Research Initiation Award: Robust Control for Nonlinear Systems

本课题旨在探讨非线性系统的鲁棒控制理论。非线性系统鲁棒控制技术的发展将为非线性控制分析和设计提供有价值的工具。建议的研究方向是：(1)将增益调度发展为一种系统的设计方法；(2)研究非线性控制设计方法的输入/输出特性。增益调度的研究涉及到“线性变参”系统的理论。LPV系统构成了非线性增益调度控制的基本框架。这种系统的理论将消除增益调度对进化缓慢的系统的基本限制。非线性控制设计方法的输入/输出特性研究是将重要的线性鲁棒控制概念引入非线性系统的一种尝试。非线性控制设计方法通常依赖于状态空间表示。输入/输出分析将有助于更好地理解这些设计方法的能力和局限性。

The research is to pursue a theory of robust control for nonlinear systems. The development of robust control techniques for nonlinear systems would provide valuable tools for nonlinear control analysis and design. The proposed lines of research are (1) the development of gain-scheduling into a systematic design methodology and (2) an investigation of input/output properties of nonlinear control design methods. The research on gain-scheduling involves a theory for "Linear Parameter-Varying" (LPV) systems. LPV systems form the underlying framework for nonlinear gain-scheduled control. A theory for such systems would remove gain-scheduling's fundamental limitation to systems which evolve slowly. The research on input/output properties of nonlinear control design methods represents an attempt to bring important linear robust control concepts to nonlinear systems. Nonlinear control design methods typically rely on state-space representations. An input/output analysis would lead to a better understanding of the capabilities and limitations of these design methods.