Quadratic Lyapunov Functions and State Feedback via InteriorPoint Optimization

通过 InteriorPoint 优化的二次 Lyapunov 函数和状态反馈

• 批准号: 9222391
• 负责人: Stephen Boyd
• 金额: $ 19万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-09-01 至 1997-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9222391&HistoricalAwards=false
• 关键词: Quadratic; Lyapunov; Functions; State; Feedback

9222391 Boyd One of the most useful qualities of a properly designed feedback control system is robustness, i.e., the ability of the closed- loop system to continue working well despite large variations in the (open-loop) plant dynamics. This property is also the source of some of the hardest problems in control system analysis and synthesis. For example, the problem of determining a feedback law that is guaranteed to work well when connected to any plant model from a given set of models-the robust synthesis problem-is in general quite difficult. A recent advance is an analytic solution to a specific type of robust synthesis problem. This analytic solution can be derived in several different frameworks: Hoo-optimal control, linear-quadratic game-theoretic control, or linear exponential quadratic Gaussian (LEQG) optimal control. In contrast, this research centers around a method that couples Lyapunov theory with (numerical) convex optimization (but is closely connected with the analytic solution method mentioned above). In particular, newly developed interior point optimization methods will be applied to some convex and quasiconvex problems that arise in control theory (analysis and synthesis). Preliminary investigations suggest that the impact of interior point methods on Lyapunov function and state feedback search problems will be as profound as it has been on linear and quadratic programming. The goal of the research is to develop the foundations for method of control system robustness analysis and robust controller synthesis that substitutes convex optimization for the computations required in the analytic solution mentioned above, but in return solves a much larger class of problems. Moreover, with interior point optimization methods, the increase in computation effort over that required for the analytic solution, may be quite modest. ***

9222391 BOYD正确设计的反馈控制系统最有用的品质之一是稳健性，即，尽管（开放环）植物动力学发生了较大的差异，但闭环系统的能力仍在继续运行良好。 该特性也是控制系统分析和合成中一些最严重问题的来源。 例如，确定反馈定律的问题，该法律可以保证与给定模型组合的任何植物模型连接时可以很好地工作 - 强大的合成问题 - 通常很困难。 最近的进步是针对特定类型的鲁棒合成问题的分析解决方案。 该分析解决方案可以在几个不同的框架中得出：最佳控制，线性 - 季度游戏理论控制或线性指数二次高斯高斯（LEQG）最佳控制。 相比之下，该研究围绕着一种方法，该方法将Lyapunov理论与（数值）凸优化（但与上述分析解决方案方法密切相关）。 特别是，新开发的内点优化方法将应用于控制理论（分析和综合）中出现的一些凸和准认证问题。 初步研究表明，内部点方法对Lyapunov功能和状态反馈搜索问题的影响将与线性和二次编程一样深刻。 该研究的目的是为控制系统的鲁棒性分析和鲁棒控制器的合成开发基础，该方法将凸优化替代上述分析解决方案中所需的计算，但作为回报，可以解决更大的问题。 此外，使用内点优化方法，计算工作量的增加比分析解决方案所需的增加可能是相当适度的。 ***