Optimal Reference Tracking, the Next Step in the Design of Controllers for Markovian Jump Linear Systems

该建议概述了一个为期两年的研究计划，开发的第一个收集的方法，设计控制器，实现最佳的参考跟踪，随机时变系统。作为第一步，PI采用马尔可夫跳跃线性系统公式，因为它保留了线性确定性情况下的易处理性，同时具有其底层结构的随机变化。最近的结果提供了解决方案的H2和H_inf最优调节器（无参考）的问题，马尔可夫跳跃线性系统。然而，本提案中所述的范例，即必须跟踪参考的范例，尚未得到研究，也无法通过基于经典的最佳监管理论调整的方法来解决，例如内部模型原理。PI预计，一个有效的设计方法将依赖于一个新的框架，用于联合设计的状态估计器，状态反馈控制器和前馈项，使用线性矩阵不等式技术。本提案中概述的研究还将揭示在随机或间歇性故障存在下实现最佳参考跟踪的伺服机构的结构特性。现代工程系统通常由机械部件、机电设备和传感器的复杂组合构成。由于环境的突然波动、组件故障或装配互连中断，这样的系统可能会在其结构中表现出突然的变化。这种变化往往是不可预测的、随机的或间歇性的。能量收集设施，如太阳能发电厂，是动态行为直接取决于可能随机波动的环境参数的系统的示例。其他例子比比皆是，例如汽车和制造设施，其中可能发生致动器或传感器间歇性故障。在这项提案中，PI计划开发第一套工具的性能分析，并设计控制器，实现最佳的参考跟踪存在的植物，其结构变化的随机和不可预测的方式。PI预计，拟议研究的结果将使控制系统的设计更安全，更有效，在存在随机和突然的变化，在物理工厂？的结构。

This proposal outlines a two year research program for developing the first collection of methods, for designing controllers that achieve optimal reference tracking, for randomly time-varying systems. As a first step, the PI adopts a Markovian jump linear system formulation because it retains the tractability of the linear deterministic case, while featuring a stochastic variation of its underlying structure. Recent results provide solutions to the H2 and H_inf optimal regulator (no reference) problems, for Markovian jump linear systems. However, the paradigm described in this proposal, where a reference has to be tracked, has not been investigated and it cannot be addressed by methods based on classical adaptations of optimal regulation theory, such as the internal model principle. The PI expects that an efficient design methodology will rely on a new framework for the joint design of the state-estimator, the state-feedback controller and the feedforward terms, using linear matrix inequality techniques. The research outlined in this proposal will also unveil structural properties of servomechanisms that achieve optimal reference tracking, in the presence of random or intermittent failures. Modern engineering systems are often made of a complex assemblage of mechanical components, electro-mechanical devices and sensors. Due to sudden fluctuations in the environment, component failure or assemblage interconnection disruptions, such systems may exhibit abrupt changes in their structure. Often, such variations are of an unpredictable, random or intermittent nature. Energy harvesting facilities, such as solar power plants, are examples of systems whose dynamic behavior depends directly on environmental parameters that may fluctuate randomly. Further examples abound, such as automobiles and manufacturing facilities, where actuator or sensor intermittent failures may occur. In this proposal, the PI plans to develop the first set of tools for the performance analysis, and the design of controllers that achieve optimal reference tracking in the presence of plants whose structure varies in a random and unpredictable way. The PI expects that the outcomes of the proposed research will enable the design of control systems that are safer and more efficient, in the presence of random and abrupt changes in the physical plant?s structure.