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

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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.