RIA: Robust Control of Nonlinear Uncertain Dynamical Systemsand Applications

本课题主要研究机械系统的鲁棒控制问题。由于这类系统的非线性和不确定性，对系统的鲁棒性提出了更高要求。鲁棒控制问题是设计一种固定的或确定性的状态反馈控制，以使具有显著有界不确定性的动态系统在满足设计要求的情况下稳定下来。李亚普诺夫稳健性方法是当前流行的几种方法之一，将在该项目中使用。目前与该方法相关的缺点包括：(1)控制只使系统一致最终有界，而不是渐近稳定；(2)控制只适用于满足所谓的匹配条件的系统；(3)通常需要对系统不确定性的允许大小做出假设。该项目的目标是克服这些缺点。研究的目的是使非线性系统的鲁棒控制成为一种实用的工具。

This project focuses on the topic of robust control of mechanical systems. Robustness is required because of the nonlinear and uncertain character of such systems. The robust control problem is the problem of designing a fixed, or deterministic state feedback control to stabilize a dynamical system with significant bounded uncertainties while meeting the design requirements. The Lyapunov approach to robustness, one of several currently popular approaches, will be used in this project. Current shortcomings associated with the approach include (1) the control makes the system only uniformly ultimately bounded and not asymptotically stable, (2) the control only applies to systems which satisfy the so called 'matching condition', and (3) it is usually necessary to make assumptions about the allowable size of the system uncertainties. The objectives of this project are to overcome these shortcomings. The research is aimed at making robust control of nonlinear systems a practical tool.