Centralized and decentralized control with limited information.

摘要

In this dissertation, we address the problem of developing systematic tools to analyze and design control systems with limited information, where limitations of information exchange may come from the controller structure (topological constants), and/or communication channels connecting components of the system (non-topological constraints). We provide a unified view of topological and non-topological constraints in the information exchange, and methods to design controllers with these constraints.;Traditionally in control design, one assumes that system measurements are fed back, without latency over infinite bandwidth channels, to a centralized location where processing and actuation take place. In many cases, this scenario is justified. But as more flexible and aggressive control is sought, these traditional assumptions may no longer hold, especially in the newly emerging networked control system, where many components of the control system may share common network resources. In these settings, due to physical or implementation constraints, the controller may have to adopt a decentralized or distributed topology. Meanwhile, the communication network itself introduces new issues, such as limited bandwidth, latency, and packet loss, to information exchange. Finally, in order to share network resources among multiple components of the system, it is necessary to introduce the resource allocation problem into controller design.;The limited information relayed to, from, and among controllers is the common difficulty behind these constraints. In order to design more flexible and robust controllers, structural constraints and communication constraints may need to be systematically and explicitly considered during the design stage. Specifically, we provide results to address the following problems: For a decentralized control system over a bandwidth-limited communication network, whose controllers are not allowed to communicate with each other directly, we provide an explicit way to construct the associated encoder, decoder, and controller to achieve asymptotic stability. We also present robustness analysis of the control algorithm.;Then we focus on the stabilization problem of Markovian jump linear systems with log-arithmically quantized measurements in mean square, stochastic quadratic and almost sure uniform exponential sense. We present a convex way to determine the coarsest stabilizing quantization density. We also give explicit constructions of the stabilizing logarithmic quantizer and controller. Finally, we show that the problem of stabilizing a linear time invariant (LTI) system over an unreliable channel can be cast as a special example of the framework developed here.;On the performance side, we show that for LTI systems with quantized state feedbacks, logarithmic quantizers and associated controllers are sufficient to achieve finite ℓp gain (or bounded pth-moment of the state for stochastic systems) stabilization. We give explicit quantizer and controller designs along with the upper bound of the system gain (or the pth-moment of the state for stochastic systems).;Last, we address the resource allocation problem for a networked control system. By using a sampled-data system over a bandwidth-limited communication channel as a simplified model, we illustrate the trade-off between the sampling rate and the data accuracy given fixed average throughput, under a linear quadratic Gaussian (LQG) setup. We demonstrate that more frequent communication is beneficial given a fixed amount of information.