Multiobjective Robust Control: Linear Versus Nonlinear Controllers

鲁棒控制经历了广泛的发展，已成功地应用于具有挑战性的实际问题。然而，这些技术受到以下事实的限制：在它们的上下文中，必须用用于评估稳定性的同一标准来衡量性能。显然，单一规范通常不足以捕获不同的、经常是相互冲突的设计规范。因此，设计师被迫使用称重函数和相似尺度，再加上广泛的试验和错误，试图将现实规范转化为符合理论框架的形式。在这项研究中，我们建议开发一个综合框架，明确考虑到多种性能规格和不确定性。建议的研究将结合功能分析，线性系统理论和可行性理论的元素。在线性控制器的情况下，多目标问题可以被转化为凸优化形式，可以精确有效地求解。在非线性反馈的情况下，利用生存理论的初步结果表明，使用非线性静态控制器也可以达到线性动态状态反馈控制器所获得的任何性能水平。因此，在线性动力学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鲁棒控制框架，能够解决现实问题，而不需要多次试验和错误类型迭代的潜在保守近似，从而导致改进和更低成本的设计。有关硬控制约束下的多目标控制器的合成及其在厌氧消化器中的实验验证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，该小组由Rodolfo Suarez Cortez博士（数学）领导。本研究得到了NSF- contact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. ***