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arXiv 1108.3540eess.SYcs.FLcs.SYmath.OC
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鲁棒软件综合理论

A theory of robust software synthesis

UC Los Angeles(加州大学洛杉矶分校);Max Planck Institute for Software Systems(马克斯·普朗克软件系统研究所)

Rupak Majumdar, Elaine Render, Paulo Tabuada

AI总结:

提出一种基于度量自动机和不动点算法的鲁棒控制器综合方法,用于离散转移系统上的ω-正则性质,确保系统在扰动下行为优雅降级。

摘要:

系统在运行环境中面临不确定性时的一个关键属性是鲁棒性,确保未建模但有界扰动对系统行为的影响仅成比例有界。受鲁棒控制和耗散系统理论的启发,我们提出了鲁棒性的形式化定义以及用于离散转移系统上ω-正则性质的最优鲁棒控制器设计的算法工具。形式上,我们定义了度量自动机——在状态上配备度量的自动机——以及度量自动机上的策略,这些策略保证了ω-正则性质的鲁棒性。我们提出了多项式时间内构造最优鲁棒策略的不动点算法。与经典图论方法计算的策略相比,我们的算法计算的策略确保受控系统的行为在扰动作用下优雅降级;降级程度由扰动幅度参数化。我们展示了该理论在控制器设计中的应用,该控制器能够容忍无限多次瞬态错误,只要这些错误发生得足够不频繁。

英文摘要:

A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by ideas from robust control and dissipative systems theory, we present a formal definition of robustness and algorithmic tools for the design of optimally robust controllers for omega-regular properties on discrete transition systems. Formally, we define metric automata - automata equipped with a metric on states - and strategies on metric automata which guarantee robustness for omega-regular properties. We present fixed point algorithms to construct optimally robust strategies in polynomial time. In contrast to strategies computed by classical graph theoretic approaches, the strategies computed by our algorithm ensure that the behaviours of the controlled system gracefully degrade under the action of disturbances; the degree of degradation is parameterized by the magnitude of the disturbance. We show an application of our theory to the design of controllers that tolerate infinitely many transient errors provided they occur infrequently enough.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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