Multiobjective Robust Control: Linear Versus Nonlinear Controllers

9625920 Sznaier鲁棒控制已经经历了广泛的发展，并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，即在它们的背景下，必须按照用于评估稳定性的相同标准来衡量业绩。显然，单一的规范通常不足以捕获不同的、经常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标度，再加上大量的试验和错误，试图将现实的规范转换为符合理论框架的形式。在这项研究中，我们建议开发一个明确考虑多个性能规范和不确定性的综合框架。拟议的研究将结合泛函分析、线性系统理论和生存理论的元素。在线性控制器的情况下，多目标问题可以被重塑为可以精确和有效地求解的凸优化形式。在非线性反馈的情况下，利用生存理论的初步结果表明，用线性动态状态反馈控制器获得的任何性能水平也可以用非线性静态控制器获得。因此，在线性动态和静态非线性之间存在潜在的权衡。这项研究工作将产生一个扩展的稳健控制框架，能够解决实际问题，而不需要对多次试错型迭代进行潜在的保守近似，从而导致改进和更低成本的设计。与在严格控制约束下合成多目标控制器及其在厌氧消化池中的实验验证有关的研究部分将与位于墨西哥大都会大学的一个跨学科控制小组合作进行，该小组由Rodolfo Suarez Cortez博士(Mahemat ICS)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. ***