundamental design issues in the theory of nonlinear control for underactuated mechanical systems. On the basis of our recent work on underactuated ship control, we will take a further step toward the problem of controlling a surface ship with incomplete state information and in the presence of environmental disturbances. Under these constraints, achieving robustness of global stability is hard because the ship often is underactuated, and is highly non-linear. The lack of the separation principle, the general nonlinear observer design, and general robustification tools make this problem challenging. To make advances on this issue, we will use analytical techniques from ordinary and partial differential equations, together with recent results in nonholonomic mechanics and nonlinear control. This research project will pay particular attention to stabilization with incomplete state information and trajectory tracking with robustness to environmental disturbances. Underactuated mechanical systems are systems with less number of actuators than the degrees of freedom. They appear in ocean ships and many other aerospace and marine systems such as satellites and underwater vehicles. A major goal of this project is to develop a mathematical framework of high-performance control for practical applications involving these systems. Performance-oriented controllers derived from this research will be validated via computer simulations and experiments.