Multiobjective Robust Control: Linear Versus Nonlinear Controllers

小行星9625920 鲁棒控制已经经历了广泛的发展，已成功地应用于具有挑战性的实际问题。 然而，这些技术受到这样一个事实的限制，即在其背景下，业绩必须以用于评估稳定性的相同规范来衡量。 显然，一个单一的规范通常不足以捕捉不同的，往往是相互冲突的，设计规范。 因此，设计师被迫使用加权函数和相似性缩放，再加上广泛的试验和错误，试图将现实的规格转换成一种形式服从的理论框架。 在这项研究中，我们建议开发一个综合框架，明确考虑到多个性能指标和不确定性。 本研究将结合联合收割机的功能分析、线性系统理论与生存力理论。在线性控制器的情况下，多目标问题可以转化为凸优化问题 形式，可以准确有效地解决。 在非线性反馈的情况下，使用可行性理论的初步结果表明，任何性能水平获得的线性动态状态反馈控制器也可以实现使用非线性静态控制器。 因此，在线性动力学和静态非线性之间存在潜在的折衷。 这项研究工作将导致一个扩展的鲁棒控制框架，能够解决现实的问题，而不需要潜在的保守的近似多个试验和错误类型的迭代，导致改进和成本更低的设计。 与硬控制约束下合成多目标控制器及其在厌氧消化器中的实验验证相关的研究部分将与位于墨西哥自治大学的跨学科控制组合作进行，由Rodolfo苏亚雷斯Cortez博士（数学）领导。 这项研究得到了NSF-CONTACYT合作研究机会的支持。 ***

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. ***