On LQR Control with Asynchronous Clocks and Control Oriented Code for AWGN Erasure Channel: Two Control-Communication Problems

This thesis deals with two control-communication problems. The rst problem deals with control of a system over a constrained channel, while the other problem deals with using control techniques to analyze channels with state. The rst problem considers an LQR control when the sensor, controller, and actuator all have their own clocks that may drift apart from each other. An ane clock and a quadratic clock model are considered. For aquadratic cost function, an analysis of the loss of performance incurred as a function of how asynchronous the clocks are is performed. This also allows us to obtain guidelines on how often to utilize the communication resources to synchronize the clocks. The second problem dealt in this thesis concerns capacity of an AWGN channel corrupted by i.i.d. erasures.Transmitter and receiver do not know about the occurrence of erasures. A novel control oriented feedback coding scheme is presented and capacity of this channel is analyzed. It is also shown that Schalkwijk-Kailath Coding Scheme and its variants fail to achieve any rate above (1-e)½ log(1+P), where e is the deletion probability of the deletion-corrupted channel.