Control over Low-Rate Noisy Channels

Networked embedded control systems are present almost everywhere. A recent trend is to introduce radio communication in these systems to increase mobility and flexibility. Network nodes, such as the sensors, are often simple devices with limited computing and transmission power and low storage capacity, so an important problem concerns how to optimize the use of resources to provide sustained overall system performance. The approach to this problem taken in the thesis is to analyze and design the communication and control application layers in an integrated manner. We focus in particular on cross-layer design techniques for closed-loop control over non-ideal communication channels, motivated by future control systems with very low-rate and highly quantized sensor communication over noisy links. Several fundamental problems in the design of source–channel coding and optimal control for these systems are discussed. The thesis consists of three parts. The first and main part is devoted to the joint design of the coding and control for linear plants, whose state feedback is transmitted over a finite-rate noisy channel. The system performance is measured by a finite-horizon linear quadratic cost. We discuss equivalence and separation properties of the system, and conclude that although certainty equivalence does not hold in general it can still be utilized, under certain conditions, to simplify the overall design by separating the estimation and the control problems. An iterative optimization algorithm for training the encoder–controller pairs, taking channel errors into account in the quantizer design, is proposed. Monte Carlo simulations demonstrate promising improvements in performance compared to traditional approaches. In the second part of the thesis, we study the rate allocation problem for state feedback control of a linear plant over a noisy channel. Optimizing a time-varying communication rate, subject to a maximum average-rate constraint, can be viewed as a method to overcome the limited bandwidth and energy resources and to achieve better overall performance. The basic idea is to allow the sensor and the controller to communicate with a higher data rate when it is required. One general obstacle of optimal 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 is shown that the proposed method gives a good performance compared to some other rate allocation schemes. In the third part, encoder–controller design for Gaussian channels is addressed. Optimizing for the Gaussian channel increases the controller complexity substan-