A New Optimal Control for Networked Systems
Date Issued
2015
Date
2015
Author(s)
Yu, Jen-te
Abstract
This dissertation aims at extending classical optimal control theories such as Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) control, and Kalman Filtering (KF) to Networked Systems (NS). There are many important and active subjects in NS research, and this dissertation focuses on two of them. The systems and network topologies under consideration are linear and time-invariant. The first subject of this dissertation is concerned with LQ control where signal dropouts could occur. Under TCP-like protocols, the overall loop considered here is closed by lossy communication networks. Only the class of static and latest signal based compensators will be considered. We cover from simpler case of state feedback and output feedback LQR with one lossy network to more complex case of LQG control that involves two lossy networks. A new optimal control will be developed to deal with the signal dropout problem, which also links the compensator selection to the minimization of the LQ cost. The second subject covers two synchronization problems of Multi-Agent Systems (MAS). The first problem concerns with how to achieve state synchronization for a MAS consisting of homogeneous linear time-invariant systems, given that the initial conditions for all agents are different and arbitrary and only output can be used. The second problem deals with how to reach synchronization for distributed Kalman filtering consisting of heterogeneous sensor networks and a linear mobile target that is to be traced, under the condition that the initial estimates of the target’s state are different and arbitrary for all the agents. We introduce novel notions such as relative-input-output and agent-wise coupling strength and propose a unified approach to tackle these two synchronization problems. Using the new designs proposed in this work, we will be able to eliminate all the observers used in existing designs when dealing with the first synchronization problem. For the second synchronization problem, both designs that achieve exponential synchronization and finite-time synchronization will be provided for the distributed Kalman filtering in heterogeneous sensor networks in comparison with the asymptotic synchronization presented in a popular work. Unlike many existing works, the controller and coupling strength in our new designs do not involve the full knowledge of the Laplacian matrix. Nor do they require consensus region analysis. Our agent-wise definition of coupling strength also brings in an additional benefit – its fast adaptation and high adaptability to network topology changes. We will provide numerical examples to validate the new designs and compare their performances against that of existing works in the literature.
Subjects
LQ Control
Lossy Networks
MAS Synchronization
Distributed Kalman Filtering
Type
thesis
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