Control over Low-Rate Noisy Channels

Sammanfattning: Networked embedded control systems are present almost everywhere. A recent trendis to introduce radio communication in these systems to increase mobility and flex-ibility. Network nodes, such as the sensors, are often simple devices with limitedcomputing and transmission power and low storage capacity, so an important prob-lem concerns how to optimize the use of resources to provide sustained overall sys-tem performance. The approach to this problem taken in the thesis is to analyzeand design the communication and control application layers in an integrated man-ner. We focus in particular on cross-layer design techniques for closed-loop controlover non-ideal communication channels, motivated by future control systems withvery low-rate and highly quantized sensor communication over noisy links. Severalfundamental problems in the design of source–channel coding and optimal controlfor these systems are discussed.The thesis consists of three parts. The first and main part is devoted to the jointdesign of the coding and control for linear plants, whose state feedback is trans-mitted over a finite-rate noisy channel. The system performance is measured by afinite-horizon linear quadratic cost. We discuss equivalence and separation proper-ties of the system, and conclude that although certainty equivalence does not holdin general it can still be utilized, under certain conditions, to simplify the overalldesign by separating the estimation and the control problems. An iterative opti-mization algorithm for training the encoder–controller pairs, taking channel errorsinto account in the quantizer design, is proposed. Monte Carlo simulations demon-strate promising improvements in performance compared to traditional approaches.In the second part of the thesis, we study the rate allocation problem for statefeedback control of a linear plant over a noisy channel. Optimizing a time-varyingcommunication rate, subject to a maximum average-rate constraint, can be viewedas a method to overcome the limited bandwidth and energy resources and to achievebetter overall performance. The basic idea is to allow the sensor and the controllerto communicate with a higher data rate when it is required. One general obstacle ofoptimal rate allocation is that it often leads to a non-convex and non-linear problem.We deal with this challenge by using high-rate theory and Lagrange duality. It isshown that the proposed method gives a good performance compared to some otherrate allocation schemes.In the third part, encoder–controller design for Gaussian channels is addressed.Optimizing for the Gaussian channel increases the controller complexity substan-tially because the channel output alphabet is now infinite. We show that an efficientcontroller can be implemented using Hadamard techniques. Thereafter, we proposea practical controller that makes use of both soft and hard channel outputs.