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。在我们最近关于欠驱动船舶控制的工作的基础上，我们将进一步研究状态信息不完全且存在环境扰动的水面舰船的控制问题。在这些约束下，实现全局稳定性的稳健性是困难的，因为船舶经常是欠驱动的，并且是高度非线性的。由于缺乏分离原理、一般的非线性观测器设计和一般的抗差工具，使得这一问题具有挑战性。为了在这个问题上取得进展，我们将使用常微分方程和偏微分方程组的分析技术，以及非完整力学和非线性控制的最新结果。这一研究项目将特别关注不完全状态信息的镇定和对环境扰动具有鲁棒性的轨迹跟踪。欠驱动机械系统是指执行器的数量少于自由度的系统。它们出现在远洋轮船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。从本研究中得出的性能导向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.