State estimation for networked control systems with intermittent data transmission

Classic control theory relies on the assumption that sensors, estimators, controllers, and actuators communicate through transparent links. When the communication between these elements is subject to effects like quantisation, delay, and loss of packets, the links can no longer be considered transparent and the basic theory must be revisited. These effects are typically present in systems that use digital wireless communication to share information amongst the different components of the system. This thesis helps to answer the question of how the loss of packets containing measurements from a system affects the performance of its state estimator. In particular, due to its wide use and optimality, the Kalman filter is the state estimator studied. The natural way to evaluate the performance of an estimator is to study the covariance of its estimation error. When measurements are subject to random packet loss, the estimation error covariance does not converge to a steady state, but becomes a random variable whose statistical properties are studied in this thesis. The main contribution of this thesis is the development of a necessary condition and a sufficient condition, having only a trivial gap between them, to determine whether the asymptotic expected value of the estimation error covariance is bounded or not. The conditions apply for a fairly general class of systems and packet drop models, extending previous results and creating a unified approach. Other contributions include bounds on the expected value and bounds on the cumulative distribution function of the estimation error covariance. In both cases, numeric methods to obtain a sequence of upper and lower bounds that can be made arbitrarily tight at the expense of increased computational effort are presented. A detailed example showing an important application of such bounds is also presented. The theoretical tools developed here contribute to the area known as networked control systems, which in turn provides guidance for the design and implementation of network protocols, devices, and integrated systems benefiting from wireless technologies.