Research Initiation Award: Robust Control for Nonlinear Systems

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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.