Metric Uncertainty and Robust Control of Nonlinear Systems

小行星9505995 提出的研究代表了我们目前的计划，在开发理论和计算工具的建模和控制的动力系统的延续。 我们的方法依赖于图的概念。 模型的不确定性量化使用差距度量，衡量潜在的图形扰动，和适当的裕度，以确定性能和鲁棒性的不确定系统的稳定性。 在我们过去的研究中，我们已经开发了计算和理论工具的能量型（L2范数）性能指标的线性系统的鲁棒控制。 这些工具的使用已通过应用研究得到证明，相关软件已在标准商业软件包（u-tools）中提供。 在接下来的三年里，我们提出了一个密集的计划，开发非线性系统的鲁棒控制的理论和计算工具。 将使用适当的间隙类指标量化稳健性。 特别是，我们介绍了各种可能的距离措施，这可能是适当的，在不同的情况下。 我们建议计算适当的鲁棒性保证金的稳定性和性能的鲁棒性。 这些裕度可以针对各种L0、L2、全局和半局部稳定性和性能要求进行定制。 此外，我们将开发相关的工具，在这种度量不确定性的鲁棒反馈设计。 重点将放在计算问题和应用研究。 ***

9505995 Georgiou The research proposed represents a continuation of our current program in developing theoretical and computational tools for modeling and control of dynamical systems. Our approach relies on the concept of the graph. Model uncertainty is quantified using the gap metric which measures potential graph perturbations, and suitable margins are developed to ascertain performance and robustness of stability for the uncertain system. In our past research, we have developed computational and theoretical tools for robust control of linear systems with an energy-type (L2-norm) performance specification. The use of these tools has been demonstrated via application studies, and related software has become available within a standard commercial package (u-tools). Over the next three years, we propose an intensive program to develop theoretical and computational tools for robust control of nonlinear systems. The robustness will be quantified using suitable gap-like metrics. In particular, we introduce a variety of possible distance measures which may be appropriate in different situations. We propose to compute suitable robustness margins which guarantee robustness of stability and performance. These margins can be tailored to a variety of Lo, L2, global, and semi- local stability and performance requirements. Further, we will develop related tools for robust feedback design under such metric uncertainty. Emphasis will be placed on computational issues and application studies. ***