Constrained H-infinity Optimiztion: An Approach for the Robust Control of Systems with Time-Domain Constraints

我们建议开发一种Hoo优化方法，除了习惯的频域规范外，还允许明确的时域规范。后一种规范包括通过要求阶跃响应位于给定包络内来塑造系统的瞬态特性，指定执行器信号不超过某些硬界限以避免饱和等。我们将这种方法称为约束Hoo优化。在该方法中，引入时域规范作为Hoo优化的约束。我们期望将后一个问题分解为i)有限维凸优化问题和ii)标准Hoo优化问题。该方法将能够以与Hoo优化方法（如u-synthesis）相同的方式处理结构化模型的不确定性。该方法还将继承Hoo优化方法的算法特性，并系统地提供冲突规范之间的权衡，包括直接在时域中提出的规范。它将能够以合理的计算成本揭示可实现的性能限制。我们期望在此框架内生产的控制器将具有保证有效程度降低到标准Hoo最优控制器水平的特性，并且将开发专门的控制器降低方案。​总之，我们的预期结果应该为具有结构不确定性的鲁棒多变量控制系统设计提供一种通用、系统和实用的方法，其中明确地纳入了时域中已建立的性能度量。同时完全保留了标准胡法的适用性。我们认为所提出的研究为约束系统的鲁棒控制这一重要课题提供了一种独特的方法。

We propose to develop an Hoo optimization approach which will allow in addition to the customary frequency-domain specifications, explicit time-domain specifications. The latter specifications include shaping of the transient characteristics of the system by requiring that the step response lies in a given envelope, specifying that actuator signals do not exceed certain hard bounds in order to avoid saturation, etc. We refer to this approach as Constrained Hoo optimization. In the proposed approach the time-domain specifications are introduced as constraints onto the Hoo optimization. We expect to establish a decomposition of the latter problem to i) a finite dimensional convex optimization problem and ii) a standard Hoo optimization problem. This method will be capable of handling structured model uncertainty in as much the same way as Hoo optimization methods such as u-synthesis do. The approach will also inherit the algorithmic nature of Hoo optimization methods and systematically provide trade-offs between conflicting specifications, including specifications posed directly in the time-domain. It will be capable of revealing the achievable performance limits at a reasonable computational cost. We expect to establish that the controllers produced within this framework will have properties that guarantee effective degree reduction to the level of standard Hoo optimal controllers and specialized controller reduction schemes will be developed. In summary, our expected results should provide a general, systematic and practical approach for robust multivariable control system design with structured uncertainty, in which established measures of performance in the time-domain are incorporated explicitly, while the applicability of standard Hoo methods is retained in full. We believe that the proposed research offers a unique approach to the important subject of Robust Control of Constrained Systems.