Multiobjective Robust Control: Linear Versus Nonlinear Controllers

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9625920 Sznaier Robust control has undergone extensive developments that have been successfully applied to challenging practical problems. However, these techniques are limited by the fact that, in their context, performance must be measured in the same norm used to assess stability. Clearly, a single norm is usually not enough to capture different, and often conflicting, design specifications. Therefore, designers are forced to use weighing functions and similarity scaling, coupled with extensive trial and error, in an attempt to translate realistic specifications into a form amenable to the theoretical framework. In this research we propose to develop a synthesis framework that explicitly takes into account multiple performance specifications and uncertainty. The proposed research will combine elements from functional analysis, linear systems theory and viability theory. In the case of linear controllers, multiobjective problems can be recast into a convex optimization form that can be exactly and efficiently solved. In the case of nonlinear feedback, preliminary results using viability theory show that any performance level obtained with a linear dynamic state-feedback controller can also be achieved using nonlinear static controllers. Thus, there exists a potential tradeoff between linear dynamics and static nonlinearities. This research effort will result in an expanded robust control framework, capable of addressing realistic problems without necessitating neither potentially conservative approximations for multiple trial and error type iterations, leading to improved and less costly designs. The portion of the research related to synthesizing multiobjective controllers under hard control constraints and their experimental validation in an anaerobic digester will be carried out in cooperation with an interdisciplinary control group located at the Universidad Autonoma Metropolitana, Mexico, headed by Dr. Rodolfo Suarez Cortez (Mathemat ics). This research is supported under NSF- CONTACYT Collaborative Research Opportunity. ***