Practical Anytime Codes

Sammanfattning: The demand of an increasingly networked world is well reflected in modern industrial control systems where communication between the different components of the system is more and more taking place over a network. With an increasing number of components communicating and with hardware devices of low complexity, the communication resources available per communication link are however very limited. Yet, despite limited resources, the control signals transmitted over the link are still required to meet strict real-time and reliability constraints. This requires entirely new approaches in the intersection of communication and control theory. In this thesis we consider the problem of stabilizing an unstable linear-quadratic-Gaussian (LQG) plant when the communication link between the observer and the controller of the plant is noisy. Protecting the data transmitted between these components against transmission errors by using error control schemes is essential in this context and the main subject to this thesis. We propose novel error-correcting codes, so-called anytime codes, for this purpose and show that they asymptotically fulfill the reliability requirements known from theory when used for transmission over the binary erasure channel (BEC). We identify fundamental problems when the messages to be transmitted are very short and/or the communication channel quality is very low. We propose a combinatorial finite-length analysis which allows us to identify important parameters for a proper design of anytime codes. Various modifications of the basic code structure are explored, demonstrating the flexibility of the codes and the capability of the codes to be adapted to different practical constraints. To cope with communication channels of low quality, different feedback protocols are proposed for the BEC and the AWGN channel that together with the error-correcting codes ensure the reliability constraints at short delays even for very short message lengths. In the last part of this thesis, we integrate the proposed anytime codes in an automatic control setup. We specify the different components necessary for this and determine the control cost when controlling an unstable LQG plant over a BEC using either the anytime codes proposed in this thesis or block codes. We detail the relation between parameters such as channel quality, code rate, plant instability and resources available and highlight the advantage of using anytime codes in this context.Throughout the thesis, the performance of the anytime codes is evaluated using asymptotic analysis, finite-length analysis and/or simulation results.