Team optimal decentralized estimation and control of networked linear quadratic systems

In this thesis, we investigate team optimal decentralized estimation and control of networked control systems (NCS). NCS refers to multi agent feedback control systems where agents are connected over a communication network. The salient feature of such systems is that the information is decentralized i.e., agents have different information and need to coordinate their actions to minimize a common system-wide cost. As a result, the separation between estimation and control does not hold ingeneral, and, therefore, even for systems with linear dynamics, quadratic cost, and Gaussian noise, affine control laws are not optimal in general. We start by highlighting the role of common information in decentralized control of linear quadratic Gaussian systems. In particular, we investigate a static team with common information and show that the optimal strategies have two components: one is a linear function of the estimate of the state based on common information and the second is a ``correction term'' which depends on the ``innovation'' in the state estimate based on the local observation.We then investigate the problem of decentralized estimation of a linear Gaussian process by agents connected over a graph. We show that the estimates which minimize the team mean square error (MTMSE) have the same structure with two components as identified for the static problem. Next, we consider a decentralized control problem with a major agent and a collection of heterogeneous minor agents, where the state of the major agent is observed by all agents while the minor agents have a noisy observation of their own local state. We do not impose the assumption that the noise is Gaussian. In this setup, linear strategies need not be optimal. We develop a completion-of-squares based proof argument to characterize the optimal and the best linear design of such systems. This proof technique combines the fundamental ideas of linear system theory (viz., state splitting and completion of squares), with the fundamental ideas in stochastic systems (static reduction and orthogonal projection) and fundamental ideas in decentralized control (common information based approach). We show that both the optimal as well as the best linear strategy have the structure identified earlier.Finally, we consider the problem with major and minor agents: the state of the major agent is observed by all agents, the minor agents observe their local state perfectly and transmit it to the major agent over a communication channel with packet drops. We identify the structure of optimal controllers using the completion of squares proof argument developed for the previous case. Again, the optimal strategies have the structure identified earlier. As a corollary to this result, we are able to re-derive the result of NCS with local and remote controllers investigated recently in the literature

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