Risk Sensitive Control of Hybrid Systems

混合系统的风险敏感控制

• 批准号: 9629866
• 负责人: Thordur Runolfsson
• 金额: $ 19.13万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-09-15 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9629866&HistoricalAwards=false
• 关键词: Risk; Sensitive; Control; Hybrid; Systems

ECS-9629866 Runolfsson Dynamic systems that depend on a auxiliary parameter that characterizes the mode of operation of the system arise in many applications. In some applications this parameter can be measured, in others it can be estimated and in still others it is completely unknown except for, perhaps, some apriori estimate about its size. The methods that are chosen in incorporating the auxiliary parameter in the design of a control systems depends on the characteristic of the parameter. If the parameter is deterministic and can be measured, gain scheduling methods are frequently employed in the design of real systems. If the parameter is (deterministic) unknown and not measurable, robust design methods are usually used. If, on the other hand, the parameter is stochastic with known statistic, stochastic methods are usually employed. A particular case of this situation is the case when the auxiliary parameter can be modelled as finite state continuous time Markov chain. Such systems arise in various applications and system formulations such as power systems, manufacturing systems and fault-tolerant control system. In this research we study risk-sensitive control for hybrid systems with a Markovian jump parameter. In particular, the objective of the control is to minimize the infinite-horizon risk-sensitive cost functional. Preliminary investigations show that the relationship between H(_ control, linear differential games and risk-sensitive control does not hold for hybrid systems. The main reason for this appears to be that the risk sensitivity cost functional measures the risk sensitivity of the system to transitions caused by the random jump parameter as well as the noise input. The risk sensitivity of the cost functional to transitions induced by the jump parameter may be of a great value in the design of systems where it is desired to make the system performance as insensitive to the effects of the jump parameter as possible. In this research we will develop risk sen sitive control of hybrid stochastic systems and study in detail both system theoretic properties and design techniques for such systems. Furthermore, the benefits of the developed techniques will be evaluated for the applications described above.

ECS-9629866 Runolfsson 依赖于表征系统操作模式的辅助参数的动态系统出现在许多应用中。 在某些应用中，这个参数可以被测量，在其他应用中，它可以被估计，而在其他应用中，它是完全未知的，也许除了一些关于它的大小的先验估计。 在控制系统的设计中引入辅助参数的方法的选择取决于参数的特性。 如果参数是确定的并且可以测量，则增益调度方法经常用于真实的系统的设计。 如果参数是（确定性）未知且不可测的，则通常使用稳健设计方法。 另一方面，如果已知统计量的参数是随机的，则通常采用随机方法。 这种情况的一个特殊情况是辅助参数可以建模为有限状态连续时间马尔可夫链的情况。 这样的系统出现在各种应用和系统配方，如电力系统，制造系统和容错控制系统。 本文研究了具有马尔可夫跳变参数的混杂系统的风险敏感控制问题。 特别地，控制的目标是最小化无限时域风险敏感成本泛函。初步研究表明，H_控制、线性微分对策和风险敏感控制之间的关系并不适用于混杂系统。 其主要原因似乎是风险敏感度成本泛函测量了系统对随机跳变参数以及噪声输入引起的转换的风险敏感度。 在系统设计中，期望使系统性能对跳变参数的影响尽可能不敏感时，成本泛函对由跳变参数引起的转变的风险敏感性可能具有很大的价值。 在本研究中，我们将发展混合随机系统的风险敏感控制，并详细研究这类系统的系统理论性质和设计技术。 此外，开发的技术的好处将被评估为上述应用程序。