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

本提案概述了一个为期两年的研究计划，用于开发第一批方法，用于设计实现最佳参考跟踪的控制器，用于随机时变系统。作为第一步，PI采用马尔可夫跳变线性系统公式，因为它保留了线性确定性情况的可追溯性，同时具有其底层结构的随机变化。最近的研究结果为马尔可夫跳变线性系统的H2和H_inf最优调节器（无参考）问题提供了解决方案。然而，本提案中描述的范式，其中必须跟踪参考，尚未被调查，并且无法通过基于经典的最优调节理论的适应方法来解决，例如内部模型原理。PI期望一种有效的设计方法将依赖于使用线性矩阵不等式技术的状态估计器、状态反馈控制器和前馈项联合设计的新框架。本提案中概述的研究还将揭示在随机或间歇性故障存在的情况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而成。由于环境的突然波动、组件失效或组件互连中断，这类系统可能表现出结构的突然变化。通常，这种变化是不可预测的、随机的或间歇性的。能量收集设施，如太阳能发电厂，就是其动态行为直接取决于可能随机波动的环境参数的系统的例子。进一步的例子还有很多，例如汽车和制造设施，其中执行器或传感器可能发生间歇性故障。在本提案中，PI计划开发第一套用于性能分析的工具，并设计控制器，以在结构随机和不可预测的方式变化的植物存在时实现最佳参考跟踪。PI期望所提议的研究结果将使控制系统的设计更安全，更有效，在物理工厂中随机和突然变化的存在。年代的结构。

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.