Metric Uncertainty and Robust Control of Nonlinear Systems

[505995] Georgiou提出的研究代表了我们目前在开发动力系统建模和控制的理论和计算工具方面的计划的延续。我们的方法依赖于图的概念。利用测量潜在图扰动的间隙度量来量化模型的不确定性，并建立合适的裕度来确定不确定系统的性能和稳定性的鲁棒性。在我们过去的研究中，我们已经开发了具有能量型（l2范数）性能规范的线性系统鲁棒控制的计算和理论工具。这些工具的使用已经通过应用研究得到了证明，相关的软件已经在一个标准的商业软件包（u-tools）中可用。在接下来的三年里，我们提出了一个密集的计划来开发非线性系统鲁棒控制的理论和计算工具。鲁棒性将使用合适的类间隙度量来量化。我们特别介绍了各种可能适用于不同情况的距离测量方法。我们提出计算合适的鲁棒性裕度以保证稳定性和性能的鲁棒性。这些余量可以根据各种Lo， L2，全局和半局部稳定性和性能要求进行定制。此外，我们将开发在这种度量不确定性下的鲁棒反馈设计的相关工具。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. ***